The Birth of Physics

The Birth of Physics

MICHEL SERRES

Translated by

Jack Hawkes

Edited, introduced

and annotated by

David Webb

CLiNAMEN PRESS

Copyright © Clinamen Press 2000 Translation © Jack Hawkes 2000 Introduction and annotation © David Webb 2000

Clinamen Press Limited Enterprise House Whitworth Street West Manchester M1 5WG

www.clinamen.net

Published in French by Les Editions de Minuit as La naissance de fa physique dans Ie texte de Lucrece © Les Editions de Minuit, 1977 7, rue Bernard-Palissy, 75006, Paris

All rights reserved. No part of this edition may be reproduced, stored in or introduced into a retrieval system, or transmitted, in any form or by any means (electronic, mechanical, photocopying, recording or othetwise) without the written permission of the publishers.

A catalogue record for this book is available from the British Library

ISBN 1 903083 04 4 (hardback) ISBN I 903083 03 6 (paperback)

7 9 8 6 4 2

Typeset in Adobe Garamond by Koinonia, Manchester Printed and bound in the UK by Redwood, Trowbridge, Wiltshire

CONTENTS

Introduction-vii Editions of Lucretius-xxi

Translator's note-xxii

PROTOCOL First model: of declination in a fluid environment page 3 Turbulence 6

MATHEMATICS An analysis of the hydraulic model 9 Archimedes' work 13 Archimedes, or the concept of deviation 19

RETURN TO THE MODEL Turba, turbo 27 Slope and extrema 31 Flows and paths 49

EXPERIENCES The Meteora Experimentation: magnetism

CONDITIONS Epistemological conditions Observation and simulacra IOI Cultural conditions Violence and contract: science and religion I07

APPLICATION: GENESIS OF THE TEXT 135 Atoms, letters, cyphers 139 The genesis of sense 144

The Birth of Physics Coding Fall and rhythm

HISTORY Antiquity, modernity

MORALITY The soul and the descent to the underworld The garden and the local

Index-I93

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147 151

165 172

INTRODUCTION

This extraordinary and passionate book is devoted to the renewal of atomism in contemporary philosophy and science. Neither orthodox classical commentary, nor traditional history or philosophy of science, the work traces a relation to the text of Lucretius that is at once exemplary in its scholarship and sensitive to the aspirations of atomism itself. In doing so, it both revises our conception of ancient atomism and challenges our understanding of the paradigms that underlie much recent and contemporary science. More specifically, it presents a philosophical basis for a distinct approach to movement and relation, to time, to language and to the question of physical law. Running through all of this are the themes of form, abstraction, the emergence of sense and the need to reach a new and less violent relation to nature. Not least, the book is also an eloquent tribute to the precision and intensity of Lucretius' own text.

Provocatively, Serres names as the birthplace of physics the text of an author, Lucretius, who is roundly ignored by most histories of science. It is thought that Titus Lucretius Carus was born a Roman citizen in the first century BC and he wrote his only known work, De rerum natura, as an exposition of the atomist philosophy of Epicurus (341 BC-C.270 BC) . Philosophically, the book is taken today as primarily a point of departure for looking back towards ancient atomism. AB a scientific text, it is not taken seriously at all.' The atomism Lucretius espoused, along with that of his precursors Leucippus, Democritus and Epicurus, is treated as a curiosity and a cul-de-sac having little or nothing to do with its modern scientific counterpart. Against this prevailing view, the claims made here by Michel Serres on behalf the contemporary relevance of Lucretius may seem fanciful. However, Lucretius' modest profile in the history of science and philosophy is no accident, Serres argues, for his neglect is of a piece with the enthusiasm for classical rationalism that has dominated our intellectual tradition from Plato through Descartes to Newton and beyond. In spite of the recurrence of corpuscular philosophy in the 17th

The Birth of Physics and 18th centuries, there is something in the ancient doctrine of atomism that has always been anathema to this classical tradition. Yet as the underlying ideals of classical and modern rationalism no longer have the force they once did, the time is ripe for Serres to reveal that there has always been a secret current of atomism running through European philosophy and science. Strangely, while atomism has been suppressed by our philosophical and scientific tradition, it has continued at the same time to inform that tradition from within: not just as an excluded negative, but as a positively contributory factor, establishing such recur­rent themes as fluidiry, inclined planes, the fall, equilibrium and disequi­librium. To recover a little of the riches of ancient atomism therefore means neither relating it to its accomplishment in modern science, nor turning against modern science and back into the past. Indeed, the renewal of atomism in Serres' work speaks of fracture, convolution and of unexpected kinships. It complicates relations: historical and discursive. And just as the scope of the ancient doctrine, and Lucretian physics in particular, extended beyond what we regard today as the province of the natural sciences, so the atomism Serres advances here bears directly on epistemology, the philosophy of language, and morality. Above all, this new translation of The Birth of Physics is a timely reminder of the important contribution Serres has made to the debate on the relation between philosophy and science.

Atomism ancient and modern

It is generally said that modern atomic theory was animated by the desire to break down inert matter into its smallest constitutive elements in order that the laws governing their motion may be determined and that these laws might in turn underpin and ultimately explain higher­order phenomena. Its determination of the smallest element of matter was in pursuit of a reductive science. In this way, modern physics set itself apart from ancient atomism by the provision of a mathematical basis that ancient atomism apparently lacked. By contrast to the law­governed behaviour of matter in early modern physics, the ancient doctrine of atoms combining as they fall through the void seemed primitive and unsystematic, an eccentric yet lucky intuition. While this story of modern science is broadly speaking true, it veils a less straight­forward series of developments.

Modern atomism grew up alongside the dynamics formalised in Newton's laws of motion. The relationship between the two was neither

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Introduction straightforward nor always free from antagonism. Newton's laws described the movement of matter in a perfectly efficient system that would remain stable as long it were not disturbed by some external force and where all change was in principle reversible. His introduction of a universal force of gravitation depended on the idea of action at a distance and thereby dealt a serious blow to the principle of mechanism that underlay the corpuscular conception of matter. The triumph of Newton's thesis seemed to cut the last thread connecting modern science to ancient atomism. However, this view was soon to be complicated by the later developments of thermodynamics, statistical mechanics, quantum theory and non-linear dynamics, where the ideals of reversi­bility and closed systems were thrown into question. It is here in the elements of uncertainty and openness characteristic of such theories that ancient atomism re-asserts itself in modern physics. Serres' work accentuates this counterpoint to the classical ideal not just by referring to the renewed importance of certain general ideas drawn from atomism, but by bringing the richness of Lucretian physics back to life, and above all by correcting the widespread perception that it lacked a mathematical language. All the components required for the mathe­matical expression of atomist physics - a geometry of spirals and revolution, an infinitesimal calculus, a hydrostatics and more - are to be found, Serres reminds us, in the works of Archimedes.

But there is more, something quite specific, that sets the body of Archimedes' work apart from the mathematical principles and ideals that have informed philosophical thought from Pythagoras, Plato and Aristotle, to Descartes, Leibniz, Kant and down to Husserl and much contemporary thinking. The geometry underlying so much of the metaphysical tradition is concerned with the construction of figures and the measure of their elements; with sides and lengths. Serres, by contrast, embarks on a 'history of the angle'. Incidental to the principal interests of geometry, the angle resists the push toward quantification and remains 'a shape, a corner, like a quality' . The problem, Serres remarks, is that in conceding to the imperative to measure, geometry has conflated the study of form with its relation to number. As a result, it has confused rigour with exactitude, and crucially ceased to attend to the qualities of form, direction and inclination that do not lend themselves to measure. In short, it developed essentially as an applied mathematics. 2

Compound this with the tendency towards uniformity arising from the need for reliable units of measurement and a bias against the irregular and the non-linear is installed from the very beginning. By contrast,

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The Birth of Physics Archimedes is interested in the minimal angle of deviation, the departure of the tangent from the curve, an element that is indiscernable to the eye and which by definition escapes measurement. It is through such imperceptible departures from an ideal path that the forms of things really emerge. The mathematical treatment of such form is concerned less with the pursuit of simplicity and purity than with the attempt to express the singular, and must therefore remain open to the complexity, impurity and ultimately the concreteness of existing things. Every form, writes Serres, 'is draped in an infinity of adherences', 'differential robes' that slide over them (BP 130:I03) . The differential geometry he finds in Archimedes is less an abstraction than 'a phenomenology of the caress, voluptuous knowledge' (BP 134:I07) . In this way Archimedian mathematics is at once closer to the concreteness of naturally occurring forms and yet less able to derive universal principles by which they may be mastered. Perceiving this as a simple weakness, history has regarded Archimedes as a brilliant yet unsystematic innovator. However, the alliance between atomism and Archimedian mathematics enriches them both, giving Lucretian physics a mathe­matical language and the work of Archimedes a new coherence. 'It no longer forms a library, a tub ric of results and methods among others; they are an encyclopedia, a monument that testifies to a world' (BP 34:24) .

The world to which it testifies, the world described by Lucretius, is a place of turbulent flows, of chaos and the emergence of order by what classical metaphysics has taught us to call chance, but which ancient atomism also knew as necessity.3 Everything begins with atoms falling through the void. Were this flow to remain laminar, the trajectory of each atom continuing parallel to that of every other, there would be no collisions and thus no combinations from which worlds are formed. Such a state is what Serres calls the 'first chaos', the absence of order in perfect order, the absence of all relation.4 But Lucretian physics is not governed by a principle of inertia and bodies do not have to await the action of an external force before undergoing a deviation from their path. Deviation occurs spontaneously, with no cause and to no end. This declination - the central concept in Lucretian atomism - is the clinamen.

The clinamen is the minimal solid angle of deviation from a laminar flow required to create turbulence, which is the condition for atoms to meet and combine and is therefore also (paradoxically) a stimulus for the emergence of order. From the chaotic turba, the confused tumult of atoms, arises the turbo, the spiral, vortex or spinning cone. Already one can begin to see that what separates ancient atomism from its modern

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Introduction counterpart is the conception of movement and relation that accompanies it. In fact, while the material atom is a necessary and fundamental component in Lucretian physics, it is not the focus of its conceptual invention and endeavour. The ancient doctrine is an atomism of angle more than of matter. Its building block is not essentially the irreducible solid unit, but the imperceptible angle of deviation from a path that peels off into a proliferation of new forms, the fluctuation around a point of equilibrium. The treatment of motion in modern physics was inspired by the revolution of the planets, that is, by solid bodies on stable paths. As Serres tells us, for Lucretius 'the subjects of physics are mass, fluids and heat' (BP I2:5) . Everything flows, and if we are not to consider atomist physics absurd and archaic, we must, he writes, give up the general framework of solid mechanics altogether. From the Lucretian perspective, fluidity is not a particular and rare case of the general condition of solids, but rather the model from which all physics begins. 5 Solid bodies are just exceptionally slow moving fluids. Stable order exists not through resistance to change, but through the temporary maintenance of structured change. Form itself is never static and local order, which from within may give the appearance of stability, is a minimally open system that will in time return to the global flow from which it arises. It is this fluidity that is constant, what Lucretius described as the fall of atoms, and not the brief and contingent pockets of order that appear within it. Homeostasis is a local exception to global homeorrhesis.6

Inceptions: against finality

In spite of the many examples of complex flows in the world around us, the idea of movement without finality can still strike us as strange. As reluctant or recovering Aristotelians, we may continue to be swayed by the idea that order is prefigured in a potentiality that already existed in advance of its emergence, and that only what is potential can become actual, can happen. This formulation was Aristotle's response to the perceived paradox of becoming: what is cannot come from what is not, but if what is comes from what is, no change has occurred. Seeing that the paradoxical nature of this problem lay in the monolithic deter­mination of Being as One, he allowed for a multiplicity of possible significations of Being, and in particular for the division between potential and actual Being. What exists as actual could then come to be from what exists as potential. In this way, Aristotle resolved the paradox,

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The Birth of Physics while preserving a commitment to the original unity of Being, re­inscribed now in the structure of change itself, whose end is in every case written into its beginning.

With the idea of original multiplicity (everything that is may be unitary, but there is a countless number of such units) , atomism intro­duced at once a new theory of movement and an alternative doctrine of contingency. Where Aristotle could only regard chance as an inter­ruption in a pre-determined causal sequence, atomism allowed for con­tingency as the outcome of an indeterminate beginning. In Lucretius, this fundamental indeterminacy is articulated via the clinamen, which cannot therefore be interpreted as a cause of any kind. To be a cause -even as accidental or chance - is to be isolable. The clinamen, however, is by definition concealed beneath the lowest possible threshold of measurement. Its angle of deviation is indiscernable. In the same way, as an event that occurs over a time span shorter than can be detected, it eludes any attempt to identify it as having taken place at a given time.? Indeed, given the continual variation of form, even in relatively stable systems, there is no reason to suppose that it is a rare event at all. When Serres follows Lucretius in saying that the clinamen occurs at a time and place that are 'indefinite' [incerto tempore, incertisque locis ] , he does not only mean that it can occur without warning, but rather that its occur­rence cannot be localised at ali.8 The difference is important. The clinamen should not be treated as an occasional 'chance' event - that is, as a 'rogue' cause that does not obey the law - but rather as the theoretical expression of an irreducible complexity in the order of events.

It is ultimately in the void that the aleatory character of Lucretian physics resides. Without it, local conditions would in every case be continuous with the universal order (an hypothesis at play in both Laplace's dream of perfectly determinate systems and in Leibniz's monadology) . Conversely, it is as a consequence of the ontological inter­ruption by the void that local states are not continuous with global states. But if the void is the physical condition of locality vis-a.-vis the global, the dynamic condition is the clinamen itself, which from the outset interrupts the chain of cause and effect linking global or universal states to the behaviour of the local environment. The clinamen is the dynamic condition of locality. And of course this works both ways, also undermining the possibility of generalization on the basis of local observations.

If, through the clinamen, the origin of every event or system is always multiple, then every attempt to reduce change to a unilinear process

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Introduction must necessarily fail.9 There is, therefore, no universal history, no unilinear development and thereby no single frame of reference within which all events may be encompassed (this is encapsulated in the idea of fluidity as a general phenomenon. fu Serres, writes, even the vessel that contains a given fluid is porous and an open system, it 'is itself a flow, although thicker and more complex' (BP 87=69)) . There cannot even be a reliable rule of translation by which we can navigate our way from one frame or region to another. For example, we can, Serres writes, identifY several orders or rhythms of time. Events do not unfold uniformly. Indeed, time itself is described as the 'fluctuation of turbulences' (BP II5:9I) that open the dimension of time as a pocket, or pockets, of local and short­lived order within the laminar flow. For there to be a navigable history that was anything more than an abstraction, we would have to integrate the times inherent within this multiple and variable turblence.

Without the vantage point required to survey the whole, thinking and writing chart their own paths as they find their way along, pro­ducing local cartographies that reflect the specificity of environments, both physical and epistemological. Metaphysical thought long ago realized that human intuition is imperfect, its grasp of the whole sequential and partial when compared to God's total and instantaneous - that is, timeless - understanding. Yet it has laboured on trying to compensate for this weakness. The ideal of epistemological certainty, the persistent tug towards unity and universality, the residual distrust of the indeterminate, the episodic, idiom and noise all testifY to the extent to which, as Nietzsche predicted, we have continued to live in the shadow of God. One of the attractions of atomism for Serres is that it was never in thrall to such ideals. Its expression of human transcendence within and through nature is not strained by a negotiation with the residual language and habits of a philosophy antagonistic to such an idea.

Let us note briefly that when Serres speaks of the event of the clinamen as an instantaneous declination that falls beneath the threshold of possible measurement, this is not just the expression of a failure in the accuracy of our instruments. Lucretius has not been simply undermined by technological progress. For the breakdown in the determinable order of cause and effect has repercussions beyond the strictly scientific question of our ability to ascribe a serial order to natural events. For the introduction of an irreducible ambiguity into the relation between the determining and determined elements opens not just on to the problem of time, but also onto that of sensibility, in the guise of our affection by things, and even on to the relation between the sensible and the intel-

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The Birth of Physics ligible, in the guise of our conceptualisation of what is given through sensibility. In short, the renewal of atomism offers important new perspectives on problems that have been at the vety heart of philosophy for a long time, and most especially modern philosophy since Kant.

Language and perception

Compared with much post-Kantian philosophy, there is a danger that Lucretian atomism may look naIve. In fact, in a certain sense it is naIve, and deliberately so. It is true, for example, that it recognises no division between reality and appearance and does not engage in a 'hermeneutics of suspicion'. The problem is less this naivety itself than the possibility that it may be mistaken for foolishness or regarded precisely as a dangerous lack of sophistication. The issue here is that of the emergence of meaning: how do we negotiate the passage between the appearance of a thing and our speaking of it. What is the relation between nature and the language in which it is expressed?

The question leads us back from a consideration of our own language to that attributed to nature itself 'Atoms, we know, are letters or are like letters' (BP 175:141) [BP - The Birth of Physics] . Finite in variety, their possible combinations are nonetheless infinite: letters link together into words and texts, just as atoms combine to form bodies. 'The analogy of behaviour is perfectly apt. It is a metaphor and it is not' (BP 175:141) . In this way, Serres proposes an intimate relation between nature and language, such that the combinations in the one are mirrored in the other. 'Language is born with things and by the same process' (BP 153:123) . Accordingly, 'Things appear bearing their language' (BP 153:123) . This is not only a thought that bypasses the whole of post­Kantian and phenomenological philosophy in its concern with how things are given and the relation between such givenness and the language in which it is ultimately expressed, it also reaches much further back into more ancient speculations on the curse that accompanies the blessing of language. When the Chorus in Sophocle's Antigone speaks of humankind as the strangest beings on earth, it seems to acknowledge the alienation from nature that the power of language brings with it.IO For Serres, however, atomism provides a theory of language that does not imply this rupture and which leaves human beings at home in the world.

A few pages after the lines quoted above, he writes: 'That atoms are letters, that connected bodies are sentences is certainly not a metaphor; were it not so, there would be no existence' (BP 185:150) ." Yet iflanguage

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Introduction is not metaphorical, a difficulty arises that seems to threaten the materialism Serres is proposing. It will be helpful to explore it briefly. Serres describes materialism as the reference of all accounts of 'feder­ation' back to nature itself, as opposed to an idealist tendency to discover in nature some pre-determined conception of order that it had secretely placed there in advance (BP 150:121) . Yet this aspiration towards a naive empiricism is not obviously compatible with Serres' own insistence that wherever one looks, one finds the same model of movement, order and relation - that of turbulent flows and the clinamen. If nature (in all its manifestations), language, economics and morality are all isomorphic, we are bound to ask after the status of the model on which the accounts of all phenomena are based. Conversely, if the rule is variation, declination and the strict locality of order, might we not expect to find departures from the model? Should we not be suspicious of the very globality, not to say universality, of the dynamics Serres discovers in all phenomena?" The answer to this question points in two directions.

First, it is significant that in discussing the isomorphism between discourses, Serres explicitly rejects any priority of one instance over the other. Economic law is not to be derived from physical law, or vice versa: 'They are the same, that's all.' (BP 68:53) . The perfection of the analogy between nature does not entail the endless reiteration of the same. In fact, paradoxically, it is precisely because the model applies everywhere that turbulence is possible not only as a feature of the phenomena described by a particular discourse, but also between discourses, in and through translation and communication. In this way, the isomorphism that seems to elevate a certain configuration above the fray in fact facilitates the declination that interrupts the perceived invariability in the instantiations of the model. Isomorphism thereby allows distortion at the local level. Given how easily materialism is associated with reductionism (a consequence of the way that materialism has been approached from within the classical paradigm), it is important to see that it is precisely by virtue of its material basis in atomism that Serres' epistemology is in fact non-reductionist.

However, and this is the second point, there is still a model said to be repeatedly instantiated in the various isomorphic discourses; namely, the mathematical model of turbulent flows. To this extent, it seems that Serres may be proposing a simple universal theory that commits him to an 'analogical unity' grounded in the mathematical model. This would indeed be a problem, were the mathematical model to be an ideal. As we have already seen, Serres' objection to geometry arises from its emphasis

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The Birth of Physics on metrics.13 The preoccupation with measurement has obscured the exploration of form itself. It is the 'applied' character that geometry takes on by virtue of its fascination with measurement that orients it towards idealism: the form it determines will be the abstracted truth of the physical thing, of nature. By contrast, for Serres it is the precisely the purity of pure mathematics that frees it from such a commitment to measurement and thereby also from any pretensions to speak the truth of nature. As pure, it is at once closed in on itself and, insofar as it is not local, universal. Above all, it is not derived from, or otherwise developed with regard to, the physical world.

The occurrence of the model therefore does not amount to the reiteration of an ideal essence. More importantly still, neither physical law nor economic law, nor any of the other isomorphic discourses can be directly read off from the mathematical model. This is encapsulated in Serres' own statement of condition of generality that keeps this from being the case: 'The theory of flows and paths is general, but ceaselessly in deviation from the general' (BP 121:96) . The model therefore cannot dictate the exact and necessary form of each of its instantiations. As Serres remarks, '[declination] interrupts the universality of the laws. It opens the closed system. It places the physical laws under the rule of exception' (BP 97:77).14

The question of law in nature

We have seen already that form is not something that pre-exists the contingent formation of things, or survives their dissolution. We have also seen that for atomism there can be no reliable map by which to navigate berween the local and the global. As a result, the longstanding model of physical law as universal must be untenable. This classical conception of laws of nature as universal formulae with which nature must comply has a theological provenance. Nature is subordinate to its creator, and by extension to anyone who can divine its eternal laws. In addition, it is, for Lucretius and Serres alike, literally Martial Law: the law of Mars, the god of war. Following Lucretius, Serres calls this configuration of law the fledera foti.

All this is called into question by the atheist Lucretius, and by atomism in general. As there is no entirely stable order, no continuity between local and general, no pure form hidden beneath the flesh of things, there can be no universal laws. There is in nature simply nothing in relation to which a universal law could obtain. As in the case of

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Introduction geometry, the universality of law is won at the price of ignoring the real complexity of open turbulent systems. In contrast to the fledera fati, Serres traces the introduction of the fledera natura - a pact, an alliance, and not a law. Serres is careful to argue that the idea of such a pact does not reflect the projection onto nature of a political convention or arrangement. On the contrary, atomism itself deals with combinations, accomodations and temporary couplings, all of which are destined to be undone in the end. It is then our own political conventions that have modelled themselves on nature, albeit often unwittingly. For Serres, this discovery draws us into a relation with nature that in principle acknowledges the fragile condition of the regularities it describes; as opposed to calling us to uphold a law that stands over and above nature as the condition of its mastery, and which at the same time attributes to the natural order a stability and resilience that excuses our violence towards it.

Philosophy, science and mathematics

For a long time, the official story has been that whatever modest dialogue has existed between philosophy and science has been confined to particular areas of shared interest: epistemology, methodology, and to a lesser degree the philosophies of mind and language. Beyond that, relations were clouded by a mutual mistrust. Science, it was said, could not think; and once philosophy went beyond the bounds defining its incipient naturalisation, ultimately the bounds of empiricism, then it lost itself in useless metaphysical speculation. What this account would not acknowledge was the possibility that philosophy and science might communicate about more fundamental matters: ontology, the nature of space, of time, relation, number, limits. Yet if established channels of communication were indeed in poor repair, many outstanding figures in both fields succeeded in opening up important dialogues outside the generally accepted borders of their fields. In addition to Serres himself, Poincare, Weyl, Einstein, Bergson, Heisenberg, Husser!, Bachelard, Heidegger, Schrodinger, Thorn, Deleuze and Prigogine are all exem­plary in this respect, and there are others.

If this dialogue is gaining momentum, there may be at least two contributory factors. First, as we have mentioned already, what distin­guishes pure mathematics for Serres is its isolation both from the natural world and from the subjective ego.I5 It was precisely this, however, that

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The Birth of Physics made it less interesting to the philosophical tradition that passed via Descartes and Kant which has been preoccupied with the relation between these two domains. Where mathematics has featured in that tradition, it has done so in the form of what Serres regards as the applied discipline of geometry, thereby introducing metrics into the original structure of our experience. This situation is now changing. AB post­Kantian and phenomenological philosophy in particular have addressed the structure and genesis of experience, they have begun to explore the limits of truth, sensibility and givenness that have characterised the philosophy of the subject. AB the subject-object framework is increas­ingly left behind by philosophy, the possibilities for thinking themes such as space, time, relation, limits, continuity and discontinuity offered by pure mathematics will become important. Second, from the side of mathematics and science, the emergence of topology from the shadow of geometry has strengthened the resources available to pure mathematics, while the development of non-linear dynamics and chaos theory has given new impetus to the critique of finality and classical ontology that was already underway in philosophy.

Once again, central to all this is the work of Michel Serres. One of his most important contributions in this respect has been to break down the exclusive and proprietorial relation that the natural sciences, and physics in particular, have had to mathematics, yet without compromising the integrity of mathematics itself. Serres' work, far from encouraging non­scientific disciplines to 'borrow' from mathematical and scientific discourse, has demonstrated that mathematics was never the exclusive property of what we now call the natural sciences. In addition, as interest in original multiplicity, non-linearity, contingency, local order, fragmented times and spaces, continuity and discontinuiry, fluidity and non-violence continues to grow, we are indebted to Serres above all for renewing our relation to atomism, and for reminding us that Lucretius is still our contemporary.

Staffordshire University David Webb

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Introduction NOTES

I Literature on Lucretius is mostly made up of philological scholarship that provides exhaustive analysis of the text in the relation to ancient atomism and other ancient and classical literature. Pre-eminent amongst these are the following editions with commentaries: H. A.]. Munro, Vols 1-2 (Cambridge, 1864): C. Giussani, Vols 1-4 (Ermanno Loescher, Turin, 1896-8): C. Bailey, Vols I-III (Oxford University Press, 1947). One full length study worth particular mention for its attempt to develop a more philosophical inter­pretation of the text is M. Bollack, La Raison de Lucrece, (Editions de Minuit, Paris, 1978). Another book that has sought to integrate the poetic and philosophical aspects of Lucretius' work is M. Gale, Myth and Poetry in Lucretius (Cambridge University Press, Cambridge, 1994), which also contains an extensive bibliography. The most accessible translations at present are: Lucretius, On the Nature of the Universe trans. R. E. Latham (Penguin,London) and the translation by C Bailey (updated) included in ]. Gaskin, The Epicurean Philsophers (Everyman, London, 1995).

2 Referring to the idea, expressed by Husserl, that the figure of the salinon could not be mathematical because it was inexact, Serres writes: 'a superb and ancient confusion of the pure and the metrical, to which all of geometty from its origins to topology, from the Greeks to Riemann, bears witness rJait justice] in its histoty and its work. It is rigorous, anexact. And not precise, exact or inexact. Only a metric is exact' [BP 29:19]. It is only with the inception of topology that the dominant link to measurement is broken.

3 For Aristotle, only what has a final cause is a candidate for necessity. The winds, for example, though always caused in the sense that there is an antecedant to every event, do not conform to such an order. For Democritus, necessity denoted this order of events, whether we can ascribe a reason to it or not. C£ Aristotle, Physics II iv-vi: C. Bailey, The Greek Atomists and Epicurus (Oxford University Press, oxford, 1928), pp. 139-43.

4 'We say of this flow that is laminar. Everything happens as if each separable lamella in the flow acts without regard for any other. Hence there is only one question: how, in this flow, does turbulence happen? Or: how does a laminar flow become turbulent?' (BP 103:82) . The further question Serres addresses via Lucretius is how order can emerge from either state; that is, how order exists as a suspension between the two extreme states of chaos. 'But what distinguishes [Lucretian physics] from modern mechanics, which will adopt the same methodology, is that shape is not metrical, and movement is not that of a solid. The form is described qualitatively, the flow is that of a liquid, a current.' (BP 124:99) .

6 The term 'homeorrhesis' denotes stable flow. As an example of the contrast that Serres intends, he discusses the well known Heraclitean fragment according to which one cannot step into the same river twice (B91a,b) and concludes that while the flow (and on a larger scale, the water cycle) is stable, the banks are continually worn away by the current: if anything, the reverse is true, and one cannot sit on the same bank twice to watch the river (BP 189:153).

7 This interpretation has been advanced and explored by G. Deleuze, Logic of

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Seme, trans. M. Lester, ed. C. V. Boundas (Columbia University Press, New York, 1990), cf esp. pp.266-277.

8 The phrase incerto tempore incertisque locis (Lucretius, II, 218-19) 'does not signify the nullity of place or time, and thereby the passage to the soul outside of sensible quality, but simply aleatory scattering.' (BP 140:112) .

9 Deleuze makes this point too in the text cited above. C£ also Foucault's affirm­ation of an irreducible multiplicity of causes, for example in his interest in Entsteheung (emergence) as opposed to Ursprung (origin) in his essay 'Nietzsche, Genealogy, History', P. Rabinow (ed), The Foucault Reader (Penguin, London, 1984) pp. 76-100.

10 'Greek wisdom arrives at one of its most important points here. Where man is in the world, of the world, in matter and of matter. He is not a stranger, but a friend, a familiar, a companion and an equal' (BP 162:131).

II 'That atoms are letters is not an arbitrary theory or a decision or a metaphor. It is a necessity of what Lucretius and his predecessors called nature' (BP 182:147] .

12 C£ Shoshana Felman: 'De la nature des choses ou de l' ecart a l' equilibre' in Critique January 1979 Vol. XXXV, No. 380, pp. 3-15.

13 'Mathematics and Philosophy: What Thales Saw . . . ' M. Serres, Hermes: Liter­ature, Science and Philosophy, ed. J. V. Harari and D. F. Bell (London: Johns Hopkins Press, 1982). 'Ce que Thales a vu au pied des pyramids' from M. Serres, Hermes III: La traduction (Paris, Minuit, 1974) . The Origin of Geometry', 'Origin de la geometrie V' - originally appeared in Diacritics 8, no. I (spring 1978).

14 Finally, the separation and relation between the model and its instantiations in various phenomena and discourses cannot itself be regarded as metaphorical, since deviation, the ecart is itself 'the primary space in which every metaphor finds its place and time. The clinamen is transport in general' (BP 185=150).

15 C£ M Serres, Hermes I La communication (Editions de Minuit, Paris, 1969), p. 72.

EDITIONS OF LUCRETIUS

This text has used a number of editions, in Latin and English, of De rerum natura. Where a specific translation has been used in this book, a reference has been given. All other translations have been prepared specifically for this edition by Fiona Forsyth and Clinamen Press.

Michel Serres used the Alfred Ernout French/Latin edition in the preparation of the original text.

Latin texts: Bailey, C. (ed.) Lucretius, De rerum natura Vols I-III (Oxford University

Press, 1947) Costa, C. D. N. (ed.) Lucretius, De rerum natura Vol. V (Oxford,

Clarendon, 1984) Giussani, C. (ed.) Lucretius, De rerum natura Vols 1-4 (Ermano Loescher,

Turin, 1896-98) Munro, H. A. J. (ed.) Lucretius, De rerum natura Vols 1-2 (Cambridge,

1864)

Translations: C. Bailey in: Gaskin, John (ed.) The Epicurean Philosophers (London,

Everyman 1995) Humphries, Rolfe, Lucretius, The Way Things Are, De rerum natura of

Titus Lucretius Carus (Bloomington, Indiana University Press, 1969) Latham, Ronald Lucretius, On the Nature of the Universe (London,

Penguin 1994)

Parallel Texts: Latin/English - Rouse, W. H. D. (trans. & ed.) Lucretius, De rerum

natura (Loeb Classical Library, Harvard 1975) Latin/French - Ernout, Alfred (trans. & ed.) de Natura rerum Vols 1-2

(Paris, Les Belles Lettres, 1972)

XXI

TRANSLATOR'S PREFACE

In a story entitled 'Averroes's Search' Borges describes that situation which is the secret nightmare of every translator. The great twelfth­century Islamic philosopher, responsible for the preservation of much of what Greek philosophy remains to us, is busily at work translating Aristotle's Poetics from a version which, tantalizingly, still contains both the section on tragedy which we have and the section on comedy which subsequently perished. Averroes is pleased with his work, but there are still two little details which trouble him: he is unable to find an adequate translation for two words, 'comedy' and 'tragedy', two words which are, as we know, absolutely those most critical to his text. Furthermore, we recognize what Averroes cannot: not only doesn't he know what these words mean, he is incapable of understanding them, since he belongs to a culture to which the very concept of drama is foreign.

Translating Michel Serres' Birth of Physics reminded me of Borges and Averroes, since two of Serres' most important words in this work really do not go into English very well. The first is tourbillon, which can mean a vortex, an eddy, a whirlwind, a waterspout, a whirlpool, a whirling or rotational movement, and has associations both with the Old Testament and Cartesian philosophy. The second is eeart, (from the popular Latin *exquartare, to quarter), which can mean a deviation, a spatial or temporal separation, a difference, a discrepancy, a gap, or (with overtones of the clinamen) a swerve.

In both cases I have opted for consistency,: I have translated tourbillon as 'vortex' and icart as 'deviation' throughour. In this way I hoped to make the reader aware of the importance of these two concept to Serres' argument, and of the structure of that argument; but some of the richness of his text has thereby inevitably been lost.

Jack Hawkes

XXil

THE BIRTH OF PHYSICS

For Jacques

PROTOCO L

First model: declination in a fluid medium

Everyone knows, everyone concedes that atomic physics is an ancient doctrine but a contemporary discovery. It is a scientific matter, the science of Perrin, Bohr or Heisenberg; the ancient doctrine is only 'philosophy,' or even poetry. Like history in general, the history of the sciences has a pre-history. Just as there is no mathematics before the Greek miracle, that ofThales or Pythagoras, so there is no physics before the blessed classical age, before what has been called, roughly since Kant and the Enlightenment, the Galilean revolution. During this pre­history, 'philosophy' slumbered. We recognise, I believe, ideologies, religious or otherwise, by their use of the calendar as a dramatic device: before or after the birth of Christ, before or after the foundation of Rome or the first year of the Republic, before or after the establishment of the positivist doctrine, before or after the Galilean revolution. Nothing will ever again be as it was. Here is the metaphysical age; there is the positivist age.

From Cicero to Marx and beyond, down to us, the declination of atoms has been treated as a weakness of the atomic theory. The clinamen is an absurdity. A logical absurdity, since it is introduced without justification, the cause of itself before being the cause of all things; a geometrical absurdity, in that the definition that Lucretius gives is incomprehensible and confused; a mechanical absurdity, since it is contrary to the principle of inertia, and would result in perpetual motion; an absurdity of physics in general, since experimentation cannot possibly reveal its existence. No-one has ever seen a heavy body swerve suddenly from its path as it falls. Therefore we are not concerned with science. The clinamen, consequently, finds a haven in subjectivity, moving from the world to the soul, from physics to metaphysics, from the theory of inert bodies in free fall to the theory of the free movements of living beings. It is the last secret of the decision of the subject, its inclination. Lucretius' text itself points in this direction, speaking soon enough of the will as torn from destiny, and of horses that throw

3

The Birth of Physics

themselves from their stalls at the races. Modern materialists are most unhappy with this rupture in determinism and its reinterpretation as the idealism of a free subject. The entire discussion of indeterminism will subsequently reproduce the classical debate on the subject of the clinamen in the domain of the sciences.

On the other hand, the absurdity of such a principle is another proof, and a decisive one this time, of the prehistoric status of Greco-Roman physics. This was not a science of the world, but an impure mixture of metaphysics, political philosophy and musings on individual freedom, projected onto the things themselves. Hence the crude finding of criticism: there was no atomist physics in Antiquity. What is more, no applied sciences in general; and the clinamen on which it is based is just an immaterial property of the subject. We must read Lucretius' De rerum natura as humanists or philologians, and not as a treatise on physics.

Let us go back to Book II, where declination is introduced. It is characterised primarily by two phrases. Paulum, tantum quod momen mutatum dicere possis (II, 219-20) : atoms, in free fall in space, deviate from their straight trajectory 'a little, just so much that you can call it a change of movement'. Their deviation is as small as possible, and the alteration in their movement is as small as description allows. Lucretius repeats and redefines this deviation a little further: nec plus quam minimum (II, 244) , 'no more than the minimum' . classical editions remark on a rhetorical device in these lines. The thing is so absurd and so far from our experience that the physicist minimises it, as if to hide it. Now, anyone who has ever read any Latin texts on mathematics, and more specifically on differential calculus will recognise here two canonic definitions of the potential infinitely small and the actual infinitely small. This is not an anachronism; the relationship of atomism to the first attempts at infinitesimal calculus is well known. From the outset, Democritus seems to have simultaneously produced a mathematical method of exhaustion and the physical hypothesis of indivisibles. We can see here one of the earliest formulations of what will be called a differential. The clinamen is thus a differential, and properly, a fluxion.

On the subject of fluxions, let us examine the atomic cataract in which this infinitely small angular deviation is produced. In the lines which precede it, Lucretius shows that the movement of bodies cannot take place from low to high. The examples he cites are instructive; to explain the movement of fire, he uses liquid models: the flow of blood, the red gush which spurts, the fluidity of water, umor aquae (II, 197) . In the same way, just prior to the long passage on the clinamen, he shows us

4

Protocol

the lightning path obliquely crossing the rainfall, and shows it nunc hinc, nunc illinc (II, 214) , now on this side, now on that. And the same rain is taken up again in the definition of declination, imbris uti guttae, like the drops of rain. There we have it.

The absurdity of all this to critique, and perhaps the whole question, arises from what has always been considered the original fall of atoms in the global framework of the mechanics of solids. All the more so since the emergence of the inaugural Galilean moment within this discipline. For us, mechanics is first and foremost that of solids. It's clear cut. The mechanics of fluids is or was only a special case, which the most important texts, that of Lagrange for example, only take up in the final pages and as an afterthought. But now we must reverse the perspective. Modern science is born, or has its renaissance, in the works of Torri celli , Benedetti, Da Vinci, those of the Accademia del Cimento, which concern fluids as much if not more than solids. All of the Latin world is unified on this subject: Vitruvius expressly devotes a book of his treatise on architecture, the eighth, to the flow of water, and Frontinus writes an entire book on the aqueducts of Rome. A century before Lucretius, the works of Archimedes had raised hydrostatics to a state of perfection equal if not superior to that of ordinary statics. And both in his own time and before him the works and achievements of the Greek hydraulic engineers were remarkable.

Consequently, if it is absurd that a small solid mass might at some moment deviate from the orbit of its fall, let us examine whether the same may be said where the primary atomic cataract is like a stream, like a flux, like the flow of a liquid. Lucretius says elsewhere that the subjects of physics are mass, fluids and heat. And since for him everything flows, nothing is truly of an invincible solidity, except for atoms.

In the primary cataract, atoms are not touching. When encounters and connections occur, bodies are characterised according to their resistance. The hardest, like diamond, stone, iron or bronze, owe their solidity to the fact that their atoms are tangled, branching, knotted into a tightly-packed fabric. As we move towards the fluids and gases, the atoms are rounder and smoother rather than hooked, of course, but in particular they are less tangled among themselves .. We could even say that when the fabric is completely unravelled we are in the presence of a very subtle flow, in any case one that is not globally solid.

So there is flow; we will call it a laminar flow. This means that however small may be the lamina cut from the flow, the movement of each is strictly parallel to the movement of the others. This model is

The Birth of Physics

faithful to the description in De rerum natura. These lamellae are its elements; they are solids but the cataract is fluid. Now a laminar flow is ideal and in effect theoretical. In the real world it is very rare that all the local flows remain parallel. They always become more or less turbulent. The question to be raised, which we ask here, is the following: how do vortices form? How does turbulence appear in a laminar flow? Parallel flow is taken up in the first place as a simple model. Perhaps originary, I don't know, but in any case much less complicated or tangled than a swirling flow. Now the question that we raise and which we are in the process of resolving, through many experiments and localised theories, is exactly Lucretius' question. I will formulate it again: the fall of atoms is an ideal laminar cataract, what are the conditions under which it enters into concrete experience, that of vortical flow?

Turbulence

Now this vortex, tourbillon - OlV1], dine, Otvo�, dinos - is none other than the primitive form of the construction of things, of nature in general, according to Epicurus and Democritus. I The world is first of all this open movement, composed of rotation and translation. The latter is given by the flow and the fall, the laminar cascade. Question: how does rotation appear? Answer: the clinamen is the smallest imaginable condition for the original formation of turbulence. In the De finibus, Cicero wrote that atomorum turbulentit concursio. Atoms meet in and by turbulence.

Let us return to the text: just as a lightning bolt creates its oblique flight across the parallel lines of rain nunc hinc, nunc illinc, here and there, so declination appears in laminar flow as the minimum angle in the inception of turbulence, incerto tempore, incertisque locis (at an indefinite time and place, II, 2I8-19). A fresh argument with which traditional science may accuse Lucretius of ignorance and caprice. This has nothing to do with science, since the incident is indefinite in time and indefinite in place, and in any case undetermined. The argument says nothing about the model nor the description, but a great deal about its own ideal of science. For it to carry weight, knowledge should have nothing to say about chance distribution. What Lucretius says, however, remains true - that is, faithful to the phenomenon: turbulence appears stochastically in laminar flow. Why? I don't know why. How? By chance, with respect to space and time. And, once again, what is the clinamen? It is the minimum angle of formation of a vortex, appearing by chance in a laminar flow.

6

Protocol

The only line of Lucretius that everyone knows by heart is the very famous Suave mari magno, generally translated as a rhapsody to selfish serenity.2 It opens Book II, where declination is introduced. Now, our cultural memory only recalls the first part. The passage continues, turbantibus aequors ventis.! Here are vortices in a fluid medium, water and wind, presented as a heading, at the beginning of the world. A repetition of the Democritean dine.

A first model may already be constructed. A working hypothesis and experimental protocol. To understand the atomistic undertaking and not consider it absurd and archaic, we must give up the general frame­work of solid mechanics. It is that of our modern world, its very tech­nicality and its speculation. Perhaps the Mediterranean world needed water more than tools, perhaps it was more preoccupied with rain, storms, rivers. It built reservoirs, aqueducts. Hydraulics was important to it. What is hard to understand here isn't the local occurrence of declination, but its inscription in the framework of another mechanics, another science than that of fluids. For Lucretian physics is entirely immersed in it.

Who can fail to see that a flow does not remain parallel for long, who can fail to see that a laminar flow is merely ideal and theoretical? Turbulence soon appears. In relation to theory, the appearance of con­crete experience is contemporaneous with that of vortices. Declination is their beginning. Nothing is absurd here, everything is exact, precise, and even necessary.

We must therefore outline a sheaf of parallels. Then at some point in the flow or cataract, mark a small angle, and from this, a spiral. Within this movement the atoms, separate until now, meet: atomorum turbulenta concursio.4 But the text is still more precise: it refers to a mathemathics, a differential calculation, to the ideal of a great number, to a whole corpus implicit in the model. We need then to look for a man, one who wrote and conceived this corpus.

The work of physics begins. Here is the protocol. Here are the experi­ments, the complete models, the awaited mathematisation, and the innumerable applications.

7

NOTES

The French term tourbillon that Serres adopts to denote the turbulent yet stable structure that forms in fluid flow has been translated throughout as 'vortex'. This has the. virtue of being familiar and precise in its signification of a 'three­dimensional spiral' or 'cyclonic' structure. It is also neutral with regard to the medium in which it forms, generally water or air. Its drawback is that one loses the important etymological link between the French tourbillon and 'turbulence', 'turbination' and, ultimately, the Latin turba and turbo. It is helpful to bear these links in mind in reading the text that follows.

2 II, 1. 'How sweet it is when on the open sea . . . ' ' . . . the winds are troubling the waters.'

4 Cicero, De finibus, I, 20. Cf. also Academia, I, 6.

8

M AT H E M AT I CS

An analysis of the hydraulic model

History of the angle. When the classics try to describe will, freedom, or uncertainty, they often appeal to the image of a pendulum or balance. The infinitesimal angle of the beam, the smallest change in the balance of the pans, here is decision, determination, sometimes anguish, unrest. This is not' declination, says Leibniz, it is inclination. These simple machines are models. And poor models, because they are static. They were theorised theory, at the time, in terms of equilibrium, their machines were stators. Statues. And their psychology was a mechanics; or rather, the image of a statics. You forget about geometry and think you're talking about the subject. But in fact you're only talking about machines. This forgetting will last for a long time, enough at least so that at the beginning of the nineteenth century the angle in the atom is nothing but the freedom of the subject. Reality grows faint, like a dream of the soul. We must therefore go back to the Greeks.

Their classical method is the measurement of segments. Hence their sections and their polytomies. Their primary figure, the triangle, is in fact a trilateral; primary in the possible construction of figures on a plane, and thus primary in the world, as we see in the Timaeus. We have to wait a considerable time for the measurement of angles to be added to the measurement of other elements, sides or other things, that is, for the formulation of trigonometry. The angle remains a shape, a corner, like a quality, it resists efforts at quantification. Its trisection remains, for example, a very difficult problem. It is acute, pointed, obtuse, notice­able. Less easily abstracted than a length or a segment, by which I mean that it is less easily related to number. Perhaps more to movement; this is why figures must be superposed, thus transported, with regards to measurement; it is precisely because they are angled.

N ow the first possible angle that we may construct or perceive, or the smallest that may be formed, so that nothing can be inserted between the two lines which open, is that which lies between a curve and its tangent. In the language of geometry it may be called nee plus quam

9

The Birth of Physics

minimum; or in the language of mechanics paulum, tantum quod momen mutatum dicere possis.' In other words, the angle appears at the same time as the curvature. Between two straight lines or two line segments, this minimal angle makes no sense. If we are calculating with shapes or rectilinear solids we only need, in general, ordinary mathematics. If, on the contrary, we square or cube curved elements, we must at least switch to a differential proto-calculus. And thus to Democritus. He left two lost books on irrational lines and solids, and it is reasonable to suppose, as do Heiberg and Tannery, that the theory of irrational numbers served him as a springboard to atomic interpretation.2 In both cases, it is a question of divisibility and indivisibility. In both cases, the last division recedes beyond our reach. This is not all: we know, from a reference in Plutarch and by a section of Archimedes' Method, that Democritus provided solutions for the volume of a cone or a cylinder, or for that of their sections, and doubtless more generally for that of a solid of revolution. Heiberg and Philipps on think, correctly, that he achieved this by integration. This presupposes a differential division, and so once again an atomist interpretation. Democritus is the Pythagoras on the side of things, of the irrational and of the differentiable. It is inevitable that the first integrator should take things to be formed of a crowd of subliminal atoms. Not yet of an infinite 'sum' of infinitely small things, but of a very great number of subdivided things. In this way, one crosses the threshold of perception at the same time as that of operation.

This is still not all, this is nothing compared to the fact that the man of the philosophical pentathlon - the gold medal conferred on the Abderitan by Diogenes Laertius - indeed left a treatise, lost like all the others, concerning contact between the circle and the sphere. In which he discussed the angle of tangency, opposing Protagoras' view that the straight line touches the circle at more than one point. We do not know the detail of the polemic, but we know that it concerned osculation and the elements of what we would call differential geometry. What happens in the closest proximity of the curve to its tangent? What happens in the case of the smallest angle possible? And for the sake of symmetry, in the case of contact between two circles? For tangency and contingency? In passing, it is interesting to read the classics on this matter: when they write about mathematics, they speak of the angle of contingency; when they discourse on metaphysics, they write of contingency for what exists without necessity. Physics is indeed an affair of angles. End of demonstration: what we can re-establish of this sleeping pentathlon is coherent with the physics that has come down to us. Not only did the

10

Mathematics

atom have to be born by way of the treatment of curved elements, in the irrational and differential, or by way of the indefinitely divisible, stopped short by arbitrarily determined limit, but also and especially by way of this minimal angle, this atom of angle, this first angle, whose idea long appeared so monstrous to modern scholarship, and which, nonetheless, is more logical or more obvious than that of the atom. This is because the angle of contingency may not be subdivided: it is demonstrably minimal. It is null, but without the lines which form it overlaying one another. It is more atomic, so to speak, than the atom. As a result of the first infinitesimal calculus, there can be no atomism without curved elements; and no curve without a tangent, no curve without a minimal angle; thus, no atomism without declination. No atomism without the full schema of an inflected path. Cogitur flecti (II, 283) . The clinamen, like the spiral, is present and possible, from the beginning, in the geometry of the first atomist. I am not saying that Democritus himself immediately made a physics of it; we have no record of this. Except for the turbulence which, in Diogenes Laertius, is said to be the universal cause. I am just saying that his mathematics, at least what remains of it, gives all these outlines a geometric coherence, a systematicity. What is called rigour. Atomist physics has never forgotten geometry; witness Lucretius and his definitions: nec plus quam mini­mum, and so on. It is the commentators who have forgotten it. As, later, they forgot the angle, in their pathetic dissertation on contingency and subjective freedom. And, as far as I know, in the first of Euclid's Definitions, the angle is in fact called clisis, XAWU;, bending or inclination.

What we need for the model proposed - that is, the link between atom, angle, curves - is thus certainly to be found in Democritus. We will never know how this writer, who wrote a treatise on liquids and a debate on the clepsydra, was able to realise this model in what we would today call fluid mechanics. We will never know either, parenthetically, if his three books on the plague and pestilential illnesses furnished inform­ation for the closing lines of the De rerum natura. But there are too many vortices in Epicurus' Letter to Pythocles, for the resources of hydraulics not to have occurred at one time or another to one author or the other.

I am looking for a man, I wrote above, as I finished drawing up the protocol. I am looking for a man, an organon.

So here, once again, is the model. First a sheaf of parallels, where a laminar flow slips by. At some point, that is to say by chance, a deviation, a very small angle is produced. A vortex forms at once from this point on. I will break down the model, I will divide it into elements.

II

The Birth of Physics

1. A large atomic population. 2. A tangent to a curve, an angle of contingency.

3. A solid angle, a cone. 4. A curved vortical line. 5. Infinitely small elements. 6. Balance and deviations. 7. Flows, a fluid medium.

To mathematize the model successfully, I therefore need:

1 . A mathematical or arithmetic theory of elements. 2. A geometrical theory of the tangent. 3. A geometry of forms of revolution. 4. A theory of spirals. 5. An infinitesimal calculus. 6. A mechanics of equilibrium. 7. A hydrostatics.

Now, as if miraculously, this list of requisites corresponds exactly to a very well-known catalogue of works. Suppose a mathematician had written:

1. A book entitled the The Sand-Reckoner. 2. A theory of tangency to the spiral. 3. A treatise On Conoids and Spheroids, and On the Sphere and

Cylinder. 4. A book On Spirals. 5 . Treatises on Measurement of the Circle and Quadrature of the

Parabola. 6. A book On Plane Equilibriums 7. A treatise On Floating Bodies.

He would fulfill the requisite conditions. This man is Archimedes. Born barely twenty years before the death of Epicurus, murdered about a century before Lucretius' work. I have found the corpus. The whole corpus and nothing but the corpus.

I am in a position, then, to demonstrate several propositions. First, to show the general unity of Archimedes' entire work. The list of what remains to us will no longer be just a rubric, a catalogue, it will designate a global system. A system which describes, in a refined mathematics, the physical model of the Epicurean world. Next, and conversely as it were,

12

Mathematics

to show that atomist physics is not non-mathematical, as was believed, but that on the contrary it is analogically given mathematical expression in the Archimedian model. From which follows, in general, that the Greeks did not conceive of mathematical physics in the same way as we have done since the Renaissance. We mix experiments with equations. And we accompany the protocol, step by step, with formalism and metrics. Without this continual proximity, no experimentation, nor law. The Greeks would, I believe, have been strongly repulsed by this mixture. They did not have, as we do, a unitary mathematical physics. Theirs was double. They produced rigorous formal systems and dissertations upon nature, like two separate linguistic families, like two disjunct wholes. And, since they are often signed with completely different proper names, no one dares to think that they are structurally isomorphic. We would need a local and subtle blend of the two and we have only scattered monuments. Hence the strange idea, common to the history of the sciences, that there could have been no mathematical physics in Greece. There was, but we have to see it. And to see it by way of an example, we might carefully link Epicurus to Archimedes. Or Lucretius and his theory to the work of the Syracusan.

Archimedes' work

Silius Italicus: 'He knew the cause of the movement of the waves on the sea, what law the ocean follows in the ebb and flow of its waves. '3 He had repulsed the ordered Roman armies, from the heights of the city's ramparts to the shores of the sea. A sophisticated genius, serene, in high places fortified by the science of the wise. I like to see his great shadow there at the beginning of the Book I1.4

What is, first of all, the subject of the The Sand-Reckoner? Technically, it concerns numeration, series, the theory of increase. The first discovery of large numbers. Now, ancient atomism, like all atomic theories in general, implies the manipulation of very large populations, since the elements are subliminal. In any case, one must apprehend the per­ceptible, and the world, in fairly compact assemblages. That said, what good is it to think of filling the sphere of the fixed stars with grains of sand gathered, or fitted, together in larger and larger balls, if we don't to some extent want, by means of an arithmetic, to make a certain model of the world rational? At least to make it possible?

This was the reasoning followed by the calculator Leibniz in the Baroque period, encouraged by his own conception of monads and by

13

The Birth of Physics

the animalcules discovered with the microscope.5 Archimedes, like Leibniz after or Democritus before him, is a geometer of the infini­tesimal. In the end he arived at indivisibles, in the manner of Cavalieri, like Leibniz with the monad and Democritus with the atom. Or Giordano Bruno with his unities, or Pascal with some mite. And so he had no choice but to refer to the grain. To any grain, taken in general, a grain of sand, for example. And to dream for a moment of constituting the universe by these simple means, as every circle, every sphere and every spheroid had taught him in geometry. Thus his scales of order. Thus also this model which has remained canonical. Each time it is reconstructed in history, it is redesigned by a worker of the infinitesimal who is at the same time, from a certain point of view, an atomist. Bruno, who quotes Lucretius by name, Leibniz, and a few others, holds together what was separated, but analogous, in Archimedean mathematics and Epicurean physics. Hence the sphere of the fixed stars is filled with a sea of sand. Relatively filled, to be sure, since voids appear, lacunae at the tangencies or the contacts of the grains among themselves. A first model, naive, minimal.

The Sand-Reckoner achieves results and forges methods: the theory of ordered intervals, what we may call an approximate arithmetic cubature, what we may call Archimedes' axiom. But this harvest, brilliant as it is, may hide the essential point. The Sand-Reckoner builds a world and places all these means at the service of a model. So powerful that history will take it seriously, though as false, and will reiterate it each time the new calculus encounters arithmetic. Now this schema, there is no getting round it, is atomistic. In the final assessment, the universe is filled with grains and their lacunae, that is to say atoms and voids. Of course, here, things are homogeneous, the model is set up as closed, static, without movement, almost geometric; but we should not forget that Archimedes always thinks of this in terms of maxima and minima. There may exist at least the ten to the power sixty three of these grains. Elsewhere, in The Cattle Problem, even more, perhaps: bulls and cows, different colours. The model is naive, the model is the limit. This is the infinite in Gauss' sense: mathematically finite and physically infinite. Finally, the strategy of progressive orders clearly suggests that one may as well never stop. This clarifies the discussions of the finite and infinite; either by the formation of large numbers, or by the notation of ordered progressions. Epicurus' reflection on the limitless whole in the forty-first paragraph of the Letter to Herodotus, elucidated by Lucretius at the end of Book I by the example of the archer who shoots an arrow beyond the boundaries of

14

Mathematics

the universe, rests on nothing but the theory of excess, canonised everywhere in the Syracusan corpus, and summed up in what we shall from now on call Archimedes' axiom.6 Technically speaking, the atomist universe is Archimedean.

By way of confirmation: the term tomos, rOfloC;, rare and late in Greek geometry, is introduced by Archimedes to signifY the section or frustrum of a cylinder or a cone divided by rwo parallel planes not perpendicular to the axis of revolution, or for the part of a parabola divided by rwo parallel lines. The turbo delimited by rwo inclined planes is thus called tomos. We see the whole model in a phrase.

The work in its entirety is now replete with meaning. It gives expresion, in the purity of form, to this world described elsewhere in terms of the compactness of things. It is the poem De forma rerum. In six books. An arithmetic of sand. An infinitesimal calculus, by the integration of indivisibles. A plane geometry of vortices and spirals. A stereometry of the volumes of revolution, conoids and sphereoids. A statics of levers, of equilibrium, of inclined planes. What is an inclined plane, if not a lever generalised to rwo dimensions? A hydraulics of floating volumes. The whole, without exception, focussed around a single locus. It is a matter of grains and wholes, and of counting them. Of the constitution of the geometric idealities by a multiplicity of elements. Of weight, of fall, of drives. Of equilibrium and the loss of equilibrium through inclination. Of the formation of stable spirals and spiralling vortices. Of the immersion of this mechanical, geometrically constructed model into liquids. Everything we need is here, nothing is missing. No omission, no repetition. It is rare, it is miraculous, that we may read openly, in a syntax as transparent as a work of mathematics, the coherent semantics of a universe already constructed. Yet none­theless this is the case.

This certainly stems from the fact that Archimedes was never a compiler, unlike Euclid or Apollonius. He is one of those rare writers who doesn't burden himself with repetitions, who is compelled to write only in relation to the new. Consequently, the space he describes and the forms he considers are plain to see without the need for laborious sifting.

This, in geometry, is a world of revolution: spheres, cylinders, and quadratics. But, first, in a single plane. Why, essentially, spirals? Why, in practice and technology, the water-screw? The water-screw, whose achievement is to overcome gravity for the flow of liquids? This is the form of the waterspout, which, precisely, breaks the law of gravity in the Lucretian model.

I5

The Birth of Physics

It is striking that for the first time in history the author gives a kinematic definition of what relates to the screw (henceforth called Archimedes' screw) . Before atomist physics, a mechanics emerges. The fall in the void and inclined movement. Before Archimedes' geometry, this same mechanics becomes established; as though it were indicative of an analogy between the two bodies of work. Hence the spiral: a point moves on a line, uniformly. Like an atom in the void on a gravitational geodesic. And this line will turn; we shall come back to it. Now, consider the last propositions before the definitions, seven in number, that open the analysis of these very curved lines in the book On Spirals; that is, preparatory statements ten and eleven. There we see, drawn on the plane of configuration, an infinite sheaf of parallels or lines, along which points spread out one ahead of the other. There we see atoms fall. Or move with an equal speed. From top to bottom, if you will, or in whatever direction you like, it's not important. Lucretian physics speaks in both ways, as far as I can see without any contradiction. Globally, no­one can imagine a top or a bottom to the universe. Locally, for a mechanical model, which has points of reference in relation to which a movement is described, direction is defined. It is, in general, unimportant. The explicit thesis of the plurality of worlds gives added coherence to this distinction between the global, the local, the whole, the part. Better still, our reading is thoroughly borne out by the double affirmation that there can there be no privileged direction, yet that we can still outline a single schema for the fall: it is a laminar flow, in particular vertical. Ultimately, it opens the possibility of a formal model: that of Archimedes. This concerns a kinematics in general, in which the movements of heavy bodies is a special case. Atomist physics was already general and abstract, at least sufficiently to require a geometry or a kinematics. Or to make them possible.

So here is the model. In which points run on from each other without being able to catch each other, arranged on parallel geodesic lines. What is this but a spiral? What else but this line in which the points are brought to one another and related mathematically? The vortex conjoins the atoms, in the same way as the spiral links the points; the turning movement brings together atoms and points alike. From Archimedes to Epicurus or to De rerum natura, the relation is the same as that which separates and unites the physics of gases and the kinetic models appro­priate, more or less, to account for such phenomena. From the vortex to the spiral, the relation has the same operative function. The idea belongs less to classical physics, dominant until the beginning of the nineteenth

16

Mathematics

century, than to a conceptual grasp of the operation of models that came later. It is not anachronistic to claim that it was established in Sicily or elsewhere, and before our era. We have forgotten it, that's all. In mathematics, too, the end of the nineteenth century brought a return to the Greeks. And it was the same return.

I can reveal them - this relationship, this operative relation - not only in the global form of processes, but also in a singular decisive point. So now the line turns. I have said that in Lucretius the clinamen was a differential. And, according to him and his predecessors, the minimal angle of tangency, or, better, of contingency, between the geodesic of the fall and the beginning of the spiral. Indeed, it turns out that the determination of the tangent to the spiral, in the propositions which follow in the same book of Archimedes, forms 'an isolated result, the only one that we have to cite, strictly, as the ancient source of differential calculus.' And it is not I who says it, you don't have to trust me. Bourbaki himself proposes it. In the two ensembles to be compared, declination appears as anaS, hapax, once only, and likewise the tangent to the spiral. They are two remarkable singularities of analogous form, of a similar kinetics. Their definition is the same, according to differential calculus, and their function identical. Therefore, these two singletons are in perfect correspondence. Do we need to rush to the aid of such a marvel? Yes, soon, when we have examined the corpus of statics, itself entirely oriented towards inclination.

A remark, nonetheless, in passing. In an old work, not yet published, I thought I had established, geometrically, that the general method of division into dichotomies, as Plato develops it in the Republic, is formed, precisely, as a spiral. This curved line, defined by diagonals, beginning at a common point, of successive squares, increasing or decreasing, gives coherence to the dialogue, to the cosmology of two times, direct and retrograde, to the paradigm of the weaver. From which we see that the Greeks did not neglect to establish a relationship between the spiral form, movement and shape together, and the operation of polytomy. That is to say, elsewhere and physically, between the atom and the vortex. The relationship exists in Epicurus, but it is there too, in its pure and abstract formality, in Plato. It is there, we could say, as an idea. It is in Archimedes and it is in Lucretius. It is physics on the one hand and mathematics on the other. Hence the modelled relation. Quod erat demonstrandum.

Archimedes is a very difficult author, lofty, as we say of mountain passes. Deeply rewarding and dense in style: an intense intelligence

I7

The Birth of Physics

bridges meditations. So much so that Viete, for example, sometimes thought him counterfeit. He works in adamant, in this luminous density that he holds in the hollow of his hand. Just as Pasteur maintained that he had only had one idea, widely-held, followed, scattered, repeated everywhere, that of asymmetry, so the 5yracusan meditated until his old age and his death by the sword, on the notion of deviation and of excess. He too only ever had one idea.

It is true for the arithmetic of sand, for the chains of numeration. True too for his famous axiom. It is true of the spiral line that con­tinually deviates from the circumference, that locally exceeds one and catches up with another, for as long as one likes, and which curs a polar line into breaks. It is true of chiliogons inscribed and circumscribed to sum the area of a circle, of polygons, of stairs, constructed for quadra­tures and cubatures in general. It remains true of the methods which he gives in place of integral calculus, the inequalities or the framing of the 'Riemann sums.' This is said again in the first lines of the Stomachion: 'I will next describe the angles which, taken two by two [forming two right angles] , so as to conceive of the arrangements of the shape which may be obtained, whether the sides presented by these shapes have the same direction, or whether they deviate a little from this direction so that they are unnoticed; for it is a question of skill, and if these sides deviate slightly, tricking the eye, this is nevertheless not a reason immediately to reject the shapes which are formed. '7 It is with thinly disguised pleasure that 1 cite this game of completion of a given space by elementary forms,8 in which composition takes place, in which the assembly of elements occurs, taking into account a deviation, a slight discrepancy, so slight, he says, that it is imperceptible. Does one often speak in a text on pure geometry of deceiving the eye with regard to an angle? And if one does, isn't it under the constraint of another vision? 1 continue, it is always the same. This remains true for the whole set of problems collected under the heading of VEUOU;, neuseis, or in Latin, inclinatio. It is such an important core in the system of Archimedes that Thomas L. Heath devotes an entire chapter to it in his seminal study.9 We know, of course, that the technique of the VE'UOEL<;, neuseis, is commonly used, among others, in solving the famous problem of the trisection of any angle. It is true, moreover, for deviations in equilibrium. Which brings us back to statics.

18

Mathematics

Archimedes, or the concept of deviation

A remark, nonetheless, in passing. The Book of Lemmas is absent from my inventory. But no one is really sure about the authenticity of this text. Its style is not at all that of the author, and moreover the world it reveals is not entirely consistent with the rest of his work.

Even so, there is a way to defend it. As everyone knows, the whole thing turns on the establishment of that curious shape, the aUALvov, made up of four semicircles, in which three are on one side with their respective diameters aligned, the fourth forming the other. Proposition fourteen (fig. I) .

Mathematicians, beginning with Barrow, have argued about it.'O Either this is a aeALVOV, selinon, a half-moon, or a salinum, a salt-cellar. Barrow's opinion aligns itself with the geometers and the lunules of Hippocrates. But Heath's reasoning in favour of the table implement is impressive: he quotes Sicilian dialects, mentions archeological digs." Heiberg nonetheless chooses acALvov, selinon, celery leaf, with the accord of Paul Ver Eecke.'2 The decision, here, is Husserlian. Consider it as a morphology 'toothed, notched, in the form of a lentil, an umbel,' of which Ideas said, comically, that its inexactitude keeps it, in essence, from ever being mathematical:'3 this is a superb and ancient confusion of the pure and the metrical, to which all of geometry from its origins to topology, from the Greeks to Riemann, gives credence in its history and its work. It is rigorous, anexact. And not precise, exact or inexact. Only a metric is exact. In short, moon or salt, celery or umbel. Which leads me to notice Greek words in which the vowel of the initial syllables changes. Examine, if you please, the term aUAo�, salos: it means the roughness or

19

The Birth of Physics

the flood of a stream, the turbulence of the sea or the unrest of the soul. OUAEllW, saleuo, the verb: to shake, agitate, wreck; set a horse inro motion; to be balanced, as in a boat that rolls; to be unsure, hesitant or confused. The semantic field here is Lucretian, Archimedean as well. If you now turn to the inflection indicating matter, you have the reduced model of this discord. The Salinon of the Lemmas is a fluctuating curve, the disequilibrium of the swell, the pure matrix or model of the turbantibus aequora ventis, and distant ancestor of our unfolding systems. Archimedes and Lucretius, as the predecessors of Rene Thom.I3 Cantor, already, in his great Geschicte, had timidly proposed the term salos, before we could see as clearly as we do today. The singular form of salinon comes back again to the same world, and The Book of Lemmas is original.

And, once again, Silius Italicus: he knew the waves of the sea, their roughness, the law the ocean waters followed in their ebb and flow. The Salinon was better than On Floating Bodies.

The world, in geometry, of the Co no ids: cone, in Latin, may be rendered by turbo; the hydraulic world, in which, for the first time in history, mathematics modelled liquids; a world deviating from equilibrium.

And so I come back to statics. The text On Plane Equilibriums begins with three propositions that define not so much balance as the angle of inclination. By the inequality, on the balance beam, of weights and distances. From which it follows that the simple machine called the lever is nothing but an inclined beam, that the inclined plane, which will play such a great role in history, is nothing but than the extension of the lever in two dimensions; in other words, that a lever is nothing but the section of an inclined plane by a plane which is perpendicular to it. Everything begins with balance, but on condition that it tilts. The theorems of statics generally lower the angle of inclination and the inequalities that cause it to zero; it is a negation of the same kind as will reign over this science, up to Lagrange and his principle of virtual speeds, and even beyond. As Archimedes points out at the beginning of his book, equality or equilibrium are only special cases of proportions or angles. Thus statics would have had nothing to say, and practice would never have done anything rational, if no one had ever gauged what happens when there is a deviation from zero, or away from balance, in all phenomena of inclination. They would not have known what must be brought back to equality. Hence the first lines of the book, which in effect make possible the whole discourse, the discursive nature of this science;

20

Mathematics

otherwise it would only have repeated forever the horizontal identity. As elsewhere one would have repeated the principle A is A. And this is mutism. Statics, henceforth, is a discourse on inequality, which cancels itself out as it grows. It evaluates the deviation, describes it, measures it, and brings it back to zero. From which arises an unexpected coherence in Archimedes' work. In the procedures of rectification, quadrature and cubature, it was also a matter of framing a state by more and less, for example by inscribed and circumscribed polygons. The procedure is invariable. We evaluate what happens to the left and the right, and we bring it back to the mean. We were outraged that the demonstration of the parabolic segment uses a lever; it is not proper say the moderns, it mixes mechanics with geometry. On the contrary, it is superior as a system and testifies in favour of the unity of method and the coherence of a world. For it is a matter, in both cases, of making a perceived difference vanish, as one might say. Without this fundamental step, statics would have yet to be born. It is he who made it possible and expressible. Without him, no lever or simple machine, no block or tackle, no polis­paste or winch. No human praxis in general.

This idea goes to the heart of philosophy, that is, metaphysics. If we had only the principle of identity, we would be mute, motionless, passive, and the world would have no existence: nothing new under the sun of sameness. We call it the principle of reason that there exists something rather than nothing. From which it follows that the world is present, that we work here and that we speak. Now this principle is never explained or taken up except in terms of its substantives; the thing, being and nothingness, the void. For it says: exist rather than. Which is almost a pleonasm, since existence denotes a stability, plus a deviation from the fixed position. To exist rather than is to be in deviation from equilibrium. Exist rather. And the principle of reason is, strictly speaking, a theorem of statics. If things exist and if there is a world, they are displaced in relation to zero. And if there is a reason, it is this inclined proportion. If there is a science, it is its evaluation. If there is a discourse, it speaks of inclination. If there is a practice, it is its tool. We do not exist, do not speak and do not work, with reason, science or hands, except through and by this deviation from equilibrium. Every­thing is deviation from equilibrium, excepting Nothing. That is to say, Identity.

This is the locus of Archimedes' first discourse, the condition of his unitary science of forms and numbers, measures and perpendicularities. It speaks incessantly of inequalities apprehended or else, on the other

21

The Birth of Physics

hand, beyond apprehension. Better, it is the deviations which allow him to speak, as is the case for every speaker. Which make him walk like every walker. Which make him reason straight, that is to say slopingly. Against Platonism. Which make him, in particular, invent statics, in the heart of an eJtLa"t'Y]!l'Y], episteme, which has the same root. The old Sicilian is at the root of the old principle of sufficient reason. Thus at the source of existence, of speech, of calculation and of the efficacious act.

And this is, once again, the locus of the first atomist discourse. Nature runs, indefinitely, down the river of its heavy elements, towards an equilibrium. The beam no longer has a balance-point. Here or there, yesterday or tomorrow, deviations appear stochastically. Or differential angles of inclination. Here is something rather than nothing, here is existence, here are vortices, spirals, volutes, all models out of equili­brium. They are brought back to zero by deterioration, ruin and death. But, temporarily, they form. If they exist, it is as deviations from equi­librium, and if they form, it is by the differential of deviation, its suspended inchoation. Now atoms are letters, they are combined into sentences, and join to form volumes. Thus, ifI can speak, it is once again by this deviation, by this incipient volume. Archimedes brings rigour to our principle of reason, which is simply existence; Epicurus and Lucretius find its realisation in the world, and, as we say, naturalise it.

And this is, today, the new locus of our science. We have learned that repetition is redundant, we are beginning to suspect that laws are empty of information. Knowledge is a function of rarity. What exists, sand, pebble, bull, cloud, galaxy, neighbours on the improbable, in view of the principles of equilibrium. This overthrows, point by point, the ancient knowledge, according to which we know in the end that what is certain is the non-existent. Existence. And yet all this exists. All this is formed against the old laws, even if it dies by them. And the old science is that of death. Or of Mars. What is born exists, in the sense of the old principle of reason, rather than the redundant nothing, exists out of phase with regard to any equilibrium. We are, this morning, Archimedeans for forms and stabilities; and we are Epicureans for angles and vortices. And by the grace of Aphrodite. All is, all is thought, spoken or worked, in and by the deviation from equilibrium. Here, once again, is the nature of things. And great Pan is reborn.

Aphrodite emerges from the waves. If you will forgive me, she is a floating body. The proof begins once again. Here is the birth of hydrostatics. Lagrange, like all the historians and commentators, cele­brates the famous principles. He is right, but he forgets, as does the

22

Mathematics

tradition, to pay attention to the contents of the theorems. Now, they overwhelmingly repeat just one thing: put a body in a fluid - will it lean, will it float straight? It is still a question of the same angle, of the same deviation, and the same inclination. In Book I, this is contained in propositions eight and nine, the last, relating to the segment of a sphere; throughout Book II from the second statement, relating to a right segment of a paraboloid. Thus the entire text of On Floating Bodies, or almost so, attempts to resolve only one question. To efface, to maintain an angle, for volumes of revolution. As if a cone reappeared, in a hydraulic medium, in these things which come from cones. De turbine turbinum. Our model is still there.

He is finally in his true medium, that is to say fluids. He rediscovers the flux of the Epicureans. But the annulment and return of the angle also announces a technology, offered up to fortune: the architecture of vessels, and this by the theory, mastered at last, of rolling. Spheroids and conoids are pure models of keels and hulls. Now every French sailor must know that until recently the common term for pitching and rolling, was the turbination. One of the elements of the restoring couple was, for example, called the centre of Archimedes or of turbination.14 Here, in a way, is the first meditation on a turbulent medium. This is indeed a statics, but it goes beyond statics. It is almost a dynamics. Of course, the theory of couples will lead the above-mentioned movement back to rest, but, for the moment, it will still have mobility. The statics of floating bodies consists in erasing an angle that will reappear without rest. It subsits indefinitely on one side or the other of zero. An effect of upheaval in high seas, of the wind on the waves. The proto-dynamics of Lucretius consists in asking 'what really happens when this angle appears or subsists over a length of time?' And the answer is 'everything'. That is to say nature, the birth of things. And the appearance of language.

The theory of equilibrium in a fluid medium imposes, once again, a deviation. It occurs, annuls itself, reappears. It vanishes and is reborn, differentially, at the whim of the turbulence, indefinite in time and place. It expresses turbulence, it is its inchoation. The frigate Venus is meta-stable on the waves.

Nothing is missing, now, for the mathematisation of the model. It is furnished with a geometry, with a theory of numeration and numbers, with an analysis of series and large populations, with an axiom of the infinite, with a metrics and a refined description of the forms of revolution (in general conic) , of spirals or vortices, of the agitated profile of the flow, with a statics and a hydrostatics of the declining angle. And

23

The Birth of Physics

its disciplines, taken together, are not disparate: they are focussed, like the model itself, on a global theory of deviation. Towards the principle of reason. Towards the inclining reason of what exists or will be born. The Archimedean De forma rerum is also a De natura.

On one hand, the model as it is gives the works of Archimedes a systematicity that the history of sciences does not recognize in him, the unity of an idea arranged in a coherent space. It no longer forms a library, a rubric of results and methods among others; they are an encyclopaedia, a monument that testifies to a world. None of his theorems is exempt from i:his convergence and this testimony, and nothing that this world needs is absent from the inventory. Everything is there, nothing is lacking, with no error or excess. The inventory is exhaustive. Archimedes is the Euclid of the Epicurean world. His system is abstract; what is more, his system is physical. The way is opened between the pure sciences and the applied sciences, from the latter to technology.

The misfortune, or rather culture, history, was such that the appar­atus was only put into operation on the walls of Syracuse against the Roman armies, trained in columns. Only on the field of Mars. Hence Lucretius' detestation and silence. Of all the ancient sciences, the highest and the deepest, and the most faithful to the nature of the real and the closest to human practice, crumbled before the martial impulse, before violence, war and death. It was no longer a matter of birth and nature, but of the plague and the pyre. Athens is blockaded in Syracuse. Archimedes dies by the sword, cut down by the plague of violence. Multo cum sanguine saepe rixantes potius quam corpora desererentur (shedding blood in battle rather than desert the dead; VI, 1285). How can this wisdom now be saved from the dominion of Mars? How to check the downward spiral to Book VI? This is Lucretius' problem, it is his despair. To save Aphrodite's nature from the talons of war, to found a Venutian knowledge. To preserve the work of Archimedes by changing the contract, the fledus.

On the other hand, the model is no longer exclusively descriptive. It is mathematicised throughout. As Archimedes' results are adapted to the model without omission or exception, so in just the same way the model is mathematicised without exception or omission. Everything is there, nothing is lacking, the inventory is complete. Atom-grains in the infinite void, the minimal or differential angle of the vortex produced, and the deviation from equilibrium in the fluid medium. And so on, until the end. Better, no discipline of the mathematical organon, known or

Mathematics

unknown (or discovered at the time) , is absent from the rubric. Arith­metics, numeration, geometry, plane and solid, new calculation by exhaustion, mechanics and hydrostatics. We can no longer read the atomist physics as a naive phenomenology of things, it has rigorous support. Or rather, a well-formed analogon. It begins with Democritus, and the edifice is completed, crowned, by Archimedes. A mathematical physics, close to the world and proven, in fact existed among the Greeks who were not supposed to have one. Traces of it abound in the De rerum natura, but Lucretius, I repeat, tried desperately to change the contract ­as we must urgently do today.

Let us consider, as carefully as possible, the Renaissance renewal and the institution of the science that foreshadows Out own. What is torn from Aristotle, is, once again, the Archimedean world. The inclined plane, statics, hydraulics, differential pre-calculus. It is indeed said in The Sand-Reckoner that the world is heliocentric, following Aristarchus. It parallels the model taken from the Epicureans: the vortices and the fluids, an equilibrium of solutions, meteors. This is not only the Timaeus; practices and experiments are instead turned towards hydrostatics, collisions, weight, and inclined planes. Everything indeed takes place as if the institution of applied modern sciences was not, as has long been thought, a break, but the slow resumption of this analogon, formed before our era. Of course, Leonardo, Galileo, T orricelli and company up to Descartes burn their bridges with the Middle Ages and scholasticism, but Epicurus and Archimedes too already form a non-Aristotelian universe. No, physics and mechanics were not born in an instant, from the void or contemporary pressure alone, at the moment of the Renais­sance, they are reborn, that's all. And they will also take a long time to arrive at Archimedian perfection. Until Pascal, until Leibniz, who speci­fically acknowledged him. The true founders of modern science, and I'm not talking about its first halting steps, saw themselves less as the heirs of Copernicus or Galileo, than as having learned their trade from the works of Archimedes. The perspective is reversed by Kant, for reasons which stem from Newton and Bradley, as I have tried to demonstrate elsewhere; it is consecrated by the lay ideology of the end of the last century, in which the crucial battle was to wrest pedagogical power from the Church. Hence the need for eponymous marryrs. Contemporary historians repeat the discourse of their founding fathers. From one religion to another.

The Birth of Physics

NOTES

I II, 220, cited above, p. 4. 2 P. Tannery, Pour l 'histoire de la science hellene (Paris, Gauthier-Villars, 1887).

Silius ltalicus (25-101) Punica. 4 II, 7-8: 'to stand aloof in a quiet citadel, stoutly fortified by the science of the

wise (doctrina sapientum) . . . '

5 Le systeme de Leibniz et ses modeles mathematiques, (1968, P.u.P.), Vol. I, p. 368-71. 6 I, 968-73. Epicurus, The Epicurus Reader, Selected Writings and Testimonia, ed.

B. Inwood and L. P. Gerson (Hackett, Indianapolis, 1994) . 7 Texts of Archimedes: P. Eecke, Les Oeuvres completes d'Archimedes (Paris,

Blanchard, 1960); The Works of Archimedes, ed. T. L. Heath (Cambridge, CUP, 1897); Archimedes, trans. C. Dikshoorn (Princeton, 1987).

8 The problem of the Stomachion is well defined by Lucretius, on the subject, precisely, of color vision: 'just as often some square thing is made up out of different forms and diverse shapes with a single shape, then it were natural that, as in the square we perceive that there are unlike forms, so we should, etc.' II, 788-801.

9 T. L. Heath, A history of Greek mathematics II (Oxford, 1931). 10 Isaac Barrow, Geometrical Lectures: exploring the generation, nature, and properties

of curve lines, trans. E. Stone (London, 1735). II Op. cit. 12 J. L. Heiberg, Mathematics and Physical Science in Classical Antiquity (London,

1922). 13 Rene Thorn, Stabilite structurelle et morphogenese, W.-A. Bengamin, 1972, passim

and p. 101-5. Structural Stability and Morphogenesis: an Outline of a General Theory of Models (Perseus Press, 1989).

14 Couples are opposing forces acting along parallel lines in such a way as to produce rotation.

RETURN TO TH E M ODE L

Turba, turbo

The physical theory of turbulence contains a paradox. Laminar flow, the figure of chaos, is at first sight a model of order. The atoms pour out in parallel, without mixing or sticking to each other. These preliminary rows are already a taxonomy, as the word itself indicates. Turbulence seems to introduce a disorder into this arrangement. This is what the language means: turbare means a disorder, a confusion, a disruption or, as we say, a perturbation. Disorder emerges from order.

Yet it is precisely the reverse that is to be described and that occurs. Physics tries to explain how things and the world are formed naturally out of the atomic chaos, in other words how an order, or several orders, emerge from disorder. And it is turbulence that secures the transition. This seems contradictory.

The description of the chaos-cloud, of the first nebula is canonical, it is repeated in many places, and in particular in the Book V, on the birth of the world. It deals with the multiple distribution of the great elementary population at the heart of the stormy mass. The terms employed in this description belong to two families, topological and mechanical: intervals, paths and connections on the one hand, weight, movement and collision on the other. These determinations fluctuate. They fluctuate in and by turbulence. The turbare, here (Book V 439), is the fluctuation of figures and movements. Order or disorder, it is difficult to decide.

The vocabulary of the following lines provides a local index of the problem. Everywhere else in the poem, terms with a prefix of separation like division, disjunction and so on, indicate a drift towards disorder and what seems to be a return to chaos. Things which are already formed scatter by wear and tear, they disintegrate because they are only porous conjunctions. Everything flows and turns to dust, nothing is stable but the atom, the void and the whole, to which the operator of division can do nothing. Here, on the contrary, disjunction is arrangement, segregation constitutes coherent parts. By earth, air, fire, and water,

The Birth of Physics

distribution will lead to the order of the world. The interesting term here is discludere, to close by a limit, which has no equivalent in the French language.! The dichotomy does not cut, it defines, it surrounds the closure of a limit, it delineates a boundary. Within the space thus enclosed like meets like. Or rather, conversely, the specific convergance [convenancel or identity, the assembly of the analogous, delimits zones in the disorder which are distinguished from each other. The earth is separated from the waters, air divides from fire. Thus the operator whose task in general is to pulverise, works here towards distribution, towards an inchoate organisation.

Weight and complexity are the engines of separation. Fall assures difference, as creation. Once again, the fall gives order, as well as drift, decline, disorder. Always the double operator: the fall, here, is productive.

What is true of the divisions and of the fall is not completely so for turbulence. When the ether was separated from the air by its lesser gravity, it tore itself from the tempests, immutable as the Pontus (which also flows) , and seemed to enjoy a certain ataraxy.2 Now these troubled storms are the place both of turmoil (turbantibus, turbare)3 and of vortices (turbinibus) .4 There is a distance between turba and turbo. The first designates a multitude, a large population, confusion and tumult. It is disorder: the Greek LUQ�1'], turbi, is also used of the mad dancing in Bacchic festivals. But the second is a round form in movement like a spinning top, a turning cone or vortical spiral. This is no longer disorder, even if the whirl is of wind, of water or of storms. In fact, the turning shifting movement is that of the stars, of the heavens, now and originally. The world in its globality may be modelled by vortices. The origin of things and the beginning of order consist simply in the narrow space between turba and turbo, an incalculable population tossed by storms, by unrest, in vortical movement. Perhaps there is an analogous distance, in French, between turbulence and vortex, if we take these words in their everyday sense, apart from fluid dynamics. The first is simply disorder and the second is a particular form in movement. Form and movement, linguistically closest to what has no form and whose movement is only fluctuating agitation.

The behaviour of the cone or the top is worth analysing. Throw this toy and describe, as Plato did, what happens. It is in movement, this is certain, yet it is stable. It even rests on its point or its pole, the more so as

its movement is rapid. All children know this. But its rest is still more paradoxical. The top may move about, by translation, without ever losing its stability. To repeat, it can do so as long as it turns very quickly.

Return to the Model

Even better, its axis may lean, take on an inclination, without putting the movement of the whole in too much danger. It may again rock, by nutation, oscillating around a mean location. This very ancient and quite childish machine is marvellously instructive.

First of all, it combines all the movements known and thinkable at the time: rotation, translation, fall, leaning and swaying. An integral model, additive, overcharged, yet simple. Second, and above all, it conjoins in a simple one-off experiment phenomena judged or presumed to be contradictory. It is in movement and at rest, it turns yet does not move, it rocks and is stable. The simplicity of a complexity, firsi: and foremost, an additive machine; a synthesis of contradictions, beyond anything else. Now it may serve as a little model of the world, for a naive, simple and local orrery. It quivers, at rest, it moves forward, turning, like the heavens, like the stars.

Plato passes a little quickly over the spinning top [Republic 436d ff] . He describes the claim that tops are at one and the same time both stable and in movement as subtle but playful, since all that is required to escape the difficulty is to distinguish the immobile axis and the rotation circumference. In his eyes, this separation of the elements eliminates the contradiction. It can be done, he adds, on the condition that the axis does not lean to either side (OUOUIt'l1 YUQ anoxALv£lV) . If, in fact, it does lean (EYXALV'I1) left or right, forward or backwards, then it is clear that the top is no longer at rest. Plato has no notion here of rest in and by movement itself: the axis of the top sways around a position of balance, there is an invariance by variation. And the interlocutor, more wise than playful, can still assert that this distinction of the axis and the circumference does not lay to rest the opposition of movement and rest, nor their union, and that the top remains whole, at once whirling and stable. The fact remains that this little model in practice reunites what the dialogue holds to be contradictory. The fact remains that Plato did not give any thought to inclination, did not consider deviation, even in the angle of nutation. Lucretius, and atomist physics, covers these areas abandoned by Platonic geometricism, covers the temporarily meta­stable leaning and whirling, the concrete contradiction, the turbo of the top, unstable, immobile and mobile.

The children's top, 0LQO�LAO£, strobilos, the QOIt�O£, rhombos or bull-roarer, games and magic rituals frozen in the diamond-form of Euclidean space, here reveal a solution, easily formed, to all the difficulties of a self-same operator functioning, almost at wilL towards contradictory results. Is it stable? Yes. Is it unstable? Yes, again. Is it

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The Birth of Physics

rotating, does it follow a circumference? Yes, ever again. The top is a circum-stance. Can it move forward, lightfootedly? Yes. Can it lean? Yes, in all directions. So ask some questions constructed around yes and no; the possibility of finding, building and observing an object that will not be destroyed by this difference is hereby established. The vortex is unstable and stable, fluctuating and in equilibrium, is order and disorder at once, it destroys ships at sea, it is the formation of things. And so on: the sun dries the earth, it melts wax; fire melts gold and shrinks leather; the wild olive is a feast for goats, but bitter to men; marjoram is poisonous to pigs and a remedy that brings us back to life; atoms can be pathogenic germs. What is more, a single plant, for us too, may kill or cure us. This pharmacology is under the sign of the top. Not only is the thing decidable, but it is constructible, look at the top. That is how it is, in the thing itself, and no discourse can change it. As if the contradictions separated themselves, as if they repelled each other, in the battle of reason and language, while the contraries cohabited in the black box of things. If, one day, some subtle and playful dialectician disconcerts you, be quiet, don't answer, join the children, play at tops.

Hence there is a chaos-cloud, the turba, the stormy combat of atoms. The chaotic unrest or perturbation is a limitless empty space traversed by movements, collisions, intervals, paths and weights, distributed at random, without conjunction, scattered, opposed, disjunct. The Epicurean rediscovers Empedocles: struggle, war, hatred. Collisions and encounters without union. And so here are translations, rotations, chance vibrations, here are the places of rest for the points of collision, momentary equilibria, deviation. Is it possible that at indefinite times, in unforeseeable places, here or there, yesterday or tomorrow, all these phenomena may suddenly add up, all the conrradictions resolve? There is no reason why all these characteristics should not, somewhere, be co­present. Yes, it is possible theoretically. But it is also possible in practice, since we know how to construct an object that harbours within itself this combat, these oppositions, and these disjunctions, motionless and in movemenr, vibrating and stable, and so on. In such a place, in such a time, dissemination precipitates, as we say for a solid in solution. If this is possible and if this is constructible in practice, it will take place under the sign and the movement of the turbo. Figured against the backdrop, the vortex appears against chaos, and the turbo against the turba. Let there be no mistake, this has been shown.

Lucretius describes two forms of chaos: the streaming-chaos, the laminar flow of elements, a parallel flow in the void, drawn out like

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fibered space; the cloud-chaos, a disorganised fluctuating, Brownian mass of dissimilarities and oppositions. With declination, the vortex appeared against the backdrop of the first; now it reappears against the backdrop of the second. Whatever chaos may be, whatever may be its linguistic origin: yawn, pour, whatever the material movement of disorder may be, the solution is unchanged, the original figure and move­ment remain the same, it is the Democritean dinos. The vortex is thus the pre-order of things, their nature, in the sense of nativity. Order upon disorder, whatever the disorder may be; the vortex arises by a fluxion in the first hypothesis, which is that of chaos-flow, and by fluctuation in the second, which is that of fluctuating chaos. There are indeed no stabilities except in a universe in which everything flows, unstable. Yes, the solution is the same; yet, it is not the same, neither for epistemology nor for the history that will follow. The first of these hypotheses opens a classical knowledge, in which disorder is minimized: it is the path which leads from Archimedes to Pascal and Newton, mechanics, hydraulics, and an infinitesimal calculus, the science of fluxions. Here, coherence is preserved between the local and the global. During the course of this history, which goes up to Laplace, and up to a dominant positivism, the second hypothesis lies dormant. Today, it is reawakening, out of some of Leibniz' dreams and from the other side of Laplace, where chaotic multiplicity slept. Order by fluctuation has become our problem, and our world has become that in which the local and the global no longer harmonize. How can something, rare, emerge from a noise? Or from a radical disorder, and not already ordered.

Slope and extrema

Lines of rain traversed by the oblique flight of the thunderbolt; at one point, then another, lightning pitches all about, tearing itself from the clouds. This is the visible model, as it is realized in nature: the obliquity of a flash on a parallel field, aleatory quasi-ubiquity. The theoretical schema is given at once. Declination, angled obliquely, traverses the field of atoms moving in a straight line. They are parallel to each other, in their movement, like drops of rain. This comparison goes back to the concrete model. The lightning declines, the clinamen blazes, amidst the sheet of water. The notion of the vertical only arises in discussing the fall of more or less heavy bodies. In fact, everything remains equal in the infinite void, including the directions of the field. The crucial thing remains the parallelism of the flow, of the transfer, and the weight,

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The Birth of Physics

homogenous throughout, that sweeps it along. It is an average laminar field. Traversed by declination in its obliquity, aleatory as lightning. Now it is minimal.

Let us return to the clinamen. To acknowledge an almost null angle where turbulence forms is accurate but not enough. First, a detour. Leibniz says somewhere that, from a young age, he debated at length whether he should keep the void and atoms. How the monadology was decided is another question. The fact remains that declination always followed him. His psychology of freedom remains linked to a deviation in balance, to an infinitesimal angle of the beam, to an imperceptible rupture of spatial symmetry. Determination and decision introduce, of themselves, a differential asymmetry, which makes, as we say, all the difference. There is something not at rest here, disquiet, as in the pendulum of a clock. It deviates from equilibrium. Leibniz' universe is doubly regulated, by the principle De aequiponderantibus and by that of the small difference. By that of identity, by that of indiscernibles. The principle of sufficient reason breaks the stability with a small deviation. Such phenomena discerned in the entrails of the subject are no different from those which constitute the world. Coherence is invariable from one structure to another, psychology and metaphysics. Regulating the production of things at their root is the law of the steepest descent of heavy bodies. In which the form of the raindrop is given, once again, for example. This law is differential, by maxima and minima. Things are drawn into existence along the steepest route. They seek equilibrium, following a determinant or decisive deviation. For Leibniz as for Lucretius, the combinations that we must call atomic are linked to the idea of a sloping path. Extreme in both cases.

Whereupon for Leibniz, the maximal thalweg along which existents pitch. For example, the brachistochrone, or the straight line, which will become, by variational calculus, the principle of least action. Maximisation, or optimisation, will occur only if account is taken of the constraints, the global system of limitations, that are said to be inherent in creatures. It passes around obstacles, as close as possible. Even the straight line, for which space counts as a constraint. Existence is the loop of a river that has flowed to a better bed. But there is a bed, that is to say a terrain, in which the inclination hollowed out by the thalweg optimises the flow.

For Lucretius, the whole system of constraints tends to zero as a result of the void. Equilibrium, therefore, is not set upon a plateau: where, in infinite space, could such a plateau be found? Nor can there be such residual original terrenum or residual matter in Leibniz. Equilibrium is

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evaluated on a parallel self-referential plane. Atoms tend, indefinitely, towards stability. Nothing can happen, nothing is produced, in a homogenous field. One could almost say that the primal flow remains in a state of final equilibrium. In Leibniz' terms would this be the greatest slope, that which would overcome all obstacles? No. The maximum, the minimum, are only extremes. They optimise the constraints, but they do not get rid of them. The superlative is relative, it is neither all nor nothing. Now, here, the void has removed the constraints. But, in so doing, it has made direction relative. One could say, if one wished, that the fall of atoms has a total slope or a null slope. It is flow as such, homogenous, endowed with singular force. In a certain sense it is equilibrium, though more akin to a pre-equilibrium. Thus, declination defines a slope. It is the slope that begins with a loss of equilibrium, with a difference in relation to this pre-equilibrium that is the homogenous. Now the clinamen is indeed well-defined by Lucretius, twice over, by a minimum. It is the smallest possible slope opening the path to existence. Could this be a law of the smallest descent of heavy bodies?

Are the De rerum natura and the De rerum originatione radicali complementary to each other, in the way we speak of angles? Do they in fact describe the same process, at right angles? To the greatest slope there corresponds the smallest angle, to the maximum a minimum, to the drop of rain the drop of liquid. In fact, it is one and the same theory of extreme descent. And since declination may be reckoned from the vertical, there will be at least one figure for which the two models become identical. Slipping at some point onto a minimal clinamen, atoms follow the greatest slope. The birth and the origin of things flow from the same source.

Henceforth the clinamen is indeed the smallest deviation and the optimal slope. Here is the descent, the thalweg, the XQ11W011 ' chreode. It is the optimised road to constitution. A track opened through which the flow is swallowed up, a funnel for atoms towards conjunctive existence. Here is the bed of the river: designed, calculated, set down, as the condition of genesis. The inclined plateau where the laminar sheet hits the rapids and rolls in spirals. In annular turbulence which remains stable for a moment and then unwinds slowly down the length of the flux flowing on the plane.

At the dawn of things, in the past and to come, here and there, indefinitely, at the heart of the universe, there exists an inclined plane where coils roll by the temporal flux of matter. Where then does one place the Galilean revolution? If it has balls roll down an inclined plane,

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The Birth of Physics

it is doubtless because it constructs a singular case of the global model conceived by the atomists of antiquity. Galileo knew how to read. The Renaissance, as far as I know, was well named.

The world, objects, bodies, my very soul are, at the moment of their birth, in decline. This means, in the everyday sense, that they are mortal and bound for destruction. It also means that they form and arise. Nature declines and this is its act of birth. And its stability. Atoms join together, conjunction is the strength of things, through declination. This signifies the whole of time. The past, the present, the future, the dawn of appearance and death, tenacious illusions, are only the declinations of matter. They decline and are declined like the tenses of a verb, a word made up of atom-letters.

"

The world, objects, bodies, my very soul are, from the time of their birth, adrift. Adrift, down along the inclined plateau. This means, in common terms, that they irreversibly fall apart and die. The De rerum ceaselessly reveals mortality. Bur their very birth is a drift. And their stability, their conjunction, their existence, are given up to homeorrhesis. The drift is the whole of time: the dawn of appearance, a life marked our by finitude, disintegration, the aleatory fragmentation of multiple temporalities in infinite space. Everything drifts, whatever happens, from the original atoms, the backdrop. Everything drifts from the elementary roots: and so it is with words, these shifting aggregations of atom-letters. Here is the origin of meaning, the transverse lightning­flash on the backdrop that is the background noise. Sense is nothing but its slope, it is the sense of the slope. It is another drift.

Existence, time, meaning and language go down the inclined plane together.

Just like the poem which, slowly and by stages, leans and plunges towards the plague at Athens. Intercut by flashes of lightning, their shafts dispersed by the sun. Inclined hatching that impose, time from time, a new slope. It rolls its pseudo-circular versification, its vortices of conjoined words, on a thalweg intercut by catastrophes. The text declines, it drifts like the world. It follows the law of the extreme slope. The law of creation, as they used to say.

A great deal of pretentious drivel is parasitic on just this model. It drones on incessantly of the pessimism of Lucretius. Its flat Euhemerism reconstitutes intentions and blinds things. As if the Epicurians had never said that the law of the lightning flash was found in the lightning itself and not in the wrath of the subject Jupiter. The law of the text is in the text and not in the ashen breast of the man, long dead. This feeble

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discourse for those who feed off the dead is irrepressible. The author was called mad even in classical times. At least this was a sublime mania, shot through with flashes of intuition, the province of saints, geniuses, heroes. Romanticism was at play in Plutarch. It was comic, but grandi­ose, like the circus. It was at least in the order of the world as seen, where lightning pierces the clouds. We have changed all that. Reduced all to mediocrity. How sad and courageous the poet is. See how he weeps before death and decadence, before fleeting time and the degradation of things. Times were hard, it must be said. Terrible things happened in Rome. Hence the disease: Lucretius was anxious, melancholy, depressed. And since he had a master, he sought an originality that would make him stand out from the great shadow of Epicurus. How he suffered! Look, he has turned into a reactionary little professor, neurotic, narcissistic. We're wasting our time.

The model of time is of an unassailable precision. Physics is con­cerned with weight, heat and fluids. Hence with falling, with the irreversible and with flow. All this needs a slope. The clinamen produces just this inclined path. It quantifies a minimal sense, by which all things have existence and meaning [sensl . This global model is of such fecundity, for the physical and natural sciences, that it is at the horizon of four centuries of research. A horizon that is perfectly clear and not, as one might have thought, obscure. Reexamined, taken up again and redeemed by the great figures of the Renaissance, Leonardo, Stevin (the new Archimedes), and Benedetti, though in relation to quite specific mechanisms: hydraulic projects and the mastery of turbulence during flow, inclined planes, etc. In terms of both experimentation and principle, we still speak of communicating vessels, without seeing that it is a case of a singular hollow body on levelled plane, of just one vessel with a relatively unusual form. It is the old theory of the vessel, and that's all. The mqdern scientific revolution consists in playing Archimedes, that is to say the atomists, against Aristotle. Playing Stevin, whose whole work could have been written by the maestro from Syracuse. In the classical period this play became a strategy, and the particularity of experi­mentation became general theory. This is the century of descent; from Galileo to Leibniz and from Pascal to Maupertuis, the rules of the fall are extended to a universal principle. It was with good reason that the Descartes of vortices was regarded at the time as an atomist. All the resistance to Newton in continental Europe, up to the end of the eighteenth century, bore this influence. The model may have variations, but its structure is always present.

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The Birth of Physics

Here is the crucial experiment, and rightly by a Newtonian. Open the Universal Natural History and the Theory of the Heavens by Kant, the first scientific cosmogony, and one that has aged rather well. It opens with the principles of mechanics in the manner of the atomists, it cites Epicurus, while apologising for this reference to an atheist. That said, it introduces two forces, the Newtonian, that is to say gravity, and another, unspecified, in which we recognize deviation: it produces a plane, said to be a systematic distribution, in which we recognise the obligatory plateau, and in which are grouped the dense conjunction of agglomerated things. There we have it. There follows necessarily a sublime description of rings or spheres, concentric and stable-unstable, of deaths and rebirths. All across the plane, a plurality of spiralling worlds emerge and dissolve. Quasi-stationary or oscillating model of the universe, where degradation is traversed by reprise, origins are traversed by disintegration, and so on, according to a flow constant in direction. Kant never abandoned Lucretius, he thought, perhaps, of leaving him behind in the intro­duction, but he remains an atomist for the whole of his discourse. He takes over the idea and carries it through to its conclusion. Thus he remains a Cartesian beyond Newton, and an Archimedian beyond Descartes. And, when all is said and done, an Epicurean.

For the question raised never strays far from this one: what is genesis in general? The response in Lucretius: atoms, of course, elements, primordial letters, and a disseminated material cloud; but also a deviation, which dissipates a given equilibrium in which nothing comes to life, of a rather, a slope, a declination, a path, and meta-stable vortices which ensue from them. The story continues in Laplace and Comte. And in Poinsot. And no one was really prepared to read as a palimpsest the established plan of the world as conditional on two coupled forces inclined on the equator. As if out of equilibrium. On it are projected and summed all the rotations of the heavens according to the law of a certain minimum. On a stable slope vortices, once again, come together. This is the constant plane of Laplace, displaced from the equator, index for the circular stabilities of cosmology, and for the originary turning cloud (fluid, atomised) of cosmogony. And this is the plane of Auguste Comte, still inclined to a similar degree, and upon which is built a new oscillating model, by the death and birth of models that turn. Behind the writing of the French school, that of Kant reappears. Behind the writing of the cosmogonies reappear the classics, the original slope of things, the curving sphere of the drop of fluid. Under this, the plane of Galileo or that of Stevin. And so on back to the atomists of Antiquity. It

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is through the variations in these writings that what remains invariant shines as brightly as a thousand midday suns. A finite group of con­stants: angle, deviation, slope; calculated, posed, functioning in relation to an equilibrium, an equator, to something homogeneous or indifferent; circles, vortices balls, drops, couples or rotations; two forces and extremes; and the question, finally, of genesis. Vary these constants all you want, and you will still come up with the real flavour of history.

This demonstrates the long tradition in which our present-day efforts stand. Via the Carnot cycle, circle or circulation, the thermodynamic revolution redefined stability: the invariability of the first principle, and the negative deviation of the second, slope, loss or shift, through which fall and disintegration run randomly to maximum entropy, to this final equilibrium from which no genesis can emerge.

Modernity, it is said, comes about by way of this reappearance in a new setting of the same group of in variables. It is as though in the classi­fication of Lucretius, our direct ancestors had thought only of fluids and weights, whereas our closer fathers chose heat. Better still, the heat of fluids. We must begin again. Set in place a new deviation and new geneses, a slope, other curves. Thus, in part, Bergson, whose philosophy concealed, I have argued, an energetic mechanism, and whose vocabulary is taken from Carnot or Ostwald, and who translated, or rather estab­lished, the Lucretian text; thus Waddington and his chreodes; Prigogine, the deviation, open system, vortices once again, dissipative structures, hence Thorn and the mathematisation of the model. Thorn, the new Leibniz and the new Archimedes, in relation to these new Epicureans.

All this is so clear that we may wonder why and how this road, which has never been missed in scientific research, has yet been erased by the historians. In whose interest was it to cut us off in this absurd fashion from .the materialists of Antiquity? Another scholasticism, another Middle Ages?

The pleasure of recovering ataraxy. I am myself deviation, and my soul declines, my global body is open, adrift. It slips, irreversibly, on the slope. Who am I? A vortex. A dispersal that comes undone. Yes, a singularity, singular.

The sea, plain and weighty, receives the wind and its inclined flow. The eye of the wind. The swell, hollow, rises, spreads. The wind picks up, as they say. Under the action of two forces, its passive weight and the angle of the breeze. By the bar of the waves, oblique on the bitter plain, the cyclone forms, it sweeps the new slope. Complex sinusoid, imperfect circle, spiral. Turbantibus aequora ventis.

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I roll my fluid body on the same Sisyphean plateau as the sea itself, disrupted by the squall. A vessel adrift, by the angle of the tiller, that's me. Soon, a few scattered planks will float, here and there, atoms returned to atoms. Now, how do I steer with no angled tiller? I have embarked, and so the angle of the rudder is always there, the condition of my existence, of my birth and of my time. This slanting lightning­bolt governs me, as it governs the universe. If something exists, it exists only as a stone which rolls on the flank of a hillside, as Spinoza says, only as a rolling vessel, have to, in the eye of the wind. And, without this angle, there is nothing. Yet things exist. Thus everything is taraxy, everything is unrest. And the world is vile, so be it.

But the Master Epicurus, many-faced, proclaims the law of physics, that of nature, mine. Irreversibly, turbulence comes and comes undone, as ifby chance. It runs down the inclined plane, re-forms elsewhere, here and there, on the slope. A spiral figure on a laminar background. Meteoric cyclone on the space of sky. Disrupted passage on the stable chreode. Fat sea on the background of smoothness. Ataraxy is the material background of the being, the permanent murmur against which the flying words are outlined, birth and death. Epicurus and Lucretius, before Spinoza, released Sisyphus from hell. Returning him to the whole of nature, they imagined him happy. I accept my dissolution in the burning plasma of matter. And the rest is turbulence. The eternal silence of these infinite spaces soothes me.

Archimedes, in the Lemma of the Salinon.5 The circle, beginning in the hollow of the swell and passing through two neighbouring crests, includes the same space as those which delimit the high and low waves. A stable ring that includes unrest. Local figure of ataraxy. The drawn circle does not calm the waters, it transforms their instability into law. Sophisticated theorem. Ataraxy generalizes the salinon: it traces its path from the troubled hollow to the top of the cliff. The cycle of happy Sisyphus.

Morality is physics. An exact knowledge of natural things. So it is not surprising that right in the middle of the treatise on atoms, there intervenes a treatise on the soul. Its reduction to the objective is a part of the system. It is mortal, neither more nor less than this or that thing and this or that world. It knows all the same, this is the point. And this exception must be reduced. Hence the book of perception and simulacra. Types, replicas of the homologous forms of solid objects, scales, envelopes or skins, ultrastructures.6 The theory of knowledge is isomorphic with that of being. Quod erat demonstrandum.

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But first, as is natural, let us sacrifice to Venus. The text on per­ception ends with conception, in the genetic, generic, generative sense. Genesis of knowledge and genesis of bodies. In other words, how to make love? How to make love to achieve optimal fecundation? Like the four-footed animals: the seeds of the seminal flow thus come effortlessly to their goal, thanks to the lowering of the breasts and the raising of the loins. Here, once again, is the angle of the best slope, the descent of genesis, the optimal flow of fluid. Here is the reduced model after Venus of the physical model. Nothing of our rubric of constants is lacking, not the deviation, not the inclined path, not the fluid solutions, not the maximalisation, not the question of genesis. We are born like many things, in the voluptuous spiral. The flux of the atomic insemination flows by the feminine clinamen. The male weeps over the feminine declination

Lucretius keeps on and again reduces the model. At the end of the book, he refines the apparatus of Venus. And returns to those drops of waters which once plumbed the depths of the void. He has them fall on the stones. The flow, of course, skirts this obstacle, the most impene­trable dam to water. Eventually, it crosses it. It finally pierces the rocky block, it rejoins the greatest slope. And the book ends there.

And here begins, like a sequel: the pleasure of approaching the virgin springs, and of drawing water from them. The pleasure of making crowns. The pleasure of the sweet honey around the cup. The pleasure of the verse. The constants are always there, traversing the whole system of metaphors, the sexual included, however we choose to take them. Invariance by the variation in transports. I say transport, in the sense of ecstasy too.

And so the theory follows. And the question is well-framed: the elements flutter through space; the simulacra or membranes flutter here and there, ultroque citroque,7 on this side, on that, uphill and down; the spectres also appear to flutter, through our infernal anxieties. Thus: to reduce these flights one to the other, the spirits to the simulacra and these to atoms. To describe this movement.

There is a flux given off by things. By things taken as limiting cases: summo de corpore (surface of the body) , used eight times in forty lines (IV, 40 ff). The surface is the summit, it is an upper face. I said a moment ago an ultrastructure. The simulacrum detaches itself as the optimal form of the volume occupied by an object, as a sur-face.8 Far from being naive, the reasoning that makes a transmitter of everything is a subtle calculation of the best path, adopting a principle of least action.

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The Birth of Physics

The interior of the object, the background, its intimate secret, is situated on high: ex alto (IV, 70) . From here the flux descends, spreads to the edges, following paths strewn with obstacles; it is deflected, weakened, its path is not straight: the body, hollow and full, is formed of a conjunctive network in which the stream is ceaselessly captured. It divides, dissipates, diffuses and disseminates. Heat of iron or smoke of green wood. These tortuous paths, in the complexity of the material fabric, are the paths of the fragile soul: it flows, broken, to death, through the twists and turns and confluences of the corporeal channels. It goes around obstacles, breaks up to overcome them. These eman­ations lead to the mouths of bending rivers, ending at the same pores, the same gateways, whatever the barriers may be. As if there were a law of the most difficult action, of a path of the smallest slope. Of the greater complexity of the delta. In the vicinity of its banks, the object is no more than a spray of chreodes.

By contrast, at the surface, at the terminus of the conjunctive network, all constraints are removed. From this first front, it remains the best path. The constraints of the fall, for the atoms, were lifted by the void. Only air remains around the thing, in every sense. Thus the outermost edge, unloosed, may move without delay or break. It can now take the optimal paths, both for the flow and for the invariability of that which is transported. Upon its reception, the edge is all but the same as when it was emitted, and is in principle intact. This river is by far the most rapid and the most faithful to the source. Simul, at the same time, and simulo, simulation.

As for the place of a flux of perception, the envelope has a superior site. Not necessarily the highest in level: the fall through space is a metaphor, as in the tradition of our science, from Leibniz to Carnot, or a special case. So it is for atoms, and for the relativity of directions in the infinite void. But take the ensemble of points from which delays become minimal. From the centre to the periphery of things, they are maxi­mised. At the edge, this reverses: it becomes in this way the best centre or pole of transmission. The stream flows from two springs: non solo ex alto, verum de summis (IV, 74) , not only from on high, the interior, but from the summits, the surface. We perceive very little of the entrails, but essentially the periphery. This is indeed best placed. The thing is a black hole, a hollow crossed by the highest of walls. From them the flux falls; it falls, it flows, it diffuses: cadant, diffosa, fluitare. It fluctuates. Trementia flutant, it floats, it undulates, it ripples. Turbulences. Towards the bottom, subter. It preserves the forms,jormai servare figuram. Now, here

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is the point: the flow takes place according to a law of extremes: multo citius, quanto minus . . . , the more rapid as it encounters fewer obstacles. This is how it is in the interior of the body, where the dams become more common. It is still the same on the errant journey of signals, where obstacles are rare. Except for mirrors, except for echoes and except for other clouds. Where, naturally, we think we see some giant coming down from the high mountains, from where the rocks torn off from their sides roll: where the myth becomes a model.

Review, alongside this, the history of least action, and you might conclude that Fermat and Descartes, Leibniz, Maupertuis, Euler and Hamilton added nothing to this established and finely constructed model but a mathematical formulation. This is not nothing, it must be said, but the thing was formulated by the Epicureans in the tongue which we call vulgar and, quite explicitly, against the doctrine of final causes. The reason why Book IV takes on the Stoics, and also Aristotle and the Timaeus, over the question of finality is because his principle of explanation by extremes leads to him think in this way. One finds the same concern among the classical authors. Yet on the other hand all of history, the whole development as we say, of the principle aligns itself simply with the unities of mechanics, as they are gradually formulated. The shortest path, space; the smallest time; the greatest speed; resistance, work, action, energy, right up to the most complex state, that of the tensor quantity of movement-energy with the invariances of Cartan. Epicurus and Lucretius mark the kinematic state of this question, bereft as they are of power. But for all that, neither Fermat nor Descartes sees much farther, nor Leibniz at the extreme, none of whom could make the vague idea of resistance mathematical. In the middle of the eighteenth century, Euler always - or already? - spoke of a river and its bed, of the speeds of the flux according to the topography of form. In the final analysis, the ones who have given positivity to physical teleology and, let it be said in passing, to the teleonomy ofliving systems, and peeled them away from their adherences to finalism, are, on evidence, the Epi­cureans. Scientific modernity does not enter history by a fault or a break, but by the revival of a philosophy of nature that has been spreading ever since Antiquity. The so-called break is an artefact of the university: one of those ecological niches designed by specialised animals. As if knowledge should have its ground in ignorance.

And if we think about what comes next, if we extrapolate on the sequence of concepts? Might we obtain a highly refined model of sensory perception? Let us imagine a flow of information issuing from a

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transmitter and displaced by a deviation from every receptor, rushing towards equilibrium, among the aleatory turbulence, according to one or several laws of optimalised structure. This is the reiteration of the model, where information has replaced energy at the end of a chain. It is the reiteration, too, of an atomistic metaphor that likens what is transmitted to a mask of damp plaster that retains its invariant features, and which will bounce back from an obstacle, beam or pillar, yet whose pliancy means that it can enfold itself around the form of its target. One day we shall have, if we do not have it already, a theory of perception very close to what is proposed here.

Let us now confirm that the model of perception is reducible to its physical equivalent. We need only follow the text. We have the flow and the descent: perpetuoque fluant ab rebus lapasaque cedant, abundat, iaculentur, perpetuo fluere . . . (IV, 145). This river never ceases to flow. Here is the formation of turbulence: liquidissima caeli tempestas, perquam subito fit turbida Joede (IV, 168), all this is so clear that it would be inelegant to translate.9 Upon reception, the images form quamvis subito, as quickly as one could wish. The quamvis recalls, as a virtual infinity, what was given as quam dicere possis at the definition of the clinamen.1O Which we see, as soon as the law is given, absolutely speaking: thus know, now, the speed of simulacra, with what mobility they fly through the air, such that they traverse a great distance in a brief instant, whatever the place might be towards which they tend by their inclination. The clinamen here bears the name of numen, which is not unexpected for the simulacra; some linguistic attraction has brought the expression to the simulacra numinum, the everyday statues of the gods. Overthrow the gods, topple their statues and you will have, conversely, numina simulacrorum. The elements of perception stand out. The thunder passes, we were waiting for it too, the principle recurs: inmemorabile per spatium transcurrere posse, temporis in puncto (IV, 194), the simulacra are capable of crossing inexpressible distances beyond all reckoning in an instant of time, an infinitely small yet actual minimum or atom of time. Why? For two reasons, one of which in fact relates to the medium's resistance, while the other is the parvula causa that is reputed to be so obscure, yet which is necessary to the proof. II

Declination, in the physical model, was a minimum; if the model of perception is materialist, if the simulacra are formed of atoms and if their flow is governed by the general laws of propagation, then one model is reducible to the other, and the numen is minimal; it is, absolutely, the smallest cause. The principle of extremes is reiterated so

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often in the text that we wonder how and why this parvola has remained unexplained. It is the ciinamen, that's all, it is once again the law of the smallest or the greatest descent. However, it is also true that the declination of atoms remained obscure. The two illuminate each other at the same time. We must note that the parallel is renewed in the classical period: the genesis of the world, grasped fundamentally, occurs according to the same law, at the limit, as that which presides over the propagation of light. For Lucretius as for Leibniz, the order of things is originally formed in the same way as knowledge. From knowledge to being, the inference is sound, and vice versa. This means: in the real as in the perceived, the sequences are identical and preserved.

These inexpressible distances are now actually givens. The space traversed by the light of the sun is equipotent to the whole of the world. It flies, in a point of time, through the seas, the lands, the heavens. This is a limit theorem: in a temporal atom, the totality of space. Now the law of the extremum is so powerful that it imposes the extremum over and again, not only as an upper limit. Light and heat, in fact, are emitted from the heart of bodies, ex alto, and this is why, as we have seen, they are diffused as particles, disseminated here by the conjunctive network within the sun, the most difficult paths. How much quicker and further, quo eitius et longius, will be the propogation of the particles that come from the envelope, fronte prima, from the edge, from the superior site, by the best paths, the constraints removed? Response: in the same time, a multiple space. The speed of light is a point of reference for cal­culation. And this calculation is rigorous, well-known in mathematics. However large a number one may imagine, there is always one larger. Archimedes again. He is no longer the Syracusan who mathematises a model, he is the physicist who applies a theory, a theorem. He gives himself a very large number: the totality of space traversed in the atom of time. It is, properly speaking, the infinite speed. The principle of the maximum applies: this great number, in which this infinite is actually expressed, is only reached by a road filled with obstacles. If the con­straints are removed, the number is exceeded. In fact, quod erat demonstrandum. The flux of simulacra is thus Archimedean. Even light cannot be thought more rapid than this: quo eitius nee lumen eogitari possit. Proof by the (mathematical) idea of the infinite that tradition generously attributes to Descartes. One can see how for this physicist of optics and dioptics God might be spoken of as light. And knowledge. Light of light, true God of true God. Metaphysics is a metaphoric physics.

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The logic of mathematics used here is of an unassailable rigour. Even though it far exceeds physical experience, even its possibility. However, this is an common discrepancy with a long history: the so-called experi­mental sciences were rigorous before they were exact. They did not suffer from a lack of mathematics, but from an excess. Like our human sciences today. This is everywhere to be seen, from the Classical age to Fourier. In short, stars seen directly in a mirror of water are not, for us, a proof. We know only too well that the speed of photons is for the moment a physical limit. But this instantaneous image remains a proof for Lucretius: it is formed simul ac primum, immediately, it does not wait an atom of time. Simulacra simul ac, this equation is in the text. And, once again, the flow descends, it falls. From the edges of the deep heavens to the banks of the earth: ex oris in oras.

A time for reflection, in the midst of a dissertation on physics. Towards the middle of the Book IV, there is a passage, nine lines long, that raises a counter-example to the model.I2 Lucretius must either overcome it, or admit to having spoken falsely. Here it is. Take a building. To begin with, if the measuring-stick is false and the square inaccurate thanks to a deviation from right angles (in the plural, of course, and not only for the particular case of the verticals), if the level (of a plumb-line or water level) is off one way or the other (either by the angle of the line or a deviation of the bubble), then by virtue of this defect and this inclination everything will be built leaning, askew, sloping to the front, pushed backwards, discordant; the building already seems to want to collapse, it collapses, betrayed by errors in the initial judgement. And so it is that reasoning is necessarily false and irregular when the senses [sens] from which it arises are false. End of quote. Every concrete Latin term that reproduces the deviation from equilibrium, the angle of assymetry, or the inclined slope, around the xavwv, canon, the canonical, the rule of the Epicurean mason, is here brought together all at once to reduce my thesis to nothing. Since this material builds only what is false.

Or rather, out of true. The local theory of hollow bodies and the global thesis of mortality show clearly that things, around us as well as in us, seem already to want to crumble. Our soul, an amalgam, of atoms and void, is mortal. The universe, as it is, as it goes on, as it transforms itself, is mortal. The earth shakes and the house falls. All conjunctive tissue is sapped by the void. Nothing is full but the heart of the atom, that is to say the atom. And only the void is immortal, like the particles. Death is this return to particular clouds, the crumbling into dust and for

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dust. Parenthetically, it is the return to immortality, an implication that Leibniz, and, perhaps, ataraxy, have made coherent. So if these buildings, which is to say all of nature, are in danger of collapse, it is simply because they were, at the manifold dawn of times, erected, built, on a deviation from equilibrium. Their duration even increases as the angle grows smaller. My soul is briefer, the greater its declination. Consequently, the model is compatible with the canon. Nothing crumbles except by pronation or supination, by original deviation; thus everything crumbles - except for atoms and the void. And so on the first morning, declination must necessarily have taken place, in the middle of the void and the particles, aligned canonically. The canon, far from suppressing declination, requires it, and requires that it be small and original. Everything in nature is out of true.

The universal mortality of things that may be known, and their original distortion from the square, nonetheless cannot prevent our knowing in a stable fashion, our arriving at elements which themselves are immortal. The out-of-trueness of nature does not dictate a false physics. We can and must think rightly. Science is a matter of rigour as well as rectitude. That is the way it is: when I describe the clinamen, whether I estimate the greatest fall or calculate the slope, I compare these angles, necessarily, to some rectilinear trihedral and in particular to that of the mason. Nothing may be seen or thought to be inclined without reference to something which is not. And nothing can spill, in fact, without these axes. The canonical text defines the point of reference: a water level, a plumb-line, a measuring-stick. A cube in space, a Eucli­dean system. And if things fall and are born to fall, or, better still, fall to enter existence, it is by virtue of the laws of statics defined around the trihedral of reference. The very ones by which the elements are aligned according to the fall of heavy bodies or laminar flow. There are thus two systems of axes: that of the atoms raining down, and that of natural phenomena. We move from the first to the second by resemblance: a displacement of some kind and a very small rotation by which the slope and the inclination are made to appear. This transformation is the formation of things, their canonical formation, related to the canon. It is also the passage from fundamental physics to the science of phenomena, from ontology to phenomenology.

Once again, Leibniz, in a parallel text. The production of things, taken at their root, follows the law of the greatest slope, and thus on a deviation from equilibrium or perpendicularity. The image of con­struction is taken up once more: again, and as ever, we are concerned

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here with putting up a building. With its site, its foundations, its plans and its walls. The canonical core accompanies the law of the extremum. The classical God of philosophers and wise men thereby became the architect of the universe. He had only the level and the plumbline, the reference, the canon. He took the place of Euclid. Lucretius says the same thing, leaving God on his Olympus. We have the mason's tools in our hands, thus referential space. Deviation [l'ecart] is now counted as discrepancy [teart] . This invariance between two texts is easy to understand; a static system is never different from its canonical model: establishment or the building, I was going to say, as elsewhere I have spoken of the statue.'3 The rule of the canon is equilibrium or rest, stability. Hence Euclidean space, the space of the mason and the geometry of statics.

Now things are not motionless. Everything is in a perpetual flow, adsidue quoniam fluere omnia constat. '4 The void and the atoms, im­mortal, are invariable. There exists nonetheless a third eternity: that of the movement by which particles are carried in space. We must here understand a very difficult thing: a perpetual motion that is produced by nothing and which produces nothing, that is to say a stable movement. It is eternal because it is stable. This is nonetheless quite clear: for example, atoms in free fall move towards the equilibrium that is inaccessible and, as such, their parallel flow is an equilibrium. As if there existed, without paradox, a statics of movement. The river is not at rest, but it remains stable. Nothing creates it, it creates nothing. Nothing creates itself, nothing halts itself: the flux of atoms is inert. The eternity of the atomic stream is the equivalent of the principle of inertia, recognized by the Epicureans. One could say, strictly speaking, that in Book II this movement materialises the principle of Book 1. It is the movement of the canon. Now here is the deviation or the declination. This angle, for us, is much more than an angle. It is so for geometry. Not for mechanics. Lucretius could ignore it, but not Leibniz. For it introduces acceleration into the flow. The slope, precisely, of the inert river. Thus a force. And dynamics appears. It appears at the same time as things in the world. A foreign body in the heart of statics.

What produces things is, here, a motor. A producer of movement, a force, that no one knows how to produce; neither Lucretius, nor, as a result, Leibniz. We will have to wait some centuries before learning how to make a motor work. And so the question clearly poses itself. How do we avoid the production of the producer, and so on? How do we avoid having, once again, to treat the production of forces itself? How do we

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stop ourselves in the flight of origins? How do we avoid, behind a possible sequence of Third Men, a transcendent prime mover, outside of the world and nature? The answer is as lucent as the question is clear: since I have a universal canon constituted by statics, all I need do is relate everything to it. Restore this foreign dynamics to it. And to treat movement as rest, force as an equilibrium, and acceleration as an angle. Everything is then reduced to geometry. Aristotle himself did not overlook such a step and his prime mover is rightly motionless. avaY%l1 a811wm could be translated as 'statics is law. ' The episteme is stability. The canon, the rule, are just cessations. The solution of the Epicureans is still more brilliant, and so profound that Leibniz in the Classical period had no choice but to adopt it. First, it is established that the movement of the atoms is stable (see above) . And the eternity of this flow assures, even before the origin, the reduction of the question of movement to statics. Second, for things in formation, from the time of their birth and throughout their duration, the law of the optimal path permits the same reduction. Simple falling is replaced by a path on a plateau, the extreme descent. Now acceleration and force are brought back to the angle of this plane in view of the reference. Whereupon all that remains is to describe the movement in relationship to its end. Which is attained, depending upon circumstances, by overcoming obstacles, by slipping through the middle, finally, to the maximum, by far surpassing the infinite speed of light. The path is never described or conceived other than by the limiting presence or absence of strong or weak constraints that help or hinder access to this goal. Which is neither an object nor a function - there is no finality - which is simply rest, equilibrium, base.

Such a crossing repulses it, differentiates it, postpones it. Hence the process, the calculation of optimisation: the faster as the path is less encumbered. All movement is thus related to stability: it takes place more or less easily. In the first physical model, this signifies the encounter of an element with another atom, with other atoms: these hinder the first in its journey to rest. Collision is nothing but a hind­rance, a brake, a difficulty, to the precipitous rush towards the base. These constraints are necessary so that the movement only be maximal. All in all, in a region of space, objects, as entanglements and complexes, are throughout no more than temporary obstacles, thick shields, either more or less solid, more or less resistant to the general tendency of each of its elements to dissolve towards equilibrium. They impede each other with hooks, frictions or viscosities. All of nature is an obstruction to its

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own canonical law, that of stability. It is, through its birth and through its time, this generalised deviation. The global fluency, as a state of the tide, is itself only a barrier to immediate access to the low point. The stream is its own dyke, the river its own wharves. Statics is triumphant, renewed in vigour. Everywhere, in fact, there are formed only temporary cessations, provisional, that defer the cessation. Obstacles, atoms, bodies, world, are in their turn just stabilities, but transient. The dynamics of force, misunderstood, introduces, by the minimal angle, collisions, interlacings, fabrics. It is reduced to friction. Far from being motive, it slows. And kinematics is calculated solely in relationship to statics. The whole of the schema is reduced to the canon. The only law is that of rest: of the level, the line, the measuring-stick. Time is just what is necessary to attain it. And this is why there is no time but that of objects. Even that of kinematics is reduced: it is only an intermission. This inter­mission which we call history or the brief duration of the world. Raise an obstacle here or there, on this or that channel, duration comes to nothing. Time is the interruption of rest. Its quasi-stable interruption.

The fundamental state of the void and of atoms, the phenomeno­logical state of things in the process of being born and of using up their duration, are states in the static sense. Objects deteriorate [s 'usent] because they find themselves accidentally in the middle of a path and an element or a group of atoms tries to get through them as quickly as possible to rejoin the state, the base and rest. The door now open, these objects, damaged, in their turn find better ways to this state. The drop of water pierces the stone and kills time. The canonical reigns, it expels dynamics. Nature, deviating very little from level, plunges towards the line and the measuring-stick, in what it seeks to make a minimal time. Thus dynamics, deviating very little from geometry, comes down to this in theory. There remains space. The lines cited are not a counterexample to the thesis, but are, on the contrary, the principal paradigm of the model, in which its reference is mapped out. Quod erat demonstrandum. Homeorrhesis, or its equivalent, was already there. It is, in its own way, an original recuperation of movement by rest, as stability in direction. To maintain this is not to succumb to its recurrence, to the retrograde movement of the true. We might also admit that the re-written history of the sciences is filled with feed-backs. We will speak more of this later on. Physics, at this time, seemed to have to chose between the mobility of Heraclitus and the base of Parmenides. At least Plato formulated the problem this way. And resolved it othetwise. The atomists founded, and for all time, the science of things themselves, in the absence of dynamics,

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by saying yes to both sides: everything flows, there is a canon. By a rigorous statics of movement. By a canonics of fluency. By the proposed model.

Everything flows, objects are springs. Fluunt, flu viis, undis aequoris, fluenter, fluendi. Waves and fluxes of fragrance, of voices flying in the wind, of heat and cold, spume and bitterness. The perceptual space is dense with waves. All things are transmitters, without interruption and in every direction; our senses ceaselessly receive. We are plunged into the space of communication. We bathe in an interlacing of channels. Rivers regulated by the same law: quanto plus, tam procul, always repeated. The space of signals is physical space itself. The streams of waves move no differently than objects themselves or their elements. These are subtle objects, that's all. Thus perception is an encounter, a collision or an obstacle, one of many intersections on the way. The perceptive subject is an object of the world, plunged into the objective fluencies. Receiver, in its place, transmitter from every point of view. Beaten, struck, wounded, sometimes ravaged, burned, painful. Sometimes pierced, but sometimes obstructed. The sensory channels are no different from the conjunctive channels of any other hollow body. The soul is a material body, the body is a thing, the subject is just an object, physiology or psychology is just physics. And, consequently, the senses are reliable. For them to lie, a thing would have to be capable of betraying things and conversely. Where would such a discrepancy come from? Why this rupture of the contract?

The pact of nature associates things among themselves. The pheno­menon is well founded by it. The atomist, a friend to Venus, does not feel the hatred by which a subject is invented, or the detestation of the body that makes it other to the world; these are vices of Mars and of his philosophical followers. The senses are faithful, like all other receivers. They are under a contract to Venus, as are the objects among them­selves. This natural pact is something like an equivalent of harmony, and functions like it. Established by an immanent Venus. The fluctuating network is stable for itself The so-called errors of the senses can be reduced to the canon.

Flows and paths

The first model is local and original. It simply simulates the look of a fluid. Atoms cascade in a laminar flow down an infinite channel without banks. The void is a generalized hollow body. Inclination, then, imposes itself, the precursor of turbulence. It is produced, as experience shows, in

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an aleatory manner, at indefinite times and places. Every nascent object is initially a vortex, as indeed is the world. Hence the phenomenal universe as described by physics and mathematized in the work of Archimedes: spirals, angles and cones, differential calculation, the axiom, sand and floating bodies.

The second model is global. It takes the whole path into account. To the inclination, defined as minimal, there necessarily corresponds a maximal descent. The law of formation, the law of the duration of things and of the world and the corollary law of the flow of perception are expressed as the law of the greatest slope. From which arise the formulations of equipoised comparatives, forming a sequence that often determines the sryle of the poem, through a series of pulses. Just as the prefix dis-, through its repeated occurrence, legislates for the division of the elements, the dichotomy over words, so this syntactic peculiariry legislates for the complex and its paths. Linguistics, here, is simply the equivalent of mathematisation. If the rule relates to elements, the frequency is decided by words; if the rule is of movement, its iterations are observable in the syntax and its linkage. Hence the optimised universe, hence reliable knowledge, hence the stability of the canon.

Let us now construct the third model. Every object, naturally, emerges like Aphrodite from a flux of elements. By the above­mentioned models. Born from this and, as soon as it is born, complex, twined, twisting its long thick hair, it begins to transmit, in floods and in all directions, a star of flow: its wear and its time. It radiates various waves: heat, odours, sounds, simulacra, subtle atoms. In the same way or inversely, it receives the flow emitted around it, from the vicinity and the edges of the open universe alike, whether it be rock, harvest, horse or woman. The world, in total, flows in itself and for itself, exchanging its rivers at the maximal thalweg, to the point of consumption and return to the cataract. At birth, the singular atomic cascade is transformed: no longer here and there, in and for some local object, but integrally and for its global flow, in a multiplicity of rivers, streaming by all paths, trans­verse, diagonal, intersected, complex. The summation of the dispersed inclinations in space and time in the cataract produces, in the maximal descent, a complex weave of flows that begin from the unified nappe. The world is a vortex of vortices, interlacings or networks of waves. It is, as was to be expected, a generalised object of some kind. Connective and fluent. It deviates from the singular fall, ultimately returning there as to the common mouth; the death of the world is generalized from the singular death of one of its aggregates. What, then, is physics? The

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theory of nature natured, as it appears, once its nascent state is past? The first two models took account of nature in its the naturing, in the course of its birth. The fluctuating network simulates one already born. Answer: physics is reducible to two sciences: a general theory of paths and routes, a global theory of flow; and a topology of interlacings, a hydrology of what flows through the network. Now the first design, the plan of a local object, was drawn only a short time ago in the guise of geometry, combinatorial mathematics. The world extends this plane to a space without edges. The universe differs from things by its absence of borders. It does not have high sites: which explains its directional relativity and the compensations in its flow. There is no Olympus. It is enough that we let ourselves be led along by the second science, that we follow the paths taken by the flows.

The classical or Cartesian distinction between figures and move­ments, which is only a reduction, an abstract planing down, of this double science. Form, here, is a simplex; space is rich in complexities, it is divided, it bifurcates, it is filled with knots and confluences, it is the conjunctive web of the topology and of the ars combinatoria, it is the tattered strips of the ars coniectandi, of the event, of circumstance. The Cartesian figure refers back to Euclid's geometry, it is a metrics, domin­ated by the algebra of proportions. Metred, masterable. The master and possessor of nature metricates his space. The Venutian contract leaves it as it is, venturesome and complex. In Descartes, we can see the presence of Mars, arranging things in fronts and battlelines, coordinating them along axes. Method or strategy. The atomist flow is a material move­ment: heat, weight, light, liquids . . . Cartesian mechanics is theoretically independent from states. Take everything away, so I can see. Ancient physics is stronger than modern physics. And it is not by this excess that it failed to be a science, in the eyes of many.

Flows circulate on paths. Now the law of circulation is henceforth known, it is extremal. The flows spread as fast as possible, always taking into account the conjunction of constraints; they plunge towards equilibrium in minimizing the difficulties as best they can; the obstacles are only a sub-assemblage of other paths. The maximal slope, in the last instance, better, in the first extance, must be evaluated by declination.

That said, the new question arises, or the oldest question in history. On the global circuit as physically constituted, other circulations, others or the same, must now be recognized. Not only heat, the luminous, the ejecta of wear, the perceptible in general. Now it is a matter of early humanity. Thereby the circulation of violence, of force. It obeys the

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same laws, the rule is an extremal. The greatest force sweeps it away and passes on, overwhelming constraints weaker than it is. Violence is an increased flux, just like another. It occupies the mountaintops, the summits, everything that surpasses the common level, by hostile paths. Ad summum, e summo, iter infestum viai, per iter angustum (V, II23ff.) . This is an ordinary physical flow and it follows the recognized rules. I t is comparable to the fire of the heavens. Kings found their citadels, for defence and refuge: a high site, and barred roads. The same with beauty: flocks are given up, and lands as well, to the strongest and most magnificent. The strong is the strongest, the handsome is the most handsome, the intelligent is the most ingenious.

Hence the creation of wealth. As soon as cattle and lands are distributed, property takes the place of qualities. Still according to the same law. Gold easily diminishes,focile dempsit (V, III5) , the prestige of violence. It removes altitude from force and beauty. The proof is that the wealthy man drags behind him, in his retinue, in his sequence, quamlubet, whomever he desires, the most valiant hearts and the most beautiful bodies. The rich man has more power than the strongest, more beauty than the most magnificent. The rule repeats itself. The circu­lation of wealth, of gold in particular, makes the other circulations seem secondary and less easy. It is the best possible, the extremal, with respect to the best known: and substitutes itself, consequently. Money is not calculated as such, in its general equivalency, it is evaluated as a flow, as the thalweg of the greatest descent. Conceived not by equation, but by subtraction and excess. Plutocracies always take power through speculation on the fall. Money is substituted for everything, not by a universal equality of value, but by its optimalised dynamics. Not on a balance, but on a better flow on a better path. The whole world rushes in, cultural relief is irreversibly eroded higher upstream, or lower downstream: the economic flux, well named, transforms everything in its passage to alluvial cones. The proof in the fifth book returns to the topic of simulacra from the fourth. Take a maximalised movement, the speed oflight, understood as an upper limit, and images propogated still faster by far. In the same way, take an steepening path, such as the advance by utmost violence towards the summits of sovereignty; the flow of gold exceeds such a summit and thereby diminishes it, sculpting the valley to a lower level. The marvellous flux of money is isomorphic with the movement of simulacra.

Epicurus and Lucretius were most fortunate, they didn't know that they were materialists. This word was invented much later by Leibniz,

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for reasons of categorisation. Antiquity experienced that free age in which philosophers did not exhibit themselves in cages; in easily distin­guished pigeonholes, easily defended, and good hiding places. Wearing cuirasses and doruphora. Schools were not smothered beneath the classification of ideas, which forecloses history and the possibility of invention. Here is a local proof: the isomorphism between an economic law and this economy of the laws of nature. Not that one leads to the other, or vice versa. They are the same, that's all. A little while ago, this was quite rightly called a materialist assertion. For if you perform a reduction in either direction, you must justify the first or project the second; either way, if you want to see the internal connections, that is idealism. What is important here is not classification. What is important are the results. The trees to their fruit. The precise knowledge of this isomorphism leads, in fact, to the rejection of those channels of rarity that level the slope, underline singularities and produce competition. As a result, no one commands nature except by obeying it. Parere. As you read this, erase the vocabulary of command, obedience. No one acts without knowledge. No one speaks without listening. Here, to be rich, fabulously, beyond comparison, is to be equanimous, aequo, level, smoothed out, only just alive; on just a little, which is not penury, neque umquam penuria parvi (V, 1120) . This reverses the extremum. This erodes the high spots, stops the waves, evens up the slopes. The little abounds point by point, there is always as much. Movement ceases; hence the absence of the vortex, ataraxy without disorder. The ills of the world come from comparison. From comparatives, competitives. From the world in relief, mountains and combes, valleys of tears. From crests and citadels, the acropoles of royalty, streams of violence. Men and things, rivers of gold. This does not cease, Archimedes' axiom watches over it. The most powerful is overcome by the one who is more violent than he, the strongest is never the strongest, the most envious never envious enough, the landowner never rich enough. A perpetual auction, escalation, excess. Now imagine someone master of a high point or holding a summit that far exceeds the average: envy strikes him and hurls him down to Tartarus, the crest is only a hollow; the thunderbolt with a movement more rapid than light once again exeeds and chooses the peaks. The Archimedian logic of excess is the law of history: nee magis id neque erit mox quam fit ante (V, II36) . No more today or tomorrow than in the past. The meaning of history is that of the extreme thalweg. Enjoy equality, you enjoy little. Ataraxy corresponds to the canon, to the water-level and the measuring-stick. It is the true

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calculation: ratione vera, not the true doctrine, but the faithful report and the exact proportion. The balanced reference. No point of this place exceeds another, neither master nor slave. The physics of flow, the science of their law, and the Archimedian logic of maximal paths immediately produce a moral technology. That of balanced level­headedness, of equanimity. Or of calmed materialism.

We must begin once again to pass from these local laws of passage to their historical generalisation; to demonstrate the isomorphism globally. The Book V, on the world and nascent humanity, is traversed by the same laws as the Book IV, on perception; and these are the laws of matter found in Book II. Always the same whole, a multiplicity of elements, and always the same operations at work on these wholes. The method by structural invariants, generalised to the global stability of flowing movements, establishes materialism.

The world was going to die in the second book; it is mortal here. Like every other body and every other fabric, like the fabric of our soul, in Book III. Like the Athenians, in Book VI, in the city, a scaled-down model of humanity. Everything flows, everything crumbles, and the walls tremble, everything comes apart, returns to atomic dissemination. Nature is deathbound, moritura matura, what is born must die, without exception. I will show you how the world was born, how it will perish. Two parallel lines: I will show you by what force governing nature moves the course of the sun and the phases of the moon. Qua vi jlectat natura gubernans. By what inclination of the helm do the stars turn in their inflected orbits? I will tell you of the crumbling of the world and of crushing earthquakes. Perhaps tomorrow. May sovereign fortune turn this misfortune far from us: quod procul a nobis jlectat fortuna gubernans. The translation of the optative is extremely weak. May governing fortune turn [ecartel this far from us. Now there is only a single govern­ance, nature is fortune, physics is aleatory. Natura sive fortuna, nature and fortune. Now nothing is exterior to things themselves, a physics of immanence. The governance of the rudder is enough. Now here it moves. Which means that it deviates, that it makes an angle, that it is inclined, and begins a turn, a sweep, a circle. That of the sun, of the moon, of the stars. It grants birth, as necessary if the hour of death, here and now, is to be avoided. And death moves off when chance, by the declination of the rudder, bends it, makes it turn, makes it turn away from us. And the angle of the rudder is existence itself, the deviation from the universal grinding; this existence is the cycle, the stellar and solar vortex. The clinamen is enough, the deviation from equilibrium.

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Everything takes place through declination, everything declines under the same angle. The same event inclines to death as to birth. Everything is subject to nature, to be undone in the end, by the same deviation: minimum obliquity that engenders turbulence. The world is a global vortex, but it is disturbed by turbinations, and it will crumble, ravaged by whirlwinds. Time as a whole is the time of the storm. From the tempestas nova, primitive, new and originary, to that of destruction and fragmentation. The proof of mortality evolves a single theorem: tanta stat praedita culpa (II, r82) . Nature, we say, arises marred by many faults. The moral connotation attached to cUlpa inundates the whole assertion, and it engulfs physics. Now it is a question of equilibrium, stare, of a lack of equilibrium, culpa, in the singular. Nature is given, endowed with, dita, this disequilibrium; it leans, it leans forward, prae, tanta, so much, it overhangs the greatest slope. The translation puts original sin in the declining origin. It pathetically moralises a proposi­tion of statics. I won't hide the defect or the fault. Lucretius has both, together. Yes, nature is moribund, since it has, as if before itself, a defect in balance. The train of the theory gives a value to this deviation, producing the vortices. Now the theorem itself comes after an exposition of the fundamental state of atoms, a moving and combinatory whole, a state taken up again, term for term, outside the cosmo gonic exposition, which will follow. It is the lemma of the clinamen.

So then the famous section on childhood (V, 222-7) . What is birth, our birth? The receding waters have cast the seafarer on the shore. We have seen above how the storm works: a rupture of equilibrium, water­spouts and precipitations on an inclined plane. The castaway comes to the end of his slope. How sweet it is to read about and see Ulysses, rocked by the waves, stretched out, naked, on the shore, waiting for Nausicaa. Sisyphus at the foot of his hill. In the same way, the child comes to rest. facet humi, to earth. In the low places. He falls. Poured out from above and forward, profodit, to the shores of light, from the maternal chamber, where he was stable, an obscure mariner in calm waters. Storm in the amniotic waters, rupture, shipwreck. The river Nile that carried Moses. A fall to depth, to nudity, cries and misery. fndigus omni, in the state of total lack. Every vital help forsakes this newborn, all succour that could make up for what he lacks. Auxilio indigus, augeo egeo, every possible increase is withdrawn, all growth is suppressed, nothing can be added to his whole ebbing. He is at the lowest low point, birth is already death, it transpires by the keenest descent. The hollow fills with doleful cries; this is the same idea as the valley of tears. Wells

5 5

The Birth of Physics

full of cries and supplications. Legitimate complaint, aecumst, in compensation. The threnody balances the hole. From the depths of the abyss the clamour rises to the high sides. The funeral song of this dawn is canonical, it cries out for the measuring-rod, it requires the line, the level. Because law recommences. Past, fallen, poured out by the blocked path, through the storm, pushed, jostled, thrown out at the end of the fall, the naked newborn sets to living, that is to passing through, by paths strewn alike with so many obstacles: tantum transire malorum.I5 Slope to death from the end of the slope to life. The cradle-boat goes down the same river as the funeral barge. Through the same storms, and similar vortices. The birth of the child of man is precisely through nature. Except perhaps that its deviation from equilibrium is stronger than that of animal young. Who need neither rattles nor nursery­rhymes, nor clothing, nor weapons, nor walls: in sum. His disequi­librium is so great that he is an orthopaedic animal. He tries, desperately, to recover his inevitable fall. Thus he makes his time. Thus he makes the time of nature, no less unbalanced, by the apportionment of seas, forests, swamps or deserts, putting his weight behind the handle of his plough, or bending to his mattock. He recovers the death of the world, as his own. But in this game he succumbs to the odds, the fall wins every time.

In general, nature seeks an equilibrium in the midst of the fluencies, and seeks fluency through equilibrium. We would say today that there are fluctuations, homeostasis, then homeorrhesis.I6 The demonstration establishes them one after the other. Since it concerns the four elements, states of matter science now regards as outmoded, we have forgotten it. In its form, or rather whatever the contents of the flux, it remains exact. Indeed, for the atomists too, earth, air, fire, water are outmoded states. The reasoning is valid for any composition of atoms. It is just more suitable and more easily established for the traditional states.

Of the earth: it exhales clouds of dust; diluted by the rains, swept up by the winds and the waters, it ebbs, it flows. Fluencies. Now what it produces always goes back to it. Universal mother and common grave, thus she dries up and, increased, mends herself. Equilibrium. The earth is homeostatic in its fluxions as a whole. Of water: waves abound, everything goes to the sea. All is flood and flow. Everything loses but water is lost, the hot wind dries the moist surfaces, bears back to the springs those liquid floods which, risen up, will return by the hollowed­out path, the slope. Equilibrium. Nowhere does the ocean overflow. See, below the flood, stasis and stanzas. Of the air, another ocean: it receives

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the emanations and gives them back to things. It blows but equalises. In short, by descent and return, birth and death, solution and resolution, borrowings and restitutions, three cycles are in place. The circuits of earth, water and air, are circulations. Fluent and stable. We almost always bathe in the same rivers. What I, with Epicurus, Lucretius or Descartes, call a vortex corresponds very precisely to these (quasi) homeostatic circulations. We must now generalise the models. For the air, a whirlwind, a cyclone: these are turbulence. The global vortex, that of physics and its laws, is the circuit de rebus et in res, which leaves and returns. Likewise for the waters: here and there, you can experience the formation of the vortex; in general, the waters circulate, they turn, from the spring to the sea, and from the depths to the heights. All is engendered from the earth and goes back to its dust in the end. The vortex, at this level, is a homeostatic cycle. But, once again, not com­pletely in balance: global, quasi-stable and out of true, it will descend by the slope. The death of the world will undo these pseudo-balanced cycles, temporarily almost fixed. But, right away, nature has formed them. Before plunging the stabilised vortices into the flux, it gives rise to the circulations of fluencies. Hence the first of the theorems: adsidue quoniam fluere omnia constat. This is of an extraordinary precision. There are two terms that belong to statics define a term of fluency, furnished with a universal quantifier. Constare means holding together by the union of constitutive elements; the sum of the whole of the flux yields a base. Adsidue, if it is translated by 'continually,' finally means its opposite, since, for us, the continuous is almost always that which moves. Adsideo, even so, is to be seated, to have a seat, near someone or something. To be fixed, fixed with respect to some reference. It is thus certain that everything which flows is quasi-stable. Or, for the daring: the totality of fluxions holds together in a relative fixity.

This first account does not point directly to the death of the world, it describes what is going to die, what on a large scale exists as an ensemble of detours. It saves the great phenomena by the establishment of a circuit of exchanges. If everything flows continually, eternal death is deprived of even a fleeting existence. Nature adds nothing to the underlying cataract. A declination is necessary, and it is enough. Hence the lemma of the ciinamen, after the initial picture of the atomic cloud. Imagine now the great members of the world. We must show that they are mortal. If everything flows continually, they are not yet born, they are not formed, natured. Once they are born, nature exists: an inclination has taken place. Thus a vortex. From the local to the global the

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consequence is preserved. This principle founds the possibility of integral calculus. A thing in its particularity is a turbulence induced by an angle to the current; an element, in the sense of earth, water and air, is what circulates in the vortex through a deviation from equilibrium. If there exists a time of things themselves, the time of physics, it is because these vortices are stable. Hence the homeostatic cycles of the fecund and funerary earth, of waters at the infra-diluvian level. Now, and this is the point, if these circulations are perfect circles, then the movement finds its equilibrium, the world is immortal, it proceeds to eternity. This is the stroke of genius in atomist physics: there is no circle, there are only vortices. No exact rounding off, no pure circumference, spirals that shift, that erode. The circle winds down in a conical helix. The Pythagorean or Platonic circle becomes the Archimedean helix. In other words, nature is not endowed with perpetual motion.

There is only a laminar flux. The world is a multiplicity of flows, each inclined in relation to the others. And every stream runs its slope. The ensemble of fluencies forms a cycle, by a generalised inclination to the global state of the materials of nature. These circulations are not circles, precisely on account of inclination. A circumference plus an angle, however small it may be, produces a spiral. The thing is in Lucretius and the theorem in Archimedes. From models to laws, or to theory: here is a nature, oblique form on a parallel background, birth has vanquished death; death is eternal, bur time has formed. There exists something rather than nothing: deviation wins our over homogeneity. Yet time is not in perpetuity: every movement ends by stopping. Theorem of the world: neither nothingness nor eternity. Neither straight line nor circle. Neither laminar flow nor stable cycle. Nature, that is to say birth, that is to say death, is the line inclined by the angle that produces a global vortex, which the wear of time brings back to the straight. Neither circle nor line, everything is stable and unstable at the same time. By the angle of deviation, lines and circles join to form Archimedean vortices, which unfold while rolling on inclined planes. Resumptions, revivals, re­provisions, quasi-stability until final death. A physics of fluctuations without eternal return. This is the high point of the Hellenic sciences and, perhaps, of our own.

Finally, fire. The rays of the sun, of the splendent and of oil-lamps are exhaled from their source; in the manner of liquids, liquidi fons irrigat, they disperse, irrigate space. Heat is lost and light flees. Here are irreversible fluencies. They evaporate when they are caught: like the shadow of the clouds. Earth, air and water were at once source and goal,

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fountain and reception, transport and reservoir, movement and stability; as if each flowed from itself to return to itself, flux and stock, invariant and variable. The fire dies out, the light is blocked, the rays do not come back to the hearth. Hence the difficulty.

It is not until the arrival of Baron Fourier that we can evaluate thermal exchanges within worldwide stability. Alternatively, at least Halley, regarding this movement and its equilibrium in meteors; or, at best the legacy of Carnot for cosmology. This is the subject of our histoty. Now the cycle of fire and the loss of fire were already known to Heraclitus, who, as I have shown elsewhere, intuited with precision what we now call the second and first principles, as well as their local and global conditions, and their apparent inverse, which we shall henceforth call the negentropy of information: otherwise, what would it mean, for him, that the logos increases by itself? The histoty of science has become infantile, strewn with those who would murder their fathers and who assume great ignorance and obscurities in the early reaches the better to mark progress in the later. Heraclitus, on the subject of fire, knew, roughly, what we know, that's all.

The present solution to the difficulty remains learned and refined. Fluency is universal; its allure is, here, rapid, thundering: light hastens, it is precipitous, fulgurant. The law of the maximum brings the path back to the instant: confestim lumine lumen.I? It is obvious that evety obstacle makes it disappear immediately, but no less evident that it bathes the world and things: irrigat adsidue, always, and in a quite stable fashion. The birth of new flames thereby hides the death of the old flux. Lucretius goes back to the source of the irreversible river instead of examining, as elsewhere, its mouth and its return. Repair, re-provision and feed-back do not occur in and through a cycle of exchanges, but at the beginning of the programme. At its origin and in its production. The demonstration regarding the sun begins with largus liquidi flns luminis, the immense source of the liquid light, and ends with lucis caput ipsum, the very sum oflight.I8 From the fountain to the capital which in a single word comprises the grandeur and the quantity, the throng, the origin and the concentration; from lumen, the ray, the instrument, transport and mediator, to lux, the active fire emitting the flash or illumination, we clearly pass from the phenomenon as such to its pro­duction. The cycle of provision takes place in the caput and not in the general circulation. Flowing or evaporated water leaves the sea and returns to it; the entire air, the sum of the winds, is another ocean; the earth, mother and burial ground: for the first three elements, the total

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reservoir is transmitter, receiver and path, it integrates the circulations. Fire represents a local reservoir: principally the sun, and then some others, torches, stars. From now on the transmission will not return to itself, it is produced at the head of channels, it expends. A third term evaluates this disequilibrium. For the whole world, the lemma said: tanta stat. For three-fourths of the elements, fluere omnia constat. For the trembling fires, we must say: instant, instant. They press forward, the new behind the dead, thus the continuous hides the intermittent, they are in the vicinity of each other, on top of each nearly, but above all they are in a state of instability. Fire seeks fluency through equilibrium, as if it reversed the circuit of other composites. As proof of this, the text immediately refers to crumbling rocks, high towers in ruin, and stones that roll down trom the summit of the mountains.'9 Fire succeeds fire like rocks do rocks, down the thalwegs of deposition. The source and the hearth are on the crests, where matter trembles, in unstable balance. It threatens to fall, it falls as fast as possible. The gods cannot protect their own statues; they crack as they fall. This is the law of nature, the contract. Light wastes away. It wastes its capital. The reservoir empties just as stones roll: everything falls.

To seek an equilibrium through flows and to seek fluency through equilibrium amounts to one and the same law. Otherwise, no one could understand how or why the proof of death takes place through the evaluation of the reservoirs: nam quodcumque alias ex se res auget alitque, deminui debet, recreari, cum redipit res.20 Everything that gives of itself to feed the growth of others must be diminished, and be restored when it receives them back. Here is the cycle, or the elementary vortex. For fire, it is open to question. What is it that comes back to the capital?

The three terms or theorems, stat, constat, instant, form a dialectical sequence. Two hundred years of philosophy have accustomed us to dif­ferent arrangement. It seems clear to us that movement is produced by being and non-being, as though by thesis and antithesis. Now, moving has nothing to do with being or nothingness; the idea relects a crucial confusion between a mechanics and something else. Or rather, it is the admission that everything is projected onto kinematics. Ontology conceals itself behind the theory of movement. This is an outdated thesis: all of physics reduces to mechanics. It is called mechanism. Ontology is the motive force of mechanism. Metaphysics is even less than a physics, it is what precedes phoronomy. Astronomers were quite correct when they described phenomenology as celestial mechanics itself. This said, movement is no stranger to our thesis, if by this we

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designate the act of posing, of placing, of establishing; that is, the state of rest, static equilibrium. To say thesis, antithesis, movement would at least be comprehensible as a sequence. But dialectics would disappear, since movement is the contrary as such and contradictory to rest. We would need to produce it. The sequence stat, constat, instant, is physi­cally exact and far more faithful to the concrete. There first exists equili­brium and deviation. Together they produce flows, whose total is in equilibrium, but only relatively, since it remains unstable. This sequence clearly produces time. It preserves, at every point, the deviation from stability. The praedita culpa, the omnia jluere, the prefix in third place, always accompanies the verb of state, statics. The clinamen does not cease. It grants birth, it preserves a moment of existence, it leads to death. Or: it grants being, it grants movement [se mouvoir] , it leads back to phenomenal non-being. If we were to write an informed dialectic, it would adopt the following order: being, movement, non-being. It would be compatible with the second law, would avoid perpetual motion, would go beyond the purely mechanistic model. This is the series that the last century spurned in favour of the eternal return, in all its diverse forms, like the long march on the sublime. As soon as we go back to the production of movement, to its source or its caput, to its energy, to heat, to the sun or to the thousand suns of our practical technologies, a perennial re-fuelling is inconceivable, just not feasible. At the end of the time constructed by this productive dialectic, at the end of all the necessarily staggered cycles, it returns to rest: as a thesis as such it is absolutely unproductive. So an initial thesis, a thesis furnished already with its differential or minimal deviation; and without this 'rather' nothing could exist. Thus, but only thus, movement, furnished in its turn with an associated pseudo- or quasi- equilibrium; that is, once again, with deviation. Finally a thesis, a sub-thesis, a base without devia­tion, perpetual rest, non-being, as it were. The essential part of the entire business is inclination, declination, as you prefer, which is more faithful to the real, to the concrete, to that which exists and happens, in the time of equilibrium of false perpendicularity, of birth and of obliteration, than the Aujhebung which is in part clinamen, and in part its contrary. Stances, constancies, instances, all things in nature, as they appear, exist and scatter, are unstable. The only precise dialectic is that of circum­stance. There can be no last instance, there are only instances, and every­where, within cycles and elsewhere. We will come back to this problem.

Why would an atomist physicist deal with the four elements? At first sight, this is a retrograde step in scientific progress. The answer is

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perfectly predictable and provides the thread of the text. The element, in fact, is the atom. It is immortal, without birth or end, like the void. Eternal, because residual in every possible analysis, and every real decomposition, by collision or otherwise. Residual, because minimal. This leads us to draw a balance, a picture, a table.

The void is the zero state of matter, the atom is the minimum state. To these will you kindly add the angle: the clinamen is minimal, too. In a certain fashion and, perhaps, in all, it is also eternal. Indefinite in time and place, it is the first instance, it is the last instance, it is the instance in general, the deviation from equilibrium of birth, death, and temporary existence. Eternal in kind, as the vectorial motive force of time. The atom is eternal as pure circulation, the void as pure reservoir, declination as pure vector. Atomist physics is based much more upon a vectorial space than on a metric space. At the other end of the table, the universe as a sum of sums, or as a whole of wholes, is also eternal. In that it has no exterior to which its fluencies could be lost or from which it might be threatened. There is no opening from the sum of creation. It is the total reservoir of all circulations, the whole of transports. In the first line, the infinity of time is valued as a minimo, in the last it is counted a maxima maxima rum, a summa summarum. Between the two are the columns of time, the walls of the world, composite things, nascent tissue, complex, connective. Between the two lies the relational. The void, atoms and the angle, as pure elements resistant to analysis, and the universe as a maximal totality without door or window, are eternal because non­relational. All the rest is born from relation and dies by it and with it. By the hole, the door, the hiatus. It was by no means insignificant to speak of hollow bodies, their pores are their stereo-specific relativity: their very nature, understood as their essence, as their temporary existence. Every­thing in nature is hollow, and nature is everywhere hollow, the reverse of the full and dense Leibnizian universe. Atomic physics is lacunary, in that it comprises the definition of thresholds, minima; it is non­monadological. Lucretius says: everything dies, where Leibniz will say: there is no death, strictly speaking. But to demonstrate the mortality of things, one would have to review all places and regions, differentiated by the aleatory distribution of relationships, of repletion and orifice. Best of all would be to state it, and to calculate as though a fortiori. So why elements, in the traditional sense, earth air, fire, water? Because they are maximal compositions, maxima membra. Death is given value a maxima. If these members die, then obviously everything dies. The equilibria and the disequilibria between these limit composites must be

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described. What is an ordinary element for an atomist? By a total reversal, it is the very opposite of an element: the atom is minimal, it is, itself, maximal. It is the highest material complex in the table, as if it were the heaviest in the classification. The table, constructed by evalu­ations of extrema, as everywhere else, frames the finite with the infini­tesimal and the i'nfinitely large, the phenomenal by the fundamental, nature and time by eternity.

Depending on whether it is evaluated for a thing in isolation or between two given objects, equilibrium assumes a true invariance or a relationship of equivalency. In the quaternium of the elements, earth and air are fairly stable in themselves, and are defined as such by Lucretius: they recapture what they give away, and vice versa. The reservoir wins out over circulation, and perhaps exchange over pro­duction. They only vary by an invariance, within narrow limits. The instance tends there towards constancy. It is otherwise for fire and water. Always in disequilibrium, in increase or decrease. Fire spreads like a flood, spreads like a torrent, and flickers to extinction as quickly as the swell retreats. Dry bed or ashy hearth, deluge or sudden blaze, the limited excesses of the out of true, reached with thundering rapidity. The flow, here, wins out over the resource. The maximal members are of extreme stability or instability.

These evaluations are not prompted by a vain material imagination, but by the different tissues of matter itself. The civilizations of the earth vary only very little, agrarian practices and sailing ships are connected by the weak circulations of reservoirs in equilibrium. Therefore their history is more or less flat, like the minor flow issuing from the resources in which their symbiosis is situated, issued from them, to them returned. The common design of the stable equilibrium: every deviation of position is inevitably restored. As in one of Archimedes' theorems or Montesquieu's theories. This is all of a kind with the earth and the winds, with their marginal movements. Civilisations of fire are dazzling, in the end they are only concerned with increase or decrease. They are connected by extremely rapid circulations, in which the reservoir fills and empties, with hyperbolic rapidity. As soon as the motor is built by the industrial revolution and its general systems of theory and practice, all the questions, abstract and concrete, suddenly go back either to escalation or entropy. Since the construction of the first motor by the industrial revolution and its general systems of theory and practice, all questions, abstract and concrete, are uncompromisingly reduced to either escalation or entropy. The motor, that is to say the producer of

The Birth of Physics

movement by a deviation in the equilibrium at the source, the motor, that is to say this or that machine of fire or fluid. Cultures, but why am I using the plural, the culture of flood and fire, of plethora and exhaustion, of vertical growth and sudden fall, of accumulation and drought, in which history, fatally and by the unassailable laws of nature, rises and descends, as if on the high seas under the movements of the hurricane. A culture whose elements come down to the energy of fire, after the forgotten cultures of the unchanging earth, without either inflation or deflation.

The work on fire is science, technology and history. It is urgent and dangerous. We are embarked on extreme fluctuations. The time of history is nothing more nor less than the increase or descent of the greatest slopes. This stems from our exclusive connections with energy, we eat only fire. Our time is traced on the duration of the flames. Their vertical propagation and their blazing extinction. Maximal movements by disequilibria of limit. Extreme fluxes arise from harnessing reservoirs accumulated across the globality of times, and from the exhaustion, in a minimal time, of quasi-eternal stocks. Without doubt, the dominant illness over the last century or more, times of fire and flood, has been manic-depression. And doubtless too, it is the illness of the dominant. Crisis, in the same way, is an extreme notion, a singular point, high or low, either a peak of ecstatic exasperation after a sudden escalation, or a hollow of drought, of exhaustion. Crisis, for us, is no longer a rare state in our movement, but the current state of our movement. Hence those theories that wish to pull us in from the storm. They are all regressive. They coax us back to minimal slopes, to historic curves that are nearly flat. But this would mean returning to the ancient reservoirs, to the general stores of weak circulations. In a word, quitting fire and water to recover air and earth: leaving industry and its energies for agriculture and its slow meta-stabilities. Sailing and tilling. The proposed choice between perpetual movement, impossible without destruction, and a perennial invariance. Materially: either fire or earth. Equilibrium or dynamism.

The new science escapes the dilemma. Everything is conceived by it as a deviation from equilibrium. It is no longer archaic constancy, nor the movement produced by the destruction of equilibria, it is the instance, understood as disparity. This is what life does to elude death temporarily, this is how material substances subsist in spite of degradation. Theory and practice of circumstance, space of renaissance.

Lacking the right technologies for working fire, or for setting it to

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work along the channels and circuits through which its force is made accessible, a merely local mastery that we took for global, some ancients nonetheless recognised, either directly in physics or geography, or through myth c or prosopopeia, its rapid expansion and its lightning decline. Gradient to death, in both senses. Earth and air, aparat from temporary exceptions, invite us to think of a stable equilibrium: the seismic shock and the storm last for a short time, a tolerably short time. Their stability may thereby be assessed in isolation, each for itself, as though independent one from another. Fire and water are held in a logic of extremes, as if they passed with all speed towards everything or nothing. Terror, anxiety, and birth of the gods. Phaeton. Hence the idea that we find in Homer and elsewhere of assessing equilibrium across several elements that are in themselves catastrophic. To play fire against water or, conversely, growth against growth, before the point of rupture is reached. Thus Achilles is delivered from the flood of Xanthus, or Scamander, by limping Hephaestus, who sows the brilliant flame. In other words, how can we deliver ourselves from raging violence, from the sea in fury and from armies who slaughter each other, from frantic growth and the labour of competition? There is still a lucidity to the wisdom of the sages who esteem equilibria from the height of the sheltered passes. Fire and water vary respectively in a terrifYing fashion, but they are covariant. It is enough to conceive of them as concrescent. Elements of war, but evenly matched: aequo certamine. The variance of the one nullifies the growth of the other. Here is the zero pass [col zero] of comparatives and superlatives. The sun disperses the sea and dries up the waters, forbidding the floods to exceed their low-water mark. Heat grows, the flood recedes. Equally, the fires of the universe would devour the flood if the rivers did not strive to overflow and extinguish them. The balance is delicate, it is fragile and temporary. There is always deviation, and it is rupture, and the end of the world.

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NOTES

I V, 444. While French has delimiter, i t has no word corresponding to the Latin discludere, as in English we have disclose.

2 Reference to the Pontus (Bosporus), the Black Sea. Cf. Bailey Vol II. p. 1393. V, 501, 504-

4 V, 504-5 Figure I, p. 19. 6 Cf. below: Epistemological conditiom, observatiom and simulacra. Here it is a

question of the speed of their propagation; below it is a question of their form. 7 IV, 4I. 8 Le simulacre se detache comme forme optimal du volume occupe par l'objet, comme

super-ficie. [La naissance de Ie physique, p. 52] Hyphenating the usual term for surface, Michel Serres emphasises the separation of the simulacra from the thing on which it lies. The translation itself borrows from French in attempting to reproduce the sense.

9 ' . . . just when the climate of the skies is clearest, it turns most suddenly dark and foul.'

10 Cf. above, p. 4 and Lucretius II, 220. II IV, 193. The expression names a 'tiny cause' that acts as though from a distance.

Bailey suggests that this describes the effect of the impact of a single uncom­bined atom moving at great speed [Vol II, pp. 1204-5] . The adjective is thereby referred to the material bearer of the cause, the atom, whereas Serres goes on to identify the expression parvola with the clinamen as itself minimal.

12 IV, 513-22. 13 M Serres, Statues. Second livre des fondations (Paris, Franc;ois Bourin, 1987). 14 V, 280. 15 The whole phrase reads: tantum in vita restet tramire malo rum: it remains in life

to pass through great trouble (V, 227). 16 Homeorrhesis signifies stability through movement. 17 V, 283, 'Without delay (it supplies) light with new light.' 18 V, 281-93. 19 V, 306-17. 20 V, 322-3.

66

EX PE R IENCE S

The meteora

Scientists can predict the time of an eclipse, but they cannot predict whether they will be able to see it.

Meteorology is the repressed content of history. Of great histories and small, of the sciences and of philosophy. I don't mean the climate, but meteora:I clouds, rain and waterspouts, hailstorms or showers, the direction and force of the wind, here and now. And I don't mean the prevailing wind. Meteors are accidents, occurrences. A chance proxi­mity, an adventitious environment of the essential, the stance. This only interests those in whom the learned have no interest: peasants and sailors. Those whom the learned meet on holiday, when the things that they consider serious are put off until tomorrow. They scornfully deign to speak about it with the doorman, on the street. The time of meteora does not match up with the time of history, and their kind of order and disorder has only recently begun to be of interest to scientific rationality.

The sages of yesterday, of long ago, were passionately interested in the Meteora. The physicists of Ionia, Plato, Aristotle, Renaissance thinkers, the writers of the Pleiade. Modernity, to my knowledge, is announced like a play; by the trois coups, Geometry, Dioptrics, Meteora. Of which we only ever hear two. Can't the curtain be raised all the way? Suppose

'that it were drawn wide, the landscape perceived would be all

new. This is the science of today, of tomorrow. Meteora bear an incre­dible knowledge.2

So no one reads the Meteora, not those of Lucretius, of Descartes, nor of anyone. Why this repression? Because philosophers, historians, the masters of science, are concerned only with the ancient idea of the law. With exact determination or rigorous over-determination, and with the god of Laplace. With absolute control, and thus with mastery without vacillation or the ambiguity of margins. With power and order. The weather now and the weather to come infinitely surpass our account of them, so they are of no account. Because it is the place of disorder and the unforeseeable, of local danger, of the formless. Because it is the

The Birth of Physics

weather of another time. Because it is the weather of clouds, and one must not have one's head in them, nor have them in one's head. And yet, what good does it do me to know the exact second of the next eclipse when a thick mounting wind keeps me from seeing it? What good are all the tools in the world when snow and mud prevent their use? This is why physics takes place in camera. The laboratory, and every closed system, are a protection against turbulence. Science is shut inside. It proceeds from its beginning, from the Meteora to the furnace, and will never leave this closure again, which excludes chance and the uncontrollable, what today we would call hyper-complexity.

Lucretius' physics is outside. And ours is too, once again. The old closed systems are abstractions or ideals. The time for openness has arrived. Lucretius is prehistoric by comparison with Descartes, Laplace, and every thermodynamic, that is to say metaphysical, closure; now these are prehistoric with respect to us. And the De rerum natura is there ahead of us. Outside in the storm and the rain. On the banks of the Nile.

After the praise for Athens, called the bearer of fruits and harvests, before becoming the focus for the plague, in book six, the Meteora, opens with a re-examination of the theory of the vessel. The body is a vessel which contains the soul as it would a finer fluid. Figure or metaphor, this vessel is first of all a model. The proof is that Book Three leaves open the possibility of imagining others, on condition that conjunction, cohesion and connection remain intact. But, since the soul is still more fluid than water, fog, smoke, since it is a mobile cloud continually impressed with the simulacra, we have no choice but to conceive of relations between fluxes and not solid relations, like knots of connection or the friction of cohesion. To imagine other objects, other models, is a weak translation. Better: construct. The vessel can be built, it models fluid relations. It is a hydraulic basin, whose form is pleasing. We may imagine any basin. Suppose we shake the vessel, the liquid it contains spills and runs out. Similarly the basin can crack, it is always porous, and its contents spill. In this way, the subtile soul dissipates into air and space, through flaws in the body, in a fabric less fluid than itself. Hence dreams, death.

We should note here, and this is a stylistic constant in Lucretius and therefore a physical law, that effusion is a diffusion: diffluere, discedere, discedit, diffundit, dissolvi, this dissolution, dissipation or dissemination, these divisions or discrepancies, are repeated five times in four lines in Book III, in relation to the vessel.l It is, in fact, only a local accumu­lation: the dispersion of the prefix is almost homogenous throughout the

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text, it is the operator of dichotomy, the elementary rule of atomisation. Things naturally wear out and spill, they return, dissolved, to the individual cloud.

So the vessel is porous, the basin crazes. It is, very precisely, an open system. Very superior, in its complexity, to an automaton in an interior medium. By the channels that it has left free the animated fluid flows and escapes. Effusion: it leaves; diffusion: it spreads. It loses its concen­tration, it spills everywhere, it takes up the volume available to it. From the locally open to the globally open. Everywhere and at random, the soul returns to the world and to chaos. It is therefore mortal, by a physicalist death, aleatory diffusion; it cannot exist without the body, this basin that ensures it a concentration, at least for a while. It would spill if it were not constrained.

But the vessel itself is a flow, although thicker or more complex. If it can split locally or be undone, it must carry through its own diffusion to the end and spill, finally, broken up. The open system, contents plus container, is delivered whole to the operator of atomisation, the dichotomous prefix. This Lucretian law, evident in the frequency of words like dissolution which for a series that sets the style of the poem, this law is strictly equivalent to what we call the second law of thermo­dynamics. It is at work in the whole poem, like a physical torrent, ravishing the senses, nature, it is the destruction of vessels by water­spouts and storms, the wearing away of statues under the lips that kiss their feet, the precipitation of the whole poem towards the plague at Athens, the inclination of the text, the fall of the atoms and the cataract ofletters. But this law concerns open systems. Hence the obsolescence of the text in the interlude between classical and modern physics. Hence its renewal, this very day.

The vessel and its fluid leak. But they are stable for a time. They can postpone, for a little while, the end anticipated by the law of dissolution. Which shows that the flux lends balance to that which leaves. By the channels left free in the walls, thick or fine, the simulacra penetrate. And this is only one flow among many. Some less subtle, like the wine which invades the tissue of the veins, others more subtle, like the philosophical teaching of Epicurus. Whoever excludes his words or writing from physical or atomist laws cannot be deemed a materialist. This is his stroke of genius: the body, an open system, is the place or the seat of an exchange of flows; they enter, they leave. But these flows are, unitarily, food and drink, Eros or perception, and intellectual information. The exchange of teaching may be assessed in the same terms as the circuit of

The Birth of Physics

other fluxes. Even Descartes saw this clearly: one need only translate his circulation of animal spirits into the language of information to make it readable today. Epicurus is the source of a flow which enters my body. But, once again, the body can lose it. Either by the porosity of the walls, or by a hole pierced in the bottom. The classical translator writes of this vessel that is is bottomless, a proof that he failed to understand the physical model. No one has ever seen a bottomless basin, except in a sexual or metaphysical dream. It is riddled with holes, quite simply, and the text says so. By these channels Epicureanism escapes. I don't impugn sex, the text begins with an Aphrodisiac prayer and strongly recommends certain positions which prevent the loss of semen. But there is a hole, simply, by which true philosophy can enter or escape. Simply. That is to say, the contents already there have so strongly impregnated the cask, it is revolting to the taste, says Lucretius, even so far as to soil, besmirch, corrupt, the new spurt that enters. Here is a chemistry that we will speak of again when the atom becomes seed. And so we must clean the basin: Epicurus, who built it, washes it. He purges it. This said, and yet to be said, the fact remains that the vessel cannot fill completely: never in any way. It is too permeable. And on the other hand, it cannot empty, except in the case of death. This expresses a theorem that is true within the system, or a law of nature: boundaries exist. A law read again in a sequence of repetitions that reveals the Lucretian style: the dense repetition of the imposition of limits. The residual flow, as the flux enters and leaves, rises and lowers in the basin, within a bounded, limited interval. Except in case of death, of course; that is, in the temporal interval in which the system, open site of the flowing exchanges, averts the end of the necessary dissolution. The average level thus fluctuates, relatively stable, until final destruction. And the flux always has the same direction, more or less, and the same end, absolutely. Thus the porous hydraulic model is locally homeostatic and globally homeorrhetic. Quod erat demonstrandum.

We now know how to construct open systems and to describe homeorrhesis, as examples of complex and relatively well-ordered models of the states of inert or living things. Perhaps the discourse of nature, as written by Lucretius, may now be audible to us without a dictionary of any sort. Without archeology or fossil examination. The thing is simplicity itself; it has safely crossed the breaks in communi­cation: the classical closure, where experimental physics can only be born when it is shut in the furnace, either in the laboratory or elsewhere; a thermodynamic closure conditional to all knowledge and all reason,

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since all knowledge presupposes quantifiable evaluations of energy, of force; all those closures reflected in institutions or metaphysical discourse. Thereafter Lucretius was excluded, not at all for his material­ism, other materialists were not excluded, but because his physics was a complex evaluation of open models: nothing there is simple or closed. Hence the unthinkable, absolutely speaking. Once knowledge, on the other hand, overcomes the energetic and definitional conditions of its formation, once it regards the closed as no longer anything but an archaic and abstract ideal, once it has more and more to do, down every avenue of the encyclopaedia, now ill-named, with opening as such, Lucretius will be there to welcome it, intact and as yet unread. When we twice cross the line of a closed curve we find ourselves in the same space. Old physics or old discourse, not pleasant: we had shut ourselves away so as not to hear them.

The vessel is a small hydraulic model. Now for some large systems that work in like manner: the earth forms the basin of the seas. If the laws and the rules remain invariable between the model and the system, then the latter becomes theoretically constructible, just as the first was in practice. Physics is possible as the science of nature. It will be able to describe a program of construction. Now the large vessel is precisely homeostatic and open, it is the site of an exchange of flux, for exactly the same reasons as the small model. In the ocean basin, the level of the water is constant within a narrow window. Why? By the evaluation of a statistically authoritative account; statistical because it is based on chance and large numbers. In the addition column, the sea is the receptacle of rivers, of rains, of storms. The entirety reckoned in an aleatory space: blockages are distributed everywhere, the rains wander, the storms fly. The whole flow stochastically distributed. What is more, the basins are essentially filled with holes: the aquatic plain covers its interior springs. Note that, just now, when the small vessel received a sum of flows, the estimate too was aleatory: the simulacra roam and fly, and we encounter precise philosophical information by chance, for which we must thank Aphrodite. Once again, the great number: compared to the immensity of the sea, this pile of contributions are of a lower order of magnitude, like a drop of water. A plane of retreat, in face of the sum: the sea emits fluxes, evaporation, clouds, and the winds sweeping the surface remove a certain mass. The vocabulary does not fail: all this happens as far as the eye can see and over a vast extent; the sun breathes up small quantities here and there, but there is a considerable distribution of such points across the retreating immensity of the seas,

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The Birth of Physics

and the total withdrawal will be large. Finally, the basin is essentially full of holes, permeable and porous: channels for the escaping the salt waters. In the general evaluation, through a multiplicity of causes and not through one alone, this accumulation and fanning out are important, the window does not move, or only very little.

The text, however, seeks to prove too much. Examine the balance scrupulously and it is not really in equilibrium. On the side of additions, the fluxes make a sum. It is evaluated down to the last drop, in relation to the enormity of the actual volume. On the side of subtractions, the fluxes are judged sizeable. Lucretius demonstrates homeostasis, bur his discourse is swept away to speculate on the fall. A trace of anxiety in the multiplied chain of reasoning. The terror of the flood. It is sweet to watch the raging of the sea from land.4 It is sweet to see battle upon battle spread out on the plain, if one is our of danger. Assuredly sweeter still to occupy the high fortified places of knowledge, from which we drop our gaze on the rivalries of men. The sweetness of living is to live our of water. On dry land, above the highest seas, in a place overlooking the plain and with superior knowledge. With dry feet. The problem is growth. Perceived as a threat, as a danger, uncontrollable. The rise of the tides, that is to say the propagation of violence and the intensification of rivalries. It is thus crucial to show that the waters' rise is bounded. To scatter the text with limits, thresholds. Growth cannot exceed a given maximum. The reduced vessel does not fill itself and in the great Medi­terranean basin the storms are not strong enough to cover the highest ground. And we are gods, for our Olympus is now down here. The sea does not rise. The homeostatic system is scientific, because of the flow, the opening and the evaluation of great numbers, because it allows the construction of a theoretical order. Bur the demonstration causes a panic deviation, strangely pushing the flood to subside. It speculates on the fall, against the swell of the sea. Is this a lost cause? Perhaps, for soon the Athenian region will be flooded by the plague. Many cities were swal­lowed beneath the waves, along with their inhabitants. Uncontrollable growth or regulated growth?

The water is contained in the basin, the earth contains it, although it is open and everywhere in ruins. It is the vessel, built like the vessel; and it is not I who say it, but the text, which twice returns to the comparison between the system of earthly physics and the little model: ut vas, ut horor in nostros artus.5 We shiver in the cold and our limbs quake like the earth. The soil is worked by the laws of disruption and discord, the text is sprinkled with the prefix dis-, like the subsoil with pockets and caves:

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derupta, disserpunt, disturbat, dispertitur, dissolvat, distracta . . . ruina. The vessel is porous, this is an understatement, it comes apart. The body of my mother the earth breaks up in pieces: the fantasy of scattered limbs gives rise to atomism. Demolition, mole by mole: the only permissable expectation, at the end of the rule, that and frantic anxiety. Fiat mundi confusa ruina:6 the dreaded end of a time that began with the fiat of atomic construction. And this disintegration, which is the whole of time, operates by flux. Of air and water, of scree. The demonstration begins again. In the depths as in the shallows, here as everywhere, the earth is full of voids, filled with caverns in which winds blow; lakes, swamps, subterranean rivers. Flow which travels through solid ground, which rolls the stones, blocks and the dissolved mass of fallen rocks. The flux splits the resource. Avalanches, vortices, tremors, and the vessel of vessels vacillates. The earth quakes. Fall of threatening things, rush to death. Flows and paths, maximal slope, vortices, all the models are experienced at once.

Local experiment. Suppose that all the flows gather together at a point. They press on the epicentre. The earth leans. It leans to the resultant side, the summed power of the hurricane. The constructions upon it, buildings, houses, lean: lean at the same angle and in the same direction. The beams, pulled forward, hang at the limits of equilibrium. The earth tilts, the walls, by the plumbline, lean, the vector and its angle appear in the wasted frame. All in the immediate vicinity of the fall. The structure is here the constructable and constructed model. Its limit is a structural reduction of it, in fact it is the same word, the same Latin word, at the limits of the theoretical. The paradigm and its schema. The framework delimits the field of forces. It is thus easy to read off from the two together, the statement of the system's laws. Laws of fall and inclination. The vectorial field of gravity, the differential angle of the deviation from equilibrium. The earth tilts, like the roof of its own crumbling basements, the wall leans, the beam reveals the law, geo­metrically, under the shifted roof. Vertical vector, but not completely.

Plunged into events, the phenomenon witnessed, the appearance of its schema, the soul quakes, like the earth. It loses its serenity, the calm full of equilibrium. Restless, it deviates from repose. The vessel-body leans and the level of its liquid tilts. Anxiety of falling and terror of death. The waters of the craven soul are ready to overflow.

We must return to the system. The house threatens to give way, yet is still standing all the same. Why? By the estimations of the general fluxes. In fact, they are alternatives. Their course spreads out in all directions,

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like that of the atoms in the chaos-cloud, their forces increase or cancel each other out. Violent, gathered, they inflate, here is the first experiment. We must display it over time. Tomorrow, they subside, then withdraw, repulsed by reversed flows. The whole of the evaluation is homeostatic. The flows which run through the large vessel obey the global laws of the sea. Their impetuosity, in the final assessment, is within the window. Now the earth threatens to give way, but it does not fall. It tilts, recovers, goes to the limits of falling, but does not pass them. It leans but wavers, it trembles around a solid angle. And if the inclination is a solid angle, then it is a restatement of the window. The earth is homeostatic. The conical angle guarantees stability in the deviations of equilibrium. Better still, it produces stability in the general domain of falls. Now follow the nappe of its opening: the more you move, the more the fall prevails over equilibrium; the less you move, the less the invariant is swept away. The top of the house trembles more than the middle, and the middle more than the foundation, and the foundation very little. Limit. The inclination is a solid angle and a differential angle. In truth, an atom of angle. Hence the definitions, of a perfect rigor, in book two: paulum tantum quod momen mutatum dicere possis . . . nec plus quam minimumJ Which is not by any means a precaution of language, bur precisely the deviation from equilbrium, mathematically measured by the infinitely small, either virtual or actual. Declination is an indivisible angularity in three dimensions. Scattered stochastically in space-time: incerto tempore incertisque locis.8 The local experience of the quaking, of the vacillation and the limit deviation, a window or small cone appearing in the models, is iterable whenever and however; and clearly without it there can be no physics, that is, no theory. Thus the whole of the terrestrial system, the great basin, becomes in its turn a model, that of theory. Now, by virtue of the reduced model, a beam supporting a roof, bowing in the middle, it is erroneous to affirm that the earth tilts, but will not pass the boundaries of the fall. We must speak in the intensive: it threatens give way more often than it falls. It is a low place, but contains still lower low points. This is Pascal's principle. It remains stable, but sometimes it falls. Collapse is perpetuated by the persistence of certain states around the solid angle. And this is a general theorem: the fall of atoms continues around knots built by declination. They rush towards equilibrium, like a flux that surrounds islands temporarily saved from the fall by the differential deviation from this equilibrium. The terrestrial system is not static, it is homeostatic. Now this situation obtains, as we have seen, by virtue of the alternation

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between flows and fluxes, winds and liquids. Thus the homeorrhesis produces homeostasis. And produces it locally. The window is the first inclination, the liquid interval is the first solid angle. The general fall of atoms is a flux. Homeorrhesis precedes homeostasis, we would put it no differently today.

The atoms, in their heavy flow, plunge to the low point. To the lowest low point, and so on indefinitely. The beam buckles and the mid­point dips. And this is the rule of balance. Atoms, together, are in search of equilibrium. This fall is the law and it is the same law for the dichotomy. Things fall and break. Dichotomy, extended polytomies, thus ultimately atomism. The law of disintegration, of dispersal, of dissemination or of dissolution, whatever you like, the the prefix remains invariant, it is the law of the fall and vice versa. The rocks roll and destroy themselves, mole by mole, scattering atoms. The movement towards the limiting state of equilibrium is a type which has two exemplars: the fall of heavy bodies is the first kind, atomising and chaotic dissemination is the second kind. And this law, unique and double, is universal: the atoms fall, that's why they're atoms.

It does not pause for a moment in the exercise of its power. Its ravages spread both everywhere and always, through the course of nature and the rest of the poem. It is not that there is a time of fall, the advent of lightning, then a time of aggregation. A chaos, declination, a world. No. Each centre of aggregation, hardly formed, breaks apart and falls. The flux does not stop: a race to death, a search for rest. The movement towards equilibrium is the universal of the law and the organisation of this or that state of things cannot stop it. The cataract, the torrent, the flux of collapse, is the core the being, the fabric of the core, the noise of the core, the theoretical closure, the fundamental opening.

Now underground rivers erode the earth, hurricanes tear off the roof The wall threatens to give way, it leans, it is going to fall. No, the flow, reversed, soon straightens it and pushes it back. By the unevenly starred wind rose, it slowly describes a very small solid angle. We would not notice it, perhaps, without the shaking of the beam. This small differential cone saves the building from collapse. It marks the bordered, limited space, in which such an aggregation is temporarily removed from the universal legislation. Now it very faithfully reproduces the alternation of ravaging waves, charged with the execution of the law and obedient to it. This is because their forces are distributed on spreading beds, they run to the east, the south-west, the north, and so on. Thus a general turbulence. The solid angle which protects the wall and which

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The Birth of Physics

General rush to balance, towards maximum entropy

F I G URE 2

MECHANICS First kind:

FALL

Opposite

PHYSICS ATOMISATION:

Second kind

�E

. 1 ' qUlva ence

Op osite

'if Equivalence 'f

Exception deviation from equilibrium

First kind: CLINAMEN

MECHANICS

� '"

AGGREGATION: Second Kind:

PHYSICS

The universal law of rhe rush to equilibrium is double. lfit is the fall of heavy bodies, it is mechanics, if it is automation, it is physics. The fall is the mechanical equivalent of atomisation, and it is more simple. It says, in pure movement, what dissemination says in matter. Now, if something exists, this is because aggregation takes place, physically speaking, by and in matter. There is an exception to the general rule of irreversible atomisation. Hence its mechanical equivalent, simpler in pure move­ment: the clinamen, as a local deviation from equilibrium.

describes the beam is identically the starry circuit of the flow. Solid angle, or cone, that is turbo in Latin.

Let us return to the cataract. It rains down universally, everywhere and all the time. Declination is the minimum solid angle that introduces a change in the general movement. Or, quite precisely, the smallest turbulence. In the light of the constructible models and the phenomena experienced during the meteora, things become clear. An instant and a minimum deviation are enough. An instant later, turbulence forms a pocket in the three-dimensional flow. A local pocket where the flows, adrift, go back upon themselves. In this place of singularity, these flows change their direction, their force, their volume. And this exchange can be, by chance and temporarily, homeorrhetic. The world as we know it, for example, is such a pocket. Fragile and protected by the round roof of minimal declination. Stable-unstable through homeorrhesis.

Experiences

This pocket, this seed, this island, this turbulence, holds for a certain time before disintegration, before being carried away by the cataract, the current of atoms that wear it out and break it. They preserve themselves by their differential deviation from every static law. This appears a paradox and yet is not: this temporary stability is only possible at the price of a small discrepancy in relation to the law of universal stability. For every static law is in fact either a law of falling, the first type, or a law of disintegration, the second type. Why does this hold? Simply because it does not hold completely. Every case will be a minimum degree out of true. There has to be a minimally open solid angle. Yes, it holds by a miracle. And by a miracle I mean the case statistically of extreme rarity. And Lucretius says just this: incerto tempore, incertisque locis, by chance, here and there, amid the universal cataract, by a stochastic dispersal, these deviations happen, these micro-turbulences or minimal cones occur from out of these islands or pockets. Bolts of lightning in the clouds, waterspouts. At the heart of some of these singularities, the flows equilibrate, the sea does not rise, the Nile regulates its floods and its falls, the compass card is roughly symmetrical. And so, it holds. Homeorrhesis, homeostasis, miracles at the heart of the general torrent, extremely rare local cases. To be wholly precise: exceptions to the static law. But, once again, exceptions as close as possible to the common root of the ordinary law, by this differential deviation. Hence the scandal of declination in the eyes of classical and modern physicists: it interrupts the universality of the laws. It opens the closed system. It places the physical laws under the rule of exception. Under the protective roof of its solid angle. And yet, that is the way it is. Lucretius is right.

He accomplished the revolution being carried through by the sciences of today and which philosophy continues to neglect. If the fall is universal, if its law, both kinds, can never suffer any exception, then every construction becomes impossible: there will be no world, there can be no physics. Correlatively, there will be neither discourse nor sense. And this indeed is the case, at least for closed systems. Now it happens, and no one can do anything about it, that at least something exists some of the time. This pebble, as it rolls along the thalweg, this house built with my hands, the smooth body of this woman, and this world under the sun. Our science has said, without really knowing it, that all this must not be. It is impossible. Reason delivered up to the death instinct and tending towards chaos. And every discourse is impossible. Yet, you speak and I understand. Thus there are open systems. Thus there are exceptions to the rule. Thus there is a nature. By this I mean that in the

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sheet-water of the cataract, an aleatory scattering of turbulences and singularities are in the process of being born, at indefinite places, at improbable times. In the vicinity of birth, in generalised death. In this sense, at once rigorous and statistical, without nature there could be no physics. Without nature, that is to say, birth, the open, the exception, the miracle, the deviation. Science is no longer within order; order is equilibrium, death, and chaos. It is entirely within the extraordinary. Science is, throughout, the organon of the miracle, and the miraculous discourse. Science no longer partakes of the general, but of the ultra­rare. Discourse is not ordinary, sense and sign are exceptional. And the minimal condition of this displacement, of which I have said elsewhere that the Copernican revolution was by comparison but a child's game, you will call declination. The principle of reason defines two reasons. Closed reason, equilibrium and chaos, cataract, indeed maintains that there is nothing. And shows it. If there is something, it is a nature. The rare formation of pockets, of islands, of waterspouts and seeds. The ultra-rare and aleatory birth, by the little deviation within a vicinity: that which is ready to be born, what is going to be born or to appear, in the open proximity of the differential inchoation. So the term of nature, in its very grammatical formation, makes declination inevitable. In the cataract of the meaningless, in which the atom-letters rush towards their fall, here is the birth of meaning. Discourse is a deviation from equilibrium as this or that state of things. As exceptional, as rare, as declined. It too, breaks the flow, the flow of things themselves. Atomist physics is a critique of closed reasoning. No. Not a critique. It is an architectonics of the opening in false perpendicularity founded on the irrepressible flight of the stable. Not a critique, but a clinic. The stable flees, and only the unstable can hold. The clinamen. This is how it is. And it is only this way as long as it turns. Lucretius is among us, he speaks the same language as we do, his feet on the same earth.

As a consequence, things, phenomena, the world in its entirety, are all models for theory, and wrought by these two laws of nature. The law of death, universal, flowing in waves towards equilibrium, infinitely, and the stochastically distributed exception in the cataract, under the differential cones of declination, where the flow inclines, returns in a waterspout, diversifies, develops locally and constructs an aggregation that is temporarily stable because unstable. From which the vessels, the family of vessels, basins opened by declination itself, ceaselessly inclined, or in rupture of equilibrium, holding by a miracle and threatening to fall, whole sections crumbling into the cascade of the great flood if they

Experiences

pass the limit of rupture, but retaining their organisation for a time under the leaning roof where the beams bend. The framework delineates the declining world.

When we compare two or more manuscripts that have probably been subjected to successive recopies and we find that one of them has a passage or section that is more obscure than the equivalent sections of the other manuscripts, the rule expects us to choose the more obscure. In all likelihood it is the authentic or original text. The copyist, in fact, faced with a difficulty of understanding, steps back and can translate clearly. Clearly for him. For the easiest thing is interference, the simplest is the transmitter. A rule which is known by the name lectio difficilior, choice ·of the most difficult reading. Just as if the series of copies ran towards maximum entropy. Now, analysis may apply the same rule as epigraphy. The interpreter, too, helps texts along.

Up until now, I have adopted the lectior difficillima on the atomism of the ancients. Here, the obscure section, the incomprehensible passage, or better, the paradoxical fact, is the introduction, the existence, the appearance of the clinamen. Translations softened the difficulty for rhetorical purposes. I have shown that it concerned an infinitesimal language, thereby explaining the recourse to Democritus, who instituted differential calculus on the basis of geometry and statics. A solution that illuminates the mathematical organon of presentation, but which leaves dark the thing itself. Which remains incomprehensible so long as history lacks a physics of open systems, and has not made the deviation from equilibrium possible. Which remains the more difficult before the revolutionary reversal which makes the clinamen the exception and the law, and makes knowledge of nature the science of the rare and not the general. The deviation from equilibrium as an ultra-rare exception to the universal laws of fall and dispersion is the only principle possible for the temporaty constitution of bodies, hurled into the irreversible cataract of the second law of thermodynamics. Only contemporary science allows us to see the darkness of the fact directly and to explain why interpretation always recoils before this most difficult reading.

Now this is even more difficult than it seems. I will explain. Everyone seems to agree that there was no physics, I mean mathe­

matical physics, before the end of the Renaissance. This thesis is debatable. In fact, there was none, at least before Euler and his theory of vibrating strings, at best before Fourier, with his analytic theory of heat. Before these two moments, there was only mechanics and geometry. Optics, in Gauss' approximation, is only geometry, the treatment of

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heavy bodies is only mechanics. Then the emergence of physics occurs, in effect, in an interval around what we call the Industrial Revolution.

And so the new contribution of the classical age is precisely dynamics. For Galileo, Leibniz, the Bernoullis, right up until Lagrange. And so this means, roughly speaking, that the Ancients had nothing but a statics; and, beyond the language of the mathematician, a theory of equilibrium and of rest. And their limit is Archimedes, once again.

These historical references, simple and clear to all, make the difficulty plain. I have shown up to now that the whole question discussed by Lucretius was that of equilibrium. Bodies, aggregate or elementary, rush towards rest, either by the movement of falling, or by the scattering of their constituents. They fall and break, and it is all the same, just a question of statics; the reading returns, and it is the easiest. It is compatible with everything we know about the history of the sciences. Here is equilibrium, here is the deviation from equilibrium. But let us compare all this to Archimedes' treatise on Floating Bodies. I do not think I have yet shown the extraordinary dissymetry of the two works. From proposition VIII of the Book I and until the end, almost all of the theorems address the angle of inclination of a solid submerged with respect to its axis of symmetry. Most of the geometric proofs in Archimedes tend to show that a floating body left to find equilibrium in fluid reestablishes its axis and effaces the angle of inclination. In other words, Archimedes' hydrostatics removes an angle that Lucretius, on the contrary, introduces.

Allow me to return, for the moment, to Book VI, on the Meteora. It seems there is no rest here. A general theory of the flow. Thus a dyna­mics? No, nonetheless; for I have shown that in the end everything con­tinually returns to equilibirium, by the general process of homeorrhesis.

Hence I return to statics, and the most difficult reading is still the easiest. The homeorrhetic equilibrium is compatible with the general readings of the history of sciences.

Let us go into detail. Examine, for example, the explanation of thunder and lightning. They are produced, as we know, by the friction between clouds. And the clouds themselves are carried by the winds, on the pathways of the winds. Nothing, here, which has to do with rest or equilibrium, quite the reverse. There are the waves, sunt etiam fluctus per nubila.9 Fluctus is not only the flow or the flood, it is also agitation, disorder. But we know this well enough, those of us who speak of fluctu­ation. Then, going up the series: wave, fluctuation, friction, lightning, ripping. But the hurricane sometimes surges in a cloud, hollows it out

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and causes it to explode. Line 126 says of this process: turbine versanti. I assume that the flow of the wind was a translation, that in the encounter with the cloud its movement changes. Which leads to an interesting observation: there are flows, but fluctuations; there are floods, but turbulence. The book on the Meteora is the book of turbulence. The examples just cited are only aerial. Here is the waterspout: versabundus enim turbo descendit.IO A liquid column in movement running straight on the waters. Here is the fiery summit of Etna: ut Aetnae expirent ignes interdum turbine tanto. II The fires exhaled by the broken crater in enormous spirals. As we have seen, the process is the same in earth­quakes, in which the wind vortices in the cavities of the earth, opens an abyss and destroys cities. Turbulence at a stroke is trans-elementary: earth, air, fire, water. But, in book five, it affects the world, the move­ment of the heavens, after Democritus: quanto quaeque magin sint terram sidera propter, tanto posse minus com caeli turbine ferri. 12 The more closely the stars neighbour the earth, the less quickly they can be carried off in the circular vortex of the sky. So also with the moon: jlaccidiore etenim quanto iam turbine fertur inferior quam sol, etc.I) As it carries off the moon, this vortex is more languid in its given place below the sun . . . As for its form, at least what appears accidental, the waterspout, eruption, thunder, lightning, becomes the law of the movements of the universe. Whereupon we again find a correlation between the exception and the rule. Here, perhaps, is an opening to the words of Heraclitus, according to which lightning governs the universe. These are words on which Heidegger and his school have pronounced so many grandiose sublimities, and yet they simply mean that we never steer a vessel except by the angle of inclination given to the rudder, around which the streams of water leave their turbulence; then the lightning flashes and crashes like a perceptible clinamen, around which the winds and the clouds form their vortices.I4

The final outcome, the general theory of flow does not lead uniquely towards homeorrhesis. It also leads to a general theory of turbulence, general because trans-elementary, and generalised to the movements of the heavens. General finally because it traverses chance accidents and law-governed orders. Turbo, thus, is an important word. Quite close to turba, the crowd, disorder, number and great number, the throng, chaos and agitation, we have already seen and discussed this. Quite close to disturbare, destruction, bursting. But finally meaning a change in move­ment. Now, since the elements, in statics, are in free fall in the void, all parallel to each other, is the turbo the result of the momen mutatum?

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The Birth of Physics

Things now become wonderfully simple. Take some flow, of water, wind or fire, of matter or of atoms. Ideally, without any constraint, each of its waves moves in parallel with all the others. We say of this flow that is laminar. Everything happens �s if each separable lamella in the flow acts without regard for any other. Hence there is only one question: how, in this flow, does turbulence happen? Or: how does a laminar flow become turbulent?

From hereon I am released from any recourse to contemporary knowledge that is cutting edge, as they say. To aid my understanding I have at my disposal a classical science, a science old as Archimedes and the Greek hydraulicists: fluid mechanics. Let me say this: Lucretian physics is modelled on a mechanics of flows. This is our experience. Fluid flows in hollow bodies: clouds, rainstorms and waterspouts, seas and volcanoes (the sky and the earth receive from the infinite in sufficient quantity all the elements that can suddenly make the shaking earth quake, hurl devastating turbulence through the sea and the lands, rapidus percurrere turbo,'5 make the fire of Etna overflow and to kindle the sky) , the Nile and rivers in flood, lakes, baths, menorrhea, water from wells and fountains, finally the lodestone. All bodies sink and everything flows: perpetuo fluere (VI, 922) nec mora necrequies interdatur ulla fluendi (VI, 933), without truce or rest, and all bodies are hollow (VI, 936) . Then the clouds reappear, bearers of germs and death, to destroy every living thing (perteurbarunt, VI, I097). Perturbatus enim totus trepidabant (VI, 1280) : return to disorder. The exception, the law, the return to chaos. Everything flows, turbulence appears, temporarily retains a form, then comes undone or spreads. Physics is entirely projected on the current events of hydraulics in general. The physics of Lucretius is a hydraulics.

This remains true to descriptions of experience. From lightning to the lodestone, and from perception to the wearing away of things. Is this true for theory? Let us examine Book II. It begins with the famous line: suave, mari magno turbantibus aequora ventis, which is now suddenly stripped of its psychologism. How, in open sea, in the greatest hollow, without the various flows suffering any constraint from the shores, does the general turbulence of air or water appear. Thus a treatise on the mechanics of fluids. And the first line has the status of a title. The reading is thereby made easier. Yet no. For the problem raised, that of turbulence, is no longer a static question, it is a dynamic question. Not of hydrostatics, but hydrodynamics. And this is incompatible with the state of sciences in Antiquity. We fall, once again, upon a lectio

Protocol

difficilior. It seems obvious, but it is impossible. Inversely, homeorrhesis was not obvious, but it was possible. It was an equilibrium. Rhesis, here, is a movement.

It is obvious: atoms fall in the void. We always read this as readers knowledgeable about the laws of the fall of heavy bodies. In fact, Book VI and the whole range of phenomena described in the text impose once again the consideration of the theoretical schema as a flow. Flow in general and without constraint of walls. A theoretical streaming, ideal. The question now is simple: does a streaming remain laminar? And the answer is equally simple: in fact, in practice, physically speaking, a flow always is or becomes turbulent. The clinamen is the infinitesimal turbulence, first, but it is also the passage from theory to practice. And once again, without it, we understand nothing of what goes on. It is thus a matter of experience.

Now fluid mechanics has understood what happens, if it understands anything at all, only recently, and on the condition that it abandon its abstract and general perspective.

Let me briefly turn back up the path that I am going to open. In his Analytic Mechanics, Pan II Section X, Lagrange begins from the theory ofJacques Bernoulli, generalised by d'Alembert, that reduces the laws of movement to those of equilibrium. D'Alembert himself applies it to fluids in general in his Treatise on Fluids, 1744, where he resolves all the main questions that one could ask about the movement of fluids in vessels. Broadly, however, this whole theoretical framework falls before the critique of Daniel Bernoulli. For these solutions suppose: 1. That the different sections of fluid precisely maintain their parallelism, in such a way that a section always takes the place of the one preceding it; 2. That the speed of each section does not vary in direction, that is to say that all the points of one section are assumed to be of an equal and parallel speed. One can see immediately that the two suppositions are those of Lucretius, for the first fall of his atoms, considered as a laminar flow. Now, paradoxically, Daniel Bernoulli declares that these hypotheses may be confirmed experimentally in very narrow bore pipes, but never under conditions far removed from this. For the larger the pipe, the higher the probability that turbulence will appear. Henceforth, the clinamen appears as a necessary and non-paradoxical physical reality, in as extended an environment as one could wish.

Beginning from these remarks, either I can either turn back through history or carry on ahead. If I turn back, I establish the text; if I turn ahead, I resolve its problems.

The Birth of Physics

1 . I turn back. And I shall shed a new light the relation between incipient physics and hydraulics. The importance of the latter in the emergence of the former. From Bernoulli to Archimedes, via Torricelli and Pascal: liquids. To understand why this discipline, which we think of as very specific and specialised, is found at the centre of these preoccupations, from time of the Renaissance and the Classical age. Why the magnificent drawings of Leonard da Vinci on the turbulence in hydraulic veins, the channelling and control of the Arno. And why this central relation, why this importance? On this question, we need only go back to the contemporaries of Lucretius and read their works patiently. We see that the learned are not as learned as we think or as they would have us believe. Read Frontius, read Vitruvius. These are practitioners, technicians, technologists. It is remarkable that in the treatise On Architecture, Book VIII is entirely devoted to hydraulics. An encyclopaedist engineer concerns himself with architecture, hydraulics and astronomy. This is the normal degree course. Although later than the De rerum natura, Vitruvius' text contains numerous intersections with Lucretius': the regulation of the Nile, theory of fountains, springs and wells. The same is true for F rontius, in the treatise Aqueducts of the City of Rome. The questions raised here relate to flow in various conduits. And why at the conclusion, at the exit, the flow is never the same as at the spring, and why conduits can break, why the flow never occurs ideally. The technological conditions of the whole question are assembled. The text establishes itself by itself. The hollow earth is a complicated composite of aqueducts and aeroducts. Here and there, it bursts, because turbulence appears. The technological model is in place. It is a physics of water supply. Our physics was first a mechanics of fountain-builders, well-diggers, or builders of aqueducts. Hence the foregoing history. The Mediterranean basin lacks water. And he who holds power is he who can channel water. Hence this physical world in which the drain is of the essence, and in which the clinamen appears as freedom because it is precisely this turbulence that refuses forced flow. Incomprehensible to scientific theory, incomprehensible to the master of the waters. It is not necessary to live under the rule of necessity. Hence the great figure of Archimedes: master of floating bodies and military machines. Just like da Vinci. And just like Lucretius who ends with the plague at Athens.

2. Now I shall head down through history and ask present-day scholars for solutions to this problem. The formation of turbulence in a flow takes place:

Experiences

a) by chance: incerto tempore incertisque locis, in the reference text; b) according to viscosity, plus speed. Hence the hooked atoms. A

certain relation of speed to viscosity must be fairly large. These conditions are found together in Lucretius' model, fall and hooks;

c) the appearance of turbulence is, finally, like a return to statics within hydrodynamics. The flow, losing energy, attempts to recover its initial equilibrium.

Thus: r) the clinamen is necessary within the experience of flow; 2) it must be produced under the conditions of the theoretical model; 3) it is the sign of return to statics in a domain that appears to be

dynamic, it is thus the only phenomenon that makes Lucretian physics compatible with the current state of the sciences. An atomism without clinamen would be non-scientific under the same conditions. Quod erat demonstrandum.

The book of the Meteora closes with the plague at Athens, which is odd in itself. As though a contagious plague, an epidemic, were regarded as a scourge from heaven. What astonishes us today is nonetheless of the utmost coherence. A germ is a quasi-atom, or else what we have since named materialism is thwarted. Retrospectively, this was an error as well as an important discovery. Like a question well-posed, though badly answered. Lucretius, one suspects, is a pre-Pasteurian and the only path remains, for him, that of hylozoism or, should you wish, of heterogeneity. The sowing of life or death requires no other seeds than the elements of matter. Now, to formulate the question in this way is to betray it, it is to formulate it in modern language. The coherence of the poem does not quite run true here.

Book VI reveals physical theory in the concrete. In a field to which we are unaccustomed. Our science, our mechanics, generally takes place, from Newton to Auguste Comte, on earth and in the heavens, the fall of bodies and the orbit of stars. Almost never in between. Atomist physics, accomplished, complete, is carried out in the Meteora, its basic model in the open set of Nature; not its reduced model and its formal schema, not an object as large as the state of the things that it describes, chaos, the formation of worlds and the history of mankind, but a sort of middle ground, visible though immense, and functioning according to contracts. This site, excluded from classical science, occupied entirely with the movements of bodies, and the planets, this middle ground

The Birth of Physics

between mechanics and astronomy, is the true domain of atomism, since it is a matter of very global laws, of the aleatory and of great numbers, of a very complicated mixture of the reversible and the irreversible, and of non-closed systems. As soon as rri:odern physics formulates, by shapes and movement, by quantitative and controlled experimentation in closed sub-systems, it abandons the phenomena which resist its abstraction to contemptible minor trades. Lightning, rain and clouds, are incomprehensible to it, and so they do not exist for it; they are the business of the peasant or the sailor, of the agronomist, geographer, of the oceanographer. Applied sciences that are denied positive classification, yet which have nothing to do with the instruments furnished contemptuously by those which this rubric sanctions. Lucretius' science is anterior to and posterior to this interlude, archaic and contemporaneous at the same time, it doesn't cover the same history, and thus is not at ease with the same objects. Its preferred phenomenon is precisely the one which, after or before, was or will be excluded or exceptional. This middle ground of the sailor and the farmer, of the hydraulic engineer; the turbulence within their locales, the scourge of work in the open.

The song of the Meteora is now simpler to read. There we find, placed with exactitude, all the pieces of theory and them alone. Just as though the text ended with a finite and perfect montage, on the natural spectacle of physics itself. The phenomena are saved, in the old sense of the word. Here is the world.

Thunder and lightning, first and foremost, can only be produced among the clouds. And the clouds are primordial. They model chaos. Chaos is cloud, cloud is chaos. Formless mass of elements, fluctuating and colliding. Within these groups, declination appears, visible, sonorous, dazzling. The thunder and lightning model the clinamen, make it seen and heard, they illuminate experience.'6 In the minimum of an instant, I see it, I hear it and the world is full of it. Hardly the time it takes to say it and no more than the minimum. The lightning-bolt governs the universe and declination produces it. Now, what is pro­duced is indeed a vortex, a vortex, vertex, whose sharpened point is thunder, the vortex that the Latin calls fulmen, thunder, turbine volvitur. The clinamen, in the chaos-cloud, brings turbulence. And thus imme­diately, the waterspouts and presters, spirantibus, turbo, involvat, the vortices of air or water, in the sea and the wind. Theory of cyclones. Theory forms before our eyes, nature deploys its spectacle under the contract of physics. Chaos, declination, turbulence: cloud, lightning and

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waterspouts; thunderclouds, thunder, cyclones. Science is experimental, theory in the storm. General repetition.

A return, then, to the clouds, these primordial wholes. If they form, it is by the flow, waves of vapour, rivers of wind. Amorphous gathering of certain currents emanating from the earth and the water. Gathering, that is, confluent crossing. The clouds knot the fluids together. And, immediately, the chaos-cloud is transformed into chaos-pourer, at the demand of the model. It rains. Heavens, sprinkle your dew. It is raining molecules, it is raining drops of water, as it rained, it rains, it will always rain atoms. The theory of the flow leads back to the hydraulic state.

This said, we still have to elucidate the questions concerning equi­librium. The earth is a hollow body, like all other aggregations, blocks and caverns, conjunction, disjunction; it is formed of fullness and hiatus. The surface and the sub-surface, as such, faithfully model the simple and dual law of the constitution of things: cavernous bodies of matter and emptiness, atoms and void. So the earth quakes, from the flow crossing mines and trenches. Terrae motus, it moves, but little. The earth crumbles and does not crumble, just as the house falls and does not fall, hesitant and entreated in the middle of the wind rose. A constellation of forces and flows delineate a cone, a solid angle, at once protector and destroyer, thus inclination, equilibrium and disequilibrium; a decisive deviation from the edifice of the canonical. Here the earth and the house enter into time. Into the real, history and physics. The house of the canon, fashioned by the measuring-stick and the water level, this was the plan, the blueprint and the utopia. I never stop fixing the roof under which I live, repairing the leaks and keeping it clear of water.

Everything falls and yet nothing falls. Everything falls when the time comes. And that time is defined by the deviation from the fall, or that which defers it, the interval of real time. Finally, deviation fades away and no longer defers the accomplishment of the static contract, the building, the earth and the world collapse, the city, a group of construc­ted buildings, is destroyed: this is the plague at Athens. The foreseen and foreseeable end, prepared by the beam that hangs from the roof in ruins.

The Meteora dramatise the fundamental variable of physics, this deviation from ruin or declination. Creator of time contretemps. Here is a statics, in excess, in default, with regard to its own canon. It is a dynamics and it is not, judged in the closest proximity to statics. Heaven's scourges make the inclination of the balance-beams visible. The roof beam, hesitating right and left, behind and before, in a starry bed of the flow, beats the time of clocks; and the other time is that which

The Birth of Physics

wears out the clocks, demolishes and defeats them, that which ruins the house, and cools the crackling funeral pyres in plague-ridden Athens. Two times considered together for the first time, equilibrium and disequilibrium for the first time evaluated one in relationship to the other. Theoretically linked in the same schema, flow, declination, and experienced at the heart of the greatest phenomena. Meteora fall, thunder, rain, snow and hail, and their etymological sense says that they ascend, rise, lift. This is not an error in the fall of bodies, of heavy bodies. This is a significant decision. The meteora are neither stable nor completely unstable, they are the visible models of existence itself, this word of statics outside statics.

Hence, with the greatest precision, after the description of seismic tremors and their explanation by flows and the deviation from ruin, by equilibrium and disequilibrium together, Lucretius gives us the calculation or the estimation of the oceanic homeostases. The sea, subject to constraints of growth and shrinkage, deluge and drought, remains within the frame of the level. It is stable and unstable, in other words homeostatic. Its global base is a sum of deviations. No matter how great the waves and the storm, my situation on the shores is safe: I am saved from the waters. I risk as little from them as do the gods. There remain some exceptions: Etna's eruptions are floods or fiery blasts (ignis abundare Aetnaeus) that produce vortices (per mare ac terras rapidus percurrere turbo) ,I7 and the regulation of the Nile, alone of its kind, is subject to floods. But, while volcanic activity is irregular and almost pathological, St. Anthony's fire of the earth, or sacred fire, the floods of the Nile are regular and foreseeable. The flow of the sands forming the sandbars, the flow of the winds, of rain and snow, together form constraints, conjugated or dispersed, and produce a homeorrhetic river, beyond homeostasis. The periodic innundation leaves its coutse stable, as also the blocked delta or the breezes which retain it. The river [fleuve] is constant in its floods [fleuves] , even as they push it out of balance.

Nothing is lacking in the schema and everything finds its place. Book VI has rebuilt it in the open experience of the world.

In general, the analysis, simple or multiple, goes back to a flood. Far from speaking of a solid system subject to constraints, that is to say to forces, Lucretius sets in place a fluctuating system, we would like to say a diarrheme, a syrrheme, constrained, in its turn, by a multiplicity of flows. Force is less a quantity than a direction, a tow. The meteora reveal the mechanics of fluids in action, at least as they occur. Thus the relative stability of the Nile is understood as a flood or vortex of floods,

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generalised turbulence maintained by the exterior flow: the wind pushes the waves, these push the sand, which, blocking the river, diminishes the slope (proclivis fiat minus impetus undis) ;'8 the North Wind pushes the clouds, which run to the mountain-springs and burst into rain; so precipitation and the melting snows push the waters of the Nile along the diminished slope; Thereafter they vary little; the slope is unstable, but the flood, as a flood, is stable. All in all, this is the most complex model, the most composed or the most confluent of syrrhemes. But simpler phenomena, clouds or presters, are also syrrhemes or conflu­ences of flows. A word is needed to express the simple element: a word like rheme. When the vortex constitutes it in form, it is called rhythm. And the flow, primary in the analysis, as it is primary in the construction of the theory in the form of the laminar flow of atoms, this pulling of matter down a given path, turns up everywhere in the phenomena which follow.

Emanations from lakes above which birds cannot fly, bitter smoke of extinguished lamps, effluvia of musk that makes the woman recline, sleepily, streaming with her menstrual flow, burning waters of the bath, vapours of charcoal and wine, with sulphur, with asphalt and iron mines, rivers everywhere, demonstrating the importance of fountains, hot springs and cold springs. Everywhere there are models of the most general theory, that of floods and paths, of elementary rhemes, capable of intertwining, here and there, into syrrhemes, connective rhythms. Everything flows, everything falls apart without truce nor rest. Every object spills, being both the source of flow and flow itself. Every body is hollow: every body is a well and every body is a fountain. Nature fluctuates, physics is written in a hydraulic language, it is a mechanics of generalised fluids. The lesson we learn here in the sixth book, which describes visible and tangible nature, confirms, again, the theory and the idea of the atomic river in which turbulence is formed. But it also come back to the workings of perception: it reconsiders its theorems, as in every book of science, where one principle is recalled in order to link up with other phenomena.I9

That the space of the world be a space of communication; this accounts at once for both sensation and the nature of things, for being and knowledge, for science as knowledge and science as the theory of the world. Everything is formed as a flood and is perceived as a flood. The sea is bitter and leaves a salty spray on our lips. Everything flows and spreads, and everything transmits to us, as receivers, through obstacles and interceptions.

The Birth of Physics

Now, just as turbulence or waterspouts give form to things yet drag them to their end, just as the same operator of construction, of con­junction, effects a return to the elementary, to ruin, to destruction, so also as the rivers and the flow, eddying sometimes and thereby making the world's objects, are the operators of disintegration: cataracts drag­ging on to cataracts. Declination is also decline, it conjoins, it disjoins, the waterspout is discord, it makes things, unmakes them; order comes stochastically from disorder and returns to it, the flows are of matter and of germs, principles, seeds, roots, genetic and primal bodies, for the edification of the inert or the insemination of the living, but they are also pernicious principles of contagion and epidemic. Every operator is of transformation in general, it works just as well for formation as for deformation. Thus flow kills the birds, puts epileptics to sleep, makes women doze off at their time of the month. Rheme and rheums, diarrheas or menorrheas.

Experimentation: magnetism

The global model of fluid mechanics, constructed by theory in order to save the phenomena, and readable in them by the whole of the senses, makes us recognise how nature functions, and how we ourselves function as nature in nature. Which means this: how things are born. and how we are born, how we form knowledge of these things which we in fact are. They are formed of atoms, conjoined at the heart of the vortices that form in the cascade, by chance, beginning with a differential declina­tion. Here, for objects, as for us, turbulence is productive. Subsequently, as I will show, it emits simulacra. In every case, it has a positive constructive function, for reality and for knowledge.

Now, beginning with the suave mari magno, things are otherwise.20 Rivers of churning air and water disturb the world. The templa serena, the temples of serenity, fortified by the wisdom of the sages, are removed from the cyclones, from agonising labours of seamen thrown about on the deep-sea plain, from evil. Turbantibus, magnum laborem, vexari quibus malis. Turbulence, then, is a trial, a torment and a mortal threat. We ourselves, born from the vortices, like naked Aphrodite in the foaming seas, are troublemakers full of troubles. This postulate can never be refuted. The cyclone passes over the world and the text, destroys them, shakes the walls of the universe, dismantles what is conjoined, disseminates the semina, casts disjointed spars on the waves. Collapse, decadence and the return to dust easily vanquish constitution. The vortex is devastating.

Experiences

These two ends of turbulence appear to repel one another. But not as much as it seems. If the spiral, in fact, begins in the infinitely small declination, we must recall the local results already obtained regarding the clinamen in order that they may be integrated, dare I say, to the global figure of turbulence. Things are born from deviation. They are constituted out of this difference from equilibrium or this minimal angle. From this little solid cone called turbo. In their nascent state, or their inchoate formation on the nappe of the fall, they are destined to return to the cataract. In the process of being born, destined to die, mortal nature. They are adrift on the thalweg of descent. And declina­tion is drift, thalweg, descent. All in all, things decline. This postulate means that at the end of their temporary existence they must come apart, undone, into their elements, but also that this only takes place by decline. Decline is time. Its length or its interval, its beginning or its end. To be born is to decline. But to exist too, and also to die. One and the same operation accounts for their appearance, their wear and destruc­tion, for their synthesis and their analysis, for their generation and their corruption. There would be no world and no things in the world but for the clinamen, in their existence, their beginning and their end. And it is the same with words, texts, with language, always in decline, always adrift. Formation is, in every final analysis, only a particular case of transformation in general The clinamen is thus the phenomenal and theoretical minimum operator of transformation in general. See, at your leisure, other applications of the same law: the history of men, like that of the world, is in decline. The famous Lucretian pessimism is only a psychological translation of a physical contract, committed by commentators that are blind to the world and who, pressed for the time, put their name to impressions instead of searching for results such as might follow from this universal law of transformation in general, this physical contract.

All that is required for understanding now is to go from the local to the global, from declination to the vortex that it initiates. Turbulence is the functional figure of constitution and formation, everything happens as if it integrated declination. This is the dine of Democritus. It then becomes the global figure of transformation in general, as the clinamen was its minimal or local operator. Things, and so nature, are formed by atomic conjunction in and through this very vortex; but, what is more, they exist and continue in and through it; finally, they destroy themselves, come apart, as if it were dwindling to nothing. Time is the fluctuation of turbulences, which make time, maintain it in their implications, set it going and finally allow it to disappear.

The Birth of Physics

To be born, to exist, to die, are only variations of this fundamental dinos, the figure of transformation, in which dynamics appears, timidly, in the continual deviations from statics, that is to say from the circular figure. Existence or displacement of equilibrium. If this deviation is null, there is no birth. If it is minimum, the spiral begins and the object is formed. Then it flees, it flees forward, as the word dine tells us, it develops and unfolds. At the extreme of deployment, dissemination. Existence, henceforth, can be called either vortex or disorder. T urbu­lence is productive and destructive, as the clinamen is formative and declining. It travels over the ocean, the mountains, the rivers, it travels over the living, history and language, over the stars, signs and meteors, accumulating catastrophes, leaving only ejecta, disjunctions. The vortex passes. It is the time that passes, the object which flees or the thing which falls, nature which bends, in its multiple and shifted curve, the temporary that still remains. And the movement of the cyclone, prester, or of the wind circulating in the hollow of the earth or of the waves, this is nature itself. What is nature, if not the aggregate of objects, these forms that are in a nascent state and which transform this form? Thus the open circulation of the flow in general, the indefinitely broken cycle of spirals. Pseudo-solid volumes in which implication is undone, whose resistance melts. Rivers and turbulence: rivers flow vortically, the vortices fluctuate, and all of physics is here.

I can do nothing about the vortex that brought my birth, and whose unfolding will bring my death. The science of time, that of things and of the world, teaches me that existence is disorder and disordered destruction. Through it, my time escapes me and death is near. Wisdom: avoid adding more movement to the vortex, to that which carries off the dense elements of the body, which screws down or enfolds the subtle elements of the soul. Halt the cyclone, try to escape it. Quell the disorder: ataraxy. This term of morality is built on the principal word of physics, precisely as the soul is of the body. Disorder is the evil side of the vortex, this state in which the operator of formation and of transformation becomes the operator of destruction.

Ethics enjoins struggle against the forces of death, inscribed in nature itself. The Greek words �oovr" hidone, pleasure, or �O1)<;, hidus, pleasing, reveal the root surad-, from the Sanskrit svaduh, and this corresponds to the Latin sua vis. Now Lucretius, in his most famous passage, as we know, juxtaposes suave to turbantibus, brings them together and opposes them. The storm rages, the prester passes over the waters. This physical vortex is the life of men, their movements, works,

Experiences

battles, rivalries, honours, shadows. Their movements and their short history. We have set off: this would be nothing. We are delivered to the cyclone, to bad weather, to the agitations of the tUQuXll, tarache, of the vortex and disorder, the turbantibus. Sweet ataraxy, pleasure, to withdraw from these spirals, increasing, decreasing, that work towards destruction. To withdraw to the riverbanks, to withdraw to the moun­tains, to withdraw to the temples of serenity fortified by science, which, precisely, makes theory out of these storms. To know its laws. The physical laws of statics: oUQxo� £votus£� XUtUOtll[!U, the stable condition of well-being in the body.21 The episteme, the knowledge of Lucretius endlessly repeats this term of statics. Stable on the riverbank, stable in the regions of the stable episteme, se-mota, remote, as far as possible, from every movement. And soon the classical age will repeat this lesson. Science is the fixed point and wisdom too. Then you will be like a god.

By Book II, Lucretius resolves the problem, even before he can formulate it. He sets out his argument like this: by what movement do the generic elements of matter engender the variety of corporeal things, by what movement do they dissolve the things engendered? A single movement, quo motu determines at once the formation and the resolu­tion. And a single force too, qua vi, compels their aggregation and their dissolution. Just as in morality, pleasure and pain have only a single source, an end to pain is enough to produce pleasure.

All the parts of the model, and all the elements of the theory, have now found their place, their realisation and their functioning, in the concrete reality of phenomena. Clouds in the wells, lightning in the fountains, meteora, on one hand, and the geography of the seas, of rivers and springs, naruralise physics. As experiential proofs of abstraction. We must say experiential and not experimental. What is lacking in this physics, is, as we say, experimentation. The theoretical schema saves phenomena without work ever intervening. The abstract model is faithfully reflected in the concrete model, by analogy: it is a spectacle, a speculation. The suave mari magno defines the situation of the observer: e terra magnum alterius spectaTe laborem, to watch in comfort, from the land, the labours of another. To observe fluids and turbulence from a fixed and solid point: experimentation began very late in fluid mechanics, in the twentieth century. It is not so easy. Thus this physics is an applied science, a science by applications, it is not yet an experi­mental science. It formulates explanations, it knows the multiplicity of reasons and the equivalence of hypotheses, it does not produce protocols

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of intervention. The phenomenon is thus a test of theory, on the side of the demonstration and, consequently, of the probable. It is not a test on the side of experimentation. It is a physics, a knowledge of the world through the coupling of abstraction and observation, yet still less than such by virtue of its lack of intervention. Paradoxically, it is instead a mathematics, the song of the meteora is no unlike astronomy. In which we observe and explain without being able to vary the parameters. And from which the Greeks seem to have noted the equivalence of hypotheses.22 To my knowledge, storms and rivers do not depend on us.

The success of the naturalisation of theoretical physics, and the absence of experimentation, the defeat of experimental practice. From this twofold result one can understand the extraordinary importance of magnetic phenomena, the last in the series and described in unusual detaiU3 fu if everything converged there. For once, precisely, there is experimentation. For only experimentation, intervention, can make the phenomenon appear. Here, experimentation is positioned in the immediate vicinity of theory, as is customary in canonic science. The instrumentation and the apparatus reconstruct the pure schema. This fundamental model is always a laminar flow in which turbulence appears. If nature, that is to say a ensemble of linked things, not an incoherent or chaotic ensemble of objects, but a communicating ensemble that functions as outlined, is to exist it is absolutely necessary that these vortices be in relation one to another. It is necessary that, in a certain manner, they be chained together or lead to each other. We must explain that they are rarely isolated, instead forming avenues, as con­temporary hydraulic engineers put it. So take a piece of manganese in your hand and little rings will link up; sometimes five, hanging in a row, will stick together, passing on a force one to another. So we have a finite avenue of rings, through which something is passed and lost. A reduced model of the vinculum or of that chain which is often spoken of in the history of science, and even in philosophy. Vortical rings in a fluctuating line. The theoretical model is finally completed. Not seen, but made.

From this point on the entire corpus is brought to bear in safe­guarding this new experience which, on account of its place at the end, the exceptional length of the commentary it receives and the pheno­mena exhibited in its reconstruction of them, must be taken as canonical. A general repetition of the theoretical for the experimentation of closure. In fact, Book VI presents us with a double inventory, in terms of extension and conception. Meteora, first, then rivers, seas, fountains, cashing out the initial schema in detail, they spread the coin of theory on

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the face of the world in a grand spectacle. Physics is a vision of the world and the world reveals physics. Then, as though inversely, a singular intervention, the manipulation of the magnetic rings, gives rise at the end of the analysis to a complete and general overview of theory, which is then brought to bear on the example. The recapitulation is brilliantly controlled: it gives us to understand that from the local to the global, and vice versa, the consequence may work.

Next comes the second review. A resumption of the general theorems on flow; perpetuo jluere, jluviis, jluenter, simultaneously accounting for the basic state of things, and for the knowledge that we draw from them. Fluid objects, flows to touch, odour, sound, sight, fluctuations that make a transmitter of the entire body, a receiver, a vector. Repetition of the first book: everything is a mixture of matter and void. The design of the hollow body or the porous object concretely models the theoretical com­bination, the fundamental simplex. The organism is a lacunary vessel, the earth is sown with caverns, the world is neither full, nor dense, nor com­pact. Now these veins in the fabric, these grottoes, trenches or hiatus, the ensemble of these interwoven sets are not just blank spaces on the design of the mechanical construction. They are given a function in the general theory of flow: the function of passages. Matter flows and wears out, it is conveyed (transire) through the network of pores. There are two complications, or two simplexes: the field of conjoined atoms, inter­twined series, full veins, and all the hollow passages through which the flow is conveyed. To the theory of fluids there corresponds a theory of paths. If everything flows, there must be channels. If everything communi­cates, there must be roads. And the theoretical existence of the void may alone account for these paths, channels or roads, laid out, complex, in the hollow body. The void makes paths possible. It is not a matter here of a crude or elementary mechanism, one cannot go inside as one would into a mill. It is not constructed, as we might say, of pullies, ropes and weights, that is, of elements and hooks. Not solely. The mechanism is accompanied by a complicated network of hydraulic transmissions. Now theory fore­sees it: the mechanism of fluids induces a hydropneumatic mechanism. We should note here, at least parenthetically, the distance between the atomist world and that ofLeibniz: two theories of the communication of substances, one in a mdedium that is semi-empty and the other in a medium that is full. The choice is important; and it depends on the tramire, the paths and the passages. In other words, is there a supporting structure beneath communication or not, a thing that is exchanged? From theories of light to biochemistry, this question is asked again and again.

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Thus everything flows throughout everything. There is always a network for a flow. The vault of grottoes oozes and our entire body sweats. Through the veins sustenance travels to the end of the nails. Heat, cold, penetrates bronze, silver and gold. Sounds and odours go through walls. There is thus no defence against sickness. Everything flows and illness courses. It insinuates itself. Now, everything does not flow through everything: what is true in general has particular limita­tions. What goes through gold cannot pass through glass. Each fabric presents a singular network or an original web. For a flow in circulation there are paths or directions that are forbidden, as if there were good and bad conductors. Wood is never affected by that stone we call magnetic. Everything flows through everything, but not in any manner whatever. There are conditions for the passage from the local to the global.

The theory of flow and paths is general, but ceaselessly in deviation from the general: everything flows through everything, but everything does not flow through everything. It accounts, through shapes and movements, mechanism and transmissions, better, through forms and rhythms, for what we can call specificity. What is specific is proper to a species or to a class, even to a thing, to the exclusion of other species or things. The contemporary age, ours, suddenly unites around this concept, which is plainly the question of the social, chemical and biological sciences, or of their common nucleus. Knowledge is in crisis, because it is ruptured from generality. The opposition to the positive method, the critique of truth, human nature lost and the world effaced, are only symptoms of the dissolution of the universal. But what kind of knowledge is in crisis? Not ours, that of the islands, but that of long ago. I'm afraid that we may be late for a war, or that we might only take up arms against a corpse. What we take for the foundation of Science, in the Renaissance, or whenever, was nothing but a path towards the universal or a presumption of generality. Doubtless simply a seizure of power, if power is no more than the intrusion of the particular into the universal. It is thus the knowledge of Bacon, Laplace, Comte and Hegel that is in crisis. This classical science or absolute knowledge, that gener­ally unlearned philosophers still take for science, by which specificity is repressed, forced back, ignored or otherwise not taken into account. Or, worse, that deduces it.

Now, from all sides, it pours in. From tiny compartments, from elements, from the enfolded topology of particular composites, from the stereospecificity of primordial forms, from life, local and global, from cultures scattered through space and history, and from those swathes of

Experiences

the world that one can call universe-isles. Maybe there are as many mathematics and systems as we wish. It breaks the mirror of the universal into tiny pieces, and everywhere delineates a polymorphism. Seeding the sea-chaos by sporadic archipelagos. The new knowledge finds only specificity before it. Either it is a defeat, there will be talk of a crisis, but it is the ancient universality that is lost, the old university; or it is the last death of Aristotelianism: there would no science but that of the special.

As a result of their vety generality, which is in danger of being lost. Our concepts of apprehension are dealt a blow by the specificity of the objects and contents with which we are concerned. They name specificity without saying it. By its root, by example, and not by the thing itself; then we speak of the look, we draw back to the subject that which belongs to the object. Or of classification, an ordered grid cast over sporadic polymorphism. But, on the other hand, generality dictates that, in the same circumstances, the same causes produce the same effects. Since we are plainly unable to refer with any confidence to causes and effects, we would do better to write that in the same circumstances, the same x makes the same y. There remains a repetition of the same [meme] , which is the general as such [meme] . And thus a deception in other circumstances. In the absence of a philosophy of circumstance, there is no choice but to go back to bricolage. It is the forced localisation of method. The latter is a path, virtually global. Bricolage is the ensemble of operations that the general cannot perform. In short, it apprehends the specific. Now, again, what is specificity [ie specifique] ? It is a medicine, for the treatment of a particular disorder, to the exclusion of all others. Applied elsewhere, in other circumstances, it is no longer a remedy and may be a poison, or else neutral. The traditional double meaning of the Greek word CPUQflUXOV, pharmakon, beneficial or harm­ful drug, exactly matches specificity. Or the exclusion of cpuQfluxo£, pharmakos, not of a third, but of a singleton of the whole. There is a crisis, one says: in the social group, in the text, in knowledge. But what is in crisis is the idea of the general, of the presumption to the universal. What trembles and threatens to break is none other than the bridge thrown from the global to the local and vice versa, that is to say classical knowledge and the will to power. The text of the law.

Are we so far from Lucretius? No, it doesn't seem so. The wild olive tree, he writes, is nectar to the goat, bitter to men. Marjoram and per­fumes are poisonous to pigs, medicine for us, on occasion. This question of the specific does not a concern only for the pharmacopoeia, the world itself is at stake here. Constitutive atoms may be unhealthy germs; far

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from making the world, they kill the city; turbulence is a vortex or waterspout, productive or destructive. Generation or corruption, this is a specific problem. Not merely of rwo values, but of a number of values as great as the things in nature.

And physics is summoned to this tiller or threshold: heat dries and liquifies, the sun melts the snow and bakes the parched earth, fire liquefies gold and bronze, it shrinks and dries meat and leather, scalding water hardens iron, softens flesh. It amounts to saying that all flow is a phdrmakon in its own way; in other words, it is a specificity. Thus, in particular, the flow of atoms, the clinamen, the vortex. They are des­tructive just as they are constructive. Dissemination is insemination.24 Corruption is generation. And vice versa. But this alternative is not everything. The logic of yes and no, dualism, and the dual, that is to say life and death, must be opened to plurality.25 The earth contains the elements of every species. Many, indispensable, nourish; many make sick and kill. Some are better suited some beings than to others and adapt themselves better. One way or the other, more or less, some do, some don't. And it is the projection of this pluralism of multiplicities onto the dualism that is fatal and destructive. Bringing down the multiple to rwo, and the specific to the general.

Lucretius now patches things together [bricole] . He builds local forms and traces singular circulations. It does not matter which flow does or does not go down which channel. Every body, each thing is of a particular tissue and presents its own original nerwork and web. The flow feels the effect of the channel, which itself has possible, modal or impossible paths. Now this bricolage of the tangled mass and interlacings is a method, in the literal sense. It is even exactly a combinatory topology. The atoms combined among themselves form figures and tissues. The birth of things, thus of nature, is the passage from the figure of the cloud (chaos, for theory, meteora, for experience) to that of interlacings, the fundamental mode of existence of all things, from the whole to the simplex. Already, in the second book, there abound terms like perplexis figuris, inter se plica tis, quasi ramosis, eia, intervalla, connexus, and so on. Here the topological description is mobilised by a theory of flow, of paths and pathways; but, elsewhere, it is developed as the topology of local varieties. Now the whole question in these matters, for Lucretius as for us, is indeed to link, paste, unite, adapt, incorporate, weld these varieties one to another. These are the proper terms here. Now this relationship, this local pasting, is always specific, and defines the specific. The important thing is what happens in the neighbourhood of

Experiences

the singularities. Hence the final proposition on the magnet, and on stereo-specificity: 'When the two textures of two substances are mutu­ally contrary, so that hollows in the one correspond to fullness in the other and vice versa, then connection between them is most perfect.'26 Who does not see, besides, that this is a theorem for the physics of Aphrodite? Every body is a hollow body, is a singular web of ways in which flows circulate.

Henceforth experimentation on the Magnesian stone reconstitutes the initial model. From the magnet there emanates a current of atoms, a flow, like a cataract. And the series of little rings, paradoxically attached one to the other, apparently making an exception to the fall of bodies, just as turbulence resists the cataract, lets us see, perceive, the avenues of the vortices foreseen by theoretical physics. We indeed pass here from the observation of waterspouts, presters and meteora in general, upon which intervention is impossible, to a local, precise and restricted manipulation. Where the same schema is found.

Now, the explanation of phenomena is given in terms of figures and movements. But what distinguishes it from modern mechanics, which will adopt the same methodology, is that shape is not metrical, and movement is not that of a solid. Form is described qualitatively, the flow is that of a liquid, a current. Thus fluid mechanics and topology then provide the basis for explanation in terms of surges and the filling of empty intervals.

Classical mechanics will measure, it will change its choices for the states of matter, it will prefer solids. Who can say whether this is progress? Surely not we who are just beginning to think in terms of forms and flow, and who pose vital questions about the local and the global.

NOTES

I ' . . . to the Physicists fJ,f1:fWQU denoted all the phenomena of the sky including the heavenly bodies as well as atmospheric occurrences and certain phenomena on earth, earthquakes, volcanoes, etc., which had similar causes, i.e. the contents of Lucr. V and VI. Aristotle first confined the use of the word to the atmospheric and associated terrestrial phenomena. ' Lucretius, De rerum natura, ed. C. Bailey, vol III, p. 155I.

2 Hermes IV, La distribution, Minuit, 1977, p. 9-14. III, 435-8.

4 This image and those that follow are drawn from the opening of Lucretius, Book II. 'Like a vessel, like the dread in our limbs.'

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6 ' . . . that then is a chaotic ruin of the world', VI, 608. 7 II, 220. 8 II, 218-19. 9 VI, 142.

10 VI, 438. II VI, 639-40. 12 VI, 623-4. 13 VI, 632. 14 It should be noted that in Book II, immediately preceding the description of the

clinamen, lightning and thunder hurl their flame and cross the lines of rain with their oblique flight (transversosque volare per imbris jlumina, nunc hinc, nunc illinc, here and there). The meteorological model here precedes theory.

15 VI, 668. 16 Lightning, of course, occurs nunc hinc, nunc illinc, in VI, 199 as in II, 214. 17 VI, 668-9· 18 VI, 728. 19 VI, 923-35 repeats again, very closely, IV, 217-29. These repetitions are relatively

frequent in the text. They always bear, or almost always, on canonical principles. This is the ordinary sryle of every scientific exposition. To speak of interpolation here would come down to this: a scientific treatise, by its infinite repetitions, would always be interpolated. No. This is a vortical text, endowed with long­distance attraction.

20 This citation and those that follow are taken from the opening of Book II. 21 Epicurus, Fr. II. 22 It does not seem to me imprudent here to compare the atomist approach of

multiple explanations and the aforesaid equivalence of hypotheses in astronomy. Some late commentators, like Proclus and Simplicius, attribute the idea of a multipliciry of possible hypotheses for an observed result to Hipparchus (for example, the movement of the world), without our having texts or sources in which he states it explicitly. R. Blanche, however, takes the attribution seriously (La methode experimentale et la philosophie de la physique, sub principio) and I gladly vote in his favor. Archimedes, we know, was more or less the contem­porary of Aristarchus, and considered him to be the first to propose heliocentric movement. He precedes Hipparchus by abour a half-century. Now, it so happens that the Sand-Reckoner, which in fact builds a model of the world, is perfectly unconcerned with the hypotheses in question. It is easy to suppose that he held them to be equivalent. If I have been correct in showing that Archimedes' work is the mathematisation of Epicurean physics, it follows that there is a concordance between the physical doctrine of multiple explanations and the astronomic principle of the equivalence of hypotheses. & time passes, on the other hand, we see a drift from Hellenism to Hellenistic probabilism.

23 VI, 906-1089. 24 La dissemination est ensemencement. The term ensemencement has also been

translated above as seeding [previous pagel and sowing, p. 85 . 25 The French duel may signify both 'dual' and 'duel'. 26 VI, 1084-6.

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CONDITION S

Epistemological conditions

Observation and simulacra

Of the errors of perception cited by Lucretius, the example of the tower is one of the best known. It is taught in school, and you can come across it anywhere. From a distance, a square tower looks round. Sometimes a circle may seem to be an ellipse: this is normal, and Apollonius' geometry gave a precise account of it. The eye is situated at the summit of a cone of vision, the rest is variation on conic sections. But it is not a matter of this, that is, of a plane object. Square, now, is no longer a precise term: a tower, a solid form, cannot be quadrangular; it is, rather, a parallelepiped, a prism, a pyramid. Likewise, it is not round: it is a cylinder, or a cone. A tower, isolated, built on the ramparts of a town, or in a ciry seen from afar about which the classics will speak so often, may take the shape of a cylinder, a prism, a conic section or a pyramid.

Who was the first to see this angular tower, about which school­masters speak so often and so traditionally? Thales, of course, who solved the puzzle of its measurement. But what disappears, in this vision become theorem, is the form of a pyramid and the flesh of its appearance. There remains only its height and its vertical framework: its volume and its edges have been left out. Perspectival space has given way to metric space. And who returns to revisit it, meditating on the planes that enclose it, on its ribs and its dihedra? Democritus, precisely. Democritus who, again the first, according to Archimedes at the end of the preface to Eratosthenes in his Methods, had formulated, without proof, a derivation of the volume of the pyramid from that of the prism and the cubature of the cone from that of the cylinder. The three dimen­sions are restored, the tower is a tower. We know from Plutarch and, again, from an Archimedean sequel to the problem, that Democritus, on his part, had raised the question of the infinitesimal with regard to the section of the cone and touched in general on the cubature of any solid of revolution, by an integral pre-method. There, all the forms required for a tower are found here, at the source of atomism: pyramids, prisms; cylinders, cones, and truncations of these objects. There, all the more so

lor

The Birth of Physics

since in a notable passage on theatrical set design, Vitruvius refers us to the works of the same author on the subject of perspective. Democritus had clearly composed a geometry of those things in two dimensions that one can call square or round, and which, seen from a fair distance, appear to take on relief: this organon that governs these optical illusions.

In addition, if he knew how to integrate the volume of a conic section, or of a cone from that of a cylinder and in relation to that of the pyramid, it is no doubt because, before the great Syracusan, he had conceived of the idea of exhaustion: to fill a curve with a polygonal outline, a circle with a square turned myriagon, a cone with a pyramid that has an increasing number of faces. And so, a round tower is indeed the limit form of an angular tower; the metamorphosis is accomplished. Everything happens as if sight, in the distance, resolved this problem of proximity by itself. This is the first convergence of perspective with strategies of the infinitesimal, an intersection that has a long history, via Leibniz, Pascal, and so on as far as one chooses.

But let us return to exhaustion. Imagine a square inscribed in a circle. It does not fill it, by an means. It leaves empty places, like hollows outside the fullness of its angles. An imprint inscribed in the circle, and that does not describe it faithfully. Let us increase the number of sides, this operation absorbs the voids and fills their emptiness. The imprint, little by little, begins to take up the outline, by closer and closer approximation. As the number increases, the two schema tend towards the same shape. And everyone can see that only Epicurean terms have been used in completing this process. And that the words corresponding to the Letter to Herodotus are authentically the everyday lexicon of geometry. Now this operation, strictly speaking, both has and does not have an end. In the vicinity of the smallest, we must decide. It is the passage to the limit. The curve precisely envelops this broken polygonal path. The surface is a boundary. It is an infinitely thin garment, cast upon this complex conjunction. A replication, as it were, though more of an application. Now observe the fluctuating muddle that separates and unifies the border and the conjunction, the limit surface and the infinite increase in angles. Literally and without metaphor, this space is fluent. It is the mobile deviation of a fine fidelity. Here, quite simply, is the genealogy of the simulacra, of these motile idols emanating from the surfaces, of the limit edges of the ElOOS' eidos. It is topologically so exact, and linguistically so precise, that the theory of sensation may serve, reciprocally, to show that Democritus indeed used exhaustion in his integral proto-calculus. And that Archimedes, in his resumption of the

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Conditions

problem and through his perfect mastery, had moreover mathematicised an unexpected process. It is an analogon, on the same model, of the Leibnizien theory of small perceptions. Even richer, it would seem, more complete or better constructed, since it takes account through its borders of the appearance of the shape at the limit frontiers of atomic constitution, and of the fluctuations of the phenomenon. The flying wraps are the fluctuating edges, and the surfaces the limits. Summo de corpore. The simulacra peel away from things as when addressed via infinitesimals. They peel away as you like. Each object becomes the source of an infinity of envelopes. Vision is as rigorous as the mathe­matical method. Now, since every object could only be produced in and through a vortex, or a spiral, it is turbulence as such that becomes the transmitter of its envelopes.

Hence the final analysis, close to the origin. Through his approach to irrational numbers and introduction of the infinitesimal, Democritus the mathematician produces the conditions of atomism, its instruments and its objects alike; through the question of the minimum angle in contact with the circle and the sphere, he brings out declination, tangency and contingency; through the volume of solids and the pre­method of integration, he makes the theory of simulacra quantifiable and plausible: the concrete example of the tower, the doctrine of what it emits. Every form is enveloped by an infinity of adherences, sliding infinitely from the virtual to the actual. Here are the elements of things, the requisite of their alliance in vortices, and the conditions of know­ledge. Take the world and its knowledge: a written physics in formal language, easy enough to decipher. Now, in the three cases listed, the indivisible, declination and contours, we are concerned with a local mathematics, or, as it will be called, a differential geometry, an ultra­precise analysis of proximity, which in every place repeats the question: what happens as close as possible to the singularities? They are all different from the recognised Greek tradition, the one leading straight from Thales or Pythagorus to Plato. Strictly, they are also contrary to each other. Democritus takes for his subject what for Platonists is an accident, and what for Pythagoreans was a disaster. They may be contrasted as a local and a global mathematics, as a science of idols and a science of ideas. The ideal forms of geometry are not transparent, invariable and empty, they are dense and compact, full almost to saturation, of a complex tissue, and covered, around the edges, with invisible veils which yet allow them to be seen, infinitesimal limits that nonetheless are there.' Differential robes that glide over the shapes. To the eyes of a Platonist

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the mathematics in question is false; for an Epicurean that of the Timaeus or of the dominant tradition is false. By true or false I mean these values with regard to the chosen system. Hence the two opposing theories of knowledge: idols and ideas. The latter are produced indefin­itely until completely worn away in the flow of the primordial, towards my eye that is itself made of atoms, and which is another tower, the receiver at this moment. The tower of the temple or the ramparts crumbles and the statues shatter: this is how the gods die. The thing is demonstrable, mathematically.

Methods and tools canonised in the work of Archimedes, and throughout the analogies which extend to the model established by the Epicureans. The Democritean corpus, in the beginning, brings this deviation between atomist physics and Archimedean mathematics to zero. The mathematical physics of the Greeks, the other, the other in relation to the Timaeus, is found there as though in embryo [embryonnee] .

The word dOWAOV, eidolon, is, in its development, an exceptional case. Anyone can clearly see its relation to eidos. The Indo-European suffix which completes it is participial. This normally indicates that it more closely resembles a verb than a noun. Yet on occasion the opposite occurs and in Greek some substantives are furnished with such a suffix or one of its equivalents. As these designate a productive agent, the derived term must necessarily be of a personal form, feminine or masculine. This is the general case. EidOlon is neuter, and is there we have the exception. It is an inanimate, impersonal, asexual agent. That which produces a form. A singularity of language.

The term is of great antiquity, and common in Homer. An image, sometimes, but often a phantom. He who converses with Penelope, in her sleep and in her dream, at the end of the fourth book of the Odyssey, or the pale shadows which flit through Hell in the eleventh. These same images reemerge naturally in the funeral celebrations of the Laws. Plato prescribes them, in the Book XII, describes the rites due to the under­ground divinities, and, coming back to the dead, says that the cadaver­ous body is an idol, a simulacrum (959b). The real being, imperishable, the soul, has gone to other gods to render accounts. The tomb body is a neutral phantom. And hell is here. Even better, here below. A world of dream and death; of appearance. Better still, the Theaetetus, in the famous passages on child-birth, opposes the fruit of life and of truth to the simulacrum and lies.2 The image is false, like a still-born child, after an abortion. Worse than false, it is foolishness; in the Phaedo, that book

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of the dead, it is foolishness that makes up the general sum ofloves, fears and desires. The phantasms born of anguish and libido. Plato, we might say, psychoanalyses Homer and the linguistic tradition.

The eidolon is what, in the perceived world, produces images, appearances, brightness. In water, in air and in mirrors. Illusions of the object. The eidolon is what, in the subject itself, produces false imaginings. And this happens all alone, in the inanimate neutral. In sleep and the dream, where the shades of the dead come back to life and speak of terrifYing subterranean gods. Hence the general synthesis: he who sees dreams that he sees, he who is alive is in fact dead, he who desires is filled with anguish, the body is a corpse, the world is a hell, truth false and senses phantasmagorical. Paul will have no trouble finding his images in Plato: images without words of gods dead or dreamed, the false gods.

The teachings of Epicurus save us from these terrors. And from this neuter agent, which set the phantasm to work with anguish and desire, the erotic body and the death drive. This analysis is indeed on the side of Plato, and of Paul, the Greek myths and the idols broken by Moses. His morality, it was said, opposes dreams, fear of the gods, and fear of death. It returns naively to the body, as it desires and perceives, and directly as an object of the world; it returns, naively, to the truth as true, to appearance as exact, to the object as object. It cuts the knot of the effects of language, and of the complex labyrinths of an exhausted desire that has become thanatology. The immortal eidos, unvarying and true, becomes, for him, error, and the lying eidolon, phantasmal and dead, becomes truth, tranquil appearance in a real world. See, just desire: nothing is that complicated.

Everything goes back to the workings of the idols. A science is required to secure peace, the felicity of desire in a gratified world. This knowledge is physical; through its explanations and its hypotheses it constitutes a nature. Nature seen, touched, felt, full of emanations, fragrances and murmurs, bitterness and salinity. Connective bodies exchanging the connective signal with other connective bodies. The atomic composites come together. This is how it works. Forms com­municate with forms by way of forms, which they auto-produce. This is how it works, and eidolon is a neuter agent, inanimate like an atom or a group of atoms. The id is material. If you dream, it is because you have drunk too much wine, or because you are worried about work. If you die, it is because the connection comes undone. But nothing is more delicate than the senses, more exact, more precise, more faithful. For all gnoseology is physics. No one can conceive of a more sophisticated

The Birth of Physics

receptor, of a more elaborate machine, than the sensory organs. The forms are to be found here, then, for there is nowhere else. And the neuter eidos, this atomic block, invites suffixive links. Form produces forms, the productive agent and the product each causing the other. But how can we explain this physical process, in its turn? With mathematics. With Democritus, who revealed the atomic constitution of shapes, and the infinite process of the formation of their edges. Yes, it works just fine. For the conical or pyramidal tower as well as for me, as receptor. The polygon with an increasing number of sides is the productive agent of the contour, of the exterior, of the interior. The square tower indeed appears round and the round square. Perception faithfully reflects constitution.

The eidOlon is false for the eidos, and vice versa. The theorem is true for the phenomenology of perception, as for philosophy in general. Homer and Plato, false. False for hells, corpses, anxieties, dreams. False for error and lies. Thus true. The eidolon is true. Perceived, alive, in a universe that is real and without fear. Terror is false for ataraxy. Go back now to the conditions of morality. There, we find a real physics for a world in which the here-below of Plato is false. And so, at the end of the regression along the series of requisites, there is a mathematics, a geometry, in which Democritus is false for Plato and vice versa. Which is what I said and wanted to demonstrate. The mathematics of the Epicureans, emerging with Democritus and given canonical form by Archimedes, is a science of images: neuter producing infinite multi­plicities of form. Auto-productive forms. The thing was inevitable given the realism of the compact and the dense, a prelude to physics; it opposes point by point the realism of ideal forms [idealites] , seen as empty and transparent. Either the lucid subject and the luminous object, or the subject-object compact through and through. White, black, true, false.

The exceptional neuter of the word eidolon flees, on one hand, through dreams, phantoms, anxieties, death, lies and double world, down the path of the id; or it flees, on the other, through physics and mathe­matics, nature and truth, down that of materiality. Thus the question, now resolved: on which side, as I still ask today, do happiness and rejoicing lie?

The theory of simulacra is a theory of communication: edges, envelopes, wraps, flying through object space, as objects or from trans­mitters to receptors. We know how these skins are shed, how these delicate carapaces become detached at transmission. And we know how,

lO6

Conditions

that is, at what speed, they cross the space of communication. At the end, at reception, the sensory apparatus enters into contact with this delicate film. Thus, sight, smell, hearing, and so forth, are just senses of touch. Sensation is a generalised sense of touch. The world is no longer in the distance, it is nearby, tangible. The theory of simulacra is a singular case of the general theory of flow, communication is one circulation among.others, knowledge is no different than being.

Like all philosophers passionately concerned with objective realiry, Lucretius was a genius of touch and not vision, which is the model of gnosologies that take their distance, through repugnance or repulsion. Knowledge is not seeing, it is entering into contact, directly, with things; and besides, they come to us. The physics of Aphrodite is a science of caresses. Objects, in the distance, change their skins, they send one another kisses. In the distance the square tower, angular, stiff, coarse; it comes to me, round, sleek and smooth. A phenomenology of the caress, voluptuous knowledge.

Cultural conditions

Violence and contract: science and religion

The Lucretian text is a discourse on physics. Commentary, at once critique and translation, in general refuses to recognise this, avoiding the nature of things themselves and treating the knowledge it presents as that of an ignorant pre-history, it speaks instead of moraliry and religion, politics and freedom. It cuts Lucretius off from the world. The scholiast loathes the world.

The hymn to Venus sings in praise of voluptuous pleasure. Of the original power, victorious over Mars and the death-instinct, without fighting. Of the pleasure of life and of guilt-free knowledge. For knowledge of the world is not guilry, but peaceful and creative. Gener­ative and non-destructive. There: these words already drift towards moraliry. Towards deep feelings, ataraxy and the gaze, the pose of the theatre: to view all things serenely, to contemplate calmly. To be free from the gods at last. As if Venus were not a god. As if the treatise did not begin with a prayer. An atheist, a believer? The decision is clear: there is only transcendence. Let these figures feast forever in the moun­tains. We will come back later to these heights, which the waterspouts leave untouched. There is only transcendence, and we must leave it to its strangeness. But it is a matter of immanence. Venus sive natura. Mavors

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sive nature.) It is a question of physics and not of emotion, of nature and not of cruel phantasms. Immanence: the world is traversed by laws, and is without deviation the site of reasons. But, before verse, one must choose between two laws. The law of eros or the law of death. Spring­time or the plague. Birds, corpses. And the wound of love or decom­posing bodies. Venus, verna, volucres, volnere amoris: these are the lines I want. To choose, then, between two physics, and the original hymn is the axiom of this choice. Venus, that is to say nature. Mars, that is to say nature. And the two remain true, violence and the plague descend the steepest slope, falling, without recourse, according to the law. So if I want to tell Memmius the laws of nature, I have to decide on its identity, its proper name.4 Now this decision is of such historic importance and cultural significance that perhaps nothing greater can be imagined. It so happens, and as its slave I can do nothing about it, that Western science has continually chosen otherwise than Lucretius. It has opted for war, the plague. Blood, brawls, and the bodies on the pyre. From Heraclitus to Hiroshima, it has never known anything but martial nature. What we modestly call Lucretius' pessimism, or the drift of his Aphroditean text to the plague at Athens, is the recognition that his bet is lost; and his physics too. Thus science, or what we call science, forbids us to read this lost science. The laws of Venus-nature are indecipherable to the children of Mars; who die and will die at the stake before understanding that locally, within the walls of Athens for example, but also globally, at indefinite places and uncertain times, this decomposition sends sliding down some thalweg a teeming atomic horde that will by declination reconstitute a world. The text of the poem is nature itself. That of Venus. It cames back on itself at the end of the martial action. But not in a perfect circle. The place where the atoms fall is not necessarily plague­ridden Athens, the time of the clinamen does not necessarily coincide with abandoning the dead. Space and time are thrown here and there. The circle does not complete. But, stochastically in space and time, turbulences appear. And the whole text creates turbulence. Turbulences appear everywhere in it. Venus, circumfosa, diffuses all around the reclining body of Mars, thrown at last to the low-point he had sought. She disturbs him. And unsettles his law. The physics of the fall, of repetition and of rigorous sequence is replaced by the creative science of chance and circumstance. Neither straight nor curved: a spiral.

Return to declination. To the text finally translated into its differential elements. The minimal angle to laminar flow initiates turbulence. From which comes, here and there, indefinite in time and place, a world

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among many others, things and men. Without declination, there are only the laws of destiny, that is to say

the chains of order. The new is born of the old, the new is just the repetition of the old. The angle interrupts the Stoic chain, it breaks the foedera fati, the infinite sequence of reasons and causes.5 It precisely disrupts the laws of nature. Therefrom arises the appearance of the living, of everything which breathes, and the horses rush forward. 6

The order of reasons is repetitive. The knowledge linked up in this way, infinitely iterative, is but a science of death. A science of dead things and a strategy of the kill. The order of reasons is martial. The world is in order, for this mathematicised physics, where the Stoics meet Plato, up the way, and Descartes, down, and order reigns amidst the heaps of corpses. The laws are the same throughout, they are thanato­cratic. There is nothing to know, to discover, to invent, in all this repetition. It falls, in the parallel of identity. Nothing new under the reign of the same. This is the zero state of information, redundancy. The chain of causation, the fall of atoms, and the indefinite repetition of letters, three figures necessary to the zero point of science. The per­petrators of bloody domination may well have been thrilled to find this world and seize the laws of determination, theirs, the same as theirs, those of extermination. Determination, identity, repetition, no inform­ation, not an iota of science; extermination, not even the shadow of a life, death at the end of entropy. Then Mars rules the world, he cuts the bodies into atomised pieces and lets them fall. This is the foedus fati: it is indeed the law in the sense of physics, it is how things are; it is also the law in the sense of dominant legislation: they want things to be that way. Mars has chosen this physics, the science of fall, and that of silence. This is the plague. Always the same concatenation: the epidemic spreads, becomes pandemic, violence never stops, it runs down the thalweg, atoms fall ceaselessly, reasons repeat indefintiely. Buboes, weapons, miasmas and causes, it is indeed always the same law, in which effect reiterates cause, identically. Nothing new under the reign of the same and under the same reign, preserved. Nothing new and nothing to be born, no nature. This is death, eternally. Nature put to death, its birth unwanted. The science of this is !lothing. It is calculably nothing. Stable, immutable, redundant. It recopies the same writings, with the same atom-letters. The law is the plague. Reason is the fall. The reiterated cause is death. Repetition is redundancy. And identity is death. Every­thing falls to zero: the nullity of information, the emptiness of know­ledge, non-existence. The Same is Non-Being.

The Birth of Physics

The angle heals the plague, breaks the chain of violence, interrupts the reign of the same, invents the new reason and the new law, foedera naturae, engenders nature, as it really is. The minimal angle of turbulence produces, here and there, the first spirals. It is literally the revolution. Or the first evolution towards something other than the same. Turbulence disturbs the chain. It troubles the flow of the identical, just as Venus disturbs Mars.

The first vortices. Turbantibus aequora ventis: scattered turbulence in a flowing fluid, sea air or salt water, breaks the parallelism in the repeating lamina. The sweet vortices of the physics of Venus. How can we not rejoice at heart when we see the sea in declination? The prim­ordial waters form. All more so since, upon these heights we elude Mars, elude the armies drawn up ready for battle. From these heights fortified with the knowledge of the wise, we have only to choose between these two physics. That of the troops, set out in parallel lines, in series and sequences; here are destiny's federates, laminae of atoms bearing arms, arranged, very precisely, instructa, in order, in columns, the well­educated science of instructors, the structure of divisions, the Hera­clitean physics of war, or rivalry, of power, of competition, which repeats unto death, miserably, the blind shadows of its redundant law. Form ranks, we will teach you order. The structure of order. And the series of reasons. The knowledge of rank. And of blood. Or instead that of turbulence, of sweetness, of joyous pleasure. Those who are at sea labour in the vortices: they are tossed by the deep swell that was once called turbination. They are troubled. But this vexari is only cruel for some landsmen, those who have never been to sea. 0, marine move­ments of intertwined lovers. Or voluptuous movements of the swell on the open seas. Listen to the rolling spiral line: suave, ventis, vexari, voluptas.7 This is the revolution of pleasure. This is the physics of Venus chosen over that of Mars.

A fresh return to declination. To the usual misinterpretations in the translations of the theoretical text is added the difficulty of establishing or reading it. Why, here and now, voluntas, voluptas, will, pleasure? Grammarians argue, not really knowing where the consonants should go: volu{n)tas, volu(p)tas. There is sense to this. The demonstration begins again. In the beginning we were warned: maritime turbulence, admired in bad weather from the land, only agitates fluids, waters and winds: turbantibus aequora ventis. In the theoretical text, reference to singular bodies is directed only at fluids: imbris uti guttae, like drops of water, per aquas atque aera rarum, through water or the rare medium of

no

Conditions

the air and, again, corpus aquae naturaque tenuis aeris. It is indeed a question of weight, of heaviness, but never of solids. It is the fall of heavy bodies, but not in the sense that we associate with this word almost instinctively since the dawn of the classical age. Hence the increasing likelihood of the proposed solution: the model is in fact hydraulic. Just as the scattered examples throughout the books are chosen from the animal kingdom, so the models are taken from what we would call fluid mechanics. Nature generates the living from flows. And these are laminar, parallel lamina to lamina, and declination is the atom of angle necessary and sufficient to produce turbulence. Hence the text which follows: what are these fledera foti, these laws of destiny that declination breaks? The following lines define them: they are sequences. Cause repeats cause ad infinitum. And so we have the bundle, the sheaf, the infinite cylinder of parallel consequences. Chains of reason pour down like rain. No atoms any longer, as in the model, either concrete or quasi­concrete, but laws or equations. The fall is the schema of their necessity. Now, declination interrupts this model and this theory. It disturbs them, it introduces a turbulence. And, since they are necessary, what shall we call this, if not freedom? But beware: this is not a matter of animantibus. Living beings have a degree of freedom when compared with mechanical constraints. The Latin libera remains concrete in relation to weight, to obstacles, chains and burdens. Now the laws of necessity remain those of fall and equilibrium. And so livings beings live in deviation from equilibrium. How can we explain this fact materially? Through phenomena that are visible, tangible, verifiable in relation to flow. By analogy with the concrete model. Turbulence is a deviation from equilibrium. And the beginning of the vortex is the minimal angle of declination. If living beings disturb the order of the world, then this literally means that living beings are primarily turbulence. What you see from the safe height of the cliff is the first living body in the midst of the waters, new-born Aphrodite, in the streaming of the liquid spirals, nascent nature in joyous pleasure.

This is not contrary to the laws, nor frenzied, absurd, illogical. Nor is it as opposed to Epicurus as some have said. For many of his teachings, such as the Letter to Pfthocles, are scattered with vortices and turbulent clouds; one of his lost treatises was even entitled Of the Angle in the Atom. It is a physics: in any given flow the clinamen is experienced, experimental, and is required by such experience. But it is a physics under another law than the preceding ones. The fledera naturae are in no way the fledera foti. We would say today that what we have here is a

III

The Birth of Physics

paradigm shift. Science remains science and laws remain laws, what changes is the global contract. The general design of what the learned agree to call physics. That declination has been mocked as a pulling of strings, a bending of rules, a fiction, as Cicero says, that one has remained blind to such a simple phenomenon, is all quite normal if it is considered from the perspective of another paradigm. Consider the still quite recent history of fluid mechanics and you will see the trouble physicists have had in freeing themselves from theory in order to return to the things themselves. Flow did not obey the theorems of general mechanics, formulated in the eighteenth century, and no one tried to describe flow in its concrete complexity until the beginning of this century. To become a phenomenologist again is as hard as breaking with the contracts of destiny. Epicurus, Lucretius changed the paradigm. And Marx, who saw subjectivity in the atom, as if it were a Leibnizian monad, and saw the arbitrator in the clinamen, just as if he were rewriting the Theodicy, was doubly right in recalling Themistocles.8 Athens is near to its destruction, let us abandon her and do battIe on the seas. Another Athens, another science, at sea. I shall explain myself, though I shall omit the strategy, since Mars is now asleep. The new knowledge is aware of stochastic phenomena: incerto tempore incertisque locis does not signifY the nullity of place or time, and thereby a passage to the soul outside the world of sensible qualities, but simply aleatory scattering.6 It is informed, since Democritus, by infinitesimal questions. It is inspired by hydrodynamic models and looks towards the formation of living systems. It is more physicalistic, less mathematicised (since it lacks a probabilistic organon) than Platonic knowledge, more pheno­menal, less metrical. But, above all, Athens is by the sea. The elective model is fluid. It is no longer crystal, or the five polyhedral solids, the body of the Timaeus, it is flow. Martial nature, martial physics is made up of hard, rigid, rigorous bodies, Aphroditean nature and physics is formed in the flow. The residual hardness of the atom is below the threshold of perception, what is important in experience and in pheno­mena is large numbers, the crowd of elements, the infinite cataract, that is to say the river. And we, whose own nascent physics tells something of the same story, may now understand this through flow, chance, systems, deviations from equilibrium. We understood Lucretius' knowledge very poorly because we were the children of Plato and the Stoics. Because the fundamental facts of Epicurean nature remained marginal to traditional science, which was ultimately not very Archimedian. And so we judged them irrelevant to the history of the sciences. Moreover, we placed their

II2

Conditions

nature outside of nature, in the soul and the subject. Even while, affirming the contrary, they founded materialism. Atoms are not souls, the soul itself is atomic. Consequently, and this will, I hope, raise a laugh for a long time to come: every non-physical interpretation of the clinamen remains essentially idealist, as it were, or, more precisely, spiritualist. In the classic line of philosophies of the spirit [de !'esprit] , dominant ideologies power and martial sciences. For a classical science, a classical philosophy. Take a good dictionary and see for yourself: classis, in Latin, means ' army' .

But we have come to the contract. To the Lucretian change in the contract. Why call fledus or fledera the laws of nature or the necessity of destiny? Foedera naturae or fledera fati. Pacts, alliance, conventions. Can we discern a political or strategic terminology, perhaps via the presence of the divine figures of Venus and Mars, in a work of objective science intended to free us from the tyranny of the gods, and directed towards a wisdom in which political ambitions and the negotiations of the forum will have no further place? Our very vocabulary is plunged into an ambiguity of this kind: order is of the world and of the street, law is in the courthouse and the laboratory, the rule is operative and civil, class is logical, social and scholarly, and so on.

Every war ends one day with a treaty of alliance, a fledus. Unless it continues to the point of total extermination, or the pandemic of the plague. At the beginning of Book V, the combat against nature is presented through the labours of Hercules. The first singular case of every war in general. Here, the worker is identical to the soldier. The Field of Quirinus is held by Mars. And the lands of the farmer are ravaged by the legionary, who passes for a labourer. This theft, for it is a theft or an embezzlement, is a stubborn tradition. Michelet, in the last century, always took Hercules as a model and a god; it is always the soldier who passed for a worker-hero. While the real farmer has too much to do to waste his energy on unproductive aggression. Lucretius denounces the illegitimate occupation, perpetrated, according to custom, in the name of the terror. Who is afraid, today, of the Nemean lion or the hydra of Lerna? If there are monsters, here or there, you go somewhere else, and that's it. The battle is over, Hercules is useless. Theatrical. Epicurus has set down his weapons. He speaks, he gives laws, he dictates the fledus. The new pact with nature. Epicurus brings to a close the Heraclitean period, in which war is the mother of all things, and where physics remains under the control of Ares. Thus Lucretius is harshly critical of Heraclitus, but treats Empedocles with consideration:

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The Birth of Physics

this other Sicilian had foreseen the dawn of the contract, by his introduction of Friendship or Love. Faced with Hatred or Discord, joyous Aphrodite had already arisen. Epicurus and Lucretius have laid down their weapons, have driven Mars out of physics. Can we understand this, outside of mythology and its old-fashioned naivetes? Yes, all too easily.

At the dawn of modern science, Bacon decreed that we can only command nature by obeying it. Descartes, that we must make ourselves its masters and possessors. The contract of alliance is broken. The battle resumes, and nature is our adversary. Hydra, boar or lion, we play without cheating. This is the law of the hunt: to put it into check and mate. Epicurus has just foundered, along with Lucretius' Aphrodite. It is the Syracusan in arms who gains the upper hand. The method is a strategy and no longer a contract, a tactics and not a pact, a game to the death and not an act of coitus. The return of Hercules in Bacon: he passes the columns. And of Archimedes in Descartes: he moves the world. So it is that the ancient figures of Hercules, Mars and Venus are prosopopoeia, that they are reducible to principles and conditions.

At the foundation of objective knowledge, as in its historical beginning, there lies a series of decisions or preliminary choices that often pass unnoticed. Here is one of them: either the contractual pact, or military strategy. Either the fledus which puts a halt to combat, or the tactician's game of command and mastery. Who guides science and decides? To this question the answer might be: Mars or Venus, Hercules or Quirinus, and so it seems religious or mythological. We moderns substitute the question 'what' or 'how. ' By contract or by strategy. Yet our contemporaries, behind the abstract principles of method, have rediscovered the question 'who' and the language of the ancients, behind metaphysics and the groups in power. Who? The class of producers, or the class that dominates? And thus the military and the generals. Lucretius speaks through eponymous heroes, Descartes and Bacon in abstract principles shimmering with metaphors, and we speak as historians. But the question is the same in all three languages, and it bears on the conditions of possibility of the sciences. What about this so­called nature? Is it enemy or slave, an adversary or our partner in a contract that Lucretius calls Aphroditean. This is not naive, it is not slight. It is of consequence. Will knowledge follow the slope of des­truction, of violence and plague, or else of peace, of rejoicing. Life or death, this, finally, is the question. Once again, our knowledge hears Lucretius calling.

Conditions

This is a condition, and it is a postulate. One might say: perhaps they precede science, orienting it, or, better, those who have influenced it as they profit from it. But in every case science, in its contents, its norms and its results, remains invariable with respect to them. Theorems and methodologies are not bound by these decisions. This is one of the most serious problems that we have had to face. It is difficult to imagine a rigorous and exact knowledge that could have been influenced by Venus, and not by Mars, by the desire for peace, and not destruction, by a contract, and not by strategy, by labourers and not by generals, since western science has only ever followed the weight of power. In other words: science is influenced by postulates, or by social, cultural, and historical decisions in general, which shape it and orient it; and yet it is universal, independent of the kind of contract made in advance. Two and two make four, heavy objects fall as described by Newton, entropy increases in a closed system, in every latitude, and no matter what class is in power. I do not know of any mountain, frontier or date that could broker the agreement of the learned and all on these points. Science is conditioned, but it is unconditional. No one has ever escaped this fact.

Yet it is easy to pick out conditions that give rise to their conditioned while leaving the content of that conditioned independent. We say that they are conditioning and not determinant. Moreover, they are sufficient. A little space, a chair, a table, three notebooks, two pencils, the average salary that makes them possible, and so also sociery today, its history and its divisions, all form a group of conditions that allow me to write a book. But the book may or may not come to be, and if it does, it may become a collection of equations or a dish of poems: plagiarised or inventive, exact or erroneous, hot or just warmed up. In short, in this case and a thousand like it, we can always go from the thingproduced to its conditions, but never from the latter to the former. This very simple principle has led all or part of contemporary philosophy into a retro­spective movement. Its discourse, in all its lucidity, is unfailing so long as it marches backwards and goes towards the multiplicty of conditions with its back turned, but it is powerless as soon as it begins to go fotward, from the condition to the thing. For this reason its position is unproductive; not by virtue of a poverty inherent to theory, but by virtue of the interminability and indeterminability of the theory itself.

Let us now assume that these conditions did not determine the con­tents of their conditioned. The initial contract in the practise of science is certainly of this type: mathematical calculations are independent of it, for example, as are the laws of the fall, and so on. But these conditions

II5

The Birth of Physics

determine, and strongly, what I would happily call the global cartography of the conditioned. Its disposition, the respective situation of the parts, the centre-point of its space, the classification of its consti­tuents and the schema of their relations. In short, global form and local topography. Yes, it is still the same science, but its topography differs according to its initial contract. Yes, it is still the same clay, but the mould has changed. From the same piece of iron we can make a sword or a plough. Lucretian physics, as I have shown in the models, is indeed the same as that of Archimedes, but the Aphroditean postulate and the exclusion of Mars transforms it. Here, hydrostatics is related to the theory of vessels, and there it is drawn towards the constitution of living beings. Fluid mechanics underpins both an inert technology and a biology. The model does not vary, only what is modelled changes. The parts and the proximities are turned around. More generally, the postulate does not determine the type of discourse or the methodology, but it does determine its classification. Now, what guides the practice of science is, more often than one might notice, the organisation of its parts. Science has made its own provisions, as we say. We forget too easily that exploitation is first of all a spatial term. It comes from 'to explicate,' thus 'explain' is only its brother. A tracery of folds on diversity. Classification is always already there, not only that of the sciences. It indicates where to begin, where to proceed, the most obviously optimal path, and the most strongly connected sections. This is true of knowledge, of the encyclopaedia: why such a discipline first or primarily, why a certain proposition first, why a certain experiment. The formative element of a generation is less the contents of what it knows than the apprenticeship that leads to this knowledge. And the invention, the discovery, the resumption, or whatever you wish, that follows the thread of development. Pedagogy is a guide, the word says it all, education is lead by a duce, as the term itself demonstrates, and method­ology is a path. Now the global design of this complex, the local connec­tions of its graph, are determined by a antecedent choice. So the condition is indeed determinant. And if knowledge works for death and destruction, it is because Mars or the military, the commander in Bacon, or the Cartesian master and possessor, are there keeping watch over the beginnings. This is also true outside science: there are few virginal spaces. Paths have already been cleared, and classifications are in place. Long before the forces enter into relation, before the confrontation takes place, finds equilibrium or topples, some un-named predecessor has chosen the site of combat, and the peaks that determine it. Strategy is

u6

Conditions

not only a dynamics and an energetics, it is first and foremost a topology. The condition of Mars or the condition of V enus: this is what determines the world-map of knowledge. No one has ever ordered science except by flow charts. And, thereafter, the master ignores the contents. But that is no longer of any importance.

Foedus is thus the pact of the post-war period, the peace treaty. Two enemies were at war, and now the armistice is signed. Up to this point the important thing has been science, and we have not understood the role played by decision. Postulate, decision, issues of culture. What else? Foedus is, in general, a contract. For example, social. Now this is easily reduced to this, once the war of all against all is over. This is the plague and the end of the plague. The plague is the figure of violence in general, a multiple chain with thundering power of propagation, which threatens a particular city or group with extermination. Athens, for Lucretius, or the realm of the Lion. Hence the fable telling of the invention of the judiciary after the death of a sacrificial donkey/ass. This violent communication, the most terrible calamity for the group whose very existence is at stake, is brought to a halt by a blow of force: the sacrifice of the one who takes on all the sins of the group. Justice is done. This means: justice appears, is formed and formulated, fashioned into an institution. Hence the entire poem, which turns endlessly back upon itself, like a vortex. The plague at Athens is begun: fights break out and blood is spilt before the burning funeral pyres.9 This only stops when all those fighting are themselves dead. To stem it, to interrupt it, that is, to overthrow the body of Mars, to throw back his neck

To stem it, interrupt it, to draw down the body of Mars and throw back his round neck, a convention is necessary, a pact, a foedus, a judicial institution or its equivalent.Io Now the contract can only be reached by way of a sacrificial murder. Whose? Mars will only stop at the altar of Iphianassa. The flower of Greek warriors stains the stone of the virgin Trivia with the blood of Iphigenia. This is the ordinary, trivial, tradi­tional solution, that of every religion, that of every politics. Iphigenia, that is to say the genealogy of sovereign power. Lucretius is careful to give her name in Greek. She dies, her headband untied, its ribbons falling evenly down on either side: the abolition of difference. Slaughtered by the paternal blade, a virgin who had not bled, unviolent, safe, she raises the great sea, stirred by gusting and turbulent winds. II And the storm, again, is the plague. Two figures of violence, deluge and pandemic. The murder, in turn, increases, two figures of growth, or, as we say, of escalation. Without the ritual murder of the virgin, there would have

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been war between the Greek warriors before even getting to Troy. The waters are finally stirred, the miasmas reappear. And here is the contract, the contract by blood, that of the oldest tradition, perhaps of destiny: the fledera fati.

What must be averted is first the primary threat, yet also the archaic safeguard against it. The plague, to be sure, and the storm (Lord, you sleep and we're lost) , the fatal propagation of murder; but also, but above all, the solution to this collective problem given by the sacred: human sacrifice. We must save Iphigenia. Science, here played against religion, is not a laicity played against a church, this combat of twins that we learn about in school. Foolish naivete. The problem lies in stemming a series of murders otherwise than by another murder. For the solution is only temporary, until a new crisis, a new seed, a new epidemic, in which the process repeats itself. Nothing new under the bloody sun of history. The plague flares up again in an Athens strewn with corpses. We must also save the scapegoats, put a full stop to the series of sacrifices. And so the turn: whoever speaks and through speaking founds a new history does not charge a third with the sins of the earth; he takes upon himself, of his own volition, the thunder, the rumbling of the heavens, the flame at the walls of the world, the wrath of Jupiter. He freely takes on the dangerous position assigned to him by his knowledge of the laws of the universe and of human mechanisms. In the face of these horrible threats, he goes forth, unarmed. In this way, Epicurus tears us away from the storms once again, but this time for ever, and puts us in a quiet place, on dry land. Epicurus is a god. Yes Memmius, he has the right to be called a god, there is no contradiction. Cicero and his successors understood nothing. To take on alone the fire of the heavens, not to displace it by unleashing violence on the nearest bystander, the virgin Iphigenia, but to advance, unarmed, before it, deciphering, lucidly, what is happening; this is precisely conduct contrary to all religions, to the terrifying constitution of the sacred. But it is only practicable on condition of knowing the laws of constitution, and of being a master of justice. Epicurus is a god beyond all gods. The new god of another history, having toured all through the archaic traditions, he wrong-foots them. He abolishes the sacred by completing it. So the Epicureans, atheists, were not wrong to venerate the founder of this science as a god. And by his courageous action, heroic above heroes, Epicurus brings about the birth of Venus, from the agitated waters. To know the fledus, love and friendship. The contract of nature, fledera naturae. Finally definitive, and the gods are outside of the world,

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as the ancient reiteration of sacrificial crisis is brought to a close. An end that founds Epicurean wisdom. This is how I believe Rene Girard would have resolved the whole question: a parallel solution to my own.

Now, delivered from violence, henceforth independent from a sacred space and time which has no relationship to us, our feet finally set on the high place protected from the sea, fortified by the science of the wise against the enterprises of Mars, we can produce things as objects, ourside of the mechanisms regulating our unregulated violence.

Now, delivered from violence, freed from our dependence on a sacred space and time that have no relation to us, our feet finally set on the high place protected from the sea, fortified by the science of the wise against the initiatives of Mars, we can bring things forth as objects, outside of the mechanisms regulating our unregulated violence. The sacred took intersubjectivity and polemical relations and made a knowledge of them. Nature hides behind it from the dynamic laws of the group. As soon as it is placed outside the world, in remote locations that in no way concern us, nature is born, objectively. It bears its own laws. The solution is the founder of science. Of this Aphroditean science, without violence, without guilt, where lightning is no longer the wrath of Zeus, and where the level of the waters remains stable. In the new contract the exact word can be spoken.

Might this be a general solution? Will science occur regularly in history in the shadow of figures such as Epicurus?

Foedus is the treaty after the war. The laws of nature, articulated by this science, remain conditioned, and then determined in their global arrangement by such a pre-existing contract. For example, the choice between Venus or Mars. Foedus is, on the other hand, the convention which closes the war of all against all. In the course of a primordial history, the exterminating violence freezes, congeals, halts, in the course of the sacrificial murder: Iphigenia. But it is set in motion by a new crisis, and the plague takes hold once again. We must begin anew. The sacred is formed by this repetitive and catastrophic dynamic. Epicurus the hero willingly takes the place of the virgin; unarmed, he disarms the process, founds a new history, an objective science. One can now see how Venus replaces Mars. Foedus is, in short, a political constitution.

Is calling the laws of nature the foedera naturae to project such a constitution on the world as such? Is it a ruse, a ruse of reason, to give the status of natural necessity to arbitrary power, to the domination of certain people, here and now? It is undeniable that this trickery has often been perpetrated upon us. All powers seek legitimacy, since, by nature

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The Birth of Physics

excessive, they always lack it. To establish a domination on the basis of science is even a common conventional strategy and, what is more, quite easy, since the sciences themselves are usually founded on domination. One has only to move around the circle; it is all so open that it is hardly a ruse or trick. And the Greeks, Plato himself and others, did not pass up this chance. And they have been very well imitated too, from the times that followed down to the present day.

Two things, however: one, very general, touches upon Hellenism, and the other is particular to the Epicureans, to Lucretius. No one is better fitted for the ruse than a Greek, always in part a child of Ulysses and Metis; and I have shown elsewhere how a simple effect of point of view allowed the belief in democracy, while the ancient hierarchy persisted, unchanged. An effect of optics and geometry, a scientifically­arranged illusion. But these perfect masters of the arts of trickery also and at the same time invented dichotoniy, separation, division. They founded classicism, as a theory of the specificity of regions. Olympus to the gods, the world to atoms, and an axe in the middle. I accept, I maintain that such a word or another is multivalent: that it summons up, simultaneously, myth, the sacred, power and physics. But indeed if we have the idea, poor and clumsy as it may be, of reading today as polysemous and out of joint, it is because of the Greeks. It is because of their divisions, and the clarification that they bring. They, and no one else, knew how to cut and classifY. They produced, for the first time, a distinct cartography. The constitution and the Meteora, mathematics and myth, medicine and the theory of exchange, and so on all you want. Hellenism is polytomy. The lucid awakening on every transition between of themes (pcraf3aOL� cl� a),),o ycvo�). Hellenism is dicho­tomy, from the theory of segments to the representations of separate worlds. Without this, would anyone have discovered atoms? Now, our question is decidable. Yes, the Greeks used guile, trickery, deception, cunning, fraud, almost as much as we do, and this is saying a great deal. Like us, they passed off rabbit for quail and anything at all for science, but, if they had always and everywhere practised only sleight of hand, suspicion, would they have invented geometry? No, it's impossible. If there is a distinct field in which no one can keep cards up his sleeve without a resounding defeat, it is mathematics. Let no one enter ifhe is a conjuror. Inversely, every philosophy, every discourse and every text that avoids this place keeps elbow room to cheat indefinitely, and appears to everyone never to be wrong. The criterion of truth is the risk of error. The only path towards discovery is the absolute willingness to make

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mistakes, in front of others. All the rest is only power. Now, as I have demonstrated, atomist physics does not avoid the mathematical model.

I will not say that it is therefore certain, just that it is probable that we are not dealing here with the fraudulent projection of a political model on the world as such. Polytomy, dichotomy, is the chosen field of the atomist thinkers, from the elements to their transcendent theology. And their wisdom, explicitly, tends to steer them away from the conquest of power. As does their practice of science: the method of using a cluster of multiple explanations broadens the scope for the acknowledgement of error and closes off the taking of power. On the contrary, for the first time, the world is autonomous, does not depend on command, is self­governing. On the contrary, for the first time, the ruse is absent from the game of things. And this is indeed the first physics, in the sense of Einstein, a subtle knowledge that is never deceptive.

All at once the reversal occurs. Far from a political convention being projected upon nature, it is on the contrary the natural constitution that, in the final instance, accounts for every other federation. Either I am seriously mistaken, or this is materialism. Conversely, to decide how to read the state of things starting from the state of public relations, here is idealism once again. The individual subject may be replaced by a collective 'we', its practices and its history, but the working of idealism will not vary for all that. Things remains transformable shapes for a pole furnished with force and conscience. Generalised idealism, simply: from the individual to the group, from the represented form to the whole of practicable transformations, from the instant to historical time. By the body of these concrete extensions, idealism survives and comes down to us. Materialism is always recovered. The state of things becomes State reason, in place of being, that of the transcendental T. This is precisely Lucretius' fight against Mars, against power. The natural constitution, in the last instance, is none other than the atomic constitution. Men, no less than things, are composed of atoms. Their soul and conscience. Their collective is thus a composition of compositions. What, then, does the fledus mean?

We must return to things themselves. Almost at the beginning of the first book Lucretius distinguishes the coniuncta from the eventa, follow­ing an ordinary division of Epicurean physics. What is conjoined to a body is that which is destroyed if it is disjoined. It is thus conjunction as such. The given examples clarifY the definition. Weight is conjoined to stone, heat to fire, fluidity to water. Thus all bodies are tangible and the void is intangible. This is what Leibniz in the seventeenth century would

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have called a well-founded phenomenon: one whose internal relations and specific relationships are stable. For the fundamental states of matter, atoms and void, tact is the condition of possibility of experience. It is enough to extrapolate from the tactile to conceive, at the limit, these residual bodies that are themselves limit states, and which are in turn are the condition for the existence of other things. These two conditions are the foundation of physics; which from this point on, is at once the theoretical science of the void and of atoms, what might be called fundamental physics, and the experimental science of the phenomena founded or well-founded by them. The second of these is threefold: it is concerned with weight, fluidity, and heat. Our model is confirmed. In traditional language, barology, thermo logy, fluid mechanics are the three major disciplines of the natural sciences. They and they alone are found may be found in the text again and again. Fall, atoms and non­equilibrated bodies, the formation of flow, of turbulent outflow, fire. It is these which are charged with the birth of every thing, and of living things. What is a living being? A thing in equilibrium and in disequili­brium, a flow, a vortex, heat. Like every other object, perhaps. The definition belongs to Lucretius, but also to us. Atomist physics is our own.

This said, what, once again, is the foedus? The atoms gather here in well-founded phenomena. Their meeting is a convention, a coitus, and a conjunction, coniuncta. Without this conjugation or this encounter the assemblages come apart, their phenomena are ill-founded; physics, in its three disciplines, disappears. It remains as a fundamental theory of the void and of atoms, as a knowledge of before the birth of things, but it is destroyed as the science of nature. Things are made of atoms and the void, their study consists in seeking to determine how they are made. Their matter is particular, their nature is relational. The essential thing therefore for an exact discourse de rerum natura is relation or the inter­relation. The simplex, as one says in combinatory topology; the relation­ship, as one says in chemistry, the interaction, as one says in contem­porary physics says. This ensemble of relations, without which nothing can be born or exist, is constituted in fact by the coniuncta. Which are the stable reservoirs of composition. And it is stated in theory by the foedus. In a sense, the pre-model of the fundamental physics has no laws. Take an infinite void, in which atomic clouds move. A space in which packets, wholes, move around. As soon as a phenomenon appears, as soon as a body is formed, a law can be expressed. The laws of nature are those of conjugation, there is only a nature of composites. Just like the laws governing the assembly of the letter-atoms when a text is produced.

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The alphabetic pre-cloud is without laws, and the letters are enlisted in an arbitrary fashion; they are always there, as a whole in space, as language. But as soon as the text or the word occurs, there appear laws of good formation, of combination, of conjugation. Now these laws are just a federation. The law repeats the fact itself: while things are composed, the laws express the federated. A thing, a state of things, such as can be accounted for by fluid mechanics, theories of equilibrium and of heat, are paired in fact and federated by law. But there is no difference nor distance here. How, in fact, could the laws or fledera be explained, if not in a language or by a text in which composition is reproduced. The fledera naturae, the laws of nature, are fledera coniunctorum, laws of conjunction, but they are themselves only possible through this con­junction: coniuncta flederum, composition of the laws. From fact to law, the distance is null; the deviation between things and language is reduced to zero. In both cases, but there is only a single case, every formation is nothing but relation, everything is only relation. Outside of relation, there are only clouds in the void, letters or atoms. Language is born with things, and by the same process. Things appear bearing their language. Coniuncta, fledera, they are the same words. Stable assemblies of elements, of whatever kind.

Hence the following very important point. At the same time as it produces physics, constituting it as a fundamental theory of elements and a threefold discipline faithful to the phenomena of experience, atomism resolves the radical question, that has always been asked and never straightened out: how is it that our laws, our hypotheses and our models are found to be in aggreement with realiry? Lucretius makes it comprehensible that the world is comprehensible. My text, my word, my body, the collective, its agreements and its struggles, the bodies which fall, flow, flame, or thunder like me, all this is never anything but a network of primordial elements in communication.12

What, once again, is physics? It is the science of relations. Of relations in general between atoms of various families. Of conventions, assem­blies, contests, coitus. Hence the opening prosopopoeia: the goddess who alone is sufficient to the government of nature. Venus states the fledus, the contract, as an ego coniungo vos. Venus assembles the atoms, like the composites. But she is not transcendent, like the other gods, she is immanent to this world, she is the being of relation. She is relation, identically. Venus sive nature sive coniuncta sive fledera. She inspires inclination, she is inclination. Declination is also a differential in pleasure, the first disturbance before the liaison. Aphrodite alone governs: who

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has ever governed but by the angle of the tiller? Take lightning, in Heraclitus; it is said to govern all things. How can this be, if not by the inclination of the rudder, or by the inclined streaks it cuts across the heavens? It is the furrow of the world, inscribed, traced on the clouds. The rudder's mark, solicited obliquely. The stamp of the government's seal, its sole law. The same here: nature is formed by liaison; these relations, interlaced into a network, necessarily begin by a differential angle. And Venus inclining is declination itself.

Lucretius distinguishes with care between conjunctions that make stable objects and eventa, events or accidents.I) He initiates the distin­ction between physics and history, precisely quod erat demonstrandum. For one thing, weight, heat and liquidiry are conjoined with bodies that are themselves conjunctions. These are the primordial qualities of conjunction itself, the qualities of Venus. She is heavy, she flows, she is hot. These are the ways that relation is established. These various slant­ing liaisons ensure the stability of natural things, that is to say possible experience. Our determinism says exactly this. It is the guarantor of repetition. It is reproducible, it will reproduce. Thus coniuncta: so indissociable from things that we can always be sure of finding them. Stability of their tissue, of the conjunctive network. Now events are of another texture. They come, they go. Look at the words themselves: aduenta, euenta, form a labile flow from the advent to the event. Atoms pass, upstream downstream, without constituting a convention. And events are adventitious. They are neither federated nor conjoined in coitus, but are immediately undone by abitu.I4 They spread and pour, fonditus, from top to bottom and back again. Unstable, they flow around the resistant and conjoined cores of objects. They pass. Irrevocable, gone.

Here is the complement of the model. Imagine a particular flow, an atomic flux. By declination, the first tangent to the curve formed, then by the vortex, a thing is constituted, relatively stable. It remains in deviation from equilibrium, ready to break and die or disappear, but resistant by virtue of the conjunctions established between the torrential flow upstream and the river downstream. It is a stationary turbulence. In the heart of this formed nucleus, the coniuncta crystallise into a network. Thus the thing is heavy and, liquid, it gets hot. Physics studies these stabilities. This said, all around these spirals, whose whole is the very nature of things, the endless flow continues to pour down a rain of atoms. These knotted points occur [adviennent] , they meet here and there, and match themselves vaguely to the outline of objects; then turn straight away to leave, resuming their parallel course, bestrewn and

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undone. Hardly a deviation, hardly a disturbance, comes to ruffle the water's surface. Without the objects of matter and space, without the quasi-stationary formations, this passage would not be so and could not be perceived. It is an ill-founded phenomenon, totally without con­junctions. It occurs, it passes, it expires or exhales, it is an event.

Time would be nothing without the situation of objects in space, without their respective movements, without their formation, their disintegration. Pardon me, but the clock that Lucretius sets right in the middle of nature cannot not tell Newtonian time; because it is the whole of things, between their birth and their collapse, it records a Bergsonian, that is to say a thermodynamic, time. An irreversible, irrevocable time, pointing like the endless flow of atoms, flowing, rushing, crashing towards fall and death. Things are heavy: they fall, seeking their peaceful rest. Fluid, they flow. Hot, they cool. Fall, death, dispersal; breaks, dichotomies, atoms. The atomic flux is residual: the backdrop of being, background noise. This world endlessly adrift is seeded, here and there, in indefinite places and instants in time, with pockets where nascent vortices are formed, by a pseudo-return. And clocks appear with these spiralling, discrepant objects. From their very dawn they begin to beat the time of death. The Lucretian world is entropic globally, and negen­tropic within pockets of vortical movement. Conjunction is negentropy, and the complex formed registers the quantity of information given over to the drift. The event that has hardly passed when it is almost immediately undone gives minimal resistance to the irreversible flow and bears little information. Newtonian time, reversible, is the mark of resistance to the irrevocable. It is absent from this physics, and this is why our forefathers could not imagine for a single moment that there might exist a Lucretian physics. With the possible exception of Bergson, who was nourished by it. Irreversible time is the master here. The physics of things resists it in places, but in the flow of the drift; history follows it, hardly rippling its flow. History flows around physics.

Hence Lucretius' examples. Whereas the conjunctions were heavy, liquid and hot, thereby giving rise to the classifications of physics, so events are all of a socio-political order. In the poem, servitude and freedom are placed on either side of poverty-wealth, as if they were set around the nucleus of this central pair.15 The condition of the slave and that of the free man are outlined around material and spatial objects: the scarcity of bread, or the abundance of money. O'ufl,'twfl,a1;a, sumptomata, says Epicurus, of events, O'ufl,�£�rptO'ta, sumbebekota, he says, of conjunctions.16 Slavery, freedom are symptoms of wealth or poverty,

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themselves symptoms, of more closely linked material things. History is a symptom of nature. Time is the symptom of symptoms. We will come to this. First, war. This war, or the Trojan war. Mars is only an accident to stable Venus, a passing relief around convention. It passes, poorly linked. Vulcan must capture him with his net, as Homer tells it; meaning by this a penis captivus. Otherwise, Mars will only be passing through or staying briefly. Final example, peace. And here is the foedus, the political foedus. Announced after the war and following every war. Far from projecting on the state of things, unconsciously as we say, the constiturion of political order, Lucretius strongly differentiates the conjunctional, contractual, stable relationships of the atoms between themselves, with the unstable, conjunctional historical contract, which would be nothing without the existence of the primordial, and which vanishes quickly around them. Far from unreflectively projecting the constitution of political order onto the state of things, Lucretius strongly differentiates the conjunctional, contractual, stable relations between atoms, from the unstable, circumstantial, historical contract, which would be nothing without the existence of the former relations, and which quickly vanishes around them. Politics, history, are just the purely phenomenal symptoms of the fundamental combinations.

Lucretius translates oUfJ,Jt'tofJ,u'tu by eventa. The Greek word is, once again, about fall. Things fall and meet in the process. Bodies, solid or liquid, living, whatever. Atoms, are a fundamental example. It is all collision and chance. Cournot means just this when he speaks of the intersection of independent series. Falling has disappeared from his definition, only to return in the metaphors he uses: the roof-tile falls on the head of the passer-by, like the tortoise on Aeschylus' head, and so on. Now it also disappears in the translation of Lucretius. Clearly this is still favourable to the model: less a fall than a transit. It happens, while in Greek it falls. Things come and go, they only crumble or collapse for a singular case of the form. What is more, the prefix is erased, while it is preserved in the word coniuncta, for OUfJ,�E�rpw'tu. Here is the modest linkage that events admit. As if the encounter did not produce relations, or hardly. Venus absent from history and politics. Lucretius adopts, in place and stead of the con-, a prefix of issue. This is of capital importance, for it is at the exit that we see clearly that it was only a matter of politics and history: nothing remains but ruins, and scattered parts returned to the parallelism of their fall, while the world continues to turn, quasi-stable. The symptom was a phantom. And it was only a symptom, in the contemporary sense, of natural objects. And, to my

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knowledge, once again, this is materialism. The calm of the Garden, its tranquil serenity, is called ataraxy. Now

the soul is formed of atoms, like the body, like the world. Ataraxy, a moral state, is thus a physical state, without deviation or distance. Now the physical model shows us an aleatory multiplicity of vortices in infinite space, of which one group is nature, this one, and the whole of wholes is the plurality of worlds. For Lucretius, as for us, the universe is a global vortex of local vortices. And so it is in his poem. Ataraxy is the absence of disturbance. Nature is river and whirlwind. The life of the wise man is free from turbulence. Yet it is the closest to nature. In the name of the Epicureans Seneca gives this advice: ad legem naturae revertamur. Return to natural law, to the fledus. Revertamur, morality turns, once again.

What nature teaches us is the streaming of the inexhaustible flow, the atomic cascade, and its turbulence. Waterspouts and whirlwinds. The tropic wheel in the heavens. The conic spiral that forms things. The soul, like the body, like bodies, made of warm atoms, aerial, windy and nameless, that is to say the principles of warmth, of fluidity in general, and of weight, is the seat of turbulence. It burns, it is troubled, it loses equilibrium. Like the sea, the volcano or thunder. The same space and the same matter produce the same phenomena under the same laws. Disturbances to which we give names, out of a fear of the gods and the terror of death. The soul is knotted like the world. And like the world, it is unstable, deviating from equilibrium.

Physics, psychology, give an account of these scattered knots where disturbances form. Behind the three physical disciplines, the fundamental theory goes back to the laminar atomic flow, the void and principles. Behind cultural psychology, marked by history and the gods, anxiety and disquiet, burdened by our events of relative, adventitious, competition and combat, morality recovers a primordial state. Ataraxy returns to the initial turbulence, before any disturbance in the straight line of the flow. The wise man is the fundamental world. He rejoins material being, this ground of being itself where no ripple has yet troubled the surface of the waters.

Once again, we must count irreversible time on the clocks. It beats the measure, irrevocably, of deterioration. Things, formed in the hollow of the vortex, slowly lose their atoms. They lose them in the flow down­stream. This is the time of wear, statues of the gods worn away by the kisses of the faithful. The world is mortal. This is thermodynamic time: of heat, weight and of flows, the disciplines of the trivium. This is the

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drift towards the plague and dissolution. We call this the second law of thermodynamics. It was not unknown to the Greeks, at least since Heraclitus. History, or the idea of history, is only the translation or transposition of this material principle. It is not just a copy or repro­duction of a lost mythic paradise. If, from the beginning to our own times, the earth tires and does not create any new species, it is because the downstream flow, devouring, has stolen away a share of atoms. They are increasingly hollow. Abandoned to the erosion of irreversible time. Atomic physicist take up an archaic tradition, but they place it within the demonstrable and the experimental. From now on history has two constituents: irrevocable wear, and the human labour which tends to make up for erosion. The farmer adapts to the ageing of the earth: through his labour he tears from her what she once gave freely. Pro­gressive civilisation is only one response to time's erosion. It sails upstream in the entropic river. Hence labour, of course, but also language and writing. Culture and agriculture have always been a single vector.

Now, this said, atomist physics also recognises the equivalent of what we call this the first law of thermodynamics. The universe is regulated on the basis of a constancy, an ioovofua, isonomia. This is still not the invariability of forces or energies, but everything happens as if it were so. To the degradation of one thing there corresponds the birth somewhere of another, and to the death of a world from plague and the flames of the pyres, the appearance elsewhere, no matter where, of new one. The thesis of the plurality of existing worlds is thereby made a necessity. In its agony, the world as a whole returns its atoms to the fundamental river in a cataract, it unknots and undoes itself by analysis, and elsewhere, at some indefinite time and place, a declination announces a nascent turbulence. A multiplicity is therefore necessary in infinite space in order to establish constancy in the field of eroded disappearance, of the irreversible and the aleatory. Invariance is global. Physics describes a system, but not one that is hierarchic, deductive, or tightly ordered, as in the series of the Stoics: it is a set, its general equilibrium a balance sheet that takes account of the stochastic. Locally, this meta-stability is seen on the threshold temporarily marked by rising waters; theory states as much in its immutable laws, practice ensures it by the success of its predictions. Here, once again, is a foedus: the pact is constancy, and the contract is an assurance. Lucretius goes farther still, and without a doubt deeper. It guarantees the very stability of the flow, as movement and in its direction. It attains homeorrhesis. Whatever the capricious combin­ations of atoms, whatever the obstacles before them, monsters or

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androgynes, the aleatory vortices in fact end up producing a world that is coherent and well-founded, that is to say conjoined. Beyond, this conjunction comes undone, in the streaming of mortality. Beyond, farther beyond, in the foreseeable global and the unforeseeable local, a declination reappears. The clinamen is a principal element of home­orrhesis. It ensures the stability of the chreodes. It is a differential of the chreode. If invariance is no longer to be just rest, if constancy is not to be just statis, if the system is not to be just a statue, if stability itself is to touch upon movement, what else is necessary, in the very beginning, but inclination? I'm not saying that it is sufficient, I'm saying that it is necessary. The river must have a sloping line ifit is to remain stable in its variable bed. Declination is a tremendous physical and mechanical discovery. It breaks with the common antithesis of rest and movement, of Par men ides and Heraclitus, much more completely than Plato did. In its obviousness and simplicity, in what can be touched and experienced. Through declination, it is movement that is stable, in the path of its flow, in its general direction and its passage point by point. It is what ensures the most profound and exact invariance, although tradition down to the present day has seen only paradoxes there. For it is the condition of a great synthesis between statics and dynamics. Hence the recapitulation: the old unitary being is multiplicity, here are the atoms. Stable being, at rest, is movement: atomic flux, streaming, cascade. Global fluidity of local solids. Here is irreversible time. The atom of angle, the angle of contingence hollows out a direction, which needs no reference other than that which is intrinsic to the flow: and so we have a thalweg. A stability is recognised, exists, is thinkable, tangible, in and by the fluviatile flow, it is a homeorrhesis. A reunification is possible, by conjunction. The physics of things has come full circle around ancient physics, while leaving the cardinal gods on top of their mountain. ] ust as the analyticity of being produced atoms, so the analyticity of the vectorial directions of space produces the clinamen. Movement and rest are wed in turbulence: constancy and variation, life and death. Nothing truer, perhaps, was ever said or seen in Antiquity.

Everything is degraded irreversibly in accordance with the first time, atomic erosion. The increasing labour of humanity seeks to halt this irrevocability. There is progress, and no progress: history advances across the surface, while it retreats at depth. It heads upstream against a current that descends more quickly than it can advance. The excess is discrepant, the plague will return. The eventa slide on the coniuncta, history skids on matter. The first global vortex. Humanity constructs weak coherences

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on material cores of great coherence, in the course of coming undone. Athens, that eminent city of culture, vines, fig-trees, theories and science, must end up, in spite of its labours, in a scattered heap of atom­ised bodies. Ashes from the funeral pyres are returned to the cataract. The irrevocable destiny of labourious transformations. This history is lost in advance. We should not therefore expect anything from struggle, competition, agitation, from activity or growth, for they are no more than a little Brownian motion on the surface. Superficial disturbances hide the irremediable erosion of matter, of things and the world.

Everything is constant, but in the aleatory and the directional. Venus watches over the renaissance, a whim of springtime desire: the very first time of encounters, of collisions. Here and there, yesterday and tomorrow, for the perpetuation of the species. Athens lost, the city eradicated from history, the universe brought to collapse, a turbulence begins again, flickering somewhere in the infinite void. Formed in the blink of an eye, or solidly welded. It is born, autochthonous, while else­where there are smoking ruins. Troy. Second global vortex, but globally splintered. The dead and the constitutions are distributed and dispersed in an infinite space-time.

And so the wise man returns to the pacts of nature. He takes up everything at the beginning. He is well versed in the time of degradation. He knows that vortices come undone. Not only the vain agitation of turbulent men, mere ripples on the water, but also and above all things and the world, born from turbulence. All these distur­bances return to the primordial streaming. Born from this dust and returning to dust. Thus the soul, my soul, a thing among things. Not only here today, troubled by terror and anxiety, by fear and labour, but as born one night from chance impacts and encounters, inclination and disturbance. This morning my soul is tumultuous, convulsive and stormy, but by its birth and essence, it is just a troublemaker. Produced by a storm in the atomic cloud. By an inclined lightning flash. It is a taraxy, just as my body is. And things themselves. I know it, I learned it from the contracts of physics. And I make my revolution. V ortical physics is revolutionary. It goes back to the first disturbance, towards the primordial clinamen. And from there to the streaming. To the con­stancies of movement. To the general invariances, whatever the random variations may be. To the primordial paths of matter itself, pitted here and there, wracked with convulsions. So ataraxy is a physical state, the fundamental state of matter; against this background worlds are formed. Disturbed by circumstances. Morality is physics. Wisdom accomplishes

Conditions

its revolution. It climbs back up the spiral towards the primary state, ataraxy is the absence of vortices. The soul of the wise man extends to the global universe. The wise man is the universe. In repose, he is himself the pact.

Greek wisdom arrives at one of its most important points here. Where man is in the world, of the world, in matter and of matter. He is not a stranger, but a friend, a familiar, a companion and an equal. He maintains an Aphroditean contract with things. Many other wisdoms and many other sciences are founded, conversely, on the violation of the contract. Man is a stranger to the world, to the dawn, to the sky, to things. He hates them and struggles against them. His environment is a dangerous enemy to be fought and kept in servitude. Martial neuroses, from Plato to Descartes, from Bacon to our time. The hatred of objects at the root of knowledge, the horror of the world at the foundation of theory. Epicurus and Lucretius experience a reconciled universe, in which the science of things and the science of man are in accord, in identity. I am the disturbance, a vortex, in turbulent nature. I am an ataraxy, in a universe where the foundation of being is undisturbed. The wrinkles on my forehead are the same as the ripples on the water. And my repose is universal.

The sacrificial murder resolves the crisis, for a time. Iphigenia is put to death, the wind rises, the Trojan war will take place, a new crisis of violence. Here, the war unfolds in Athens, terrible brawls amid the pyres. The plague like the ocean unbound, like the river in flood, is the figure of violence. In Book Six, no sacrifice will interrupt the new crisis. No Iphigenia in plague-ridden Athens. Piety has fled. In place of a single trifling pyre, a hundred flaming pyres, one at every crossroads. Have we benefitted from the exchange? In other words, suppress violence, and it will reappear. Do away with its local setting, that is to say the solution of religious sacrifice and, all at once, the global space of the city is infested with violence. A formidable question that Lucretius has not avoided, yet which he was perhaps not able to resolve, and which overwhelmed him.

Violence is the only problem. So little has it been resolved that our culture is without doubt the continuation of barbarity by other means.

Violence is a major factor in relations among men. There it is, running, perhaps fatal, perhaps our destiny and our greatest risk, our greatest deviation from equilibrium. Lucretius knows sacrificial purga­tion well enough. He acknowledges the sacred solution, and dismisses it. He knows also the judicial solution, which is only an interpretation of the former by the rationalisation of guilt.

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The most revolutionary event in human history, and perhaps in the history of hominids, was less, I believe, the accession to the abstract or to generality in and through language, than an uprootingfrom the whole of the relations that we maintain in the family, the group, etc., and which concern only us and them, leading to an accord, perhaps unclear, but sudden and specific, to something external to this whole. Before this event, there was only a network of relationships into which we were plunged without appeal. And, suddenly, a thing, something appeared, outside of the network. The messages exchanged no longer said: I, you, he, we, etc., but this, here. Ecce. Here is the thing itself

As far as we know, those animals that are close to us, let us say mammals, communicate among themselves by repeating the network of their relationships in a stereotypic fashion. The animal indicates to or makes itself known to the animal: I am dominant over you and I give to you; I am dominated by you, so I take from you. What? It is not important or else is implicit in the relation. You are large and strong, I beg you. Lucretius says this of our relation to the gods.

Hence this necessitating condition obliging animals to resolve all the problems that stem from these relations within the network. There are nothing but contracts, that is their destiny.

Now the human message, while ofren repeating the network of rela­tions that men maintain among themselves, to the point of stereotype, says, in addition, says, sometimes, something on the subject of things. If it does not, it is immediately brought back to the model of the exclusively political animal, that is to the animal as such. Hominisation consists in this message: here is some bread, whoever I am, whoever you are. Hoc est, this is, in the neuter. Neuter for gender, neuter for war. Paradoxically there are no men, there are no human groups, until after the appearance of the object as such. The object as object, quasi­independent from us and quasi-invariant through the variation of our relations, separates man from the mammals. The political animal he who subordinates every object to the relations between subjects, is just a mammal among others, a wolf, for example, a wolf among wolves. In pure politics, Hobbes ' remark that man is a wolf for man is not a metaphor, it is an exact indication of the regression to the state preceding the emergence of the object.

The origin of the theatre, comedy, tragedy, where only human rela­tions exist and where there is no object as such, is as old as the origin of political relations: it is thrust into animality. Politics and theatre are just mammals.

Conditions

The discovery of the object as such and, globally, of the external world, while it may not be the first scientific invention, remains the pre­condition for every search of this kind. But, on the other hand, the discovery of the object offers an opening and a chance to escape the network of our relations, and thereby to free ourselves from the problems raised by it; in particular that of violence. The object will be, perhaps, a neutral terrain. The pre-history of a physics, the pre-history of a non-violence, given all at once. The pre-history of hom in ids. Can one conceive of an object outside of the relationships of forces?

Listen now to the lessons of Epicureanism. They come down to this: reduce to a minimum the network of relations in which you are plunged. Live in the garden, a small space, with a few friends. No family, if possible, and in any event no politics. But above all, this. Here is the object, objects, the world, nature, physics. Aphrodite, pleasure, is born of the world and the waters. Mars is in the forum and in the armed crowd. Bring your relations to little and your objects to the world, the intersubjective to the minimum, and the objective to the maximum. Your back turned on politics, study physics. Peace in the neuter. Such knowledge brings happiness, at least and end to our worst pains. Forget the sacred. This means: forget the violence that founds it, and forget the religious, which links men to one another. Consider the object, objects, nature. Yes, he who said this, ecce, hoc est, this one, Memmius, is a god, a god among men. He changed hominid nature.

Nonetheless, the plague returns. It destroys Athens, bringing violence and death. Why? Let us go back to the object. There are only two objects, constitutive of all things: atoms and the void. The void, inane, has as a root the Greek verb lV£LV, inein, which means to purge, to expel, or, in the passive, to be driven out by purgation. The void is a part of chaos, but it is also a catharsis. Iphigenia sacrificed, purge or catharsis for the little kings of Greece. But, at the end of the sacred dynamic, the Trojan War and extermination. Passage to the object, to be freed from Mars. But the first object, this is still purgation, it is only the physical concept of catharsis. Second object, the atom. The sacred solution begins by a partition of space, by an apportionment. The temple is a dichotomised space, the very word says it. Inside, the religous, outside, the profane. A logic of two values, a geometry of two values, an ontology of two values, inside outside, sacred profane, void matter. The word 'temple' is indeed from the same fomily as 'atom. ' Atom is the last or the first temple, the void is the last or the first purgation. The two objects are, in the final analysis, the physical concepts of catharsis and of the temple. We come

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back to the network of relations. For with the erasure of the sacrifice of Iphigenia in the temple of Trivia, the local manifestation of the religious inundates the global world. Atoms in the void, little temples in the great purgation. Nature is still a sacrificial substitute. Violence is still, always, within physics. Now, the germ atoms wreck havoc on Athens, the last survivors killing each other. Quod erat demonstrandum. It is not politics or sociology which is projected onto nature, it is the sacred. And beneath the sacred, violence. Beneath the object, relations reappear.

The question, for us, remains unchanged: violence is not only in the use of science, it goes to ground again in the unknown of its concepts. Athens generalised, the world after Hiroshima, may still die from atoms. Where is the madness of the irrational in our rational?

NOTES

I Hermes IL L'interference, p. 178. 2 Plato, Theaetetus 148e-151d: cf. especially 158c for mention of eidolon.

Venus and Nature. Mars and Nature. 4 Memmius was a Roman praetor to whom Lucretius addressed De rerum natura. 5 Foedera fati, the bonds of fate, II, 254. This is the expression by which Serres

denotes the conception of inflexible law that the philosophical and scientific tradition has for the most part attributed to nature. He contrasts it to a conception oflaw drawn from the Lucretian text, the foedera natura, the natural contract. See also M. Serres, Le Contrat Naturel, Editions de Minuit, Paris, 1992: The Natural Contract, trans. E MacArthur & W Paulson, Michigan Universiry Press, 1998.

6 II, 263. 7 'Sweet, winds, labours, pleasure'. The line is composed of a series of terms from

the opening verses of Book II. 8 Karl Marx, Difference of the Philosophy of Nature in Democritus and Epicurus. 9 VI, 1283-86.

10 The allusion is to I, 31-40 where Lucretius describes Mars falling into the embrace of Venus. Cf. Bailey II, pp. 599-600.

II The story is that of the sacrifice of Iphigenia by her father Agamemnon to appease Artemis who had sent bad weather to keep the Greek fleet at Argos from sailing for Troy. 1, 84-101. Cf. Bailey, II, pp. 614-15.

12 M Serres, Hermes I La Communication, Editions de Minuit, Paris, 1969. 13 I, 449-58. 14 1 457, 677· 15 1, 445-6. 16 Lucretius translates these terms from Epicurus, Letter to Herodotus, Everyman

Edition, pp. 23-4- Cf. also Bailey II, pp. 670-2.

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A P P L I CAT I O N : G E N E S I S O F T H E T E XT

Lucretian physics then goes on to respond to the usual criteria of every physics, at least as we have thought of it since the classical age. It mani­pulates models, constructs them, refines them, its mathematicisation is in place, recognised, rigorous, its fidelity to things themselves is verified experimentally, finally it is coupled with calculations and reflections concerning observability by the theory of simulacra. As for observable things, the moenia mundi, the high walls of the world enclose them for the time being.

What is more, we would need practical applications: the water mill or Archimedes' water-screw. Leaf through Vitrivius, Frontius and the hydraulic engineers of Antiquity, and you will find parallel texts. The task is not difficult, and the reader may devote himself to the work as an exercise. I have shown the way, elsewhere. I prefer to press on, and to return to the question of the text itself.

Here is a determined scientific corpus: chaos, declination, vortices, simulacra, etc. Here is a physics, here a genesis of things. Here is a theoretical and experimental tissue that tries to explain, to understand, how this thing, which I see, touch and hold, came into existence. My question, now, is the following: can I travel through this same tissue again and arrive at an explanation, at an understanding of how this text that I'm reading, Lucretius' De rerum natura, came into existence? This is an analysis, the genesis of the text.

And in some way its radical genesis. It raises the same questions as the other, with no discrepancy. Chaos is the background noise. Atoms are letters, their ensemble an alphabet. Their conjunction is intercon­nection, combination. Here are words, sentences, their filtering. A signal and a meaning emerge from the noise. How? By declination, by drift. So what is their function here? What is the function of turbulence? How does the deviated fall introduce the reversible into the irreversible? In other words, why is this text on physics a poem, why did Lucretius, writing it in Latin for the first time, write it in verse? How does this

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music emerge from the chaos-noise of the background, and how does the rhythm emerge from the pitcher's flow without return?

Application of the physics of texture to the text which expresses it. The primitive chaos is a stochastic cloud in which the atoms, in great

number, indefinite in time and place, collide with each other in the void, in thousands of ways. The primitive chaos is a liquid cataract in which the atoms' flow is laminar without ever touching, in which declination, indefinite in time and place, leads them to collide, to encounter each other. These two models do not seem compatible. We must work on them.

What is chaos? The void and disorder. The chasm and the gap, in the beginning, the shadowy abyss, at the origin. The correct etymology, the accepted etymology, insists upon the open being first. At time zero there is only opening. Hence the void. The incorrect etymology, which is excluded, and which, in any case, comes too late, points to a Greek verb meaning to pour, to overflow, to spill. False philosophy, good science. For it is a matter of falling and dissipation, not just something that falls, but something that expands. This something is generally liquid, and does not necessarily follow the vertical, but all the directions around it. The atomists follow these two paths: the forbidden direction and the one authorised by the philologists. That of the void, and there is an open void, and that of the waterfall, the cataract of the atoms. A vaporised fluid spreads through a space that remains absolutely empty.

Good science. No chaos is original if, in the beginning, there is nothing but void. For nothing is born of nothing. And the first chaos is nothing. And it is not an origin. For it to take place it needs energy. Thus a fall, a discrepancy or a difference. Now, two possibilities: either weight, some force or other, makes the atoms fall or drags them in a certain direction, or else the difference is treated generally. In the first case we have a simple difference of level, and where we once again find the act of pouring, its verb and its substantive; in the second, we must imagine a heterogeneity, a fluctuating cloud of innumerable elements, moving in every direction. As in our science, difference is condition. Nothing is born from nothing or the void, and the original chasm is noting but the place where it is formed; but everything can be born from deviation. And we can then multiply this discrepancy globally: every atom, in its place, falls and rushes. Here is disorder. Not homogenous disorder, that of the lowest low point, from which, once again, nothing can be born, because all differences and all discrepancies have been abolished in a general state of equilibrium, but the heterogenous

Application: Genesis of the Text

disorder in which deviations again arise everywhere, and which is, without any doubt, the matrix of all things. This is chaos, the first model, the global cloud. It is not the pitcher, but the ensemble of stochastic fluctuations. The other model or cataract is only a localisation of the first. The deviation multiplied, globalised, in the cloud, is restored to unity, the difference in fall, distance, and angular declination, direction and meaning. Reality is disordered chaos. To study it we approach it, and we study a model that is reduced, cut down, in which the eruption of deviations is overlain upon a simple case. We do not proceed any differently today, when we reconstruct a model of Brownian motion. Hence the cascade, and laminar flow. Now, as in infinite space, no direction can be privileged, vertical fall is just a particular case, flow occurs in every direction, and the simplified model picks up the general case: the local is faithful to the global. The chaos-cloud of disorder, and the cloud-pitcher in the cataract are thus compatible with each other.

Leibniz wrote about the radical origin of things, and Lucretius about their nature. Nature has no beginning, it is always in the process of being born. For there to be a time zero, an instant of emergence or of beginning, would require all objects, the world, living beings and things, to keep the same time, a universal time. Now time is nothing without each thing, and each thing has its own. Atomism is a pluralism, and singularly, a chronological polymorphism. Every conjunction of elements describes its own graph or travels down its own chreode. For it, as born, a time begins that will disappears on its return to the cascade, when its vortex is undone in the torrent. And so too for others, here and there. Time is only the same after dissemination. And one who died yesterday will exist no more for a time as long as one whose end dates from months or years ago. Universal time is the stable time of disorder, and chaos is eternal.

Chaos never ceases. It is for ever and forever there. The world born, or nature, does not suppress the atomic cloud. It comes from it and goes back to it. No, things, numerous, come from there, go back there, each in its time. Chaos remains, around things. And nature is plunged into it. Not like contents in a container, but like a hollow body in a subtle fluid. Chaos borders the world, and what is more, it penetrates it everywhere. It produces it, like a matrix, working its interior, to bring it back to death, that is to say to itself. Disorder produces order, and works, in the vortex, to disseminate it. Stochastic chaos, produces conjunctive vortices by chance and declination, and by the law of division, by fall and descent, it ultimately destroys what it has formed. As a reservoir of the positive, as the work of the negative.

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There is no time zero, no origin. The instant of birth is proper to each vortex, here and there, once, tomorrow, long ago, this is how the clinamen functions. Origin, dispersed, is distributed stochastically, indefinitely in time and place. My mother died yesterday morning and, since then, a crowd of beings has arrived on the shores oflight. A certain star appeared, this evening, while a thousand mortal worlds went back to the dustbin-universe. Our world will die, and this isn't the end of the worlds. The relays are not taken in sequence, as in the Stoics, but in polymorphous explosions. Meaning is formed by noise, a rare and improbable miracle, then it drifts, at its own tempo, towards noise. Space-time of flickering and decline. The signals of the universe blink from the depths of the cloud.

Chaos is forever, forever there, outside, inside. Dense everywhere in the formed turbulence. The chaos-cloud is reality, the present real. The chaos-pitcher is its epistemological model. It leads to the unities, the multiple dimensions of the primordial.

Hence the text, as it is written. On this, one may form three sequences, of which one alone is faithful

to the stated physics. A monodromic series. Here is the void and the atoms, the chaos-cloud. Then the chaos-pitcher, physics possible through the model in the cataract. Nature is born, man and his mortal soul. Which perceives, which knows, by the same laws of precipitation as by those from which things are born. Here is society, techniques and exchanges, politics, arts and sciences. Days of labour, immersed in the meteora. Clouds again, in which principles become germs, hence the plague and the death of Athens. A sequence that extends from Aphrodite to corruption, from nature nascent in the midst of troubled waters, to death in tatters. The poem runs along the chreode, the Sisyphean slope towards the flaming pyres. If the road is unique, from formation to what might be called maximal entropy, or if the series is monodromic, then there is an origin and an end. Chaos is before and after the world. And it performs no work upon it. So why the slope?

Or: the scattered cadavers, plague-ridden, corrupt, burned, decay into dust. The cloud of germs produces the dust-cloud. So, by the end of the poem, the global result is the chaos-cloud. And everything begins over again. The initial conditions have returned, the series is circular, resumption is possible, and we have the eternal return. It is Kant's text that, from similar premises, is led to a cyclic and semi-stationary model. Book Six ends with the labours of Mars, violent fighting amid the heaps of cadavers, and the poem resumes with the victory of Aphrodite over

Application: Genesis of the Text

the god of war. Venus indefinitely revives what falls by violence. The final chaos, decay, is a beginning, through conjunctions and coitus or encounters. The clinamen works like Venus' couch. Why, then, only the city of Athens? While this city alone and its inhabitants return to chaotic dust, elsewhere the spring promises multiple beginnings.

There is no longer but one solution, which combines the slope and the cycle. There must be a slope, by way of the disintegration of chaos, and there must be a circle because chaos is a reservoir of conjunctions, by way of the work of Venus, and the clinamen that produces order by noise or forms by disorder. Athens dies locally, like Troy, for example, but Rome is still to be born, on Aeneas' journey. The resumption is else­where, not necessarily at the point of the greatest fall, not necessarily at the time at which this, singular, enters the shadows. Elsewhere and it matters not where, at another time, it matters not when. Indefinite in time and place. Now, a sloping line plus a circle produces a spiral. Nature, in everything, is turbulence of turbulence. And Lucretius' poem is written in a vortex. In all, it forms a vortex. It turns back on itself without meeting itself' It dies and is reborn, but elsewhere, in another time. Furnished with the coefficients of chance. Hence the chorus of criticism since its production: it is disordered, its author is a maniac. No. Lucretius has written a text which exactly expresses the physics to be described. His discourse is rigorously true to its contents, that is to nature.

Thus this physics includes all the models of our own: the question of equilibrium and movement, inventory, difference and circulation, the first notion of a deviation from equilibrium, the idea of the stochastic cloud of elements, order arising from disorder, the message arising from noise, the temporary organisation of open systems, and this vortex which hurtles down a slope, which elsewhere I call circumstance.

Atoms, letters, cyphers

That mathematics may be applied to physics in general or to the sciences we call 'natural' astonishes the practical man, who often finds it incomprehensible that things are comprehensible. How can we explain this application? It works, but why? A stupefaction without end, of which Einstein was still the interpreter. Here is the site of an experiment that we can call crucial. A particular site of the more general problem concerning words and things, language and meaning. This is also the site in which the solution is decided. Nominalism does not stand up to physics.

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At the beginning of the seventeenth century, when what we came to call the applied sciences first made their appearance, a theory spreads that one can find in several authors, although none of them is its sole source, and which seeks to account for a harmony that is not self­evident. This discourse may be found in the works ofLeibniz, Descartes, Pascal, Fontenelle, and so on, but even before them in Galileo, and perhaps in a number of alchemists. What spreads is the idea that nature is written, that it is written in a mathematical language. Language here is too strong or too weak a word. In fact mathematics is not a language: rather, nature is coded. The inventions of the time do not boast of having wrested nature's linguistic secret from it, but of having found the key to the cypher.2 Nature is hidden behind a cypher. Mathematics is a code, and since it is not arbitrary, it is rather a cypher.3 Now, since this idea in fact constitutes the invention or the discovery, nature is hidden twice. First, under the cypher. Then under a dexterity, a modesty, a subtlety, which prevents our reading the cypher even from an open book. Nature hides under a hidden cypher. Experimentation, interven­tion, consist in making it appear. They are, quite literally, simulations of dissimulation. Experimentation is not very far from prestidigitation. And so mathematics is not a language. Locally, it is the key to a word puzzle; globally, it is the whole code. The proof is, according to Leibniz, that every calculation, arithmetical or algebraic, is never anything but a particular instance of the activity of coding.

Hidden does not only mean locked away in a secure place away from view, or, on the other hand, impudently exposed, as in the Purloined Letter by Edgar Allen Poe. To this meaning there corresponds the meta­phor of the nesting and opening of Russian dolls, the black box. Now what is perfectly open, perfectly legible, but so far beyond our capacity to number that it would take the whole of humanity at work for a time longer than history to read or see it, is even better hidden than a secret in its box. The secrets of a work, for example, are published in several large tomes. By expanding this model we arrive at large numbers, whose treatment may exceed possible experience: in which case what is hidden may remain so, but is not dissimulated in the naive sense given above. A box may always be opened, some day. In place of which experience draws the outline an island on the sea of large numbers, a singular isolate, a closed system: a phenomenon. It is lost rather than hidden. Lost like paradise or like a needle in a haystack. On the combination padlock the right number is lost rather than hidden. Hidden god, paradise lost. The purloined letter is only a text, the lost letter is a letter of the alphabet.

Application: Genesis of the Text

The actions and behaviours of the practitioner must be described in and by a subtle and general methodology comprising the situations of the game. Either the game is perceived within a field of possibilities in which a decision must intervene, and Leibnizian metaphysics comes to the fore. While God calculates, a world is created: the world is con­struct�d by coding. The real is hidden among the possibles, the possibles are hidden beneath the real. Or the game is perceived as a strategy, setting partners and adversaries in opposition, deploying trickery, guile and relations of power, and we have Cartesian metaphysics. Which Einstein continues, in an experimental setting: God is clever, but he is not a cheat. Similarly for Pascal, and so on. Attempts to introduce the conditions of experimentation to philosophy. That is, large numbers, dissimulation and the key. What emerges in the seventeenth century, all at once, is not so much the applied sciences, the practice of exactitude and precision, as the general philosophy of its possibility. Hence Kant, closing the classical age: the open phenomenon, and the buried numen.

If my thesis isn't crazy, if applied, physical or natural science is already well-formed in ancient atomism, it is perhaps not enough to have discovered mathematical coding in Archimedes' works, or, in the history which follows, its fruitfulness. We also need some general and fundamental assertions about its possibility. Now, precisely, we find them here, and their meaning is not far removed from what is common in texts of the classical age, and in its experimental practices.

Atoms, as we know, are letters, or are like letters. Their intercon­nection constitutes the tissue of the body, in the same way as letters form words, empty spaces, sentences and texts. The old discussion of finite, indefinite or infinite numbers, of original elements, recurs for the alphabet. The whole of differentiated letters remains finite, while their combinations, with omissions and repetitions, are infinite in number. But we can say, without too much error, that for linguistic atoms as well as for the letters of matter, a given element placed here or located in such and such a vicinity, is not the same as the same element elsewhere and in a different context or structure. The analogy of behaviour is perfectly apt. It is a metaphor and it is not: the correspondences or relationships there are exhaustively dominated. To project it onto the time of an evolution, we could say that the atomic idea was arose with the inven­tion of writing or non-ideographic alphabets. This is another way of repeating the metaphor: the transfer takes place in time, that's all. As if the question of the origin were a metaphoric figure or modulo of time. Now yet another is possible: everyone knows that the systems of

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numeration used by the Greeks in particular, but by the Romans too, used letters as numbers. Here the analogy is strengthened. Lettered combinations do not make valid formations in every arrangement. A random combination of letters does not necessarily form a word, an arbitrary sequence of words does not necessarily make a sentence. Arrangements lead to monsters that rules of usage eliminate. Thus, atoms are letters.

The earth, once formed, becomes productive. Matrices grow, under the sun, fixed by roots. Then the monsters are born. They have strange features or limbs. Now this strangeness is never only negative. The androgyne, for example, does not simultaneously partake of the two sexes, it is neither one nor the other, and belongs to neither. Teratology is constituted on the basis of the rule determinatio negatio. The nameless monsters, innumerable, are deprived of feet, without hands, mute, mouthless, blind, expressionless, they can do nothing, neither move nor avoid danger, nor fulfill their needs, nor increase, nor find food, nor couple in the Aphrodesian act. These negative determinations lead to their definition as closed systems: the monster has no offspring, because he has no hole. He is without door or window. Lucretius' monster is Leibniz' monad. Without door or window: without mouth or vagina. Just as if, precisely, life were only possible through the possibility of combination, that is to say by opening. Life is an open system. The monster is in himself and for himself, autistic and dead. Nature eliminates them, she gives them up as prey to the animals, selected by their positive attributes.

On the other hand, if monsters are hybrids, crossbreeds or mixtures, then nature has not made them. The androgyne existed as neuter, the Centaur did not exist as double nature (nec ultrum, or duplici, bino) . Elimination occurs either by the death of the unclassifiable, or by the contradiction of classes.

Atom-letters do not work like numbers [chiffres] . Whatever the base of numeration, in fact, or the alphabet of the cyphering [chiffrement] , the various combinations of these signs among themselves produces acceptable numbers. Thus, the interconnection of atoms in things, conjunction, is cyphered, nature is coded. Atomic physics discovered the key to the code. Now the cypher is hidden in its turn, since atoms, subliminal, are imperceptible and very great in number. That atoms are letters is a thesis that heralds the great classical philosophies, the idea of cyphering and the secret code, the global working of physical science. Now read Archi­medes' The Sand-Reckoner and you'll find a pre-combinative arithmetic

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that formalises this idea. Physics is indeed an activity of deciphering or decoding.

Let us return for a moment to this hesitation between numbers [chiffres] and letters. On one hand, all possible interconnections are acceptable, on the other, all are not. Either everything possible can be realised, or nothing possible can be. Everything has a meaning, or everything does not. Meaning is a filtered rarity. The rational is real and the real is rational. Or: none of the rational is real. Two well-known sequences of hypotheses, which can be set face to face, as in an antinomy of pure reason, and which form, on the contrary, an antinomy of applied knowledge. In the first column, the affirmative universal is stable. In the second it is possible to write: all the possible is not realisable, or all the rational is not real, this is the contrary proposition. We may also write: some of the rational is real, or some of the possible is realisable, this is the secondary proposition. Finally, we may write: some of the rational is not real, or some of the possible is not realisable, this is the contradictory proposition. The last two may be grouped together as contraries. This antinomian table, the general antinomy of applied science, represents, all at once, the ensemble of relations belonging to classical logic. It brings traditional reasoning into play, through affirmation, contradiction, clash, subordination, and so on. Now it is reducible, as in a reduced model, to the atomic hesitation between letters and numbers [chiffres] . So the whole of applied science, its decisions and developments, its history perhaps, is relative to the type of coding. To the difference between letter and number [chiffre] , to the difference between a sequence and a word, to the difference between the average and meaning, or the difference between two meanings. In this way, we will arrive at an elementary semiotics of science.

Is it possible to prove this? It would doubtless take an infinite work. But we may make some preliminary inquiries.

Here is the atomic or elementary hypothesis. There is a matrix group of seed, an alphabet or a base for numeration, a notation of musical notes, in short, unities of some kind. This is the inventory. I don't mean the original inventory, for I still don't have the time. Either this is given, or we give it to ourselves. It is the deal, the deal of the game. Without it, I'm sure, there would be no music, no identification, either oral or written, no mathematics, no physics, no chemistry, no biochemistry, and so on. The elementary inventory is, perhaps, the deal of every universe of discourse and the whole universe, broadly speaking. It is perhaps necessary to generalise what we presently call the universality of

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the code. This said, we can have a go at producing something, a world or objects, we can have a go at deploying, as one says, the resource. The most general idea of such functioning is that of a relation in general. However we take it, this is always a question, sooner or later, of the combinatory. Lucretius does not escape: it collides, unifies, forms tissues, which are simplexes. Complexes, complications, multiplications. Arrange­ments, combinations. In this jumble of the complicated the most general relation, once again, is called a permuration, since the number of the elements does not come into it. Once we have arrived at this point the question arises: monster or not, realisable or not, meaningless or not, viable or not.

Hence the schema: the alphabetical ensemble, permutations, filtra­tion. It may be translated into various languages, from mathematics to biology. The pair mutation-selection, for example, is immediately inferred. But can one speak, can one write, without deploying this schema? In the viciniry of death and monsters.

The genesis of sense

Chaos is the background noise, disorder. Chaos, you say, is non-sense.4 It is, no doubt still more the absence of a sign, the absence of a signal. Against the background nappe, nothing is in relief, nothing appears. Now there are indeed two kinds of chaos, the cloud and the pitcher. In the first image, multiple aleatory collisions within the infinite void of space send disordered atoms moving in all directions. In the second image, against the second background, encounters and collisions are not possible, and the laminar atoms move only in one direction. Disorder might be non-sense, but the only information that I can draw from chaos is that the innumerable and countless multipliciry either dissipates in all directions, or flows in one direction. And atoms are letters. Would non-sense be first the dispersal of possible spatial directions, or the necessitating uniry of one direction? Would non-sense simultaneously be the average, the anywhere, the rose of all alzimuths and the unequi­vocal?

You see the thunder, the lightning, fly obliquely across the lines of the rain, sometimes here and sometimes there. Signals flicker upon the cataract. Declination is oblique, it is an angle, it is a traversal, transversal, a change of sense. Movement is modified, momen mutatum, mutation of movement.5 The nappe falls in one sense, in the white of monodromic uniform sense. There is no sense when everything has the same sense.

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There is no sense when everything is in all senses. A unique norm or all norms, white, black, white noise, black box, black background. The lightning flickers, it declines, it winks out, as they say. Direction, sense, course, are followed by small successive inclinations. Sense is an integration of small changes in sense. Against the white noise a signal appears, a biforcation appears in the laminar flow. Sense is a bifurcation in the unequivocal. A bifurcation of the lightning, a bifurcation of the flame that rises as it is born, numerous arboreal bifurcations, examples cited before the introduction of the clinamen into the text.

Inclination is a differential change in sense, an infinitesimal differ­ential of sense on a sheaf of white parallels. Like lightning, it is trans­verse, and indicates a different sense to that of the cataract. It is transversal to the universal. To say of the fall that it is universal is simply to say that it has just one direction, just one sense. The transverse bars the universal locally. The universal, that is to say the monodromic.

I have arrived at space, at words for space, at the space or at the area of some words. I mean sense, but only of the sense of space, direction and sense. Orientation is an invariant of the topos. Semiotics is first and foremost a topology. Space is a field of vectors, of arrows which indicate sense. Either, globally, all the senses of this space; or, locally, a single sense. Hence the infinite void, chaos and the cataract. Hence the various paths of atoms, either by collisions and disordered encounters, or by the laminar pitcher. Hence the suppression of the centre common to the entire universe, which would suddenly freeze the emergence of meaning or of order. The circulation of the atoms traces the outline of the field in the void. First, the universal field. The single pitcher pours one sense. Here are words, the pointing of the arrow towards, or turned towards, as we say. All the arrows parallel, universal. But this versus is spatial, of the area of verto: to turn, to return, to change direction; and even of the vertex, vortex of water and turbulence. Curiously, two movements are associated, two fields and two paths, which may be easily distinguished in space: transference, rotation. The vector is indeed turned towards. As if it meant nothing, as if the field remained uniform. Now the spatial model is given as follows: nothing can happen in the cataract, or in the constitution of a thing, or in the formation of a word. For there to be a movement towards, vector and meaning, there must be a rotation or an angle. Now the versus is not only a preposition or an adverb, for questions of place. It also describes lines and ranges, oars, elms, in short more parallels; lines, writing, prose; verses, poetry, rhythm, metrics. We're there. A parallel ordering, for things or for words, is not given from the

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first. To form it we need something like a rotation, an angle which turns on a preexisting field which, itself, fundamentally, has no meaning, is the absence of meaning. The word versus, the verse, what the poet writes, what the rhapsode chants, describes this all at once. The organisation of the verses converts, subverts, etc., the univocal and the universal. Better, it is a version of the universal. Yet the spatial model, mute, in fact does not designate anything else: inclination, differential of the angle, is like a rotation of the pitcher. There, an order of things and a meaning for the interlaced letters can be formed only by the vortex, vertex. Inclination is indeed that which cuts across the universal. Sense appears on the nappe. The first word formed by the atom-letters is vers, the index of a sense, the arrow of the vector, it is a line, a poem, ordered parallels turning. The poem, a new field of parallels inclined on the shower falL

About the cataract again. If there is just a single sense, then there is no sense. This is true of space and true of time: if there were only one season there would no seasons, if there were only one era there would be no eras, if there were only one island certainly there would be no island. And so on. It is true of movement: when there is just one uniform movement, in one direction, it is not perceptible. When everything moves, nothing moves. A change in sense, no matter how small, intro­duces sense. The tangent to the curved line that turns is equivalent to force, to acceleration. Which are, themselves, perceptible. The mono­tony of the uniform field is the absence of sense more than non-sense. The first traverse, the first transverse indicates vers, and sense is present.

Space, time, movement, force. A small energy produces force and code. Thus small energies. The monotony of the uniform field might be called white noise. A repetitive disorder where there would only be redundancy: Washed-out chaos. Disorder scattered in all directions, noise again, but in saturation; a maximal improbability, a minimal redundancy. Everything comes from the two instances of chaos that mark the two thresholds of disorder. The monotone unity of meaning, nothing new under the sun, or the totality of the meanings in all places, where nothing is ever the same and everything is different, are non­senses by lack or by excess, by absence and saturation. The signal is born from the noise between these two boundaries, traced in metaphysics by the this wisdom of Solomon and the philosophy of Leibniz.

Whatever exists, order and sense, emerges within this window. The singular and the whole are at the limits of chaos. Sense appears in the local, here, there, yesterday, tomorrow. A small local diagonal escaping from the monotone and from the saturated whole. Sense is particular, it

Application: Genesis of the Text

is a pocket. Sense is singularity. Thus there is no law to assign its place here and its date, at this time. Otherwise the law would be universal, which is absurd. It is thus here, there, once and later. It is plural. Local and plural, it is aleatory, stochastic. Indefinite in time and place. It is improbable. And, on the other hand, it is its improbability that produces information. The singular and the whole either produce no information or infinite information, which has no sense either.

Sense is local, dispersed. How is it formed? In the most natural way in the world. By a change in sense. Thus by a biforcation: an angle of rotation on the monotone transference that announces and begins another transference. Here is the fork, an X or a Y, or an N which becomes Z when it falls and leans, as Aristotle says, or Rabelais, or so many others. From one transference to the other; here is translation. Changed movement, a transverse movement at the moment\ that we leave the universal, and thus at the moment of coding. Outsid,e of the universal there are indeed only versions, codes and translations\ As we have seen, the universal has no code. The cataract nappe follows its course. Here is one path or other. All at once, an aleatory di�ion, diversion of direction, discourse. Discursus, discurro, this is indeed a momen mutatum, it is indeed to change the movement of a path . . The elementary net of discourse is biforcation. The first knot in the inter­connection of letters is at the crossroads of inclination. The crossroads where Hercules hesitates, where Oedipus kills his father, where he deciphers the enigma of the sphinx. Catastrophe.

Sense declines. The signifier bifurcates in its semantic space. Sense is its ramifications taken together. And if there were no bifurcation, there would never be any sense. And the signifier itself in its formation derives or drifts from its root. It bifurcates in its degrees, in its prefixes and suffixes. It declines too in many languages. Derivation, declination.

Coding

That atoms are letters is not an arbitrary theory or a decision or a metaphor. It is a necessity of what Lucretius and his predecessors called nature. The latter is subject to universal laws. And first and foremost to the law of gravity. All over, everywhere and always, things fall. They hurtle towards equilibrium. The cataract is from chaos, it is the original configuration, but it does not cease when worlds are formed. Con­junctions, connections resist wear for a time, but are pulverised by the collisions, are chopped fine by dichotomy and go back to the atomic

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cloud. In the hurricane the demolished vessels are wrecked and break up. This law is universal for space and time, it is efficacious for all the worlds, and goes from the first chaos to the last chaos. Thus it has no memory. I mean by this that nature does not code the universal. When an operation is general, the necessity of preserving it, of restraining it, here, there and at a given moment, has neither place nor time. In other words, the entropic drift takes place in the forgetting of its initial condition. Or: the irreversible is without memory. You will never find a local box in which these conditions are recorded. We rediscovered this theorem in the nineteenth century. The universal does not require any memory. There is no Galilean or Newtonian code. And background noise is also the absence of code. There is no code for equilibrium, for the fall towards equilibrium. Equilibrium according to Fourier, to Boltzmann, is the forgetting of initial conditions. Whatever their origins or circum­stances may be, the end of this story is univocal, determined: universal equilibrium. 'Nature' does not code the processes that are not determined by their initial conditions. The cataract is thereby without predecessor. And Lucretius was right to call it primary, and Lucretius was right to call it permanent and final. Thus the atomistic Epicurean world is without memory, like Boltzman's world. The universal is without memory. And fall is not coded.

By this universal law, nothing is created or formed. For something to exist rather than nothing, there must be a fluctuation in this uniform flow, there must be a deviation from this equilibrium. And this is the clinamen. Thus a connection, a conjunction is produced. Turbulence remains stable in the cataract, a little time, a long time, a very long time. It is maintained, as an open system, through the flow upstream, in the flow downstream. It is the recipient of atoms, it emits atoms. Feeds and excretes, a black box with inputs and outputs. For the interconnections to be preserved, they must retain something of their initial conditions. Diamond, iron and bronze are always the same, like the tiger's skin and the birds' plumage. Conjunction is thus a memory. In other words, the coding is imposed as soon as the deviation from equilibrium takes place, the code is here, in this time, for the memory of initial conditions, outside of the linearity of the fall. Nature codes the rare fluctuation to be preserved which induces a connection. It codes the clinamen, and never the homogenous fall. Then the atom-letters indeed form a word, a phrase, at the same time as they are conjoined in a body. By no means everywhere and in all places, but now here and now there, nunc hic nunc illic. This is both necessary and stochastic. Aleatory in the place and time

Application: Genesis of the Text

of its formation, and determined, there, in its relation to the prescribed local series, to the conjoined interconnections. Determination is nothing but the retention of the code. Connection makes a phrase, this phrase is memorised. It is memorised for the very time of existence of the thing formed. The connected interconnection is the thing or its first core, it is its coding, and it is a writing. Writing appears in things, it appears from things, it is not different from things. Just as declination produces connection, so precisely it produces the coded sequence. But this is not a comparison, it is a single and unified beginning. The code flees entropic fall, it deviates a little from this universal non-sense, which is the spatial sense of the fall, its univocity. Writing is negentropic. It is memorised information in the core of connections. The clinamen that produces writing outside of the redundancy of repetition is a deviation from equilibrium, a deviation from the universal. It is remarkable that we define information by its complexity, by the number of complexities in the state of things, and that Lucretius defines things and their code by very similar words, such as conjunctions, connections, perplexis figuris (II, 102) .

The body coming into existence is directly the tablet of its own law. It does not bear it written upon itself, but it is from end to end the key to its code. It is what I call elsewhere a circumstance, a vortex circulating on the nappe of the fall in deviation from the fall; it is a circumstance, a case, a chance, a miracle; it is a circumstance in code that will offer this up to be read: in this circumstance, here and now, in this local pocket, this island, a particular cause produces a particular effect. The same cause produces the same effect, taking into account these initial con­ditions. These limit conditions are the here and now, distributed in an aleatory fashion by the universal nappe of the fall, and preserved, in the irreversible. Local determinism introduces the reversible. That is to say a series that goes down like the cataract but that goes back up as well, since it remembers its own conditions. The spiral is thereby a valid model. The same is maintained even while it evolves. And on the other hand a sequence may be needed for the formation of its own predecessors. These chains turn back upon themselves.

Circumstance and its coding are the place where writing emerges as the mnemonic preserver of this initial condition by chance within the interconnections of things themselves. Atoms are not only an alphabet in the universal of the drift, they are connected letters, words, phrases, a written text, in adamantine crystals, bronze, foetuses, trees and stars. Everything that exists only exists in the form of writing and code, only in the form of the law, the tablet of the law, of the Joedus naturae.

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Conjunctions are federational. Things and words are negentropic tablets and by declination they escape, for the time of their existence, that is to say for as long as the code is memorised, the irreversible flux of dissolution. And all this is necessary, it is perhaps the most advanced discovery of ancient atomism: the code avoids entropy for the time of memory. For we have today no other conceptual means to draw order from noise or a system from disorder. That atoms are letters, that connected bodies are sentences is certainly not a metaphor; were it not so, there would be no existence. And since existence only appears in and by deviation from equilibrium, physically speaking, I'm willing for this deviation to be the primary space in which every metaphor finds its place and time. The clinamen is transport in general.

So here are the fledera naturae, stamped in the core of things. They code weight, heat, liquids, resistance to the touch of every connection. I have used the word 'core' for the physical particularity of things, what Lucretius calls 'conjunction'. Remote from the core, on the periphery of circumstances, farther along from equilibrium than the minimal declination, there slip possible accidents. Servitude, riches and poverty, freedom, war, peace. History, law, sociopolitical constitutions. They are not coded, natutally. And thus we code them, remote from equilibrium, we make them into laws, written texts on tablets, or graven in stone. Laws, contracts, narratives. These are our fledera, civil law and constitu­tions, social, political, historical and cultural institutions. Since nature does not code them, we ourselves must do it to give ourselves a proper history and a time. Our collective memory. And so we repeat, we imitate, farther from equilibrium, the native activity of nature which it itself codes near the fall. The laws of nature are not federational by imitation or projection of our own laws, but the reverse. Our writings, our memory, our histories and our times are negentropic, go back to the initial conditions, preserve them and maintain them, as nature has shown them to us. History is a physics, and not the other way around. Language is first of all in bodies.

The fall is without memory, it is without code. Nature does not code the universal. Whatever their initial conditions may be, things fall. The clinamen sets the first coding, it introduces a new time, writing, memory, the reversible and the negentropic. And space is strewn with the tablets of the law. Local physics is regulated by the fledera naturae. At the extreme edges of these circumstance-bodies our history is an even more labile flow, which we restrain by civil laws, our contracts and our texts. The forgetful universal, memorious nature, and history, second nature.

Application: Genesis of the Text

Thus atomic physics, where the code emerges, is written, a second time, in the text called De rerum natura.

Fall and rhythm

Introduction, finale, overture, closing harmonies. Music moves. It begins, it ends. Or rather: a music moves, moving from silence to silence, having as it were a source and a point of termination. Another, interminable, stops and does not stop, as at an ill-defined edge, and begins so little that we are disconcerted by it, submerged by it. Music flows like a river, the other is the sea. Music and time.

River, sea, this is not entirely a group of metaphors. Until a certain point in its history, music describes paths. From this point to this other, irreversibly. It follows a secret slope, a line of time, a loxodrome, a thalweg. From the past to the present, from the fleeting now to the future, or from some upstream to some downstream. It moves, it descends. The great overwhelming texts of this time descend, restraining this descent. Music, then, is the practice and theory of irreversible descent. Of irreversible descent restrained.

Without this retention it would be a brachistochrone, following the steepest slope it would draw too quickly to its end, death and silence in the heavy bodies, the fall of heavy bodies, precipitated towards the lower equilibrium. It would flow like the water-clock, the clepsydra. Like time, and in the silence of the irreversible. Thus to climb back up this slope. To go back, to invert, to reverse time. If musical time were the pure irreversible or pure and simple descent, music would cancel itself out by itself. To exist, it requires the reversible. Vibration of a vibrating string, or the vibration of a column of air, these are movements that turn back upon themselves. Acoustics as a whole is just the reversible. This is perfectly general: every sound, every signal is in the domain of periodicity. Thus of the repetitive, of reversibility. The measure that ceaselessly repeats, rhythm, these are returns. The clock or the metronome's pendulum recaptures its fall, it too vibrates. Even the various styles of writing and compositional techniques. Coda, double bar and repeats, voice and countervoice, point and counterpoint. Music is an irreversible saturated, swollen, dense with the reversible. It descends but restrains its descent, it traces a path of the smallest slope. Its time is directed from the past into the future, but its time is that of the return. Ritornello, refrain. Sense everywhere packed with misinterpretation, with inversions, or reversals of sense. It flows, while always restraining itself from flowing.

The Birth of Physics

So it is for the torrent and the river that journey irreversibly from their springs to the sea, moving by the thalweg, the line of the level, by the greatest slope, yet which, as they strike a rock or the arch of a bridge or some such unforeseeable thing along the banks, form vortices that turn back on themselves. Unstable by the continual crumbling of the fluid, but quasi-stable, here and there, by casual turbulence. Such is time.

Maintenant, now. What is the maintenant? The present participle of a verb like hold (tenir) in the hand (main), or to maintain. Maintenance. Now this solid object, the statue of a god, tablet or basin, I hold or have it in hand. I cannot do this for a liquid, or fluid in general. Now time flows. I no more have time in hand than I can dam the water with my palm. Montaigne plunged his into the water: if he does not move it the current flows by running through his fingers and around his palm; if he withdraws it, he does not keep a drop. There is no main-tenant, no maintenance, quod erat demonstrartdum. Now nothing is proven by this experiment from the Heraclitean library. Did Montaigne ever see or cross the Garonne? Plunge yout hand into the flow, once again. Almost everywhere, the esayist is right. But here, where a vortex forms, he is caught out. If your hand is downstream from it, your hand will not move upstream at all or only very little. Yes, in this quasi-reversible place, it maintains itself. Everywhere else a vortex will form downstream from the barrier, and the water will fall back on itself. Thus there is a main-tenant, quod erat demonstrandum. Unlike Montaigne and Pascal, all sailors know very well that you cannot always go down a river effortlessly. Countercurrents can sometimes immobilise them, sometimes carry them upstream. The river is not always a route that takes them where they want to go. There is some local reversibility in the global irreversibility. The course of music is saturated with it, the course of the river is strewn with it. Ophelia's boat goes upstream, here and there, Moses had a good chance of not dying at sea, the poetic waters of dreams know little of river transport and hydrodynamics. Everything does not go uniformly to death. The contretemps is a pocket of memory. The vortical flow saves the main-tenant.

Music, in its descent, restrained, maintained, makes the present flame out.

Now, later. No one, he says, steps twice into the same river. It flows, irreversibly. Now, from springs to the river's mouth, along the whole of the route, water evaporates and the vapour forms clouds, which burst, it snows, it rains, and here is the water back again. A large cycle, but stable, relatively. Without it, I believe, there would have been no river. No, this

Application: Genesis of the Text

is not the same river, but it is still the same river. In other words there are chances, very uncertainly distributed, that I may later step into the same river. The same, another, poor logic, not to say wretched. It is a stochastic mixture of another and the same. Is there chance [hasard] in time? Is time mixed with chance? How many fluctuations are there in a flow, in a flood, in a river? Stochastic music, the appearance of noise, in sounds and signals. In short, I can by chance bathe twice in other same waters, thanks to the global cycle. But if I plunge into a vortex, a whirlpool in this local cycle, I am more or less certain to step in the same water, more or less, or in the water held here [maintenue] . Immersion in the now [maintenant] , retained later, the bath of memory, in the middle of the waters of forgetfulness. Only the Lethe, no doubt, flows without tutbulence, hell is laminar, ideal, as they say. Heraclitus, Montaigne, Pascal, philosophers of hidden worlds. But all this is only of the contents, the water of the river. Heracitus wrote about the container, the same river. It courses down, from the mountains to the sea. Runs down the slope, its slope. If a Hercules comes to its banks, I mean a meteora or a civil engineer, and changes its course, it will eventually return to its slope and its thalweg. It is thus quasi-stable. Homeorrhetic, by virtue of its flow, its meanders, and its constrained diversions. Let its water flow as much as it wants, let it crumble, let everything flow, here the courses are in equilibrium. In equilibrium, precisely insofar as they are flows. Stability by instability, chreode, or inclined road. Thus I bathe twice, three times, a thousand times, in the same chreode, strictly speaking in the same directional river. 6 Through the global cycle of the return of the waters, the local cycle of turbulence, and the homeorrhesis of the chreode, there are subtle stabilities in the fluid instability. On the other hand, the course erodes the banks, erodes the mountains, fills the valleys, the solid flees, is atomised in the alluvial cones, I can never sit twice on the same bank. The solid is less stable than has been said, liquid is more solid than was thought. Time atomises more than it flows.

The vortex as a spiral: eadem resurgo. It reproduces itself, as if fed by its return.

Now, later, time and music. In chapter twenty-seven of his Problems of General Linguistics, Emile Benveniste questions the etymology of the word 'rhythm.' He remarks, in the purest tradition of Heraclitus, Montaigne and so on, that a flow of water cannot form a rhythm. It is monodromic and unicursal, universal. Does not turn back on itself. But rhythm comes back here. It is contradictory. How is it that the words Qu8�o£, rhuthmos, and QELV, rhein, have always been placed together? It

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is impossible. Rhythm appears for the first time among the atomists, Leucippus and Democritus, and as one of the key words of their philosophy. It signifies a form. To understand this fluent form, Benveniste proposes the word 'fluence', while the history of the sciences provides 'fluxion' and 'fluctuation.' The linguist, like Heraclitus, Montaigne and the rest, had never sailed in fresh water. Nothing flows as they thought. Direct physical experience, simple practice, reveal the rhuthmos in the rhein, or the vortex in the flow, or the reversible in the irreversible. Rhythm is a form, yes, it is the form adopted by atoms in conjunction in the first dinos. In the beginning is the cataract, the waterfall: here is the rhein, the rhesis. The dinos which appears then brings a momentary reversibility to this irreversibility: thus rhuthmos. No, it was not Plato who first made possible and imagined rhythm, it was the atomists. Linguistics meekly follows usual practice, the nature of things and abstract theory. Democritus saw the rhythm where it is, Benveniste didn't see it. Heraclitean irreversibility is rhythm, here, there, in Demo­critus and all the atomists.

The theory of atoms engenders rhythm, the rhythm of the poem speaks of the theory of atoms. Memmius, I watch my words, the Latin language is too crude for these subtleties, but do you at least hear the music of the lines, and the rhythm of the metrics?7 The form, the rhythmic model in the flowing background noise? The birth of form.

Music is saturated with the reversible. It gives rhythm to the rhesis everywhere and on all levels, it produces and reproduces the now [main­tenant] . Flux filled with fluctuations. Rhesis and rhythm, irreversible and reversible, flow and counterflow, global flow and local rhythm. Language will locally articulate a flow of signals or sounds, as music harmonises a similar flow. Here once again is the string that vibrates and returns upon itself, or the ringing bronze, vortices that are reborn of themselves. Pythagoras, it is said, once listened to the blacksmith at work. Then he reproduced these sounds on his strings, measured them, compared them, and dichotomised them. Arithmetic was born from music. Hence the sequence of the numbers called 'natural numbers' that run along numbers by the eternal return of a law. Arithmetic is rhesis and rhythm. The Pythagorean miracle has not taken place, we must go back up to the primordial fall and to the vortices, to the primitive river.

Here we are on its banks once again. Why are we fascinated by stagnant water and by running water? By the continuous collapse of liquid downstream towards death? Perhaps, certainly, because we are going to die. But the turbulent round pockets which go back up the flow

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a little, and the form that maintains them in the place where they are formed? Destroyed and rebuilt, quasi-invariant by the heavy variation of the flow? What is this process that runs irreversibly downstream towards death, and yet which preserves its form for a time in and through the flow that destroys it? This process is life itself. My body is a recurrent vortex, open, almost in equilibrium on the imperious procession of my time towards death. What fascinates us on the banks of the river is this: life in its complexity finds itself face to face with its primary model. Once long ago Narcissus was fascinated by seeing himself. In a smooth and calm water, either which was not moving, or which flowed unified and untroubled. Mirror of the waters, morose masrurbation of the subject, repetition and death. Narcissus drowned in his reproduction, in his double and his mime, when his face met the image of his face. Drowning, smothering, in adequation. Let that water, then, be murky or rough, so that the face and the body cannot be seen in the reflection of the waters, and it is here that they recognised themselves in the universality of a system of knowledge. Aphrodite pleasure emerges from the foaming waters, nurturing, fertile, living. Aphrodite emerges from the silence and the noise at the beginning of the poem, at the first interconnections ofletters and rhythm, in spiralling pleasure. This is not a dream, this is not an illusion, life is recognised as it is. In turmoil, for it is turmoil. Not fascinated, in turmoil. No more: I see myself, I Narcissus, for I no longer see myself. But: life knows itself in an application in which the two elements are other, as much as we want. Knowledge, in the first objective form, that I am this object, this form. It is not by digging through the arcana of the self that the fascination and the turmoil that I feel before the waters will be made clear, since, precisely, the T is excluded in its specific singularity. And the psychology of the senses from Kant to Bachelard disappears in this second myth of Narcissus which is experiental and a system of knowledge. The individual reflection disappears, optics is lost, while the universality of the life that I bear has an immediate grasp of the modality of its construction. The life within me, life as a local and temporary resistance to death - the universality of life is only ever local and temporary - is reflected by itself in the turbulence along the water. Narcissus dies, drowning in the reflection of the self, and Aphrodite emerges from another formation, Aphrodite the pleasure of the others.

To head slowly back up the irreversible. An order forms from out of the noise, a signal beginning from the chaos, a fluctuation on the flow. Deviating from the fall, a bifurcation. Vortices. This, this is the river.

I55

The Birth of Physics

Now, everything is finished. The generality of the hydraulic model. The code, a deviation from equilibrium. The written code from inter­connections of the letters, the local and conservative code. Directly, the birth of sense by a change of sense. The bifurcation towards [vers] , the discourse in verse [vers] , by disruptions of the flow. Thus from the reversible on the irreversible. Sound, signal and vibration. Rhythm and music. Series, measure, metrics. Time, the appearance of time with things and words. Lucretius in fact wrote a poem, a poem On the nature of things in his natural text, his natured writing. It was born, naive, from the birth of life, Aphrodite pleasure emerges from the unnameable waters of chaos and noise. Before crumbling away in the atomisation of the plague.

Note-The history of science that I report here has left some curious traces in language and words. Example: around the year 1534 Rabelais invented the word fanfreluche, which, at first glance seems to have little to do with the austerity of knowledge. Nonetheless Jean Calvin, in 1560, in the sixteenth chapter of The Institution of Christian Religion, writes in great seriousness 'Let the Epicureans answer me, since that they imagine that everything is made from little fanfreluches that fly in the air like fine dust, meeting by chance.' So here the word rises to the dignity of an atom, and, quite precisely, to that of an atom in Epicurean physics. N ow, if we attend to its formation, it is not difficult to see that it derives from the Greek Jtof,Lq:nJA'Us, pompholux, a bubble of water, a drop of steam left on a cover during boiling. Here once again, behind the atom, we find a hydraulic model, and the verb CPAVW, phlub, to well up, to flow abundantly, in which the flow and flux accompany the idea of great number. This is not all: Voltaire, who prided himself on his science, wrote to D'Alembert, who himself knew more than anyone in the eighteenth century: 'The idea that we may pass an infinity of curved lines between the tangency and the circle always has appeared to me a fanfreluche of Rabelais.' Here is the mathematical model in its exact precision. Rabelais ' word bears with it the whole of the theory, plus its Aphrodisian connotation, since fanfrelucher is nothing but making love. The physics of Venus. Plus finally all the criticism levelled against this physics: it does not explain the essential, the core, what is in the centre, but only the circumstances, everything which doesn't count. The word says everything, while minimising and ridiculing it.

Application: Genesis of the Text

NOTES

I II s e boucle sans s e boucler. NP, P.172. 2 'Key' translates chiffre, and 'cypher' translates grille. In this way, the key term,

chiffre, have been preserved from the French, albeit slightly displaced. In addition to its direct role in the discussion here, it should also be noted that chiffre denotes a sum or number. Deciphering, dechiffrement, therefore has the connotation of de-numbering, which is significant for Serres in view of his attitude towards metrics and measurement in the treatment of form. Where this has been a particular issue, chiffre has been translated as 'number' with the French included in brackets (cf. pp. 169-70). A message may be transformed into an incomprehensible text, that is, a secret, either by an organised logical system, or by an arbitrary cypher. In one case it is possible to restore its legibility, bur in the other one must, excepting miracles, have the cypher. It is a matter either of a code or of a key. On this point, definitions have never been fully determined.

I have noted on other occasions that experimental method emerged at the same time as the theoty of large numbers, of chance and games. On first inspection, it is tempting to say that in the case of deterministic physics, the question bears on the key. And that when one addresses large populations, there is just code. The cypher is organised, rational, ordered, or it is arbitrary and disordered. Now one finds that may be impossible to deal with one without the other. Physics is born on the double situation of the secret.

4 Throughout the following discussion, the French 'sens' has been translated as 'sense' in order to preserve the connotation of direction or orientation. It could easily have been translated as 'meaning', and this signification is clearly important here.

5 II, 220. Cf. also p. 4. 6 The French 'fleuve' primarily signifies 'river', but it may also be translated ,as

'stream', suggesting the experience here oflocal currents and refluxes within the general river.

7 I, 136-45. Lucretius, addressing Memmius directly, warns of the obstacles to a clear expression in Latin of ideas taken from the Greeks. He will, he adds, work calmly through the night to find the words and the poetic metre in which best to fulfill his task.

157

H IS TO RY

Antiquity, modernity

Two systems of analogies run through this work, and that of history. The first founds physics, or what we can call physics, that is in general the beginnings of the applied sciences, and in particular of statics and kinetics, and dates it to a time in which we thought it absent or at its prehistory. It is complete in the blinding short-circuit of Archimedean mathematics with the atomist tradition. Which is itself born, as far as we can tell, from a pre-infinitesimal geometry, Democritus. The play of the relations between mathematical rigour and the fidelity of phenomenal description is possible, in the beginning, and realised, in a demonstrable fashion, at the end. There is at work here a fertile circumstance that the Renaissance and the Classical age never managed to reproduce, to exploit or to mediate. That the modernist revolution did not take place, in the usual sense, that the new knowledge was an ancient invention, this is a plain fact in the history of the sciences. Yet it has failed to appear, hence the discovery of a origin hidden, willingly I believe, by those who wished to draw some glory from the continuation of a dispute between ancients and moderns: it is always easy triumph over the dead or to keep them quiet.

In narrow terms, the return of Archimedes to the bosom of the family of physicists may be of some interest: to short term academic debate. But what will follow may cause disquiet, and leaves me feeling uneasy, in any case.

The second system of analogies, in fact, takes up the same game, but at a millennial distance. Lucretius' De rerum natura, carefully reread in the presence of the Syracusan, and Leibniz' De rerum originatione radicali, which did not need two conjoined authors, are in many respects isomorphic texts. In terms of the question of their genesis, birth or origins, in terms of equilibrium in general and the declining deviation, in terms of the law of the extreme slope, in terms of the model of drops of rain, and so on, as long as you like. Combined spirals roll down a plane of determinable inclination, just as, in a unique experiment, large and small balls roll down Galileo's plane. Galileo restricted the global

History

model to a very particular case, he cut the outline of a phenomenon away from a generalised schema, brought an operator of constitution back to the local. The edge where the chisel has passed is still visible, and what is hidden by the outline is the aleatory background where the cloud of atoms vibrates chaotically; in the ancients this is the unfathomable depths of things where the elements of divisibility sleep, for Leibniz.' The immeasurable sea from which, rarely, law suddenly appears, and which we have rediscovered: for some, the point of an infinite pyramid, for others, maximal members of the world, itself infinite. Galileo is not a break, but a cutting out or away from: in present terms, he was a positivist Bridgman, not a materialist Boltzmann. This, perhaps, is the place where the science of Auguste Comte is born, as if anew, this brief historical interlude. That said, at matter of little account, from Antiquity right up to the century of the Enlightenment, in the Low Countries of Stevin and the Italy of Galileo, the atomist model did not vary greatly. It remains, stable. Sudden anxiety: what is history about?

It concerns physics, and its formation. It mirrors the world, and its constitution. It touches on discourse: Leibniz's grounds are alphabetic, the origin of words from their roots, an undeclared resumption of atom­letters. Physics is faithful to the world, since the formation of its text is isomorphic with the constitution of the natural tissue. Now, the invari­ant in question illuminates history. On one hand, I include Leonardo, Stevin, Benedetti. But, on the other, Pascal becomes suddenly clear. Here is hydrostatics and the equilibrium ofliquids, the fall, precisely, to the lowest low point, the first geometrical idea of moments; here is the roulette, this ball that rolls on a known plane, and the spiral and helices; here is the void, where we wait for him, whatever the outcome may be; the Triangle is the Sand-Reckoner, the deployment of numerical orders, and infinitesimal calculation born from scalar functions, this is the quadrature of the Syracusan; the Conics are the Conoids; everything is here, there is nothing missing. It had, at some time, to encounter the calculation of parts, game theory, in a space where chance plays such an important role. The maximal slope of the waters, roulette, spiral, helix and stairs, always the unvarying model, broken down or reconstructed, preparatory, as it stands, to a metaphysics of equilibrium, of deviation, of fall. Seated, standing, on the accursed rivers that flow. The valley of tears, and exile from this world. The important thing is not what this model tells us, it is only that it is here, present, taken up again and productive. The Archimedes of physics, that is, Lucretius. Lucretius, too, weeping over rivers.

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The Birth of Physics

Everything moves, apparently, and nothing stirs. Anxious, still, I am in search of history. Horrified by it, by what I see, which formally resists everything I have been told. At the end of the century of the Enlighten­ment, here is Kant, once again, The Natural History and Theory of the Heavens.2 And the demonstration begins anew, I have already given it: here is the inclined plane of systematic distribution, the initial nebulous chaos, the spiral of external formation and of interior collapse, death of the worlds and resumption. The text manipulates the same invariants with precision. And still nothing moves: Kant is not an Epicurean in the introduction alone, but throughout his cosmogonic model. Though he maintains that he didn't want to be. And Newton fades away, almost disappears, behind the model. Newton, nonetheless, the man of flows and deviations, like the ellipse and planetary conics, Newton who shows via universal gravitation that the celestial orbs are like the fall of bodies. Even if I go on to Laplace, to Poinsot, the series of isomorphisms is undeniable. Always the turbulent nebula, the fixed plane inclined against the equatorial level, the recovery of the stochastic, the edges or extreme places of constitution, the general couple that accounts for the fact that everything rolls in relation to the inclined plane. History still fades before the iteration of the invariances. Finally, a revolution: thermodynamics. Here is something new, and the historic thereby rushes in. Alas, the demonstration begins again, imperturbable: we have seen nothing. Here is a cycle, the Carnot cycle, certainly not closed, like a spiral, and here is equilibrium furnished with its deviation. We need, he says, a circumstance, the difference between sources. Here is the constant, in the First Law, and the fall in the Second, towards extreme entropy. Carnot himself again takes up the fall of water, and the world, through its constitution, according to irreversible time, glides along this flow. The invariant is not even translated, as though it remained in its place: Lucretius indeed said that there was no physics or science of the world without weight, heat, fluidiry. And here we are again, after Pascal's pondere, mensura, numero. This morning the sun rose upon a completely new landscape. What is important here, what is new, when all is said and done? Open systems, the deviation from equilibrium: bodies in general, inert or living, conceived as temporary vortices. These descend, as we know, along a chreode, the stipulated path, like the course of a river. Homeorrhesis is the stability of the flow on the chreode. Where once again we find the whole unchanged, in its initial lexicon; fluid mechanics. All this is easily said, but also demonstrable, assuredly, down to the least detail. Nothing new, finally, under the sun

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History

of the same. And I step back, horrified, before this flood of results. The second system of analogies is not a product of the history of the

sciences, internal to its structure or its work, as was the case earlier with the beginnings of mathematicised physics: rather, its being called into question, almost cast into doubt. This is no longer a matter of description, of a decision of detail, of knowing, for example, whether it is continuous or discontinuous, or if such a beginning should be fixed here, or there: it is a question of its very existence. Can we imagine a history in which the invariants exceed all variation by so much?

If! now proceed on this side of the Epicurean sciences, on this side of the formation of whatever applied or physical science, of some discourse, text or record, in order to be able to prove that I am rigorous or precise, I discover the Greek language as it is, and what in some fashion we call myths. Perhaps upstream, or perhaps around. Now if, in line with the vows of Epicurus', as was Lucretius, we separate the gods from the constitution of natural things, we find the old chaos once again. Chaos is the void, the abyss, the chasm, the infinite gap that the physicists have taken up again as the container of atomic disorder. But, according to a derivation widely said to be false or invented, the term does not come only from the verb 'open' or 'half-open,' but also from the verb 'to pour.' To spread, in the sense of dissipating. Water, wine, light, wind, little pieces of earth. Fluids flow, it rains, in a nappe, along the rivers. To make rain. The air, agitated, circulates. The dry leaves fall. The semantic domain of this false origin (this last word taken in the Leibnizian sense of root) exactly covers the stable model. The pitcher rolls through a deviation from equilibrium, the fluids follow the ramp. The chreode and homeorrhesis, readable transparently through two and a half millen­nia of invariant schemata, may be read anew, together with all their pre­cyphers, on this cbiotic space. What we call our science develops, arranges, combines, works, clarifies, refines, you can run through your entire lexical palette, but nonetheless iterates, repeats and leaves almost unchanged the essential meaning, form and function of the oldest word in the archeology of the world. The history of the sciences, like the statue of salt, freezes and crystalises at the first educated look back, no longer finds Eurydice at the mouth of the infernal chaos. Worse still, the archeology of science, this is what contemporary scholars concern them­selves with, in the newness of the morning. And if nothing has happened since Aristophanes and the Birds? In the beginning was chaos: and love like the ardent vortices of the wind.

All my anxiety arises from the fact that I find a relative stability where

r6r

The Birth of Physics

I expected vanatlon, a series of reversals, of stages or ruptures, of paradigm shifts, and so on. It comes from the fact that we have ideas about history, one or many theories about history, accepted or disputed models for it, but, in each case in the form of frames. It comes from the fact that we think of time in a linear fashion, no doubt because the line, dimensionless, appears to us, incorrectly, to be the opposite of space and as an analogue of time. So history appears to us drawn as a curve, continuous and discontinuous, increasing or decreasing, either straight or in zigzags and so on as much as you like. These mute models are naive, they are of a maximal simplicity, of a limit poverty, while we must account for a formidable complexity, for the strongest multiplicities, for what we rightly call history.

My experience obliges me to change ideas, to transform our theories. I believe that I have brought to light a quasi-invariant of very great duration. In which the variation from the pre-50cratics to our own time is very slight. Like a tectonic plate. Like a very heavy viscosity. The plate advances, there is no question, but its speed is only perceptible through extremely fine measurements. Above it the entire surface layer can be changed drastically. The landscape has pits, faults, folds, plains, valleys, wells and chimneys, solid parts like the earth and fluid parts like at sea. The metaphor here is geophysical, it could be mathematic. In any case, the model is complex. Locally here or locally there, I discover fractures or discontinuities, elsewhere by contrast links and bridges. A tormented surface, but sometimes, beneath, a nearly stable plate. I have already shown, elsewhere and on other occasions, a global model of this kind.3 It is quite complex, compared to the rather weak logical systems used in the philosophy of history. Why should it a logic of resemblance and of difference, of contradiction and identity, even of continuity and discontinuity, in short a naive logic of two choices, such as true/false, even if we set the two theses together so that they resonate through synthesis, ambiguity, paradox or the inexpressible, why should such a logic be able to account for anything at all, when we have known for a long time that it cannot account for the simplest things, the weakest knowledge? Every state of things is already too complex for it. And every elementary system. A fortiori, every even slightly complicated system. A fortiori, the most complex real and conceivable one, like history. A fortiori, if we try to understand how a system is formed.

The model formed is only an approximation. The visible landscape, tormented, complicated, mountains and seas, isles and continents, straits and isthmuses, faults and passages, an interconnected network of

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History

varied terrain, may be explained by the slow advance of relatively stable deep plates, of great consequence, from great distances, oflong duration. There are histories of long periods. The Epicurean or Lucretian or Archimedean block advances and works, this is not in question. It sometimes appears under an unforseen and new fissure. The inclined plane, the descent of balls along this plane, force and acceleration, this is indeed a mechanical revolution. But it is also a cut from the old block. The fall of water between two springs, the cycle which cannot reach closure, the emphasis on heat, the power of fire, this is indeed the thermodynamic revolution, but it is also another cut from the block. The local work of the plate transforms the landscape, even makes it unrecognisable. Unreadable, if we have not discovered the deep plate.

The model is nonetheless spatial. Its contours mirror time, yet it keeps us from thinking time as such. Now we know that it is itself complicated. We recognise several: the irreversible, that of entropy, the fall towards disorder; that, on the other hand, which goes against the current, that of negentropy; the reversible, that of clocks, of the solar system, of our dating, that we have so long taken for that of history, that we have so long thought a vector, yet which was just circular. Now what we are seeking in order to understand history, and not only that of the sciences, is a model that associates, combines and integrates these times. A history that did not take account of it would just be an abstraction; now it almost never takes account of it, and so it is only an abstraction. Now, certainly, whatever exists, molecule, crystal, organism, accom­plishes this performance. It is subject in and of itself to irreversible time, resisting in its negentropic order and its information, and is, in some fashion, of the reversible plunged into the fall towards disorder. It exchanges these times. It is a cluster, a star of time, yes, precisely a vortex of time. From now on I can abandon the metaphor of the earth, the geophysical model. Any object in the world, insofar as it exists by a deviation from equilibrium, and insofar as it resists the tendency to entropy, is a complex clock associating several times, all the times I recognise, and can therefore serve as the model that I am looking for.

And, all at once, things are reversed. I sought a global model to account for a quasi-invariance. But what did this relatively stable plate tell us? It told of irreversible fall, thus the time of entropy. It told of deviation, inclination; the inchoate or the departure of a direction that moves upstream. It told of the rhythm in the rhese. It told of the vortex by which these meanings are linked. It tells of a mediation on time, in fact the one that I have just set down. I no longer need any other. The

The Birth of Physics

best model is the one that moves the plate, the one that is written on its long viscosity. It carries the discursive nature of history. The best model is the thing itself, or the object as it exists, of whose constitution this discourse tells. Every thing is history, this discourse is the precise, faithful, exact philosophy of history. Again, what can it say, what can I read on things themselves?

History is chance, aleatory and stochastic. A background cloud, first, the background noise. Great populations, the parametric multitude surpassing every measurement. History is ergodic. The capricious effect of an operation depending on chance is made regular by the sufficient repetition of this operation. History is the formation of syrrheses, of systems, of orders, originating from this endless cloud. The recognition and description of these emergences. Now, what emerges from the noise may be a signal, and soon a language. The formulation may at times recognise itself as such and then describe itself. Material vortices and identifications maintain their reversible assemblage in and against the irreversible, precipitated in the short, medium, long or very long term into the fall that produced them. Local vortices, small, medium or immense, always transforming themselves or being transformed through their movement upstream and downstream, by intrinsic forces, the energies by which they are made and unmade. The old logic of causality becomes vortical, effects go back to their causes. This model, followed in history, was history itself, as if it bore within its own flanks, buried deep, the complex clocks it needed. What was born on the shores of the Ionian sea was indeed the discourse of things, physics, the formation of the existant in its matter, it was also the strongest thing that can be said about history, and which history, in the old sense of the word, bore blindly. This invariant come down to us through the millennia. It was the concept of history. We had forgotten things and what they said, variable, about the variable.

NOTES

I The forgetting of these things remains so stubborn that Paul Schrecker, towards the end of De rerum originatione translates by 'violent imagination' the fortior perturbatio of the physics of liquids. It was the time where one knew no turbulence other than that in the soul.

2 M Serres, Hermes rv, La distribution, p. n6-24. M Serres, Le systeme de Leibniz et ses modNes mathematiques, P.U.F. paris, 1968, esp. pp. 284-6.

M O RA L I TY

The soul and the descent to the underworld

Third book: the soul is material, composite, therefore it is mortal. Wisdom reminds us, in time and out of time, that we are going to die. What good is anything, to win savage battles, to seize power, to overwhelm one's peers, if we are going to die? To die at the bottom of the slope, whatever the slope may be. And to die without hope of return. What good is eternity, a metemphychosis without memory? We are not immortal, the soul decays as the limbs rot and fall away, scattered. No one, to be sure, goes down into the gulf of Tartarus. The hidden world does not appear. Neither the Acheron, nor the scenes of anguish that the fable tells of there.

The poem revisits them again, one by one, nonetheless. Tityos lies torn apart by the birds, while Tantalus is terrified beneath the rock, Sisyphus works on the rolling stone, the daughters of Danaiis fill their vases. The poem rewrites these figures at the very moment when, as they say, no one believes in them any more. It reinterprets them. In other words the legend has meaning, and our contemporaries are irresponsible to judge it foolish. When the religious man loses his way, he finds another. Thus with Iphigenia: it is a crime to sacrifice her, but it is only the sea and the wind, or the violence of men. The high places of Olympus are rewritten on the cliff, facing the unchained ocean, or in the fortification of the science of the wise. Not elsewhere, but right here and now. We must reread the legend, we must rewrite it as it was written. In bringing the distance between this world and the hidden world back to zero. Leave the gods to their business and come back here, into the practicable space and time of history. And look, read. Sisyphus exists in everyday life, we have Tityos before our eyes, each of us can be Tantalus, and, in our midst, here are the Danaids. Legends: how can we read them? In two explicit ways, and in two implicit ways.

Hell is right here. Torture, punishment, we have no need of cruel gods to invent them, to refine them. So far as I am aware, it is not the devil who roasts prisoners over a slow fire, forges arms and prepares for

The Birth of Physics

war. Or else, I know the devil, I have seen him, he is not so far away, he is not a legend. From now on I believe in the legend, as long as I read it in plain language. Its figures are not set outside of space or outside of time, after death, but here, now; they are the practices of death. They are not produced by it, but, on the contrary, produce it. No, these are not the wan shades of the Acheron, bloodless, impotent, who build the prisons, cast bodies from the heights of the T arpeian rock, pay the torturers, flagellate, fit the shackles. The torturers, with melted pitch, red torches and blades, are here among us. And it is not Sisyphus who pursues people with axes. Or else Sisyphus is everywhere here, in time, wherever I see the fasces. How not to believe it, when our bodies suffer from it? Elsewhere, in the fifth book: power, honour, ambition; empire and royalty, are a path towards the ridge and towards the summit, path of the fall towards the barathron [gulf] of Tartarus (II20-35) . Sisyphus was a historical king. In other words, hell is the struggle for power. Hell is domination. Hell is history.

The interpretation of the old legends is the direct reading of what happens. Mythology displaces history through an immense deviation of space and time, and interpretation brings this deviation back to zero. It is not enough to claim or to see there a sociopolitical interpretation of the legend. It is not enough, although it is true. For it is history written as such. Or, even better, and inversely, legend is in a position to make me read history. How must we read it? As a hell. In which the gods are our masters.

And hell is ourselves. Fearing the gods, sometimes, Tantalus, para­lysed with anxiety without object. The fear of blows, of chance, the fear of destiny, the fear oflife. Those whose principal passion is fear. Jealous, anxious and possessive, Tityos, whom the birds rent. Here, now, not around us, in us. Ungrateful, overwhelmed, but never appeased, Danaid desire without closure, losing the water of time like the seasons. But above all guilty, never not guilty. Even not punished, the soul without pardon, as if self-consciousness, unconscious of what it does, terrified, gave itself up to the goad, tearing itself, flagellating itself, burning itself, punishing itself, without ever enjoying the end of its own torture, and was reborn, guilty, of its morose affliction. Hell, the life of fools, the life of the mad, hell, life sick of itself. Tartarus is not so far off, inter­pretation brings it back, it is the torture that we each inflict on our selves. The shadow is within, the shade accompanies us. The legend gives us this darkness to read. It is not enough only to see a psychological interpretation of the legends here. It is not enough, although it is true.

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For it is we, such as we are, it is psychology, written as such. Or, even better, and inversely, this legend is a code, or cypher for reading. At the very moment when religion is lost, when the fables have lost their mean­ing, legend again takes up its literal sense: the things to read, those we must read, and how to read them. All in all, religious tales give a form to the human sciences in their archaism. And Lucretius saw this. So what do you think we have seen, since the updating of the codes and the cyphers, in the last century, master and slave, Oedipus, Apollo, Dionysus? Bits of legend struck off from the blocks of tales, and chosen for decipherment. The De rerum natura does nothing else. Some bits of hell to decode history, and to read clearly the mental and insane logogriph. Shadowy hell is described at the end of the soul, at the limiting edges of the soul, there where we are unaware that we torture ourselves. In the neigh­bourhood of the frontiers of death, the death instinct.

That is explicit, written in plain letters. This will appear implicit; yet it is written in in a displaced text, and is thus more or less explicit. Read a little farther: this man is moaning because he is afraid; not in the least, perhaps, of death, but of rotting, the body abandoned in some place, he is afraid of being consumed by the flames, or of being torn apart by the beasts, by the birds. He splits in two, he contemplates his sepulchre or his lack of sepulchre. Now, he is mistaken; for it is not more painful to be torn apart by the wild beasts or by the birds than to burn on the pyres, than to be smothered beneath a stone, than to be crushed under the weight of the earth. Here proper names appear behind the common discourse. Tartarus vomits appalling flames: this is the pyre. He who moans at seeing himself torn by the birds is himself Tityos. The tomb­stone that rolls back to close itself and closes the tomb eternally is indeed the stone of Sisyphus. He is called Tantalus, he who fears to be crushed under an enormous mass. The bits of legends, here, reproduce habits and customs relating to the dead. Some burn them, and some bury them, others abandon them in remote places, others leave them for the jaws of wild animals or the beaks of the vultures. There are those who build a coffin of stone, and those who place the corpse directly in the ground. And each group is afraid of the funeral customs of others. To leave the religious and their beliefs consists here in relativising their funeral rites. All that is immaterial, for when death comes, body and soul together become inert, and feeling has disappeared. No longer to believe, no longer to feel, no longer to suffer, ataraxy, and thus to leave these rites to their plurality. The religious person disengaged paints a picture. In a certain sense, he becomes objective. Hence the short-circuit: by the

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application of each text to the other, that of lamentations and that of hells, and prosopopoeias to narratives, we read their parallels and the repetitions of their lines and phrases piece by piece. Mythic tales form a catalogue of rites that is already ethnological, or anthropological. Each proper name corresponds to a society, each tale describes a custom. Here the grave of Sisyphus and the burial of Tantalus, and here the pyres of Tartarus. Now reproduction, representation, as we say, find their condition in the text, namely a distance, a deviation. He who laments speaks, sings and discourses, in his language and his customs, because he does not sufficiently distinguish himself from the cadaver on the earth, because he confounds himself with it and, standing beside himself, lets it mingle with his own sensibility. Words here are of a canonical precision: projection, fiction, contamination. Here is mimesis, exemplary. The text measures, annuls distance or gives birth to it: he does not see that in death there is no one other than himself who, still alive, weeps over his own loss, and shudders to see himself the prey either of the beasts or of the flames. The entire representation is a stage-setting, as are its cultural products. But what is more, the text spins it out it, and Lucretius himself is enveloped in it. Nature discourses, and asks the sated guest to leave the banquet, ifhis pleasures has not been effectively crammed into a pierced vase, pertusum congesta quasi in vas commoda peif/uxere . . . And here metaphysics (of nature) produces its theology, or is produced, behind its back, by it: the Danaids do or do not do this: pertusum congere in vas. I And Tantalus, at least in another version, leaves or does not leave another feast, no doubt the same. From rite to myth, there is projection, contamination and distance. But from the myth to the moralistic metaphor, the reciprocal deviation is the same. Hell is mimesis. And anthropological interpretation is not a bad approach to the formation of mythic figures themselves. We were not so wrong to call them interpreting as much as interpreted. Social pre-sciences.

It is notable that a lacuna in the series of infernal tales was filled by Servius, around line 1012. He seems to have read Ixion. By the wheel of the torture victim, Lucretius, he assures us, reveals the shopkeeper. 2 The application is still faithful, since the exhortations says that life is not the property of anyone, but the usufruct of us all. We are very far from a conventional Euhemerism or a moralizing allegory. From funerary rites to the feast, from the banquet to commercial exchange; anthropology suddenly abounds. Eternity ceases as little as exchange, and torture just as little as the usufruct, since they are both salva rerum substantia. Hell is here again once more, it paints a portrait of the whole of social practices.

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We are tied to the wheel of exchange, to the circulation of goods; they bear us, we can do nothing about it. The feast of immortality is never for us, the stone and death are always there, in the banquet. In the final analysis, hells are a cypher of reading for the judiciary and politics, history and social institutions, and what was once called depth psycho­logy. Portrait of the soul of the person, of groups, of their customs and their projections, admirably placed at the end of a treatise on the soul. When belief (but what is the meaning of this word?) withdraws from religions, there remains the history of religions as archeology of the human sciences. But it is enough.

Why is the cypher so faithful? Why are the models so exact? If the soul is material and formed from tiny atoms, if time is the order of connected things, if servitude, riches and poverty, freedom, war and peace are eventa, these social sciences must be supported by the science of the coniuncta, that is to say by physics. Thus the treatise of the soul, completed by a full portrait of the institutions that bear it and the shadowy edges into which it falls, begins with the atom, and must end with it. And it is so.

Servius continues, on the subject ofIxion, on merchants: negotiatiores qui semper tempestatibus turbinibusque volvuntur. These terp.pests and vortices bring us back to Book II. On the other hand, it is notable, once again, that the myth of the Danaids occurs here for the first time in literature in the Latin language. Lucretius must have noticed its specific character. All at once we leave the feast of these social sciences, rich in interpretation, to return to physics, very poor in interpretation, poor and simple. I mean by this difference that method suffices itself as a model for reading a phenomenon, or that it already needs a quasi­phenomenal figure to do so. And in the first case we are at the mini­mum. And this is the state of physics, in Lucretius' meaning: 'natural' models are naive, close to birth. We must go back to hell.

Tantalus, precisely, is there, without ordinary feast, under the hang­ing rock. First figure: the fall, the fall prevented. That Lucretius brings this figure back here, in the ordinary world and life, and he writes two words: flrs and casus, that is twice chance. Casus is overburdened: it is the fall, decline, death and dying, it is fate and chance, the aleatory unforeseeable, risk and chance, it is a medical case, perhaps that of Tantalus, it is a case of grammar and declination. Thus believing that we have entered into hell, we enter into nature: in the beginning is the fall and in the beginning is chance. We rewrite the first books in images. Second figure: nothing is infinite in space nor lasts eternally in time.

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Tityos could cover the entire earth, the birds which would cut him to pieces, which tear him into bits, would finish their task of dissection some day. And nothing is infinitely divisible. Atomisation, like the division of bodies, is a finite operation. The gallery of paintings continues, the exposition of physics. For Tantalus, the fall of the rock first occurs through ordinary law. But for Sisyphus it takes place on an inclined plane, on the slope of a mountainside. The stone rolls from the summit, seeking the level of the plains. Summo uertice rursum volvitur,3 vertex is a summit, and a vortex as well. The model is put together piece by piece. The rolling rock seeks equilibrium: plani petit aequora campi, where aequor is the plain and the sea.4 Sisyphus is a force that rolls the stone, that rolls back time. Here is the clock, eternal in hell, but temporary in life, of the reversible combined with the irreversible. Exact clock in eternity, but second fall in nature, for Sisyphus ages, weakens, cannot push the stone as high tomorrow as he can today. The high point descends in its turn, and this makes a vertex. This is not said in the text, but is implicit in this displacement of the figure of hell on earth.5 Hence the fourth figure, imported for the first time in Latin literature. We had the thalweg and the extreme slope, but we only had the liquid model by proximity of meaning. Here it is, and directly. The daughters ofDanaiis strove to fill their vases with water. Hence the pitcher, first, the hydraulic. Hence the vase which is not, and by a long shot, a figure of speech, but our body itself and our soul, which vanish through the pores in the face, little atoms which flow out by the channels of the con­nections left by the larger, but the earth itself, basin of the seas. The Danaids pour the soul into the body, rivers into the thalwegs, and oceans on the worlds. They repeat, infernally, genesis. They project their own bodies, they model them. By homeostasis and homeorrhesis. With more fidelity to reality than Sisyphus. By two cycles: that of the vase, where the loss ceaselessly disequilibrates the volume which enters, thus the level; that of water drawn from the reservoir and going back to it by the crumbling cataract from the pores of the vase. Local vortex, global vortex. Shape, simple model, suitable for reading the world, the body and its soul. We understand that Lucretius sought it out on purpose. New water-clock, eternal in hell, but temporary as soon as it is brought back here. For the vase wears out, it erodes, its flaws enlarge, which means, as well, that the daughters grow older and wear out. Then the level goes down and the torture will soon end. The knotted turbulence, local, global, comes undone; it returns to the disorder of the water. This is not stated in the text, but it is implicit in this displacement of the

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shapes of hell on earth. Hence the fifth of these figures, since the precedent, aquatic, lacked vortices. This is Servius' reading of the wheel ofIxion, which fills the gap: tempestatibus turbinibusque volvuntur. From the physical model adopted everything is here, and nothing is lacking, fall, chance and inclination, solids and liquids, turbulence, irreversible and reversible, plus the accounts of the times which change when we go from theory, external, to natural phenomena, temporary. The birds will finish Tityos.

Like Homer before him, like Virgil after, Lucretius describes the descent into the underworld. Iphigenia, after Venus, is at the poem's point of departure, there where the fleet awaits the wind. The sacrifice will not take place, must not take place, so the warriors will not cross the sea. Troy will not be taken or sacked, which means that, if Athens dies, this is not the high struggle against adversaries who come from afar, but of itself and by natural causes, the germs of the plague. Troy is too far, we will not go to Troy. Athens destroys itself for itself. The gods are far away, leave them in peace, to their laughter and their feasting, to their transcendence. Let us remain in our immanence, everything is here and sufficient. We can become gods, in nature and in our nature. Either distance is infinite and travel useless, or distance is nonexistent and travel motionless. Iliad without ships or combat, Odysseus without moving. And thus there is no descent to the underworld. No visit, no initiation, no golden bough, no guide. Either Epicurus the guide shows us stability. The initiate enters, the word says it. Lucretius leaves, he has already returned from hell, it is the exorcism. Or rather it is all of hell which leaves of its own accord, which delivers itself of itself like an inside-out pocket. Lucretius succeeds at once where Orpheus, prince of music, failed in an individual undertaking. All the repression of the shadows is spread out in the sun of knowledge. No travel there, whose distance is nonexistent, still. No golden bough flowering in Epicurus' garden: only the harvests of Aphrodite, the rich meadows, the leafY abodes of the birds. All the old tales speak of this place. Wherever you are, anywhere, on land, at sea or in the towns, you will meet Tantalus, Ixion and the daughters at the wells. Hatred and war, mad power and self-punishment, cultural rites, goods in circulation and the board laden with fruit. But this is still but little, the travels of anthropologists and anamneses are always journeys of initiation. All interpretation is still a shifting. For distance is nonexistent, to Troy, to the place of the gods, that which separates us from hell. De rerem natura: Iliad, Odyssey, or again the Aeneid, in a null journey.

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Don't move, my material soul. Take a thing in your hands, anything at all, from the earth, from the water, a stone or an animal. Read this object from the world. Read it as it was written, in the letters of its atoms. That which is written in its crystalline entrails or in its full, smooth molecules, which roll against each other, is how this thing was born, it is how it was made part of nature. It is the written memory of its formation, of its emergence from chaos. Read its atom-letters, my material soul, read the body's sentence, the text-object, or tablet-things. The thing is the fabric of its genesis. It proclaims itself to be formed by fall and by chance, by cataract and by inclination, by vortices and by interconnection, and here is the woven text. Read here Tantalus as well, this fall of heavy bodies and its retention, Sisyphus and the mountain slope, the Danaids and Ixion, or the turbulent fluids. You will read ancient shapes, not of there, but of the thing here, you will read your soul, my material soul, this jar with leaking staves that loses its water, rolling, disturbed, the irreversible slope of your own death, maintaining the level of your existence for a moment. The way out of the underworld, exorcism, this is genesis, this is nature as it is, as it proceeds, as it makes itself, unmakes itself. Everything that you say of souls, you the psychopomps, and everything that you say about us, the wise men of humanity, is simply written upon this tangible object which you hold in your hand. And which expresses nothing else but you, my material and mortal soul.

Finally, nonexistent distance from the subject to the object, or vice versa. All reading disappears, every legend, and every deviation in general.

The garden and the local

It is time to come to terms with rwo universal principles which seem to be mutually exclusive. In his work On the Nature of the Gods, Cicero translates the Greek term isonomia by aequilibritas, equilibrium. The death of a world is offset by the birth of another, and destruction by a corresponding growth. Decadence may be either delayed or averted, ruin here is contemporaneous with plenitude elsewhere. This uniform­ity, affirmed throughout by Lucretius, never means the eternal return. It is distributed in the universe. We could easily imagine that the poem describes something like a cycle. A world is born here, from the void and the atoms, from chaos, from the cataract: sun and stars, day and night; then the earth produces animals and man, in the midst of the plants and trees, who produces in his turn harvests and laws. To the cacumen

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(extreme point), the summit, Athens, Athens cradle of Epicurus, the purifier, Athens which, under the swarming germs, becomes plague­ridden, and which will die in the purulent spread of bodies, in burning pyres and scattered limbs. Return to dust and return to chaos. The process, then, can begin again. No. If the city is destroyed and if the bodies are returned to atoms, this does not necessarily mean that nature is here reborn. Equilibrium is global and distributed by chance in space and time. In uncertain places, and in unforeseeable times, another beginning takes place, somewhere else. There is no closed cycle on a local level. There are worlds which are scrap-heaps, there are worlds being born. Locally it is aleatory. Globally it is balanced. Take the rivers and seas, for example. 'This is why destructive movements cannot win out for good, nor bury any kind of existence for eternity; any more than the movements that ensure birth and the body's growth could preserve their creations for all eternity. The combat in which these principles have engaged since the beginning of time continues, with mixed success. Now here, now there, the vital energies are victorious, then defeated.' Nunc hie, nunc illic, this is the term used for the fulminating lightning­bolt, for the appearance of the clinamen, the distribution of the aleatory. Here shuddering cries of agony, there the whimpering of the new-born come to light. The sum of the whole, in which nascent nature and gradual death flicker by chance, remains a constant.

This first principle governs the global economy of the universe. The second controls the existence of the local world that has just appeared. Born of the clinamen, this place declines, drifts, it runs down the thalweg of degradation. Everything is always worse than in the good old days, say the wine-grower, the labourer and the shepherd. The sad thing is that they are right. The month of May, muscular strength, and happiness, perhaps, are not what they once were. The fecundity of the earth is at an end, it ceases to bear, like a worn-out female. It once produced rich harvests and dense pastures, without the least need for labour. Now the climate has deteriorated, sterility increased, and everything rushes towards an equilibrium in which nothing is produced spontaneously. Nature seeks dissolution and death. Lucretius introduces this principle emphatically, and he ends his Book II with the reckoning of the floods of loss that do not make up, in an open system, for the floods which enter. For a fabric shot through with veins, for a porous vase, for an atomic conjunction, simplex of paths and ways, the flow, at any instant of time, is only a meagre thread upstream, while it is a wide torrent downstream. It wears out, and loses more than it gains. This asymmetry

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of objects defines, reciprocally, irreversible time. Or rather, it defines it purely and simply, since there is no time without things. This deviation begins a long fall, space and time of fatigue and dilapidation. This dis­crepancy begins a slope, the slope, precisely, of flow, the slope, exactly, of generalised inclination. The clinamen is, stochastically, a fluctuation in the flow. It induces an order through it, an order that tends, in the end, to return to equilibrium: the vortical conjunction returns to chaos. The clinamen, too, is a differential, a flow. And, through the integration of the latter, we obtain the slope defined by this return to equilibrium. The local law of drift, the principle of systems in decline, are rigorously calculable as integrals defined by declination. Things are born of declination, and of its singularity, things die by decline, this journey initiated by declination, integrated from it, beginning with it. This takes account of the difficult bifurcation between destructive vortices and productive vortices, and of this logic, so common in the poem, in which a single operator works towards a thing and, at the same time, towards its opposite. But this especially makes the discourse of the intimist period laughable, where the principle of drift was abandoned in favour of a restless temperament, black and melancholy. An author of reason, of progress, of light, of atheism and science could only describe the decline of things if he were mad. I can't think of an example in which the distinguished spleen or the sad threnodies of the atrabilious could be founded on the precision and the rigour of a physics. Or else the Carnot cycle would be manic-depressive: nonsense or confessions?

It is difficult not to read, in the two principles of isonomy and drift, two principles which have long been familiar to us, the first since the classical age, and the second since the nineteenth century: the first, constancy, and the second, deterioration. This reading is far from being anachronistic. Heraclitus, already, and certainly Aristotle, had formu­lated them in their own terms, before the De rerum natura. It would not be in vain to ask if modern science, I mean that of the post-Renaissance, had not, for its part, repeated the Greeks. In short, we have been working for several decades in the bifurcation opened between two lines, one, shall we say horizontal, and the other, shall we say inclined. Theory has operated in this space at least since Bergson, who was not interested in Lucretius for nothing, in whom he must have seen his flows and fluxes, but above all in whom this model is already drawn, in whom it is drawn from the beginning. Whether theory has gone back to this place is one thing, but now there is a completely different question: whether, m their history and their practices, human aggregations have never

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ceased living, surviving and working there. There is the question of history.

The global description that Lucretius undertakes, at the end of the Book V, is, in its terms, of an unrivalled clarity. What we call the work, the culture and the history of mankind is produced on and by the thalweg of deterioration, is produced along the line of inclination, to compensate for the effects of this drift as a whole, to find once again at least the line of isonomy. Everything happens at first as if there were what we could call a natural history: wear has a meaning and a time, it is complete or generalised declination. On this inclined plane there can be no question of an equilibrium, except for homeorrhetic equilibrium. For example, the earth bears fruit, in its first generosity. But this only lasts for a time, defined by decline both in size and force of the living beings thus engendered. The indigenous inhabitanrs languish and become more and more deficient, until they disappear. You will see no more matrices nourished by subterranean roots, except, perhaps, some cases of residual heterogeneity, some small animals crawling out of the compost after the rains, under the sun. Spontaneous generation can only be a remnant, only a degenerate fossil of original chthonian generation. When exhaustion of mother earth comes, sexual generation takes over, at once a mutation and a new state. AB extreme a mutation as the passage in Empedocles from the time of Friendship to that of Hatred, or, in Plato, in the myth of the Republic, the reversal of the Earth's rotation. The principle of change is written with this word: omnia commutat natura, mutat mundi naturam totius aetas, mutation, and perhaps reversal as well, : vertere cogit. But the modality of change is that of the passage from state to state, or from equilibrium to equilibrium: ex alioque alius status excipere onmia debet, ex alio terram status excipit alter. Now this passage is required by the fact that a state is not a definitive or stable equilibrium, but on the contrary is unstable and temporary. We must understand the text as it is written, the variation of the forms is a function of the connection between status and mutare. From engende­rment by the earth to sexual generation, the invariable is production or reproduction, and life continues. What changes is the solution adopted, chthonian or Aphrodisian. And what operates the change is the principle of deterioration: the earth is exhausted, its power declines and its fecundity decreases. Hence this very simple model: time follows the slope initiated by the clinamen but, when deviation and decrease have lead the state of things too far from invariance and isonomy, a new solution appears, as a compensation for drift. It seeks to regain the

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horizontal line from which declination began. Then the new state drifts in its turn. Our ancestors were hard and robust, and our contemporaries are feeble and spindly.

Nothing here is different from that which has happened, is happening or will happen in the beginning of things themselves. From physics understood as the birth of the world from chaos, to this natural history understood as begetting, evolution and death of living species, the model is preserved completely. We would say today: biology is a physics, or, better: genetics falls back on the genesis of the inert. This would be to judge by our criteria, according to our categories. In fact, there is a physics, and that's all there is to it. There is a nature to things, a process of emergence, which is enough. Its function is universal. Whether we look at atoms, at species, and later, at society, the same model is always at work. That is, at first an equilibrium and, here, there, tomorrow or yesterday, a deviation. Here is isonomy, here is the clinamen, differential deviation, flow and fluctuation, which initiates the slope. By what complex paths will there be a return to equilibrium? It was the same when we considered the laminar cataract of parallel flow, bundle of straight lines, broken, interrupted, place and time uncertain, by minimal declination. Henceforth, the vortex or the turbulence will precisely designate these complex paths of deviation and return to equilibrium, during the time of the existence of conjunctive simplexes? They exist outside of equilibrium, come and go, sooner or later. What we call natural history is a genesis, a nascence in the Latin sense, in which the same process is taken up again. Hence the same bifurcation, within which open systems, receptors, emitters of flow, like the vortices, are either rushed towards disappearance, or subsist and reproduce, protected for a moment by their strength, their speed or their guile. All virtues which allow them temporary escape from the extinction imposed by the drift towards death.

It is so with history. The vagabond life, more ferarum, of the first men, the state of nature, as we will say, is first a state, in other words an �uilibrium. Tough race, with big bones and strong muscles, on a hard earth, with big fruit. The productive spontaneity of which sufficiently equilibrates needs. Sponte sua, satis: what the earth produces of its own pleased these men, to satiety. Equilibrium is evaluated on the scales of exchange: the sun and the rains gave, they were happy with the gift. They wrapped themselves in mother earth just as, at night, they wrapped themselves in branches or foliage. Acorns, water and caverns, to eat, drink, sleep. Their wandering knew no discrepancy between yield

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and need. They carried off the prey that chance offered them, new exchange with happenstance, not in gathering, but in predation. They go to the chance of meetings, like atoms, this new chaos remains in global equilibrium, by this simple algebra of the exchange between what nature offers and their needs or their acceptance.

An exception, nonetheless. As she is at the beginning of the poem, Venus is there, at the beginning of history, among these peoples without history. She conjoins the amorous bodies in the middle of the woods. Women yield to the violence of males, they yield to their own desire, they yield for the price of acorns or pears. The proof that they sometimes lacked food, that they were left to the congruent portion. This history is already a history of men, and women are in the background. They are thrust aside from natural equilibrium, and men feed them in exchange for their favours. Inclination is already there, recumbent at chance in the forests, the inclination of the scales, of injustice and of desire.

Now, in a non-evaluated time, in dispersed places, woods, moors or mountains, catastrophes appear. Animals. The wanderers in these first ages lived like the animals, more ferarum, with the animals. And, all at once, against the animals. They are prey to men, who are their prey. The animal is a part of the human niche, but man is a part of the animal niche. The lion and the boar chase the sleepers from their beds. Disequi­librium appears: the quies, rest, is shattered. Some, half-devoured, scream to Orcus and die writhing, another is buried alive in a living tomb. Death appears in the niche. Predation is no longer only an exchange, it is a competition. The predator becomes the prey. Animals, yes, but plants too. Hemlock grows among the flowers, there is poison amidst beauty. Production creates a discrepancy and need is wrong, ignorant. It pours itself a poison, nonetheless a poison which is so natural that the goats grow fat on it. What is more, scarcity appears, no doubt through variations in climate. Equilibrium is broken here and there, and these gaps launch history.

Let us draw up a list of the discrepancies through which the equilibrium of the niche is disturbed: women, wild beasts, poisonous flora. Object of violent and predatory desire, woman is on the side of the wild animal and the poisonous plant, which can kill in their own right. The natural balance-sheet of satisfaction disiquilibrates itself, the exchange is excessive or insufficient. Everything takes place as if the male were nature, as if the female were already history. We now better under­stand the dangers of love, its illusions and its suffering, in the preceding book. Hatred of women is protohistoric. Venus is there, from the

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beginning, of time and of the text, and the sacrifice of Iphigenia is perpetrated in the primitive woods. A girl killed in exchange for the wind, for the history of arms, a girl famished, then fed, in exchange for sexual generation, for history full stop. The myth of the beginning is translated in real time. History is only violence. For another thing, in fact, the exchange itself, equilibrated in the state of nature, passes to the side of death when it creates a discrepancy. Famine, death by poison or the fangs of animals. The gift becomes injury, our language has always said as much. Now, inclinations, gaps, ruptures in equilibrium, inclination in general, initiate a slope which leads to death.

The deterioration has just begun. Sexual desire, just now, compen­sated, by a new and original solution, for the exhaustion which comes from mother earth, tired of giving birth. Human history will develop by the same model as natural history, but in continuity with it. Woman is at once generative and a medium of exchange, she is the link which joins the two times. Hence the human race builds huts for protection from the wild beasts. When man killed them, he wore their skins. Here is the first trick, like the foxes' trick or the trick of reasoning, detour to escape the deterioration of the niche when it comes. Detour, compensation to return to equilibrium. Huts and skins, new solutions, wrapping himself in branches and foliage. Thus fire, the trick of fire to escape the cold which comes from climatic deterioration, to compensate for thermal disequilibrium, fire come from the canonic clinamen, lightning, or trees leaning on trees which, rubbing their branches together, heat and catch fire. Thus marriage, or its equivalent, works to offset the sequence of liabilities, woman becomes the property of a single man, she concedes everything at once. Will we regain equilibrium even so?

No. The correctives, reparations, countetweights, whatever, most often fall short of their goal of compensation. Life in the hut and before the fire makes the body more sensitive, people no longer sleep out under the stars. Venus in the home saps vigour, children run out of the magnificent fierceness of their fathers. The gaps in the niche are re-equilibrated, but the corrective measures are paid for by a new deviation in what we could call the organism itself. New drift, new diminution, which requires a solution, once again, in order to reestablish lost isonomy. We must begin again. Perhaps improve the hut, until we build palaces. Everything happens as if there were always a defect or a residue, as if the deviation were endlessly reborn in the process of adaptation. The clinamen is always there: if we fill it one place, it reappears elsewhere. Thus we no longer find a statics of equilibrium, but a dynamics of movement.

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Let us draw the level line of equilibrium, or isonomy. At any point, chosen at random, on a line, differential inclination initiates an inclined line. Here is a bifurcation. At any point, once again, of drift or decline, a compensating force tries to deny the deterioration and again achieve the horizontal: effort, solution, to go back to equilibrium. But it does not completely succeed in achieving the level line. The climate worsens, it is cold: decline. People build huts, men wear skins: compensation. Then the body becomes sensitive to the cold: new decline. Deterioration is the cause of compensation and it is its effect. Compensation is the effect of decline, and it is its cause. The earth is exhausted, and the autochthonous generation disappears: drift; sexual generation replaces it: compensation; but the family diminishes the force and the vigour of men: drift. Drift produces compensation and compensation produces drift. Desire is satisfied by the fruits of the earth; here and now, this said at random, desire can no longer be satisfied: suddenly it appears. It gives rise to solutions: fire, artifacts. It is the cause or driving force for the return to self-sufficiency, but this compensation itself brings about a deviation, creates a new disequilibrium, a rupture which brings about another desire. Desire is the effect of deterioration and it is the cause; or deterioration is the cause of desire and it is the effect. Whether the concept used be objective or subjective, an almost cyclic process takes place, in which it is, by turns, both cause and effect, producer and production, mover and moved. It is not circular, since the solution is always original and new, since discrep­ancy is always there, since inclination always reappears, since time and drift are the foundations for the drive. It is not circular, otherwise equilibrium would be reestablished, we would be victorious over drift, there would be no history. It is circular, nonetheless, for the entirety of the processes of causality. A circulation, reciprocal cause/effect, moves down the slope of decline, and enlarges its options of compensation and fall; it describes a spiral ceaselessly in deviation from itself, a turbination which, by advancing, always seeks and loses equilibrium. Here, precisely delineated, is the vortical solution: it is rigorously isomorphic to natural genesis beginning from chaos. History is indeed a physics, quod erat demonstrandum.

Solution of a rare power, in its terms and its results. Many inventions, many discoveries are explicit or implicit in it. History does without metaphysics. Without gods, without God, without the Holy Ghost, without first or final authority. It emerges from physics, it has the same form as it does. From the genesis of things to the genealogy of living beings and in the time of human groups, the process of development is

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retained, its dynamics is a structurally stable invariant. No possible separation between the matter of physics, that of natural history and that of plain history. Inclination, instability, authority as such is its driving force without a primary force. Every form, every order produces itself or reproduces itself, mutations and variations, by temporarily stable/ unstable structures of self-regulation. Lucretius discovers the processes in circular or semi-circular causality. He discovers that there are two times, that of equilibrium and that of deterioration, that history, like nature, goes about its business by associating them. As a result he discovers a third, that which creates a tension between the second and the first. History, like nature, is an interchange between three times. He discovers the usefulness of random fluctuation, and of the deviation from equilibrium: one time overflows another, is overflowed by it. Lucretius discovers the growth of complexity when deviation reappears during the cycles of return to equilibrium. He discovers this risk, this vertiginous instability, this flight ahead, in which the obligatory risk, necessary, natural, in which the risk taken, not necessary or not natural, tries to catch itself, but pays for this catching-up by an even more verti­ginous instability. I say vertiginous on purpose: disturbance, vortex. He discovers that only the insufficient is productive. But that production restores insufficiency. That labour, agriculture, navigation and the arts compensate for the effect· of deterioration, but accentuates its impact. That decline requires a dynamic adaptation, but that the latter reinforces the decline. Spiral in three times: the reversible time of isonomy, the irreversible time of the drift, the productive time of compensation. Spiral initiated by deviation. Snowball hurtling down Sisyphus' thalweg, self-productive of growth. History to death, production to death, desire for death. To live from death, to die to life. Labour of life, labour of death. Life of desire, desire for death.

As a result, is this progress? Yes, no doubt. The spiral grows in the opening of the bifurcation, and the vortex amplifies its paths, which retrace their steps back to isonomy. Up to a local high point, cacumen, summit, crest, Athens, here and now, mother of the arts, of Epicurus and of laws. But certainly not. The quasi-cyclical process leads the City back to the low point, plague and destruction. To the lowest point, past the optimum place, relative. He who attains the summit of honours, of riches and power, is soon hurled into Tartarus by the thunderbolt, the clinamen again, or envy, that vice of deviation, that ill of comparison, impossible to counteract. But especially, never on these highly complex roads, equilibrium will never come again: no matter how highly placed

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the high point, citadel, beauty, fortune, it is always lower than the level of isonomy. Every progress, globally, remains a loss.

The vortical solution, evaluated, described in the bifurcation opened between equilibrium and drift is a quasi-periodic solution. In the vicinity of the original clinamen the deviation is very small, and com­pensation minimum. The hut is protection enough from the cold or the beasts. Sufficient in the same way: gestures, for the child who cannot speak, a few differentiated cries, for animals in rut or angry, nascent words, for our needs. Gestures, cries and embryonated voices in nature, history remains a physics. We stammer out our first words like the bird leaves the nest with its first feathers. All efforts, in any case, to reduce the deviation: incapacities, needs or desires. Throughout time, the time of drift, the bifurcation widens. The forces necessary for the return to equilibrium increase. Hence the flight ahead. For defence and refuge we will need acropolises, for the group to subsist, kings, fields and flocks. Hence the evaluation of this time by much more powerful splendour: the most beautiful, the most prestigious, the most powerful, the most wealthy. Comparison leads to rage, order arrives to join a structure of order. The general dynamics leads from minimal inclination to maximal effort. The feedback spiral increases to the high point, the summits of the citadels, of royalty, of fortune, even of beauty, it falls fatally to the murder of the kings. Thus progress in the art of war turns against its authors: boars, lions or elephants, set on the enemy, turn, infuriated, trample or devour their masters. The strongest becomes the weakest. The weakest overthrows the one whom he has too much feared, in the end. The structure of order flies ahead, the strongest is never strong enough. The relation of order is never in equilibrium, it ceaselessly sUr­passes itself: it is the track of the spiral on any of its diameters. It is a singular case, just like the disequilibrated series of exchanges, in the vortical model of history. Necessary dynamic of power and violence: the most powerful is put to death, yesterday's vanquished is the victor, the excellent Town is destroyed by the epidemic. Hence the extreme degree of decomposition and unrest.

We must understand two things here. One is quantitative and the other quantifiable. That historical turbulence is a disturbance, that it is a vortex. In the first case, morality appears: ataraxy is the absence of dis­turbance. Withdraw from the quest for honour, it always leads to death and cruelty. According to the precepts laid down by Epicurean ethics. Why is it built upon a physics, why does it require a science? Very simply because physics is vortical and because it is a science of

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disturbance. Because this exact understanding of nature and history teaches valuable lessons. Henceforth disturbance is vortex and the qualitative quantifiable. Once again, morality is a well-understood physics. Of it alone we can ask the question: what is this disturbance, from which the thought of pleasure wants to tear itself away? It is the vortex itself. Which hurtles down the slope of decline as it increases. In which desire engenders desire by interposed compensation, in which deterioration is produced of its own accord by the interposed quest for equilibrium. Hedone is torn from the dine. Because if you enter into this dynamic of growth and flight ahead, you will diminish as you grow, you will loose your force as you gain power, you will kill yourself by putting someone else to the sword. Disturbance cannot be localised only at the low point of the slope, at the lowest points of this family of slopes, at this extreme degree of decomposition: it is, precisely, the whole of the processes, including the high points, fortune, royalty, power, prestige, beauty, jealousy. Disturbance is global turbulence, and the growth and the relationship to order to which it leads. Disturbance is disequilibrium which increases on its own, frenetically compensated for, counter­balanced to exacerbation. This is Sisyphus' hell. Sisyphus is right here, the happy and the ambitious of this world delivered to competition reproduce him before our eyes, produce him, rather. Disturbance is the exhausting quest for what is better, for more, along the relationship of order, which necessarily returns to the worst, to less, and with an addition, the addition which in its turn demands an additional effort. Disturbance is the local disequilibrium of the vortex itself, the global disequilibrium on the slope upon which its decline rolls. Physics dictates morality, it clearly, precisely and faithfully indicates the conduct possible. Thus the term ataraxy speaks for itself.

Limpid wisdom, simple, readable without thought about things, the world, the history which ensues. To live according to nature, nature understood as it is written, as birth, the nascent state. Not to let oneself go too far down the slope of drift, to remain in close proximity to the angle of opening in which the bifurcation is minimum, just next to the clinamen, where nature is born. The vortex here has hardly begun, no excessive deviation has increased it.

This is quantifiable and may be evaluated. In this place it is only a matter of a little. To live on little, to desire little, this little is never lacking. Equilibrium, or quasi-equilibrium, of the very first men, sponte sua, satis. Nature always has enough water to quench thirst, enough beans and figs for hunger, enough meadows for sleeping. Men are not

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lacking for women, nor women for men. Vivere parce aequo animo, to live with restraint and a steady soul. The equation is paradoxical, it operates a slight deviation. Soul level and horizontal, balanced scales, at peace. Nonetheless, keep saving, defer, be frugal. To the right, on the side of the aequo animo, this is the zero of equilibrium, it is the equanimity without flaw, without worry: repose. To the left, on the side of the vivere parce, here is the small amount of parsimony. How can this part, small but necessary, be reduced to zero? This is the whole paradox of morality, summed up in a strange equation. All the work of physics boils down to this as well: Archimidean philosophy of deviation.

No doubt the scales are never level. Without their deviation nature would be yet unborn, without this deviation we would not exist, without it the soul would never be moved. A very small deviation and nature is born, with a very small deviation satisfaction is again accessible. This small amount of morality is in the finite proximity of the minimum of declination. Parvum: a cotula of a little wine, or a little jar of cheese to make a great feast. The equation here operates another deviation. Not between a little and nothing, but between the great and the small: difference maintained. In the absence of wine, water is enough, what­ever's there. Whatever's there is at once the nearest and what turns up. Indefintie in time and place. Just a little and no more: nec plus quam minimum, this is the definition of the clinamen. Tantum paulum: as little as it would be possible to say, still, that movement has occurred. As little as it would be possible to say, still, that my desire may find itself satisfied. This little of our desires, this little of things themselves suited to satisfY, or more or less satisfY, the first, here is, in the apperceptive finite, inclination itself, that of our will, of our freedom, of our pleasure. At its root, at its birth, the movement of the soul is differential, it is a flow, a fluctuation, the same deviation in equilibrium as that which locally changes the cataract of the atoms. Life according to nature remains in proximity to the birth of things, to their changed movement: the wise man inhabits this minimal deviation, this space between little and nothing, the angle between equilibrium and declination. Place of the necessary and of the natural. Beyond there is only vain and superfluous growth: great ills and great remedies. Everything then goes back to a calculus of limits, to an evaluation of limits, and this, one more time, is Archimedean.

The minimum, the little, the near and the proximate. Nature is birth at the differential place of declination: to live there, according to nature. To avoid history and politics, ceaselessly enlarged vortex, to turn away from growth. To be content with the limited. To make one's nest in

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proximity to the inchoate, little garden where figs grow. Not far from the little and from zero, equilibrium, horizontal isonomy are within reach. To reflect on the disparities of Archimedes in which the limit value is framed with values which exceed it by little, either by excess, or by lack. Everything follows from this, from these local reasonings. The soul is tranquil in these singular places in which deviations are not large, in which it is only a question of the proximate. It runs the least risk possible, it does not venture far in the instability in which it would exhaust itself in compensation. It holds itself on the slope, it does not begin the spiral of resumptive additions. It inhabits the limit-places, the singularities.

Quantification is numerical, it is spatial, it is generalised. No more than little, no more than the minimum. This is assessed on scales which hardly deflect, just near equilibrium; this is described by the small angle of declination; this is calculated as a limit. The same proposition always comes back. Here is the example of death: it is also a place of singularity, ethics imagines it by a calculation of limits, as in a nonexistent proximity, like a particular and closed event. To its left it has not yet occurred, and I cannot fear it, I cannot suffer from it. To its right I no longer exist, and I am not here to suffer any pain. Here it is framed. Go forward forever, from the left and the right, towards its singular place, the reasoning is repeated, no matter how close to it you are. At the limit, at the limits of the partitions of time both before and after, it is no more than a hole in the line, a black well without any relationship either with one side or the other, in which affirmation and negation both disappear. I am, I am not; death does not exist, it does. In this place without parts all proximity has disappeared. This is rupture. Hence death does not concern me. But observe that immediately this limited place, without any proximity, without any membership, is exactly the singularity contrary to the one in which the wise man lives. The latter inhabits the open place in which the differential vector of declination delineates a vicinity, singularity of the inchoative in which nature is born. Death, defined rigorously by a rupture is, to the contrary, like an atom without a clinamen. Place without parts or proximity from which all inclination has disappeared. It is only self-evident or banal that death is the mirror­image of birth. It is already demonstrable that it is outside of nature. It may already be proved that the wise man who lives in accord with nature is not concerned with death. But the very technique of proof reveals how every organon of morality imposes itself, beginning with simple and easy rules already at work within physics. Nature is controlled by laws, the

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wise man in accordance with nature controls himself by these same laws. If he understands physics, he conducts himself morally. Now physics reveals how nature is born in local singularities in which atoms are inflected by declination. Here it is a calculation oflimits. Morality is the same calculation. Death is a limit, it is the inverse singularity of the place of birth in which it is advisable to live in order to live in tranquillity.

The happy life, death reduced to nothing, are questions of proximity. The wise man reflects upon them by means of local reasoning, local mathematics. The idea that guides him is very simple: to delimit a little space, a little sphere around a given point. What happens in this little domain or this little department? How can we imagine its limits? Every­thing finally comes down to this: the quantitative little, the scales which oscillate slightly around their balance point, the idea of a minimum or of tantum paulum, the calculation and the description of boundaries, the atom and declination. The interval which vanishes near the point of death is linear, it intercepts a small segment on the line of time; the deviation of the scales makes a sort of double fan-shape of this interval, a double circular sector around the same point; the clinamen, little vector around the atom, makes a solid angle, it delimits a sphere which this angle intersects. Intervals, deviations, limits, are the specific events of this small volume. Everything that is at play here may be expressed beginning from this local singularity. Now it was planned, calculated, described and applied in and by the work of Archimedes, in his world, by his science. We come back to the same place.

The physics of fluctuation thus presents local solutions: limits, singu­larities, flows, deviations, minima, maxima. It is a physics of the plurality of worlds, and of their temporary existence. Reasoning at work in the universal, global mathematics, are only power, disturbance and cruelty. This reasoning is exacting and futile, it covers the earth with the dead and spreads like the plague. Morality presents local solutions, the same. The ethics of the Garden, it will come as no surprise, is essentially an ethics of the local. The Garden is a place, it is a small place, in which we are concerned with the small and the near, of boundaries and proximity, where everything necessary is within reach, in which everything natural flourishes and is born. You can deduce all the rules, all the precepts and counsels, theoretically, beginning from the sphere, and practically starting from the Garden, its prosopopoeia. So do not cross the external limits of the place, avoid any prolongment.

Pleasure is in intensity, not in duration, the prolongment of time. Stay here safe from attack, remove yourself, remain unnoticed. What

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good is it to go aboard ship, sail the seas, extend the space of travel? There, indeed, are presters, turbulence and storms. No prolongment in space or time. Hence movement: pleasure lies not at all in movement, as the Cyrenaics held, it lies in the closest proximity to repose. Statics, its small fluctuations, equilibrium and the small deviation, are within the sphere, these are the events of this small place. Similarly, and vice versa, great pain does not last: if pain is sharp it is short, if it is long it is weak, it does not attain our tranquillity. The good lies in proximity, and evil in extension: what is necessary is close by, what lies in the distance is not a necessity, but difficult and futile. The small amount, which is natural and necessary together, is easy to procure for oneself, it may be found within reach. Thus friends, neighbours and relations: our fellow men. Caution is the art of limits, delimitation from extension, it does not exceed the boundaries of the sufficient area. And hence at the internal limit the body, the body in the middle of the sphere or the body in the middle of the garden, the body, envelope of the soul. The dwelling-place is the body, surrounded by this little space, either the soul surrounded by its two envelopes, or again the soul of the soul with triple boundaries. Autarchy lies within this compartment. What astonishing nonsense to compare the atom to the individual: for the atom without clinamen is death pure and simple, the return to chaos, or the chaos which precedes birth. The natural individual, living and feeling, is plunged into a place, he is surrounded by this field. He is atom plus clinamen, vector which, in every direction of space, describes a sphere, he is an atom plus the movements of the soul, he is atom plus liberty, will, pleasure. He is housed in the Garden, body and soul. He is not a being in the world, useless extension, he is an existent in his autarchic sphere. Pleasure regulates his existence, provided that it ceaselessly restores the limitless to limit. The sphere is a limit cycle beyond which the spiral of the supplementary is formed, that is to say disturbance and the vortex. Of which a particular event is the relationship of the order of the biggest and of the superior, which never ceases until catastrophic death, balance thrown into turmoil by large deviations.

The Stoic sage is, on the contrary, a citizen of the world. He sees and imagines extensions. His physics is global, as is his mathematics. Between the Garden and the Stoa the difference is, from the very begin­ning, that of the local and the global. The garden is a finite and defined place, the stoa is open on the world, passageway for every extension. Here mathematics is global, because it is serial. Series, series of series invade and cover totality, forming tissues of the system, of the universe,

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of necessity. In any place the series cut themselves into a star. This place then conspires with every place. This proposition is invariable. It remains true for systematic disquisition, the physics of the world, moral conduct. There is always a serial path, at least for any prolongment. The difference, first of all, between the local and the global, between the full and the empty. The effect does not fade away. The world is without any gap or local singularity that might form an obstacle or barrier to the conspiracy, the universe is open. A drop of wine, a bowl of wine, dis­solves in the sea, spreads everywhere and merges, engendering a continu­ous series, decreasing without end. It is a total part of the sea. A mathematics, physics and morality of analytic prolongment. Thus the difference, which may hold in a very simple proposition, yet be of a formidable importance: for the stoa, open, passage from the local to the global is always certain; for the garden, closed, the inference from the local to the global is always problematic. It always raises questions to be resolved piecemeal. Morals are then simple and clear: the Stoic sage lives in the midst of his family, society, the homeland and politics, responsible for the whole as well as the part, an integral sage in the precise meaning of the word; on the other hand he is autarchic, surrounded by a few friends, secluded in the garden from the noise spilling over from the forum, in a serene retreat, a dissident, separated, autonomous and differential sage. No system, no universe, no totality, concordance or conspiracy; all integral concepts. No tension or fusion; local attitudes resistant to the global. The only infinite is the void, and the seeds of the real are distributed atomically. Everything follows from the question: what are prolongments?

So if you cut short prolongments, if you attempt to reduce them, then the discourse of piety follows too. Religion is the same word as religare, to bind: to attach, to connect. Religion connects the discon­nected, this is the first definition of myth. 6 The Epicurean sage unbinds the connected, he unbinds the priest more than he unbinds himself, he unfastens the shackles, knots and connections. It is in this way that in space and the world atomism is profoundly irreligious: principles separ­ated by the void. But if religion disconnects the connected, then physics is the equivalent of religion. Then the atom is indeed the same word as templum, the temple, distinction of a local variety within the global space. And so we have the apparent paradox of an invocation to Venus immediately followed by a wholehearted condemnation of the death of Iphigenia. As if there were still a true piety: one that left the Gods happy in their Olympic isolation, in their space without prolongment, and without providence in their own Garden. We are saved from the gods,

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we are untied from them. Space is not in the least homogenous enough for a connection, for a prolongment between their space and ours to be possible. Untied, separated, we are ourselves gods in our allotted isolation. The infinite escapes, world by world, to totalising causes, history escapes, place by place, from a glance or global force. Space is a distribu­tion of gardens. Atomism.

It is not very interesting to portray two schools of wisdom, for these parallel lives end up, sooner or later, being conventional. Behind these portraits, frames and representations, two schools of thought conflict, whose contrast and asymmetry concern us. Here the decision is serious and the stakes are high. Either the world is a universe, or it is not. Either knowledge is a system, the Stoics used this word for the first philo­sophical system, or it is only plurality. Space in general is homogeneous and integrated, or it remains scattered, flowering and furnished with local singularities. Everything happens by necessity, or everything happens by chance. Two mathematics regulate these two states of things: one, global and prolonged; the other, of singular varieties.

The question arises once again, it arises today. Is a passage always possible from the local to the global1 This question is prejudicial, but it remains buried. When modern science appeared or reappeared at the dawn of the classical era, everything happened as if this question had already been resolved, and resolved in the affirmative. You will always find long chains of reasoning to secure these prolongments, or a system with a serial model, a Leibnizian network, or else an action from a distance, or else a unitary law as valid for the planet Jupiter and its little province as for the entire solar system. Seventeenth-century mathe­matics is essentially a mathematics of series, and physics can only emerge as a science by integral calculation, by a calculation which is indeed based upon the affirmative answer to the prejudicial question. Everywhere it seems to be taken for granted, although no one has ever thematised it as such, that one can always go from the local to the global. Reason, informed reasoning and the order of reasoning, masters, dominators of the world, are operators of globalisation or integration, they prolong the totality of their provincial empire. So: is it possible, is it always possible?

Is it possible? That there is a conditional interrogation where some­thing like a transcendental objective is always in play and always recovered. No reasoning that is not totalising: thereby science in general, the resurgence of systems and appetite for universality. Space, time, world and history are always sufficiently homogeneous, are always sufficiently isotropic always to ensure the passage from the local to the

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global. How do you know? Have you confirmed it? Who told you? God, no doubt.

Lucretius is strangely close to us. The garden as a place is a real ques­tion. True for space, time, world, history. Here and now are a singular locality. It is not entirely certain that I could easily leave this place, that I could plot a simple journey in the space into which it seems to be prolonged, nor that I could return once the journey has come full circle: perhaps this loop, this encyclopaedia, this history and this universe are just phantasies of reason. Now for four centuries Western reason has assured me that I can. Clearly God must have said so.

And if it were not possible? If it were only possible under this or that condition, to be met on each occasion? Then the long journey would no longer be simple or easy, we would have neither the series or the network. Method would be a road with obstacles and disasters. This would be a labour always to be begun again to link spaces, to reconnect times. And the encyclopaedia, the global form of knowledge, imagined by Leibniz, inventor of integral calculus, carried out by d'Alembert, practising this same calculus, and imagined by Hegel, reader of Lagrange, the global form of knowledge by integration through a cycle of singular localities, this encyclopaedia would not happen of its own accord. A cycle to be rethought, perhaps to untangle, to re-tangle here and there, in short to call into question and perhaps to leave pieces. Disquieting upheaval in the old kingdom of philosophy: long journies and their prolongment, methods and cycles, have their local breaks. The Garden returns, in which the Stoa was the master. Local solutions, where the global was reason. Here and now are not necessarily bearers, by dialec­tical prolongment, of all the initial conditions of the mind's complete voyage. History is no longer a unitary discourse of assembly, of remembrance. It ends this day, in the plague at Athens, and takes up again elsewhere, at some indefinite time and place, where inclination appears, a solid angle in the sphere of proximity. Another reason is in the process of being born, one delineated by Lucretius.

Now the wisdom of the Garden seems to already intuit that every prolongment has a relation to violence. Agamemnon and his soldiers sought to pass the Pontus, and killed here in order to slaughter there. As if they sought a passage, as a portico, through which to escape the becalmed area. The wind, here, was calm, and did not raise the swell. No disturbance nor vortex on the plain of the seas. Agamemnon sought the open sea, from which it is sweet to stand apart. Already, and well before sacrificing his daughter, he summoned the Greek captains, each from his

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own insula. Ulysses had left Ithaca, and each captain his city. Agamem­non summed these prolongments, centralising all these departures from the gardens. This dynamic does not stop, even the Hellespont cannot stop it. Epicureanism seeks to bring Ulysses back to his island, to dissolve the prolongments. All things being equal, Ulysses, facing Agamemnon's tragedy, is in the same position as Montesquieu facing the centralised monarchy. Go back to your city before sacrificing Iphigenia; the Trojan War, the plague at Athens, can be, must be avoided; why this long periplum of the Iliad and the Odyssey in order to return in the end to the palace of Telemachus and Penelope, to a hall strewn with corpses? Cineas' wisdom in asking Pyrrhus why so many voyages, conquests and cadavers, before going home, when he could stay there now. Iphigenia saved, the epic journey comes to nothing. Violence is first and foremost a prolongment, it opens an endless chain that tends to invade the totality. Stay in Bordeaux, in Toulouse or elsewhere, instead of bearing your sword to Versailles, where the Sun King will assemble them to cross the mountains, and perpetuate prolongment. A short-circuit strikes the Hegelian cycle: here and now find the immediacy of knowledge without the voyage-balloon in which negatives accumulate. Turbulent voyage of growth and decrease, savage turbulence that will carry its ravaging disturbance everywhere. Culture is the continuation of barbarity by other means. The plague is an exact model for this violent prolongment: its epidemic is transmitted, multiplies and kills, to the point of taking over the whole city, peopling the crossroads with pyres. The garden is first of all defensive, it is closed to the plague, a high place fortified by science against floods and pandemic. There we recount, among a few rare friends, behind closed doors, stories of pleasure in which Venus will win out. Venus born over the disturbance of the waves. The Garden is an island, a summit, a shelter. And if every king had stayed in his city, within the shelter of his walls, the Trojan war would not have taken place.

The whole question is indeed to find out if the converse of this reflection is still true. Violence is, certainly, a prolongment. But is every prolongment, of whatever kind, violence? The answer is not in the text, but everything seems written as if it were affirmative. Epicurean secess­ion, dissidence and withdrawal are the practices of peace, of serenity, withdrawn, as much of possible, from violence and death. That is to say, or almost, that away from the local, from the garden, the battle rages and the plague covers the forum with corpses. Now, and this is the point, there is a certain form of reason that, in our culture, demands and prac­tices these prolongment. Knowledge is an odyssey. Absolute knowledge

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arises after the cycle. There is thus a chance that this reason itself might demand violence and death. Can we run the risk of reason, of this reason and this knowledge: this is the question. Should we run the risk of science? The answer here is negative. The Epicureans criticised science as we would today. Not all science, not science as such, but that science or that reasoning which attracts or follows force, mastery and domination on its paths of totalisation. In this way they sought another science and another reason, finalised by pleasure and happiness. We, people of the totalitarian age of the universal and the university, have paid dearly to learn what the Epicureans were not wrong to fear. To learn from our history that the science of long chains, of action at a distance and of networked systems is contemporary to the constitution of the great centralised States in the classical age. To learn that encyclopaedias are also imperialisms. The despot is he for whom the local is erased before the global. It is thus that he writes History, through rational prolong­ments.

There are no solutions, reasons or sciences, other than the local. This wisdom of the Garden, wisdom of my father Montaigne, this wisdom of the earth is then ours. It is not ignorant of science, you have to have written or thought about thirty or more books on Physics to arrive there, one day. And we will no longer have confidence in reason until we imagine some new reason.

Once upon a time there was a golden age. Where and when, I do not know. After it, they say, came the Bronze Age and the Iron Age. Myths or history, always metal. Metal or stone: polished, shaped, neolithic or palaeolithic. We can only write of solids. Why? Because of their order and their relations. Coherence, rigour and rigidity, the local crystalline molecule is more or less the same here as there. It prolongs its identity, its monotony, under strong constraint. Thus we write history in which the local goes back to the global under the repetition of a homogenous law. The discourse is no different than the hard matter upon which it is written. A mechanics of solid systems.

Here are the waters, cataracts and flows, rivers and vortices, of Epicurean physics. Here the local rolls its weak viscosity without much affecting the global volume. Not far from its proximity, constraints evaporate. There are, as they say, many degrees of freedom. The vortex forms and fades away within uncertainty, but elsewhere the plane is tranquil, one way or another. Space seeded with circumstances.

Invent liquid history and the ages of water. October I97o-June 1977

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NOTES

III, 1009. 2 Servius. Adds lines on Lucretius: per rotam autem ostendit negotiatores, qui semper

tempestibus turbinibusque volvuntur (Note to Aeneid vi 596, pp. 992-3). The lines suggest that Lucretius had included a verse or verses about Ixion and his wheel [cE Bailey II, U62-3l .

3 III, 100r. 4 The two lines cited here by Serres are drawn from the close of a passage

describing the endless labours of Sisyphus that runs: 'To strive for this profitless and never-granted prize, and in striving toil and moil incessantly, this truly is to push a boulder laboriously up a steep hill, only to see it, once the top is reached, rolling and bounding down again to the flat levels of the plain.' III, 998-1002. M Serres, Hermes IV La distribution, pp. -219-25, where these mythical figures are discussed in detail.

6 Hermes IV; La distribution, pp. 200-9.

INDEX

Achilles 65 Agamemnon 189 Air 32, 40, 57, 58, 63, 82, w5, IIO, 151,

156 angle (minimum) 6, 7 9, W-12, 24,

32, 45, 58, 73, w3, W9-III, 124, 129, 184, 185, 189

See also contingency, angle of antinomy 43, 143 Aphrodite 22, 24, 50, 90, 99, 107,

108, III, II4, II6, II9, 123, 131, 138, 155, 156, 175

Apollonius 15 Archimedes 5, w, 14-19, 21, 23, 38,

43, 80, 101-104, 106, II2, II4, 116, 135, 141, 142, 158, 183-185

Aristotle 25, 35, 41, 47, 67, 147, 174 ataraxy 28, 37, 53, 92, w6, W7, 127,

181, 182 Athens 24, 34, 68, 84, w8, II2, 117,

II8, 130, 131, 133, 134, 138, 139, 173, 180, 189, 190

atom passim See also letter-atom

atomism 4, 7, II, 13, 15, 36, 51, 56, 85, 86, 101, W3, 122, 123, 128, 136, 137, 141, 154, 187

Barrow (1.) 19 Bergson (H.) 37, 128, 174 Bernoulli O. & D .) 80, 84 bifurcation, 145, 147, 155, 174, 176,

179, 181, 182 bodies 3-5, 16, 22, 23, 32, 35, 41, 43,

193

48, 49, 76, 80, 85, 89, 99, 109, IIO, II2, I2I-127, 137, 141, 149, 150, 155, 177, 186

Boltzmann (1. E.) 148, 159 Bourbaki (N.) 17 brownian motion 31, 130, 137 Bruno (G.) 14

calculus 4, 7, II, 10, 14, 17, 18, 25, 31, 50, W2, 136, 138, 145-149, 154, 183, 189

Cantor (G.) 20 Carnot (S.) 37, 40, 59, 160, 174 cataract 4-6, 50, 75, 76-78, 99, II2,

128, 130, 172, 176, 183, 191 cause 3, II, 72, 97, w9, 149, 179, 188 chance 6, II, 54, 68, 71, 76, 126, 137,

139, 149, 153, 156, 164, 173, 177, 191

channel 40, 49, 60, 69, 87 chaos 27, 30, 31, 69, 87, 133, 135-138,

144-146, 148, 155, 156, 161, 172, 174, 176, 177, 179, 186

Chaos-cloud 27, 31, 87, 137, 138 chreode 37, 38, 40, 129, 137, 138, 153 clepsydra II, 151 clinamen passim closure, of science 68, 70, 78 code/coding 140-143, 147-151 communication 49, 70, 89, 95, w5,

w6, II7, 123, 132 Comte (A.) 36, 85, 96, 159 cone (conoid) w, 15, 23, 28, 76, 78,

WI, I02, 153, 159

Index

coniuncta 121-124, 126, 129 contingency 10 contingency (angle of) 10, 17, 103, 129 contract/pact 24, 49, 51, 86, 91, II3-

II8, 123, 126, 128, 130, 132, 150 Copernicus 25 Cournot 126 cypher 140, 142, 169

da Vinci, Leonardo 5, 25, 84, 159 declination passim Democritus 4, 6, 10, 14, 25, 79, 91,

101-104, 106, 112, 154 Descartes (R.) 25, 35, 43, 109, II4, 131,

140 deviation passim esp. 19-25 differential 4, 10, 17, 24, 32, 50, 77,

79, 103, 123, 126, 146, 174, 176, 179, 183

dine (dinos) 6, 31, 91, 154 Diogenes 10, II division 17, 27, 68, 120

Earth 28, 56, 63-65, n 74, 81, 85, 128, 172-176, 178, 191

effect 97, 149, 179, 180, 187 eidolon 104-107 eidos 102, 104-106 entropy 37, 63, 76, 79, 125, 128, 138,

149 Epicurus 6, II, 12-14, 17, 25, 38, 52,

57, 70, 104, 106, IIl-II4, II8-121, 125, 127, 131, 133, 173, 180, 187, 190, 191

equilibrium/ disequilibrium passim Eratosthenes 101 Eros 69, 108 Euclid II, 15, 24, 29, 46, 51 Euler (L.) 41, 79 exchange 57, 59, 69, 76, 138, 169, 177,

178

fall (fa chute) passim

Fire 4, 27, 30, 56, 60, 63-65, 81, 82, 98, 178

fluid (mechanics) II, 82, 84, 89, 90, 93, 99, IIO, II2, II6, 121, 122, 125, 127, 129, 160

flux 23, 39, 41, 43, 46, 52, 70, 124-125, 129, 154

fledera fati 109, III, II3, II8 fledera naturae IIO, III, II3, II8, II9,

123, 150 Fourier G.) 44, 59, 79, 148

Frontinus 5, 135

Galileo (G.) 3, 5, 25, 33-36, 80, 140, 159

Gauss (K. F.) 14, 79 geometry 10, II, 15, 16, 46, 47, 51, 80,

102, 103, 106, 120, 133 global 5, 12, 16, 31, 48, 55, 57, 65, 69,

70, 86, 90, 91, 103, 1I2, 1I6, 127-131, 134-142, 153, 173-177,

182-191 See also local

heat 5, 37, 43, 61, 65, 79, 98, 121, 122, 124, 150

Heath (T. L.) 18, 26n7, 26n9 Heiberg and Philippson 10 Heiberg and Tannery 10 Heidegger (M.) 81 Hellenism 120 Hephaestus 65 Heraclitus 48, 59, 81, 108, II3, 124,

128, 129, 152, 154, 174 Hercules 1I3, 1I4, 153 Hippocrates 19 history 3, 24, 48, 53, 64, 67, 1I8, 125-

128, 143, 150, 158-171, 174-177, 178-183, 188, 189, 191

Hobbes (T.) 132 homeorrhesis 34, 48, 56, 75, 76, 80,

81, 83, 128, 129, 153, 175 homeostasis 57, 72, 75, 88

194

Index

Homer 65, 104, 106, 126 hydraulics 7, II, 15, 84, III, 135, 156

immanence 54, 107 inclination 20-25, 145-147, 177-181,

184 indivisibles 4, 14, 15, 74 integral calculation 18, 58, 174, 188, 189 Iphigenia II7-II9, 131, 133, 134, 178,

187, 190 irrational numbers 10 isonomy 128, 174, 175, 176, 178, 180,

184

Lagrange G.-L.) 5, 20, 22, 80, 83, 189 lamellae 6, 82 laminar flow 6, 7, 16, 27, 32, 58, 83,

89, IIO, III, 136, 137, 144, 145, 153, 176

Laplace, (P. S., marquis de) 31, 36, 67, 96, 160

Leibniz (G.W.) 9, 14, 25, 31-33, 35, 41, 43, 45-47, 62, 95, 102, 103, II2, 121, 137, 140-142, 146, 158, 159, 188, 189

letter-atoms 22, 34, 36, 78, 122, 140, 142, 159,

local 7, 16, 31, 57, 60, 69, 76, 91, 99, 103, II6, 137, 140, 145, 148, 149, 153, 155, 159, 173, 185, 187, 188, 190, 191

See also global Lucretius (T. C.) passim

Mars 22, 24, 49, 51, 107-IIO, II2-117, II9, 121, 126, 133, 138

materialism 4, 42, 52, 54, 69, 71, II3, 121, 127

mathematics 3, 4, 9-13, 16, 17, 19, 97, 103, 104, 106, 120, 140, 141, 143, 144, 156, 185, 186, 188

matter 54, 62, 76, 85, 99, 122, 141 mechanics 5, 7, 12, 16, 21, 36, 46, 76,

80, 82, 99, III, II2, II6, 122, 123, 191

Memmius 108, II8, 133, 154 meta-stability 23, 29, 36, 64, 128 meteora 67, 68, 76, 80, 85, 87, 88, 93,

98, 99, 120, 138, 153 Michelet, II3 monad 14, 32, 62, II2, 142 morality 38, 92, 105-107, 127, 130,

182-185, 187 multiplicity 15, 50, 54, 58, 72, 88, 93,

98, 127, 128, 129, 144

Narcissus 155 negentropy 59, 125, 149, 150, 163 Newton (I.) 25, 31, 36, 85, II5, 125,

148, 160 noise 31, 125, 135-139, 144-146, 148,

153, 154-156, 164 numen 42, 141

Oedipus 147 order 14, 27, 28, 31, 67, 81, 92, 109,

IIO, III, II3, 136, 137, 139, 144-146, 174, 181, 182, 186, 190

organon II, 24, 78, 79, 102, 184

parallel flow 5, 7, II, 31, 46, 145, 146, 176

Parmenides, 129 Pascal (B.) 14, 25, 31, 35, 84, 102, 140,

141, 152, 153, 159 Pasteur (L.) 18, 85 path 40, 41, 49-51, 52, 95, 96, 98, 102,

II6, 120, 129, 130, 147, 151, 176, 187, 191

perpetual motion 3, 46, 58, 61, 64 perspective 101, II2 Phaedo 104 pharmakon 24, 97 physics passim, esp. 3-7

195

Index

plague II, 69, 72, 85, 88, I08-IIO, lI7-II8, 128, 129, 131, 133, 138, 156, 173, 185, 189, 190

plane/planar 9, 15, 16, 20, 25, 33, 36, 47, 175

Plato 17, 22, 29, 48, 58, 67, I03, I05, 106, 109, II2, 120, 129, 131, 154, 175

Plutarch IO, 35, IOI Poinsot 36, 160 politics, I07, II3, II7, 126, 132, 133,

134, 138, 150, 183 polytomy (tomos) 9, 15, 17, 75, 120,

121 population 12, 13, 23, 28 Protagoras 10 Pythagoras 3, IO, 58, I03

reception (receptor) 42, 59, I04, I06, I07, 176

rheme 89 rhythm 89, 136, 145, 151, 153-156 Riemann (G.B.) 18, 19

Saint Paul I05 salinon 19 (fig), 38 Sand-Reckoner, The see esp. Protocol

& Mathematics science passim science (applied) 4, 24, 86, 93, 140,

158 science (classical) 3, 44, 51, 82, 85

See also mathematics, mechanics etc.

semiotics 143, 145 Seneca 127 signal 49, I05, 135, 138, 144, 145, 146,

154 Silius Italicus 13, 20 simplex 95, 98, 122, 173, 176 simulacra 39, 40, 42, 43, 50, 52, 103,

I04, I06 singleton 17, 97

singularity 17, 37, 50, 53, 76, 77, 98, 147, 155, 174, 184, 185, 187, 188

Sisyphus 38, 55, 138, 165, 170, 180, 182 slope 31, 32, 33-40, 45, 46, 50, 53, 55,

64, 89, I08, 138, 139, 174, 176, 182, 184

specificity (stereo-specificity) 96, 97, 99

spinning top 28 Spinoza (B.) 38 spiral 7, II, 12, 15-17, 33, 37, 38, 50, 58,

92, 103, I08, IIO, 124, 131, 149, 153, 181

statics 5, 9, 14, 22-25, 46-49, 57, 80, 85, 93, 129, 178, 186

stochastics 6, 22, 71, 74, 78, I08, II2, 128, 136, 137, 139, 147, 148, 153, 174

stoicism (Stoics) 41, I09, II2, 128, 138, 186, 188

sufficient reason, principle of 22, 32 Syracuse 24, 35, 102, II4 syrrheme 89 system 68, 69, 70, 72, 73, 77, 79, 86,

88, II2, II5, 128, 139, 140, 142, 188, 191

tangentltangency 9, IO, 17, I03, 124, 146, 156

Thales 3, IOl, I03 thalweg 32, 33, 34, 50, 52, 60, 77, 91,

I08, I08, 129, 151-153, 173, 175,

180 thermodynamics 69, 79, 125, 128, 160,

163 Thorn (R.) 20, 37 Timaeus 9, 25, I04, II2 transformation 45, 91, 92, II6, 121 transmission (transmitter) 40, 42, 49,

60, 95 trigonometty 9 Trojan War 126, 131, 133, 190 Troy II8, 130, 139

Index

turba 27, 30, 81 turbination 23, 55, lIO, 179 turbo 15, 20, 28, 30, 76, 81, 91 turbulence passim, esp. 6-7, 27-31

See also turba, turbo

Venus 24, 39, 49, !O7, lIO, lI5, 123, 130, 139, 156, 177, 178, 187, 190vessel u6, 148

violence 24, 52, !O8, no, lI4, u9, 131, 133, 134, 139, 177, 181, 189, 190

Vitruvius 5, 84 void 14-16, 21, 30-33, 44, 46, 49, 62,

95, 102, 122, 123, 127, 130, 133, 134, 136, 138, 144, 145, 172

vortex passim

Water passim See also air, earth, fire

weight 15, 25, 27, 28, 30, 37, 51, 136 wind rose 87

197