DeLanda on Deleuze

7/23/2019 DeLanda on Deleuze

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DeLanda on Deleuze

A Neo-Materialist Perspective on the Body

Jon Lindblom


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Introduction

If Deleuze is the greatest materialist philosopher ever it is because he successfully

replaced an ontology based on essences and the general and the particular with an

ontology organised around processes and universal and individual singularities. It

has been a recurring trend in contemporary philosophy to criticize the notion of

transcendental essences, but if essences must be eliminated, what is there to

replace it? It is the main focus of this text to describe how this could be done from a

strict materialistperspective, and even though Deleuze obviously is the key

philosopher here, my main resource will be Manuel Deanda!s neo"materialist

interpretation of his ontology. #he greatness in the work of Deanda lies primarily in

his clear and concise unpacking of Deleuze!s dense texts $but still giving the reader

much more than %ust an introduction& and in his re%ection of the obscure Deleuze in

favour of a very realist and practical philosophy, which turns out to be extremely

systematic and concrete. #his is the focus of his book Intensive Science and Virtual

Philosophy,' which attempts at introducing Deleuzian ontology to an audience of

analytical philosophers of science and scientists interested in philosophical

(uestions. #he first chapter of this book, entitled The Mathematics of the Virtual, will

be my primary source.)

In order to narrow the discussion down I will focus on something which is a very

important part of our existence, yet often has been neglected throughout the history

of philosophy* the body. +s a contrast to philosophies which have subordinated the

body to the rational mind, and to classification schemes which have organized

organisms after general bodily features, I will try to show how we, through Deanda

and Deleuze, may view the body as an expressive entity, actualized through

immanentprocesses andpositive difference, and organized around individual and

universal singularities.

The Mathematical Background

or Deleuze, there are no essences, but only multiplicities. +ccording to him, the

classical notion of eternal archetypes existing in an abstract space is absurd and

must be eliminated from philosophy. -o he introduces multiplicities. here, in an

essentialist ontology, one tries to find a set of defining characteristics which explain

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the identity, and relationship, between the general and the particular, in a Deleuzian

ontology there are no such transcendent archetypes, but only immanent processes.

or the essentialist, there is only being without becoming, but for Deleuze there is

only becoming without being. #his becoming may be expressed through the concept

of multiplicities meshed together on a virtual plane of immanence. It is this plane I will

focus on in this text. #he formal definition of multiplicities is highly complex and has

origins in several branches of modern mathematics, which I won!t try to fully illustrate

here. I will instead use some of its components in order to give a rather simplified

version, which I believe will be enough for our purpose, though.

Multiplicities are closely related to the term /manifold0, which was developed

through the differential geometry of 1auss and 2iemann. + manifold may be defined

as /a geometrical space with certain characteristic properties0,'and has its origins in

the analytic geometry of Descartes and ermat, but breaks with this classical

tradition since it eliminates the supplementary higher dimension of analytic geometry.

or example, a two"dimensional surface no longer has to be embedded in an x, y

and z three"dimensional space, but may be studied without references to a /global

space0. #hus, the surface, or rather the curvature, becomes a space in itself3 a field

of rapidnesses and slownesses, which is calculated as a rate of change giving

instantaneous values for infinitesimally small points along the curvature. #his was the

insight of 1auss and he did it for two"dimensional spaces. 2iemann, however, not

only went one step further, but many, when he did the same for 4"dimensions. #his is

the classical definition of a manifold* /abstract spaces with a variable number of

dimensions, spaces which 5can6 be studied without the need to embed them into a

higher"dimensional $47'& space0.)8ere we find the first two defining features of a

Deleuzian multiplicity* variable numbers of dimensions and the elimination of an

external, supplementary dimension.9

#he next step is to convert this highly theoretical model to a physical system and

this may be done by using the theories of dynamical systems. 8ere, a manifold

represents the space of possible states for a physical system, since its dimensions

represent the properties of a particular process within the system. #his may then

model the dynamical behaviour of a physical ob%ect. Deanda uses a pendulum and

a bicycle as examples, to show how their degrees of freedom $two for the pendulum

and ten for the bicycle&, that is, the ways they are able to change, may be mappedonto the dimensions of a manifold, which now is referred to as a /state space0. In this

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space we can now find the ob%ects! changes of states along a curve3 that is, we can

capture a process.: #his has led to great simplification in the study of dynamical

behaviour, but also to new resources such as certain topological features called

/singularities0, discovered by the mathematician ;oincar yet the mechanism

behind the two is very different. #his mechanism"independence of singularities is, as

Deanda points out, what makes them perfect candidates to replace essences.

-o, for Deleuze, the metric spaces of bodies perceived in the actual world are

actualized from a topological continuum. @ut what is this topological continuum?

#opology is one of many post"Auclidean geometries, and is of course very different

from classical geometry since it concerns geometric figures which remain invariant

under such deforming transformations as bending and stretching. @asically, a

topological space is a non-metricspacewhich may be twisted and deformed without

losing its characteristic properties. #his means, as Deanda writes, that*

56igures which are completely distinct in Auclidean geometry $a triangle, a

s(uare or a circle, for example& become one and the same figure, since they

can be deformed into one another. In this sense, topology may be said to be the

least differentiated geometry, the one with the least number of distinct

e(uivalence classes, the one in which many discontinuous forces have blended

into one continues one.B

#hus, topology may be described as a virtual plane where Auclidean figures aredeformed and meshed together into a single continuum. @etween topology and

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Auclidean geometry there are other geometries $differential > pro%ective > affective& in

which the characteristics of topology and Auclidean geometry are combined $as we

proceed upwards through the various geometries, figures which where highly distinct

become increasingly less distinct, until they blend into the single topological

continuum&. #hus, this morphogeneticviewof geometries and their relations shows

us how non"metric space is progressively differentiated into the more familiar metric

space of Auclidean geometry. It also shows us how these intensive processes which

actualize metric space are characterized by a /pure difference0, not subordinated to

identity, but rather /purely positive03 for example, as a rate of change orspeed of

becoming. #his is related to progressive differentiation and symmetry"breaking

transitions which we also have to take a brief look at.

#o do this, we need to discuss another important mathematical innovation, which is

the theory of groups. + group is a set of entities with a rule of combination and certain

special properties, where the one referred to as /closure0 is the most important.

/Closure0 means that, as Delanda writes* /when we use the rule to combine any two

entities in the set, the result is an entity also belonging to the set0. or example,

groups may consist of transformations which can be illustrated by a set of rotations

by ninety degrees $E, FE, 'E, )BE&, where any two consecutive rotations produce a

rotation also belonging to the group $provided 9E e(uals zero&. #his allows us to

classify geometric figures by theirinvariants, which means that if we performed this

transformation on a cube, an observer who did not witness it would not be able to

see that it had occurred. 8owever, if we rotated the cube := degrees, it would not

remain invariant. @ut this differs between various geometrical figures since a sphere

obviously would remain invariant through a rotation of := degrees3 actually to every

type of rotation to any amount of degrees. #hus, the sphere has more symmetrythan

the cube $with respect to rotation transformation&.F

-o instead of classifying geometrical ob%ects by their essences $as in Auclidean

geometry&, we classify them by looking at theirdegrees of symmetry. #he

conclusions which must be emphasized here are two* firstly, geometrical figures are

not classified by static properties, but by active transformations3 secondly, this also

allows us to envision, as Deanda points out* /a process which converts one of the

entities into the other0.'Eor example, in the example above the cube and the sphere

are related to each other $one is the subgroup of the other&, which means that thesphere can be transformed into a cube by losing invariance. #hat is, by undergoing a

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symmetry-breaking transition.'' Gnce again, this may sound very abstract, but

Deanda uses the more concrete example ofphase transitions > where physical

systems, at certain critical points of some parameter, changes from one state to

another > to clarify this. + very simple example is how temperature in water $as /pure

difference0, /rate of change0 or /speed of becoming0& reaches these critical points,

changing it from ice to li(uid and from li(uid to gas. 8ere, the gas would remain

invariant through any kind of transformation or rotation, while the solid would not.

#hrough these examples, the process ofprogressive differentiation through

symmetry-breaking transitionsmay now be connected to state spaces. or example,

a singularity in a state space may be converted into another, exactly by undergoing

this symmetry"breaking transition described above $this is referred to as

/bifurcations0& which conse(uently breaks the prior symmetry of the system. Gn top

of that $as I mentioned earlier&, this process is mechanism"independent, so the

different realizations of the process $or multiplicity& bear no resemblance to each

other. #hus, as Deanda writes* /multiplicities give form to processes, not the final

product, so that the end results of processes realizing the same multiplicity may be

highly dissimilar from each other0') $like the soap bubble and the salt crystal&. #his

gives us a perfect candidate to replace essences* multiplicities progressively

differentiated from a topological continuum to a familiar Auclidean space. e now

have the basic tools to do a Deleuzian reading of the body.

The Body and Differentiating Processes

or Deleuze, who was very influenced by Darwin, an organism is not an eternal

essence, but rather a historical entity or an individual singularity. urthermore, a

species is %ust the same as the individuals populating it, with the difference that it

operates on larger spatio"temporal scales. -pecies are actualizations ofuniversal

singularities, which allow us to connect the highly theoretical discussion in part one to

this more concrete example of species. @ecause when Deleuze speaks of universal

singularities he explicitly refers to those topological singularities which guide a

differentiation process. Conse(uently, he replaces the general category of /animal0

with a /topological diagram0, and bodies with a /body plan03 because the process of

embryogenesis, which turns a fertilized egg into a fully formed organism, is anexample of this progressive differentiation initiating from a topological diagram. #hus,

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this body plan may be described as an /animal model0 which, through bending,

stretching and folding, differentiates itself into fully formed organisms. ' #he

organisms are implicated in the body plan and differentiated through topological

singularities, resulting in the various species in the kingdom of vertebrates $for

example& in which humans belong. #his may be illustrated with the example of the

fertilized egg prior to its differentiation into an organism with tissues and organs.

Deanda writes*

hile in essentialist interpretations of embryogenesis tissues and organs are

supposed to be already given in the egg $preformed, as it were, and hence

having a clear and distinct nature& most biologists today have given up

preformism and accepted the idea that differentiated structures emerge

progressively as the egg develops. #he egg is not, of course, an

undifferentiated mass* it possesses an obscure yet distinct structure defined by

zones of biochemical concentration and by polarities established by the

asymmetrical position of the yolk $or nucleus&. @ut even though it does possess

the necessary biochemical materials and genetic information, these materials

and information do not contain a clear and distinct blueprint of the final

organism.)

-o, for Deleuze, the body is actualized by intensive differences $in temperature,

pressure, and so on& guided by the immanent self-organizing ability of matter itself.

#hus, he inverts the classical definition of morphogenesis $the birth of form& from that

of essences to that of processes, and conse(uently views the body not as an eternal

archetype, but rather as an epression of nature!s immanent power to unfold itself.

8ence, there is not only /the body0, but also the body without organs. + body without

organs is the body plan3 a body of pure intensities prior to the differentiating

processes which actualize fully formed individuals.9 #hus, we are finally able to

formulate a satisfactory classification of the body in Deleuzian terms* a topological

diagram progressively differentiated through symmetry-breaking transitions, which is

organised around immanence, positive difference and individual and universal

singularities.

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Notes

Introduction

'. Deanda, Manuel, Intensive Science and Virtual Philosophy, ondon*

Continuum, )EE).

). Deanda!s discussion of course covers much more, but the length of this text

does not allow me to go into further details. 4evertheless, I believe it won!t be

necessary in order to make my arguments clear.

The Mathematical Background

'. Deanda, Intensive Science and Virtual Philosophy, p. 'E.

). Ibid., p. '). Deanda also writes*

It is these 4"dimensional curved structures, defined exclusively through their

intrinsic features, that were originally referred to by the term /manifold0. $Ibid.&

9. In Deleuze!s own words*

Multiplicity must not designate a combination of the many and one, but rather

an organization belonging to the many as such, which has no needwhatsoever of unity in order to form a system. $Ibid.&

:. Ibid., p. ':.

+fter this mapping operation, the state of the ob%ect at any given instant of

time becomes a single point in the manifold, which is now called a state

space. In addition, we can capture in this model an ob%ect!s changes of state if

we allow the representative point to move in this abstract space, one tick of

the clock at a time, describing a curve or tra%ectory. + physicist can then study

the changing behaviour of an ob%ect by studying the behaviour of these

representative tra%ectories. $Ibid., p. '9.&

=. Ibid., p. '=.

e can imagine the state space of the process which leads to these forms as

structured by a single point attractor $representing the point of minimal

energy&. Gne way of describing the situation would be to say that a topological

form $a singular point in a manifold& guides a process which results in many

different physical forms, including spheres 5H6 $Ibid.&

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. Ibid., p. '=.

B. Ibid., p. ):.

. Ibid., p. 'B.

F. Ibid.

'E.Ibid.

''. #o put it more specifically*

hen two or more entities are related as the cube and the sphere 5H6, that is,

when the group of transformations of one is a subgroup of the other, it

becomes possible to envision a process which converts one of the entities into

the otherby losing or gaining symmetry. or example, a sphere can /become

a cube0 by loosing or gaining invariance to some transformations, or to use the

technical term, by undergoing symmetry-breaking transitions. $Ibid., p. '"'B.&

').Ibid., p. )'.

nlike the generality of essences, and the resemblance with which this

generality endows instantiations of an essence, the universality of a multiplicity

is typically divergent* the different realizations of a multiplicity bear no

resemblance whatsoever to it and there is in principle no end to the set of

potential divergent forms it may adopt. $Ibid.&

The Body and Differentiating Processes

'. #his is of course completely different from classifying animals after static

resemblances, as Deanda points out by using the example of innaeus!

classification schemes*

#his amounted to a translation of their visible features into linguistic

representation, a tabulation of differences and identities which allowed the

assignment of the individuals to an exact place in an ordered table. Judgments

ofanalogybetween the classes included in the table were used to generate

higher"order classes, and relations ofopposition were established between

those classes to yield dichotomies or more elaborate hierarchical types. #he

resulting biological taxonomies were supposed to reconstruct a natural order

which was fied and continuous, regardless of the fact that historical accidents

may have broken that continuity. $Ibid., p. 9.&). Ibid., p. '.

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9. #he concept of the /body without organs0 should not only be seen as a body

plan, but also as the virtual continuum itself. #his is how Deleuze and 1uattari

use it in"nti-#edipus$'FB)& and" Thousand Plateaus$'FE&.

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DeLanda on Deleuze