Vida Caos e Interdisciplinariedad Hodge 2007-leer.pdf

7/25/2019 Vida Caos e Interdisciplinariedad Hodge 2007-leer.pdf

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World Futures, 63: 209222, 2007

Copyright Taylor & Francis Group, LLC

ISSN 0260-4027 print / 1556-1844 online

DOI: 10.1080/02604020601172558

LIFE, CHAOS, AND TRANSDISCIPLINARITY:

A PERSONAL JOURNEY

BOBHODGEUniversity of Western Sydney, NSW, Australia

This article uses an autobiography as an object of research, to both illustrate some

principles of chaos theory in analytic practice, and give those ideas a personal andsocial context, thereby producing a unique but explanation-rich history of chaos

theory and recent intellectual history of transdisciplinarity and social research in

the West. The ideas from Chaos Theory it uses and illustrates include: three-body

analysis (Poincare); fractals (Mandelbrot); fuzzy logic (Zadeh); and the butterfly

effect (Lorenz).

KEYWORDS: Butterfly effect, chaos theory, fractals, fuzzy logic, three-body analysis, trans-

disciplinarity.

My aim is to write something useful for readers who may have different start-ing points and goals, with different levels of interest in theories of chaos and

complexity. I want to insist on the rich relationship between Chaos Theory and

transdisciplinarity, so close that each conditions and requires the other, while re-

maining distinct. My understanding of and preference for transdisciplinarity

over the more common interdisciplinarity will emerge in what follows.

I also seek to trouble this binary pair, by inserting it into a three-body problem-

atic. I get the idea of a three-body analysis from Chaos Theory, from a reflection

on Poincares seminal analysis of the Newtonian three-body problem (1943), in

which he showed that future states of even apparently stable three-body systems,such as the sun, the earth, and the moon, cannot be predicted, beyond a certain

level, using Newtonian equations. I have found this idea a rich source of models

that avoid collapsing into reductive simplicity. In this case, I add life to the other

two, to form a three-body system in which chaos, transdisciplinarity, and life are

permanently interrelated, each conditioning the understanding of the other through

countless iterations.

Hence the form of my exposition. I embed the dialectic between chaos and

transdisciplinarity in an understanding of my own life, as every reader of this

special issue must do with their own life, in ways that will be different from mine,


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210 BOB HODGE

unique in some respects, yet able to be mapped in the same terms. I also embed this

personal journey in a larger journey, my sense of a recent trajectory of Western

thought (mainly British and Australian), which was always the context of my

journey whether I knew it or not, whose structures are, I argue, a larger fractallevel of my own journey, which therefore becomes a convenient site to interrogate

the larger forms. Again, readers of my text may have a different sense of what that

larger context is and how it has impinged on them, yet the relationship, filtered

through the lenses of Chaos Theory, will I hope be valuable and illuminating,

about self and other and the universe we all inhabit. Although the object I mainly

look at through the lenses of chaos and complexity is my own life, I hope that the

challenges this object poses will be usefully similar to whatever other objects any

reader wants to address. My life is unique, but issues of chaos, complexity, and

transdisciplinarity affect everyone.

ORIGINS

Biographies naturally begin with questions about origins. So does every inquiry

into events in time, a crucial dimension in all dynamic processes. Here I have found

the concept of the butterfly effect or sensitivity to initial conditions especially

useful. I love Lorenzs famous metaphor (1993) of the butterfly flapping its wings

on the Andes (or wherever) and contributing to a hurricane in Montana (or Beijing,

or wherever) but it can also set minds looking in the wrong directions for practical

insights that can flow from the concept.Lorenzs insight came not from a biological event (an actual pesky butterfly

caught flapping unsupervised wings) but from a computer run in which he arbitrar-

ily re-started from a rounded figure, producing a pattern that diverged increasingly

from another run, which previously he assumed would be essentially identical. The

sensitivity to initial conditions, the technical name for the phenomenon, refers

to any arbitrarily chosen moment in a sequence that itself has no beginning or end.

The decision to choose to start a history at any specific point, the initial condi-

tions of the history, will lead to a different history, one which will not necessarily

converge on a single version.The initial conditions of a history from another point of view are the conditions

from which it is viewed, whose limits themselves are equally hard to determine.

Is that point, for me, 3 September 2004, the date on which I first wrote these

words? My mother died yesterday. Could that condition how this history unfolds

to a degreealong with many other factors which I am not conscious of? But the

initial conditions surely are not a point source. All 2004, then? Or the beginning

of the 21st century? The postmodern world? Each of these statements of the initial

conditions for this history has different dimensions, which contain a different,

infinite set of factors, which may prove to have an effect. Part of the conditions of

the history include the context of this special issue, making much of my personallife less relevant, even though I have reasons for still including some of it.


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212 BOB HODGE

could be represented in terms of the fuzzy logic of Zadeh (1965) as a condition of

being both A (humanities) and not-A (science). The form of fuzzy logic at issue is

only one possibility within Zadehs scheme, and not one that is prominent in most

versions of fuzzy logic. My state was not A (to a degree) and also not-A (also toa degree) but fully A (humanities) and also fully not-A (Science). This is fuzzy

logic operating at the edge of chaos, not fuzzy logic in the more stable conditions

of engineering applications like washing machines or helicopters.

Fuzzy logic for conditions of criticality is common in the turbulent and chaotic

conditions where normal logics fail. Thoms catastrophe theory (1975) illuminat-

ingly takes the case of a dog poised between fight and flight, liable to attack or run

away as the threat approaches, opposite actions that co-exist as equally potential.

Yet many dogs that withdraw do not keep running, but turn and stay their ground,

still dangerous. In a state of criticality, a single path can be followed out of a

bifurcation, or two alternatives can co-exist, oscillating between one and the other.

Freud grasped the principles of super-position and fuzzy logic. In his terms, I

could say of myself that at times I repressed my fathers side (mathematics), just

as he repressed his own mother, and my mother repressed her own father in her

life (militantly wife and mother, not headmaster and scholar). Fuzzy logic and the

concept of super-position provide a flexible, comprehensive framework in which

to make better use of Freuds important insight. His repressed is a complete

system of meanings, overlaid by another dominant system, returning after a

second bifurcation. Freud gave the Ego (or therapists) the task of devising fuzzy

solutions, in which each self has something.The logic of the unconscious, Freuds most original discovery, is still a scandal

to his scientific status, because it defies the linear logic of mainstream science. But

if the unconscious does indeed follow the weird rules of chaos, then its theorist

must describe those rules. Freud would be less scientific if he had replaced them

with linear rationality. The logic of the unconscious is a play of super-positions

in which none are definitively repressed. This unconscious is not a pathological

condition, like Batesons schizophrenia, but normal, healthy, and functional. Zadeh

did not develop this kind of fuzzy logic, but it has so many functions and applies

to so many situations that it needs to exist.Fuzzy logic came later. My immediate legacy from my family of origin was a

particular model of inter/trans/disciplinarity whose scope minimally had to include

both scienceandhumanities, not just adjacent disciplines, as in the experiments

in interdisciplinarity that became popular from the 1970s (x + y, history and

literature, language and philosophy, etc.). Nor was the relationship a weakly fuzzy

one, finding elements in common in the intersection between two such disciplines,

in a space in-between that was neither one nor the other. I came to see the value

of transdisciplinarity to describe a stronger, less stable relationship, a super-

position of prior disciplines in all their fullness onto a single coherent scheme in

which differences were part of a single structure. The fact of super-position meantthat the system containing independent disciplines in their separateness was never


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LIFE, CHAOS, TRANSDISCIPLINARITY 213

In a history that starts from my parents and their inability (as I saw it) to

manage their difference except through love, transdisciplinarity (managed super-

position) became an unexpected outcome, which for me always ultimately signifies

a reconciliation between my mother and father, my (and their) male and femaleselves, not in their lives but inside me.

REVOLUTIONS

I begin again. I arrived in Cambridge in 1965, a nave colonial from Australia

parachuted into the stable center of the Anglo intellectual universe, as I supposed,

to find it in ferment. The center of the empire of thought was a vortex. Intense

questioning of the curriculum, fueled by the flow of highly charged ideas across

the English channel (Lukacs, Althusser, Lacan, Foucault, Marcuse, Levi-Strauss,Barthes, and others) followed a power law until it exploded in the May 68 student

revolution, a radical intellectual movement that swept much of the world.

I now see the dramatic change in what students were reading and excited by as

advance warning of changes to come. Where the previous generation of students

had read disciplinary experts, now students were reading writers whose scope went

far beyond the limits that characterize disciplinarity. These authors were typically

not interdisciplinary, in the sense that they deliberately mixed more than one disci-

pline, but they were clearly beyond disciplinarity. Because of this quality, whatever

discipline was their main strength, they created a nondisciplinary space around it.

A consensus quickly formed around a new canon of authors who formed thisemergent curriculum, made concrete by an astute publisher (Collins, Fontana) in a

series called Modern Masters, edited by Frank Kermode. The label contradicted

one of the basic premises of this movement, which repudiated individualism and

bourgeois ideas of genius, but the success of the books showed that this was

a benign contradiction, super-position. In practice, these authors all had a more

dynamic complexity than any disciplinary expert. I would later see their typical

idiosyncrasy and density as marks of fractality.

There was also a pattern behind the pattern (although not subsuming or replacing

any of the elements): an intellectual current associated with a trio of masters ofthese masters. I have already mentioned Freud. I became a Freudian then, and

still am, of a kind. I was and continue to be also a Marxist, although to many

of my Marxist friends, that was a dubious, heretical double identity. I am also a

semiotician, in the line of Peirce (1966), the 19th-century philosopher of science

and semiotician, although most at the time followed Saussure (1974). Each of these

has changed for me over many iterations in a three-body intellectual system.

These intellectual movements and affiliations did not take place in a vacuum.

Life made continual demands, exerting pressure, disrupting the logic of disci-

plinarity. Politically there was much that could not be filtered out. For me there

were three special challenges. The nuclear disarmament movement projected itsecological concept of a single interrelated planet facing threats on a global scale.


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214 BOB HODGE

I use more than one three-body system to model this period. One body is

life, like the sun, exerting constant pressure on thought(the earth). But both of

these impinge on third body, the moon academia. Like the moon, academia as a

distinct force can easily seem insignificant, irrelevant, yet I believe the three-wayeffects cumulatively became decisive. Over 30 years universities were transformed

in response to changes in society and thought, and in turn fed those changes

back in.

As Prigogine says of systems far from equilibrium (Prigogine and Stengers,

1984), the world university system suddenly became or revealed itself as a system

in which ideas swept from one part to another across huge distances with amazing

speed. Linear forms of analysis can identify influences and originary sites of the

1968 movement, but what happened was non-linear. Yet the explosion seemingly

was controlled almost as quickly as it had appeared. The system made accommo-

dations, and re-grouped. In the USA, Nixon was elected president, and became

the one who ended the Vietnam War. In Mexico, a student uprising in 1968 was

brutally crushed, by a government that seemed capable of suppressing the truth of

what happened for ever. In Australia Whitlam was elected in 1971, but removed

by 1974. In Cambridge, minor concessions were made to student demands, but

no professors resigned, and the system seemed to roll on impervious, as though

nothing really had happened.

At an unconscious level, this was a major dilemma for me, as for others. Had the

revolution come and gone so quickly? How did the blight of Thatcherism come so

fast and take so deep a hold in Britain in the 80s? Yet I was changed irreversibly,involved in what has been a 30-year project that grew out of that moment. There

was a change, and there was no change: that was the contradiction that animated

me, because both parts of it were true, to a degree. Super-position, again.

In 1967 I began my doctorate. My thesis topic, on the 17th-century poet, Andrew

Marvell, seemed disciplinary enough, and was accepted as such by the English

department. The reason I chose it (not fully consciously, like a sleep-walker in

Koestlers evocative image for the creative process) was its resonance with the key

challenge that life was throwing up just as I was carrying out the project. What

was a revolution? What are its dynamics? How could I recognize one? Was whatI had seen a revolution, or just an eddy?

So my grand theme was revolutions, a case study of the century of revolutions

from the perspective of the single history, life, and consciousness of Andrew Mar-

vell. I used a version of three-body analysis before I knew the theory, to look at the

intersections between three revolutions the century was famous for: the revolution

in sensibility claimed by T. S. Eliot, the political revolution recognized by Marx,

and (driven by my still unexpressed sense of what transdisciplinarity had to in-

clude) the scientific revolution, where the still controversial work of Kuhn (1962)

was my guide.

Displacing my inquiry into revolution onto the 17th century proved productive.There I found again the same pattern; everything changed (the English King was


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Kuhns (1962) theory of paradigms and normal science was a useful start-

ing point. In between periods of normal science, he said, were entirely different

periods, crises followed by revolutions, which inaugurated the next period of nor-

mal paradigm science. But as I looked at the eye of this storm in its 17th andmid-20th-century incarnations, even without ideas from Chaos Theory, which I

needed, I realized there was a strange omission in Kuhns scheme. He emphasized

revolutions, but did not try to analyze what happened in them. I filled this gap

by asking what rules of thought revolutionaries followed.

I named these rules of thought metaparadigms (Hodge, 1978). The rules of

a metaparadigm, in many ways, contradicted the rules of the paradigms on ei-

ther side. They always produced multiplicity, wild connections, cross-disciplinary

leaps, and contradictions. What I called the rules of the metaparadigm was my in-

dependent empirical discovery of the conditions at the edge of chaos as described

by Prigogine. All great scientists, I learnt, like great artists and charismatic po-

litical figures (in Webers sense of the term) were experts in navigating at the edge

of chaos, before the term was born. This must be the case, if Chaos Theory is not

just a current academic fashion but captures how human minds grapple with chaos

and complexity.

To capture this central insight, I took a line from the poet I was studying, An-

drew Marvell: Foreshortened time the work of ages acts. The Marxist Georg

Lukacs (1968) proposed that at turning points in history, great artists and polit-

ical figures could grasp the totality, the set of contradictions that included present

and past, and the movement between them. That was the quality I found in the poetMarvell, scientists like Gilbert and Newton, and political figures like Cromwell

and Winstanley. I am now convinced that fascination with events and conditions

in times of turbulence is essential to the advance of social research. Out of that

understanding can come a clearer grasp of invisible currents of contradiction that

are always present even in normal times. Instead of disorder as aberrant, the

breakdown of order, order is a condition in which tendencies to disorder are suf-

ficiently under control to be temporarily ignored. It is never a choice of order or

chaos, but each super-posed on the other.

FRACTAL DISCIPLINARITY

I was enrolled in a disciplinary department, with a supervisor, Professor L. C.

Knights, King Edward V11 chair of English, who had pushed the boundaries of his

discipline in his time, and encouraged me to go wherever I must. Another contradic-

tion: Cambridge University, bastion of tradition, also allowed and valued critical,

innovative work among the carefully selected elite it taught. But not unproblem-

atically. The disciplinary regime that was Cambridge in the early 1970s asserted

itself. My thesis was initially failed, by another Professor, Muriel Bradbrook, an

interdisciplinary innovator in her day who ruled that my thesis was not acceptablefor a thesis in English. I was required to rewrite the thesis to remove the word


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216 BOB HODGE

Yet in important ways I was not rejecting disciplinarity, or the discipline of

English. On the contrary, I believed I was doing English as well as I could, in

a highly disciplined way. I engaged in the close textual reading that was the core

practice of English. Far from avoiding this practice, I aimed to take it to new depths,across a greater range of data, with a new explanatory framework. Super-position

again: both more disciplinary, and more transdisciplinary.

The guiding idea I used was the ancient principle that the microcosm mirrors

the macrocosm. This is beautifully expressed by William Blake To see the world

in a grain of sand, but it was also central to Marvells poetic vision. This poet of

the edge of chaos had discovered the power of fractality. In a famous poem, he

wrote:

The Mind, that ocean where each kind,Does straight its own resemblance find;

Yet it creates, transcending these,

Far other worlds, and other seas;

Annihilating all thats made

To a green thought in a green shade.

(The Garden, lines 4348)

In this version of the macrocosmmicrocosm relationship the mind is below not

above, and the fractal process continues to an infinity that is also nothing: period

doubling to reach deep chaos. It was only later that I understood Marvells poemas a contribution to the understanding of fractality. Mandelbrots fractals are not

any series that goes on for ever, producing endless self-similarity across different

scales. He defines a fractal as a shape (1993, p. 123), irregular at all scales, produced

by an iterative algorithm. For instance, in the simple formula, C+XC1, where

C1 forms the basis for the next iteration, C is an irregular whole that contains the

irregularity that affects all iterations. For Marvell, the paradox of the attempt to

escape into the mind to create alternative worlds (C1-n) out of the existing one (C)

is that all the alternative worlds contain that flaw as part of the self-similar pattern.

Empson, an influential literary critic, saw many ambiguities in this text (1935).Empson had transferred from mathematics to English, and wrote his masterpiece

on ambiguity (1930) as a series of undergraduate essays. He discovered fuzzy logic

three decades before Zadeh, and delighted in Marvells style, which like all work

at the edge of chaos was full of ambiguities and contradictions.

Disciplines as commonly understood form a linear taxonomy, each a self-

contained, homogenous regular box, produced by an iterative algorithm that results

in a structure of simple differences. History deals with the past, sociology with the

present. English deals with the past too, but it must be a completely different kind

of past, understood in a different way, and so on. Inter-disciplinarity then is a

secondary operation on a system that remains unchanged. It refers to a mixture ofcontents from two or more boxes in a way that leaves all partitions in place.


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three acted together to constitute his version of his discipline. He was a rev-

olutionary critic, source of what became known as New Criticism in USA,

which later incorporated ideas of Derrida and others to morph into deconstruc-

tionism, a major strand in literary criticism today. He was a metaparadigmthinker.

With Empson, like many founders of schools or disciplines in other fields, I

found that disciplines normally began as fractal disciplines, at a time of crisis and

creativity. That foundational moment, in which leading thinkers always carry some

of the wisdom of a metaparadigm, is a resource, neglected and denied but always

available (with strong constraints) to those who follow.

Because of this there is a paradox with interdisciplinarity. This term was pop-

ular in the 1970s, and I was committed to it pedagogically, but I found it strangely

frustrating. Interdisciplinarity in the 1970s was often an attempt to join two disci-

plines under close to equilibrium conditions, maintaining high boundaries, limiting

and controlling interchanges. In these conditions, interdisciplinarity paradoxically

becomes less transformative, less creative, than was possible within a single dis-

cipline as a far-from-equilibrium fractal discipline. All disciplines in the current

Western curriculum originated in a fractal form of disciplinarity, and that further-

from-equilibrium state is always, to some degree, recoverable. But even a fractal

discipline finally is not enough. Only when thought moves into transdisciplines

can it respond more adequately to the intrinsic dynamism and interconnectivity of

everything.

LANGUAGE

I have been fascinated with language as long as I can remember. Every project

I have ever undertaken has required an encounter with language, and I would

suggest that language in an extended sense is an indispensable component of

all transdisciplinarity. Yet I also found by long and frustrating experience that

Linguistics, the discipline ostensibly specializing in language, resists assimilation

into transdisciplinary thinking. The core problem is that language is a phenomenon

of the edge of chaos, yet Linguistics in its disciplinary form is resolutely linear.Only a chaos theory of language can participate in transdisciplinary inquiry. But

this will look so different from disciplinary linguistics as to be barely recognizable.

I had many models of linguistics I could draw on in the 1970s, all problematic.

The nature of the problems is best illustrated by describing the role of Chomsky

in my formation. Chomsky produced his revolutionary theory of language in the

1950s (1957), a beautiful fractal discipline, but I came to it in the late 60s. By this

time the Chomskyan revolution had already been declared a triumph, but Chomsky

himself was split between a normal linguist and formidable critic of American

imperialism.

My first problem with Chomsky was this split between language and society.I now see it as a super-position, to resolve a huge contradiction. Then I saw it


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218 BOB HODGE

it so disconnected from the real world, like the mathematics I craved. So I loved

his system as a denied part of my self. His super-position mapped neatly onto

mine.

I managed the problem by another super-position within linguistics, with thework of another exciting linguist, Whorf (whose first degree was in engineering).

Whorfs great work was posthumously called Language, Thought and Reality

(1956), a three-body relation that was reduced, by linear thinkers who claimed

to follow him, into what was called the Sapir-Whorf hypothesis: that language

determines thought, and hence reality. This linear model came to form the basis of a

dangerous half-truth encapsulated in what was called social constructivism (as in

Berger and Luckmanns influential book, 1971). Social constructivism has become

a dogma, identified also with what is called postmodernism (as in Baudrillards

paradoxical works, 1981). It is ironic, or paradoxical (two favored words in this

school) that postmodernism of this kind, which prides itself on its sophistication,

complexity, and up-to-dateness, is the product of linear, binary thinking of a kind

that has been around a long time.

Whorf, however, talked of conditioning, not determining. Restored to his own

three-body framework he provides a suitably complex model that allows language

to play its part, always independent to a degree, never autonomous, in all social

and cognitive processes. Chomsky also had three crucial elements: language, mind

and society, but under the weight of his adherence to linearity, the three separated

out, first into language-and-thought, with society in a separate component, then

into language and thought, now in separate boxes. In each box he generated workwith unflagging energy, producing book after book, slowly sinking beneath the

chaos paradoxically produced by his remorseless linearity.

I have not ceased to admire Chomsky as linguist and social critic. Yet I see ever

more clearly from his example the dangers of his linearity. I have come to realize

that in the 70s and 80s my own form of left politics, which I shared with many

of my generation, was damaged by a linearity similar to Chomskys, which we

mistook for a virtue. Like Chomsky, I made the core assumption of linearity, that

compromise (product of accommodation, negotiation) was intrinsically and irre-

deemably flawed. This assumption on the left helped to produce the fragmentationand ineffectiveness that always marks the ultra-left. I now distinguish between the

ideals of the left, which I share as strongly as ever, and the linear, binary logic that

is so often seen as part of the package.

At various times I have used the term discourse instead of language to or-

ganize my interdisciplinary inquiries, exploiting the intimate connections between

language thought and society opened up by Foucaults influential use of the word

(1972). There is no need to decide between the twosuper-position is a produc-

tive strategy here as well. But language has some advantages, if it is understood

semiotically, always as part of a three-body system.

One limitation of both language and discourse is the tacit limitation toonly one mode, verbal, as in speech and writing. Each needs to be seen as the


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modes). They can also include words, realities (carried by images or by other

dimensions), and inflections.

For instance, Chomsky as revolutionary linguist looked seriously at the sentence

colourless green ideas sleep furiously (1957) seeing it as the intersection betweena linguistic system (a grammar) in which it made sense, and a version of reality in

which it was nonsense: super-position again, if only he had had that theory. Or what

if he had used Marvells famous green thought in a green shade, which Empson

had already pointed out was nonsense, yet also a profound mystical vision? Or if he

had taken his sentence to a Freudian therapist, and wondered why these ideas were

green not red, like the ideas that were sleeping so furiously in the closet radical

he was when he wrote his theory? The context of Marvells line, a poem dealing

with incomprehensible, mystical experiences, becomes a third force, making it

more likely that the meaning process will resonate forever, whereas Chomsky

cancelled his potential linguistic revolution by denying the mystical or poetic

potential of his phrase. He turned it into an example of language at the edge of

his theory of language, and from there into non-language, rejected by his linear

linguistics.

CHAOS THEORY AND THE MEANING OF LIFE

I have mainly described my work before I explicitly adopted Chaos Theory, as in

my book with Gabriela Coronado (2004), to make the point that one does not haveto be a Chaos Theorist to have ideas that are illuminated by Chaos Theory. Further,

I think a story of partial emergence of Chaos Theory out of the matrix of thought

of the time is more illuminating, connecting better with the twists and turns of

many other thinkers history who never took a chaos turn, making my narrative

more useful and useable for readers of this special issue, all of whom I hope will

interweave Chaos Theory with other disciplinary backgrounds.

I have found the exercise of mapping my life trajectory using terms from Chaos

Theory a source of insight, even though I already knew my life and thought, more

or less, through having lived it. This raises three crucial questions I am often askedabout these theories. Is this exercise only a metaphor? What is the role of the

mathematics, which I have said I love yet which I have not used at any point?

And finally, is chaos always good? For instance, this argument is written entirely

in grammatical sentences, and is not an idea salad. Am I refusing chaos while

celebrating it?

The very common only a metaphor criticism comes from the old binary

between science and humanities, in terms of which metaphors should only ap-

pear in poetry, where they are beautiful or not, and not in science, where they

show lack of seriousness. As Kuhn (1979) pointed out, kinds of metaphor are also

fundamental to scientific thinking, which proceeds by proposing and testing sim-ilarities, similarity classes, models (which are a type of metaphor), and analogies.


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220 BOB HODGE

parallel, sometime unreal world, which is howevera key to the explanatory powerof

science.

By a process somewhat like a metaphor, a soul, an idea, a life, a nation or

group may sometimes be understood to behave as more or less like a particle, atother times more or less like a fluid or an organism. By super-position each can be

understood in any of these terms, in which case a common framework is applied

to otherwise different kinds of entity. Scientists do this all the time (e.g., treating

a falling body the same, in terms of Newtonian mechanics, whether it is a metal

ball or screaming human).

But dangers arise if the metaphor-like process is invisible, if interpretations in

terms of one framework are supposed to be the only truth (as mechanics for the

falling ball, psychology, or maybe theology, by that point, for the falling human).

Reductionism is a common but limiting tactic of science. It is just as damaging

when the models used are called Chaos Theory.

This raises the issue of the role of mathematics in Chaos Theory. The contri-

butions by mathematicians to chaos and complexity theories have been so rich

and important that the field today would not exist without them, and I am the

last to wish they had not written as they have done, interweaving their thinking

with mathematics. It is an additional advantage that this body of work is one more

reason to urge my humanities colleagues and students not to give up on mathemat-

ics. Yet some mathematicians have written as though the mathematical version of

Chaos Theory is its only true, legitimate form, so that applications, especially to

humanities, are not the real thing, always a misunderstanding to a greater or lessextent.

I do not accept this intellectual imperialism. The ideas of chaos mathematicians

are important because they illuminate so much of reality, the physical, biological,

social, and cognitive worlds we all inhabit, not because they are couched in math-

ematics. Mathematicians took all the great ideas of Chaos and Complexity Theory

from common language and common life, and they must be tested out and validated

or not there.

A fine mathematician like Mandelbrot is aware of this. He constantly moves

between mathematics and life. For instance, he writes: Our work on such fractalmodelling began with a bit of folk wisdom and a lot of natural history (1993,

p. 125). A three-body system including mathematics, science, and popular wisdom

is his recommended guide to chaos, not mathematics on its own.

In this respect, mathematics is like a language, in Whorfs three-body model

in which language, thought, and reality are a continuously generative system,

each constraining the other two, none autonomous. Like other kinds of language,

mathematics can produce thoughts and construct realities, just as thinking arises

from reality and demands expression in mathematics. Poetry is the mathematics of

the spirit, mathematics is the poetry of science (a statement that is only possible as

a result of language, not given in any pre-linguistic reality). Both create many newangles on reality. Neither is of interest on its own, if it were to assert an unrealizable


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used to ward off the terrors of deep chaos, to find order in chaos to use the slogan

of the chaos theorist I most admire, Ilya Prigogine (Prigogine and Stengers, 1984)

and that is what I have tried to do here. This is not a contradiction that negates the

spirit of Chaos Theory, it is the contradiction at its heart. At times, in my life as inthis article, I have veered too close to chaos to think productively, and I have also

clung too closely to limited patterns of order.

In hindsight, I believe I have more often not trusted enough that disorder will

give rise to unexpected positive outcomes, but that is only a provisional judgment

about my own case. As Prigogine notes, linearity works well, for much of the

time, with phenomena at or close to equilibrium. In physics, chemistry, or biology

I cannot estimate what proportion of phenomena, whether already explained or

still to be explained, needs a chaos perspective. With everything to do with being

humanart, thought, spirit, consciousness, language, love, power, civilization,

and all the achievements of humanityI would make a stronger claim. Everything

that matters in these areas is imbued with chaos and complexity, and no important

thinker about humanity has not been aware to some degree of them. I have been

dimly aware of this from early years, so these theories are not new, yet for me they

make a new sense. There is no revolution, yet there has been a revolution. In the

story of my life that is not likely to change in the coming years. Predictions are

still possible in a world of chaos and uncertainty, so long as they do not attempt to

become too certain or too precise.

REFERENCES

Bak, P. 1997.How nature works.Oxford: Oxford University Press.

Bateson, G. 1971.Steps to an ecology of mind.London: Paladin.

Baudrillard, J. 1981. For a critique of the political economy of the sign. St. Louis, MO:

University of Missouri Press.

Berger, P. and Luckmann, T. 1971. The social construction of reality. Harmondsworth:

Penguin.

Coronado, G., and Hodge, B. 2004. El hipertexto multicultural en Mexico postmoderno.

Mexico: Porrua/CIESAS.Chomsky, N. 1957.Syntactic structures.The Hague: Mouton.

Empson, W. 1930.Seven types of ambiguity. London: Chatto and Windus.

. 1935.Some versions of pastoral.London: Chatto and Windus.

Foucault, M. 1972.The archaeology of knowledge.Trans. A. Sheridan. London: Tavistock.

Freud, S. 1953.The interpretation of dreams.Trans. J. Strachey. Harmondsworth: Penguin.

Hodge, R. 1978.Foreshortened time.Cambridge: D S Brewer.

Kress, G. and Van Leeuwen, T. 1998.Reading images.London: Routledge.

Kuhn, T. 1962.The structure of scientific revolutions.Chicago: Chicago University Press.

. Metaphor in science. In Metaphor and Thought, Ed. Ortony, A., 409419.

Cambridge: Cambridge University Press.Lorenz, E. 1993.The essence of chaos.Seattle: Washington University Press.

Lukacs G 1968 History and class consciousness London: Merlin


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Poincare, H. 1943.La ciencia y la hip otesis.Madrid: Austral.

Prigogine, I. and Stengers, I. 1984.Order out of chaos.London: William Heinemann.

Saussure, F. 1974.Course in general linguistics.Trans. W. Baskin. London: Fontana.

Thom, R. 1975.Structural stability and morphogenesis. Reading, MA: Benjamin.Whorf, B. 1956.Language, thought and reality.Cambridge, MA: MIT Press.

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