v

Voyage(Pilgrimage) to Cythera-Jean Antoine Watteau 1721

Île des doux secrets et des fêtes du coeur!De l'antique Vénus le superbe fantômeAu-dessus de tes mers plane comme un arômeEt charge les esprits d'amour et de langueur.

Voyage to Cythera-Charles Baudelaire

AN APPROACH TO THE COMPLEXITIES OF CHAOS THEORY

by Gabriela Agüero

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Presented to Prof. Ellen Judd

Contemporary Anthropological Theory

"God does not play dice." Albert Einstein

“What you don’t get when you grasp is called the subtle”

The Essential Tao

CHAOS THEORY-INTRODUCTION

This paper will propose a design for a one week unit of

a course in Contemporary Anthropological Theory exploring the

application of Chaos Theory and its relevance to Socio-

Cultural Anthropology as an attempt to make the necessary

connections to the field. The paper will be divided amongst

several headings starting by an explanation of Chaos theory

and its importance in the field of mathematics and physics

where it originated. Further I will explain the division of

the main contributions of the theory with an explanation of

some applications to social-anthropological studies and with

a discussion of Chaos Theory as it applies to aesthetics and

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the Rococo movement. Finally I will attempt to contrast and

compare chaos theory as it applies to the ideas of Eastern

and Western Philosophical frameworks of thought.

INTRODUCTION

Chaos theory was discovered by the meteorologist Edward

Lorenz in 1960 while working on an experiment on weather

variation. Apparently this discovery happened as a mistake

while typing the numbers that were to be keyed in a computer

in order to produce a model of equations that would

eventually produce a graph symbolizing weather patterns. The

pattern that emerged was a surprise to him. Until then

physics had followed the steady pace of “linear differential

equations” in the Cartesian manner that were very predictable

and which had been until then analyzed in a myriad of ways.

By linear it is understood a theory which is predictable and

follows an order that is pre-established from beginning to

end. The Instability exhibited by the design that Lorenz

observed went against the sequence that he was supposed to

have obtained. Scientists measure of success can allow

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minimal differences of decimal places (two or three). The

infinitesimal difference between the curves was so small that

it has been labeled butterfly effect as the minimal movement of a

butterfly flapping its wings. The movement of air is so

minute yet it shows that what the atmosphere would have done

diverges from what it was expected it would have done” what

is called in Chaos theory sensitive dependence on initial conditions.

Just a tiny change in the initial conditions can affect the

outcome and behaviour of the whole system. (Odifreddi 2005)

Lorenz went on to experiment with the dripping of water.

As he observed graphed patterns of this water and what

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effects it had on a barrel of water through which it moved,

he came up with equations and another graph that represented

a double spiral and realized that the apparent disorder or

chaos actually had a particular pattern. Hence another of the

principles of Chaos theory is concealed order, Lorenz called

this the Lorenz Attractor.

What these images show and

are now reproduced everywhere and what they have

come to symbolize, are the representations of what

lies within the hidden order of things. Previously

not apparent to the eye or our perception, they

became now exposed. Lorenz being a meteorologist

did not get this paper published in widespread journals and

many years had to go by until other fields realized the scope

of his discovery.

Benoit Mandelbrot, an employee of IBM who was studying the

fluctuation of cotton prices also discovered that even

through the years and through many different historical

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events such as wars, the degree of variation of the price of

cotton had remained constant over a period of sixty years.

Helge Von Koch went further by exploring other mathematical

constructions that started by a simple equilateral triangle

and consisted of adding triangles to each side ad-infinitum

and added the dimension of fractal to define the attribute of

self-similarity as is the Lorenz attractor. This mathematical

pondering brought about the Mandelbrot set which is the

production of fractal equations by using a complex number that is

put through a simple equation z=z +c which if repeated ad

infinitum would create shapes that are reproductions of the

original set. Many applications of the Mandelbrot set have

been used in art and music producing even Bach variations

that when listened to sound “musical and creative”. 1

(Odifreddi 2000) Apply this to the information stored in the

DNA and every cell of the human body and you have a thorough

understanding of many previously hidden truths.

1 For this see: Bach to Chaos: Chaotic Variations on a Classical Theme”, Science News, Dec 24, 1994.

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The beauty at the boundary of the Mandelbrot set can be

quite exciting. It has been said that pictures of the

Mandelbrot set "demonstrate that out of research an inner

connection, a bridge, can be made between rational scientific

insight and emotional aesthetic appeal; these two modes of

cognition of the human species are beginning to concur in

their estimation of what constitutes nature”. (Talaye Minai

1993: 231) I will get to this further when discussing the

Rococo movement and the application of aesthetics to Chaos

theory or was it the other way around? As complicated as this

theory might apparently sound, its applications are endless

in diverse fields and areas of study. As we become aware that

this apparent disorder is present everywhere creating

operational systems that make visible the patterns in which

nature works (or at least seemed to have always done) the

answer will become clearer. Chaos Theory, quantum mechanics

and the Theory of Relativity have revolutionized the way in

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which we view the universe. This change is also philosophical

as it puts man as just one more piece of the puzzle and not

in any predominant position. Holistically speaking this

theory is environmentally friendly if we see ourselves as just

another component of an equation.

CHARACTERISTICS

Chaos theory is basically holistic, relational and

interdisciplinary. (Brady, 1994) Its paramount importance is

in the fact that is malleable and knowledge from one field

can be transferred to another. Mathematicians working on

catastrophe such as Tom (Odifreddi 2004) had already hinted

how this could be done in other areas but only slightly so.

As mentioned before, for the Humanities this mathematical

model was applied to the study of the Rococo period as an

example of its non-linearity and complexity and apparent randomness

something it shares with Chaos Theory. A style that was

perceived as purely decorative also had hidden order. The

essential elements of the theory of chaos fractals, butterfly effect

and strange attractors were reformulated later in more mundane

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terminology more applicable to the non-mathematical layman

as: concealed order, self-similarity, non-linearity, and constrained randomness.

(Brady, 1994)

In the concept of concealed order in Science and the

Humanities by calculus Science has been able to precisely

analyze the flow of water down a stream if the water is

coming down regularly (thanks to Newton). If the water hits a

rock the pattern changes and Chaos Theory comes in handy to

analyze the discontinuous pattern that erupts. In the

humanities the disparities account by the criss-crossing of

fields. The classical example is the a-techno tonicity of

Rococo that seems in disorder as in comparison with

classicism for example. Or the replacement of the baroque

cupola by the rococo painted ceiling that also represents a

shift in the hierarchical visual order. The other example is

the literary genre is Marivaux’s La Vie de Marianne that is

an apparently disorganized novel as is for example Julio

Cortazar’s Hopscotch that can be read from several places

within the book to create alternative and multiple endings.

(Brady 1994) Artists never work detached of their social and

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political milieu, to presuppose the opposite is naïve. The

weaving of the hidden order has many layers.

ANTHROPOLOGY

According to the application of Chaos Theory On The Order

of Chaos Social Anthropology and the Science of Chaos (Mosko and Damon

2005) much of twentieth century science has been based on

Newtonian principles which means the kind of science that

takes for granted that by knowledge of the parts we would be

able to predict the movement of the whole (as in the

planetary system). At the turn of the century Poincare

(Gleick, 1974) was able to determine that these principles

only applied when dealing with simple systems. For social

anthropology as for other disciplines dealing with highly

complex systems Chaos Theory is applicable. As specified

above, non-linearity, fractal geometry and self-similarity are some of the

conditions present. What is particular to anthropology though

is that some of the principles of chaos theory “offer an

alternative to integrate some of Anthropology’s most

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provocative and far reaching theories”(Mosko 2005: 5) already

in existence, namely :

Evans-Pritchard analysis of the dynamics of segmentaryopposition; Levis-Strauss canonic formula, Forte’sformulation of the development cycle in domestic groups;the unpredictable influence of individual personalities onhistorical events; the historical pervasiveness of binaryconstructions in socio-cultural systems; structuralanalyses of history, theory of religious and politicalhierarchy; Wagner’s “obviation theory” and particularly hisgrasp of representation in symbols standing for themselves,Marilyn Strathner’s portrayal of Melanesian sociality andAppadurai’s perception of the patterns shaping currentprocesses of globalization. (M&D 2005, 5)

According to the authors what anthropology needs is to

return to its sources in order to consolidate what

“disciplinary coherence” (Mosko 2005, 6) already exists

between its already breaking ground principles and its

correlation with the tenets of chaos theory. This

understanding is not yet complete or internalized so before

that happens there needs to be a conscience of the

limitations in theory that have been applied so far: Marxism,

functionalism, structuralism, developmental an other models

that can not count on describing or explaining the apparent

randomness of events. New ways of looking at anthropology

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have arisen that have been trying to explain or attempt to do

just that: feminism, deconstruction, postmodernism, literary

criticism amongst others. Chaos Theory will be next.

The characteristics that are underlying this apparent

disorder in the natural sciences have been described as

having the following principles: Firstly, sensitive dependence on

initial conditions which in anthropology encompasses the

particularities of culture and never despite similarity be

considered to be the same in every respect. In other areas this

would equate with Anthropology’s emphasis on qualitative

rather than quantitative research that takes us to the second

tenet of Complex, unstable relations amongst variables where the

interacting parts can produce great variables at later stages

and involves the principle of strange attractors: the movement of

a system never repeats or crosses itself as in the

sacred/profane principle elaborated by Durkheim, which

although seemingly repetitive never repeat themselves. No

analogous moment in the performance of the same rite are

perceived historical equally (M & D: 19). Dynamical

transformations in accordance with non-linear (rather than

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linear) equations could be also equated with Dumont’s studies

notion of religious hierarchy in correlation to Van Gennep’s

reformulation of Durkheim’s profane/sacred duality. Further

bifurcations and strange attractors on Van Genneps’ term

pivoting of the sacred: “within a single sequence of

separation, transition and incorporation a person arriving at

a ritually sacred condition might then consider his/her

condition to be relatively profane from which to seek further

sacralisation”. (M & D :20)

From there additional bifurcations might occur pivoting

between the two the combinations which are endless. What

chaos theory does is it takes into account the various

(infinite) combinations. This is now compared to very

predictable cases of continuity and cohesion, while also

considering discontinuity, contradiction, conflict, inversion and reversibility as

the other side of the coin. The endless possibilities that

are also present in Marxian theory of “flows and ebbs” of

capitalist production for example or in Levis-Strauss formula

of the structure of myth that could end in a spiraling number

of alternative versions to a given myth. This theory has been

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applied to explain the unexplainable as was the massacre in

Rwanda where the apparently random order of historical events

might be explained in a “strange-attractor of phase-two

alteration in a non-linear systems”2 where the author makes

sense of the massacre through the analysis amongst other

variables of the signs exhibited through popular political

cartoons inciting the population to the killings that would

take place.

As regards Fractal Geometry that I explained above as the

Mandelbrot set in the beauty of the images thus created, what

it is essentially considering is the principle of “self-similarity”

if we consider for example the repetition of the leaves of a

fern or the formation of coastlines seen from space the earth

is the “visual manifestation” of Chaos’ Theory non-linearity

that might appear as randomness or disorder. This concept goes

in opposition to concepts such as the “organic analogy by

which the functions of organs in relation to an individual

person’s bodily system replicate the functions of persons in

relation to a social system”(M&D: 25) Yet these could also be

2 See. Christopher Taylor; “ Fluids and Fractals in Rwanda: Order and Chaos” p.136 (N&D 2005)

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seen as manifestations of dualities inherent in

anthropology’s interest in the body such as gender

differences, social construction of personhood and societies

in the world’s cultures amongst others that are fractal

(self-similar) in their relationship to each other. (Mosko

2005) Or further as in Marx’s theory of fetishism where a

person takes on the attribute of the object it has produced

as he stated: "My recapitulation of mathematics and the

natural sciences, was undertaken in order to convince myself

also in detail…that in nature amid the welter of innumerable

changes, the same dialectical laws of motion force their way

through as those which in history govern the apparent

fortuitousness of events…" (Woods 1995: 16) The discovery of

non-linear constants by Mitchell Figenbuam of certain

numerical constants has added the character of universality to

the theory of chaos. What this means is that these variables

in different areas, take population changes as one example,

have always behaved in accordance with certain previously

unknown quantitative constants. If applied to Anthropology

per se we can extrapolate that apparent cross-cultural

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universals for example might happen because there is a hidden

order prevalent. This could have in itself enormous

implications for Anthropology (M& D 26)

With the work of Prigogine’s3 writings in his Chaos: Man’s

New Dialogue with Nature (1984) we come across concepts of time

that are in concordance with the second law of thermodynamics

that explains the concept of irreversible time unlike the

linear or reversible time of Newtonian mechanics. This

concept explains that it would be able to explain a complex

system backwards and forwards in time4. For Prigogine culture

and society are as much a part of the natural universe as3 Prigogine is known for his definition of dissipative structures and theirrole in thermodynamic systems far from equilibrium, a discovery that wonhim the Nobel Prize in Chemistry in 1977. Dissipative structure theoryled to pionneering research in self-organizing systems, as well asphilosophic inquiries into the formation of complexity on biologicalentities and the quest for a creative and irreversible role fo time inthe natural sciences. His work is seen by many as a bridge betweennatural sciences and social sciences. (Wikipedia)4 The classic example of entropy increasing is the case where oneadds a drop of red dye to a glass of clear water. The previousorganization or structure of the system (undiluted dye in onecontainer and water in another) is quickly reduced to just pinkishwater. The Second Law of Thermodynamics states that no matter howlong one waits, the dye will never form itself again into a singledroplet, effectively separated from the remainder of the solution,which would again be clear water.http://www.halexandria.org/dward145.htm  

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galaxies and subatomic particles and what it presupposes is

history develops in irreversible time and in pre-established

order which are labeled “natural laws of self-organization”. (M & D

2005:33)

These principles are being applied by anthropologists

who are also well versed in Chaos theory and have a

conceptual understanding of the formulas involved in the

application of the theory. Morava in his article “From Levis-

Strauss to Chaos and Complexity” (2005) himself a trained

mathematician, warns about the qualitative-quantitative

marriage that involves the application of chaos theory

without the necessary observation in order to fully

understand the application of “the numbers for making

predictions” (Morava, 39). This warning is relevant through

the readings that assume an ample knowledge of

anthropological theory and mathematical concepts. For the

success of learning about Chaos Theory in a week’s course it

would be fundamental to read several introductions to the

subject from the different perspectives and choose perhaps

one article on anthropology and another in aesthetics since

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this contra-punto would emphasize the applicability of the

theory widely. Staying on the study of one discipline alone

would therefore undermine the interchangeable capabilities of

Chaos Theory. In my own personal experience with a background

in Fine Arts the examples of Watteu or other forms of art as

subject to the application of the theory were far easier to

understand and perhaps that is also the order in which they

might be presented for further clarification. Art has always

remained a mystery to the un-initiated yet it remains that if

you are an artist or not the apparent order is always visible

and enters the mind through other hidden methods/avenues of

perception related to the fluctuations of emotional response.

EAST AND WEST

It is apparent that Chaos theory represents the accidental,

exceptional, as an intrinsic part of nature. This conceptual

shift according to Talaye Minai (1993) is hidden and had been

already explored in the ancient Taoists texts. What it turns

out to be is that the creative source and “ongoing power of

cosmic life” (Minai 1993: 156) has always been there. Quoting

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Octavio Paz the Mexican writer and philosopher Minai makes a

clear distinction between East and West

“The West teaches us that being is dissolved into meaning,and the East that the meaning is dissolved into somethingwhich is neither being nor non-being: In a The same which nolanguage of silence names” (Talaye Minai 2005:156)

As in the Tao being is not being a relativity that pervades

all things as the sum of all orders. Chaos however is not an

equivalent with disorder but with what creates time: “a

hidden law that bounds nature, cosmos and culture” (Talaye

Minai 2005:157) Having exhausted the epistemological concepts

of knowledge namely deductionism and holism Minai proposes

that we look into a “circumstantial order” neither connected

to the rules of above (hierarchical and deductionist) or

below (holistic or from below). There is a flow that is

coherent with the universe in this proposition that has

become proof through the Chaos Theory principles. Like

members of an ant colony we carry inherent “messages” and as

our bodies constituted of million of cells, we are but

particles of a bigger whole where there is no power of one

part over another but they are all interdependent in the way

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in which Zen philosophy views the universe. It is the

emphasis on the interdisciplinary that makes Chaos Theory

interesting because it emphasizes the interconnectedness of

all areas of human interest into one. According to Fritjof

Capra in his Tao of Physics (1985) phycists and mystics have to

frame their thought very flexibly in a pattern that keeps

moving as changing as with Eastern mysticism “in an organic

view of the world”.

The painting A Voyage to Cythera by Watteau amply represents

a very organic (dis)organization where shapes dissolve into

each other. The shimmering of the silk clothes against the

background melt into one. Though Watteau’s paintings are not

very large this intimacy required to view them (to the fear

of museum guards) needs your total involvement-dissolvement

into the experience. The event is highly sensual. First

censored this painting was thought to represent an emblem

against the revolution then reclaimed as a symbol of a bygone

era. More precisely Voyage to Cythera is lyrical and therefore

defies explanation. There is no simple revelation that can

challenge the visual experience, since the interaction of

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viewer to art remains highly personal. What Chaos theorists

explain in mathematics eloquently is purely and simply

transcendental un-explainable and not real in the mental

image, the illusion that is art. From the subtle shifting of

shapes into each other fractal concepts, and butterfly effect

make the most absolute sense to art. Though not within the

short scope of this paper, an interesting interdisciplinary

discussion could ensue on the subject of aesthetics-

philosophy-anthropology and Chaos theory from an ontological

perspective. Chaos theory operates as a conceptual view of

reality. Basically Chaos theory is more a discovery than an

invention it is the realization and a humbling yet powerful

way of observing understanding and studying the universe. As

stated before with consistent study anthropology is geared

towards adopting this world view. In synthesis:

The most encouraging thing about the new mathematics of chaostheory is that it represents a rejection of sterileabstractions and ivory-tower reductionism, and an attempt tomove back towards nature and the world of everydayexperience. And to the degree that mathematics reflectsnature, it must begin to lose its one-sided character andacquire a whole new dimension which expresses the dynamic,contradictory, in a word, dialectical character of the realworld. (Woods and Grant 1995)

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As in the Voyage to Cythera the characters in the painting

could either be leaving or arriving. That in itself would

change the whole perspective of its apparent hidden meaning.

If the ship represents the embarkation of a new society

tinder the sign of Venus, Cythera the destination, and love

the means, the voyage occurs whenever an audience or by

extension a society is transported across the sea of desire

to a utopia of love, pleasure, peace, and freedom.(Cowart

2001) This in itself resembles art as an illusion of nature

where the variations of love and beauty are endless where

chaos represents the most infinite of orders. The voyage

towards Chaos Theory for Anthropology seems inevitable.

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Selected Bibliography

Brady, Patrick. 1994. Chaos in the Humanities: A Syntheis Book. NewParadigm Press. Tennessee.

Capra, Fritjof. 1985.The Tao of Physics. New Science Library.Shambala. Boston.

Cleary, Thomas. 1998. The Essential Tao. Castle Books. New Jersey

Cowart, Georgia. 2001.Watteau's Pilgrimage to Cythera and thesubversive utopia of the opera-ballet. In Art Bulletin. September.

Gleick, J. 1994. Chaos: Making of a New Science. Penguin. New York

Mosko, Mark and Frederick Damon. 2005. On the Order of Chaos: SocialAnthropology and the Science of Chaos. Berghan Books. New York.

Odifredi, Piergiorgino. 2004. The Mathematical Century: The GreatestProblems of the Last 100 years. Princeton University Press.Princeton and Oxford.

Prigogine. Illya. 1989 Order out of Chaos, Man’s New Dialogue withNature. Bantman Books.

Talaye Minai, Asghar. 1993. Aesthetics, Mind and Nature: ACommunication Approach to the Unity of Matter and Consciousness. PraegerPublishers. London.

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Woods Alan & Ted Grant. 1995. Reason in Revolt - Marxist Philosophy and Modern Science. WellRead Publications.

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