"Foolishness and Chaos" Lundquist Address essay, 1993 April 30

"Foolishness and Chaos" Lundquist Address essay, 1993 April 30

"Foolishness and Chaos" was Gloria Kaufman's Lundquist Address speech that she delivered in 1993 after she was named the Lundquist Faculty Fellow the previous year.

Kaufman's essay argues that careful, linear analysis is not the only right way to think. According to Kaufman, "the mind works in a truly chaotic way." Throughout her essay, she describes several "foolish" stories of people's unique ways of thought and communication; this spontaneous way of thinking can yield better results than straightforward and highly logical thinking.

Kaufman argues that chaotic, messy thinking as well as humor can be a valid door to learning and understanding, just as linear thinking is.

Kaufman, Gloria

Gloria Kaufman Papers, Indiana University South Bend Archives and Special Collections

Lundquist Collection, Indiana University South Bend Archives and Special Collections

The version of the essay in the Kaufman Collection was incomplete, so the scan was finished from the Lundquist Collection.

1993-04-30

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Foolishness and Chaos

by Gloria Kaufman Lundquist Address April 30, 1993

The first foolish thing I'm going to do this evening is to speak about a number of events and ideas that have no apparent logical association. That is foolish because at the university we demand from students that they explain how their statements are related and that they don't wander off the subject. The LAST foolish thing I'm going to do is to contend that engaging in casual and whimsical behavior is frequently--VERY frequently--a more productive form of thinking than writing a carefully analytical essay. In between the first and the last, who · can say how many other foolish statements I'm going to make? Listen, my friends, and you shall hear....
Item number one in my disconnected, disorderly foolery. The brilliant Canadian playwright Sharon Pollock was on the IUSB campus in December of 1990 (thanks to the efforts of Tom Miller), and she spoke to my Women's Studies Seminar about many things, among them an experience she had had in Southern Alberta. The Native Americans there (or the "First Nation Peoples" as the Canadians call them or the pagans as Pollock affectionately labels them) were demonstrating against a projected dam that would destroy ecological balance in the region. Pollock noticed that the police were restrained and polite when the electronic media were present. She wondered what would happen when the media left, so she remained
with the Natives. Sure enough, when the crowds and the media had gone, out came the dogs and the vicious behavior on the part of the Canadian Mounted Police. The violence and danger became so great that the pagans thought they must decide under what circumstances it would be all right to use guns in their own defense.
Pollock went to their meeting that evening, and she listened. People spoke randomly, as the spirit moved them, and they spoke about anything and everything, even things seemingly unrelated to the subject at hand. One elderly man said, "These are the things that are now in my mind. I think none of them are related to guns or the dam, but this is what I'm thinking." And he spoke about the pleasures he had shared with his grandson that morning. Everyone listened respectfully and attentively. Others also spoke about personal matters. Some went on and on and on. There was no one in charge to cut anyone off or to decide who spoke when or to suggest brevity or staying on the subject. Any respectable parliamentarian would have had several nervous breakdowns. Not Sharon Pollock. The Natives spoke on, and she listened. After five hours, nothing was resolved, so they decided to go to bed and continue in the morning. They did so.
At the morning meeting, the same thing happened. People rose and spoke about whatever moved them. Strangely, however, by midafternoon, a consensus had been reached. They knew precisely under what circumstances they might use guns, and everyone left the meeting satisfied.
Am I foolishly suggesting we use the Native' s method for
conducting IUSB faculty meetings? It does occur to me that we have had very long and highly focused meetings over the past two and three years on particular problems that remain unresolved. So if we take TIME as our criterion, Sharon Pollock's pagans are much more efficient than we. That, however, is NOT the point of this anecdote. Let's just label it Foolish Story Number One.
Foolish Story Number Two. In the late 1950s, I was teaching freshman at Brandeis University how to think in an orderly way. In those days, we taught (and still teach) what is called linear thinking, listing things in 1, 2, 3 order, and excluding things that are extrinsic. My class was having a lively discussion on capital punishment, when a bright young man scathingly said, "This discussion is ridiculous! Obviously capital punishment is a good idea for some places and a bad idea for others." The class questioned him, but couldn't understand how he had arrived at his position. I tried to help by asking him to list the factors that led to his conclusion. "My mind," he said, with delicious contempt, "doesn't use lists."
"Of course it doesn't," I agreed. "The mind works in a messy, jumbled, simultaneous, UNlinear way. We impose artificial order so that we can communicate--which isn't happening right now." As a young Ph.D. candidate, I was enamored of logic and incisive linear thinking, and as a university professor I have also told students
to exclude irrelevancies in their anlaysis, only recently
acknowledging that the judgement of what is irrelevant is largely subjective. I foolishly thought I was teaching students to be objective when I was unknowingly teaching them to be exclusionary and arrogantly self-assured. But I was right in my class at Brandeis, which in the instance of capital punishment needed linear analysis to communicate.
Because we use logic so regularly at the university, we often fail to acknowledge that there are other modes of communication wholly unrelated to logic. When we share the smell of a good dinner, or the sight of a beautiful sunset, or a ride in a new car, a mere glance of the eye is sufficient to convey many pleasurable feelings. MOST of our communication is in fact wordless. Furthermore, in using words orally, we are careful as to how we pronounce them, because tone, pitch, pause and other auditory devices--as well as body language--often convey more than the words themselves. Few people, in listening to speakers, are moved by (or even aware of) the logic employed. Audiences are frequently more interested in asides and irrelevancies than they are in reasoned argument. In some cases, the audience is right: the asides can be more interesting and valuable--and even more important--than the trivia many of us choose to speak about.
How does the mind work? There are volumes and volumes written on this subject--in cognitive psychology, in neurophysiology, in books on theories of learning, in philosophy, and elsewhere. In
fact, we don't really know. It seems to me that the mind works in a truly chaotic way. We keep feeding all kinds of information into it, in a quite disorderly manner, and on its own--sometimes even when we're asleep, it reassembles things in remarkably satisfactory ways, whether we prod it or not. It is almost as if the mind is thumbing its nose at our intentions and at our highly directed efforts to arrive at conclusions. We've all had the experience of trying to recall something we know very well, but we just can't bring it to mind. Then we think of other things and lo and behold! it pops into our awareness. Now, what does that signify? that the mind is obstinate and spiteful? that the mind is a jokester? that it's uncooperative? that it doesn't want to be pushed? that the mind has a mind of its own? that we really can't control our mind and it has to keep reminding us because we arrogantly assume and assert control? What is the nature of this marvelous tool, the mind, that keeps playing jokes on us, without our willingness to validate its sense of humor?
In the past few years I have been intrigued by the realization that people often learn things through humor and wit--that is, in a disorganized and accidental way--things that they would otherwise not learn at all. For example, one of Muriel Sparks' characters says that another is "too cautious to live a life of normal danger"
( 30) • In discussing the meaning of that witty expression ( "too cautious to live a life of normal danger"), a student told me it had given her a sudden insight into a close friend who was
constantly indecisive. There are other people, I daresay, who do
not know that life has "normal dangers" and who also might be enlightened by Spark's witty phrase.
Sometimes humor clarifies complex concepts we had earlier been unable to comprehend. Women, for example, have perhaps never understood why men throw ·their dirty clothes on the floor rather than into conveniently located clothes hampers. Specimen A on your handout, a cartoon by Riana Duncan, humorously clarifies the source of that persistent and sadly universal habit.
When we arrive at understanding, there are usually several things simultaneously in our conscious minds, not a single conclusion standing in linear isolation at the end of an orderly process. Humor, like other modes of learning, is disorderly, and it has a large physical, physiological component.
Dr. Julian Whitaker supplies this story for my disorderly collection: "It was Sunday afternoon and I had not exercised in several days. Nor did I feel like doing it then. But I changed into my running clothes and headed straight for the beach for a 40-minute jog. It was a beautiful day with bright sunshine and early autumn air. started out slowly, and my spirits lifted immediately. As I warmed up, my mind became more active and productive. In the first five minutes, I solved two problems that had been bugging me for about a week, and wondered why I had missed their easy solutions .... More solutions came to minor problems and more importantly,
insights on how to improve my work or personal life began to flow."
(p. 8.) Exercise, it appears, is an excellent way to stimulate perception. That means I have been really wrong in advising students to come to my exams "well rested." Rather I should have told them to come "well exercised!"
The way we teach students to think at the university has been determined by prevailing views of science. In rhetoric, we taught students to be objective because we thought science was objective. Great scientists, of course, knew better and other thinkers--such as Thomas Kuhn--also knew that objectivity did not exist, but the prevailing notion was that objectivity was possible and that professionals lecturing at universities were objective. We also taught linear analysis as a part of scientific method.
But today, in the place of objectivity and linear analysis, science is offering us complexity and chaos. New and exciting paradigms of thought have been jetting their way through scientific circles in the past fifteen years, and those concepts explain the success of Sharon Pollock's Natives and why linear thinking often doesn't work and why humor is a good learning device and why Dr. Whitaker's exercising solved his thinking problems and a host of other things we have not previously understood. These new scientific concepts, I believe, will establish modes of thought in the next century that will become as pervasive and necessary as linear thinking and logical analysis have been in our century and previous ones.
This is the point at which I should bring in the band. Now
the fun begins, because our thinking habits (both in the university and out) are so firmly tied to the old science and so firmly entrenched that many of you (or even most?) will think the comments I'm about to make about chaos and chaos theory are just so much avant agarde foolishness. On the other hand, the pace of communication in 1993 is so rapid, indeed it is sometimes instantaneous, that there are probably a few among you already familiar with (and accepting of) chaos theory, which has been one of the hottest topics going in the past fifteen years.
For those of you new to the current thought on chaos, here's another story of fascinating foolishness. This is about a mathematician. As 'background, let me remind you that we are accustomed to viewing mathematical concepts in visual terms. We all remember the triangles and circles of plane geometry. Newspapers commonly use linear graphs to express all kinds of changes over weeks, months, and years. Using such graphs and other tools, economists for decades tried to understand the chaotic fluctuations in the cotton market. They did not lack data. By 1900, the South's cotton prices went through the New York exchange, and so did Liverpool's. Yet economists could not come up with a plausible analysis of how cotton price changes worked. No patterns were discernible. Benoit Mandelbrot, a mathematician interested in the abstract problem of fluctuation, was attracted to the subject ~5 It was-a rich source of data. He brought a different perspective...

(Specimen A
Comic of a boy throwing his clothes on the ground. His mother follows behind, picking up his clothes, and saying, "Clever boy!")
(Specimen B Courtesy of Heinz-Otto Peitgen
A Mandelbrot set)


...from the economists. Instead of looking at small changes versus
large ones, he sought similar patterns of change, no matter what the scale. Running the "data through IBM's computers, he found the astonishing results he was seeking." As James Gleick writes, "The numbers that produced aberrations from the point of view of normal distribution produced symmetry from the point of view of scaling. Each particular price change was random and unpredictable. But the sequence of changes was independent of scale: curves for daily price changes and monthly price changes matched perfectly. Incredibly, analyzed Mandelbrot's way, the degree of variation had remained constant over a tumultuous sixty-year period that saw two world wars and a depression." (Gleick, 86.) In the chaotic cotton data, Mandelbrot had found a nonlinear but precise pattern. What is truly amazing about this story is its sequel. No matter what field Mandelbrot plunged into, always analyzing disorderly and chaotic data, whether it was engineering or demographics or medicine or physics or geology or biology, his scaling patterns revealed UiAlimpe<.:~ed arl<:l astoundingly similar kinds of order. How could it be that heart fibrillations and cotton commodity prices followed the same chaotic patterns?! In other words, where the rest of us saw merely irregularity and chaos, Mandelbrot saw chaos with mysteriously underlying patterns--not regular or predictable patterns. Yet these patterns were shared by such diverse phenomena as trees and circulatory systems, by rivers and stock markets, by earthquakes and floods, and, in my foolish contention, by the process of thought itself.
Mandelbrot is only one of a number of mathematicians, scientists, and other intellectuals advent~rers who noted that in the real world, there is more disorder and irregularity than there is order. They felt that the regular Euclidean forms of geometry (and the linear analyses most people use) would never plumb reality and would always insult the complexity of nature. Adding all these thinkers together, we arrive at a substantial major movement concerned with what is called chaos theory. The movement's achievements are already so solid that it has earned a respectable place at major institutions of higher learning, and it has even given birth to an offshoot, "complexity theory," also deeply respected. My own alma mater, Brandeis University, for example, has just broken ground for a huge new building to house a chaos/complexity center. Even TIME magazine recognizes chaos. Last February, a cover story in TIME began as follows:
"Chaos theory likes to think that the beating of a butterfly's wings, say in central Mexico may, in the complex interactions of nature, eventually stir up a typhoon in the western Pacific. The Clinton presidency seemed determined in its first three weeks to validate chaos theory." (TIME, Feb. 22, 1993, 24.)
Like Native Americans who teach that all things (living and inanimate) are interconnected, proponents of chaos theory also preach that gospel. They contend, further, that to do the new kind of mathematics and scientific research necessary for understanding
chaos and turbulence, mathematicians and scientists must actively cultivate their intuitive faculties. According to Mandelbrot, "Intuition is not something that is given. I've trained my intuition to accept as obvious shapes that were initially regarded as absurd, and I find everyone else can do the same." (Gleick, 102.) In 1976 biologist Robert M. May stated that students should be introduced to the Verhulst equation early in their mathematical education, because "such study would greatly enrich the student's intuition about linear systems. Not only in research," May continues, "but also in the everyday world of politics and economics, we would all be better off if more people realized that nonlinear systems do not necessarily possess simple dynamical properties." (Peitgen-Richter, 8.) Other mathematicians are also
insisting on the major importance of mathematical intuition.
The language and even the experimental designs of many chaos projects are perfectly harmonious with new age holism. But the concerns that have led to chaos theory predate new age thinking by at least a century. The fact is, the tools of measurement that science has used were fairly accurate when applied to relatively static or regularly changing entities. But the world is not static and its rhythms are irregular. Scientists dealing with systems in flux have long been aware of the irregularities and the disorders that chaos theory is beginning to explain. Euclidean geometry does not really help in ~ understanding • nature because clouds are not spheres, as "Mandelbrot is fond of saying. Mountains are not
cones. Lightning does not travel in a straight line." (Gleick,
94.) The new fractal geometry developed by Mandelbrot and others "mirrors a universe that is rough, not rounded" or smooth. "It is a geometry of the pitted, pocked, and broken up, the twisted, tangled, and intertwined." (Gleick, 94. ) Mathematician James Yorke said, "The first message is that there is disorder. Physicists and mathematicians want to discover regularities. People say, what use is disorder? But people have to know about disorder if they are going to deal with it. The auto mechanic who doesn't know about sludge in valves is not a good mechanic."
(Gleick, 68.) Yorke's insistence that reality does not consist of a smooth continuum changing steadily from place to place and time to time, explains why most differential equations cannot be solved. The solvable ones in the text books, Yorke contends, have no relation to the real chaotic world.
(Please note that my comments about chaos theory this evening are generally provincial. I'm dealing largely with what has been happening in the U.S. and the English-speaking world, but as early as the 1950's the Russians were doing substantial work on disorder and chaos.)
Most of the work of the past fifteen years in the United States has focused on boundary areas where regularity turns chaotic. Similar patterns have been observed in earthquakes, heart disorders, stock market changes, etc., so that we find a remarkable coming together of professionals from formerly separate
disciplines. Thus at Chaos conferences and at the newly formed Chaos Institutes, we find, working together, metallurgists, physiologists, probability theorists, economists, Hollywood special effects designers, chemists, and others. What these people have in common is a belief that Mandelbrot's fractal geometry is the geometry of nature itself.
What is a fractal anyway? Is your intuition up to envisioning a mathematical dimension of 1. 3652? We all know the first dimension as a line, the second as a plane, the third as a solid, but what possibly can a fraction of a dimension be? Clearly we need a mathematical intuition thus far lacking in most of us. The usual dimensions we are accustomed to think of are adequate for regular forms, while Mandelbrot's fractional dimension applies to irregularities, roughness, and shapes otherwise immeasurable. Insisting that we must visualize our understanding about irregular rhythms and turbulence, he came up with one pattern now known as the Mandelbrot set and pictured in Specimen B. Think of it as a kind of graph that records all the possible behaviors of a particular turbulent system. While linear representations deal with fixed or with regularly changing entities, fractal representations allow us to envision irregular and chaotically changing systems. This is done by taking an equation (that describes a system) and graphing it repeatedly for thousands and thousands of values of x. The repetitions are so numerous that computers are necessary to do the job. In the end, we have a
picture capable of suggesting the possible parameters of change for
the particular system described by the equation. There is nothing linear about these fractal maps. For them chronological order is meaningless. Any point might have been generated at any time. Seeing the whole map of possibility is the goal. But seeing the entire map doesn't allow us to predict the behavior of single elements. Rather, the map gives us some new insights into the process itself.
One of the many reasons that fractals are important is that they account for the surprising phenomenon of rhythmic and regular systems suddenly going chaotic. This happens so frequently, perhaps universally, that scientists dealing with turbulence have been at an impasse for the past few centuries. They expected that a rhythm they had discovered in a dynamic system would persist. As early as 1845, however, Verhulst' s Law of Populations Growth Limitation demonstrated that orderly systems of growth, after a certain amount of repetition, erupt into chaos. In population growth, when the expansion was in the range of 245-256%, complications set in, and at 257% chaos erupted. (Peitgen-Richter, 6.) Whereas the stability of systems was thought to be proven around 1800, today, according to Peitgen-Richter, "we have to admit that a prognosis about the long-time behavior of the solar system (even when we restrict the problem to gravitational interactions) is not possible: the equations are not 'integrable' ...." (p. 2). Disorder and unpredictability reign supreme.
Returning to Specimen B, the Mandelbrot set, I'd like you to notice the enormous complexity that the set visualizes. The basic map is in picture a, top left. Notice the white rectangle in the center. It encloses a kind of curved angle with what appears to be a smooth edge. When the rectangle is magnified, however, we get figure b, and you can see it's full of curlicue shapes where figure a suggested a smooth edge. The white box in the center of bis further magnified to give us c, and you can see much greater detail, elegance, and refinement, along with a shape (labeled m) that resembles the buds on the set in figure a and suggests that each tiny increment, if enlarged, repeats the patterns exhibited. The box outlined in black near the top of c is enlarged to d, the box ind enlarged toe, thee-box (bottom left) enlarged to f, the f-box (in the middle) enlarged tog, the white box in the middle of g enlarged to h. This can go on infinitely. The Mandelbrot set, like other forms of the new math, demonstrates that the finite contains the infinite--which is of course at odds with some axioms of linear geometry. Fractal geometry engenders its own axioms, far different from those of Euclid.
The most disparate kinds of phenomena are explained when we understand that regular systems erupt into chaos. For example, in 1960 Sperling' s work on cognition revealed a surprising result. He flashed letters of the alphabet--very rapidly and in random, not alphabetic order--before a variety of people, to learn how many of those letters the mind could hold and feed back. His research
revealed an average consistently in the range of 4.5 on the number of letters the brain could recognize and retain in a brief period of time. This was true no matter what the I.Q. of the subject. (Reed, 23.) Since then there have been all kinds of theories about brain function to account for Sperling' s results--none of them convincing. It did not occur to scientists in the 1960s to factor chaos into their understanding of cognition, but Sperling's data exactly fits the pattern of the onset of turbulence noted in so many other dynamic systems by fractal scientists.* Fractal science works especially well on branching systems, and since cognition is a part of our neural system, it is ideally explained in fractal rather than linear terms. That is to say, we need
fractal math to understand how the mind works.
It is striking that in chaos theory along with ideas of disorder, randomness, and irregularity, we also have an insistence on interconnection. Nothing in the universe exists in isolation from anything else, and whatever we do here and now, affects everything else--be it in China or Mishawaka. A foolish idea? A dramatic example of testing interconnection is found in an experiment designed by Peter H. Richter at the University of Bremen. He mounted a double pendulum, which he set spinning in
*Note the closeness of Sperling's result (4.5) to the Feigenbaum number, 4. 669. One wonders exactly what Sperling' s number might have been, had he been able to use greater exactitude. See Gleick, 166-175, on the Feigenbaum number.
"chaotic nonrhythms that he could emulate on a computer ...." As
explained by Gleick, "The dependence on initial conditions was so sensitive that the gravitational pull of a single raindrop a mile away (my italics) mixed up the motion ~---£-i-fty--e1: · K4:¥­-rev-&3..11ti-ens. [in] about two minutes." (230). Now that's imputing a lot of power to a single raindrop! Whether or not the experiment is valid, it accurately reflects the thinking of Richter and others about the world--namely, that everything is connected and affects everything else. Nor is that so strange a scientific idea-­especially for those working with fluids.
You don't have to be a scientist to have noted that when you throw a pebble into a pond, the entire motion of the pond is affected--or that a stone in a brook affects the ways the water moves as it passes beyond the stone. Similarly, the air around us is also a fluid, far less dense than water--but a gaseous fluid nonetheless. That's why the wireless telegraph and radio broadcasts and all manner of inventions work--and perhaps that is why your cat can read your mind. Movement in a fluid medium is always transmitted, so Richter's raindrop experiment is not so bizarre as it perhaps sounds.
The aesthetic appeal of Mandelbrot's fractals has something to do with the rapidity of the spread and acceptance of chaos theory. Indeed, some of the computer-generated visual maps produced by mathematicians and scientists at the University of Bremen were so ravishing that they put together a public exhibition entitled
"Harmony in Chaos and Cosmos." The exhibit was so popular, it gave
rise to other exhibits and ultimately to a book entitled The Beauty of Fractals (1986). To suggest the visual appeal of the exhibits, these are some slides from the work of Prof. Dr. Heinz-Otto Peitgen and Prof. Dr. Peter H. Richter. As I show them, I'm going to read a few comments by mathematicians and scientists on their feelings about form and beauty.
Mandelbrot:
"Why is geometry often described as cold and dry? One reason lies in its inability to describe the shape of a cloud, a mountain, a coastline, or a tree. Clouds are not spheres, mountains are not cones, coastlines are not circles, and bark is not smooth.... Nature exhibits not simply a higher degree but an altogether different level of complexity. The number of distinct scales of length of patterns is for all purposes infinite.
"The existence of these patterns challenges us to study forces that Euclid leaves aside as formless, to investigate the morphology of the amorphous. Mathematicians have disdained this challenge, however, and have increasingly chosen to flee from nature by devising theories unrelated to anything we can see or feel." (Peitgen-Richter, v.) (These comments are remarkably applicable, aren't they, to scholars who want to dismiss amorphous multiculturalism and return to a Euclidean Eurocentric curriculum.)


Hermann Weyl (mathematician):
"My work has always tried to unite the true with the beautiful and when I had to choose one or the other I usually chose the beautiful." (Peitgen-Richter, 4)

Gert Eilenberger (physicist):
"Why is it that the silhouette of a storm-bent leafless tree against an evening sky is perceived as beautiful, but the
&-­
corresponding silhouette of any multipurpose university building is not? ....Our feeling for beauty is inspired by the harmonious arrangement of order and disorder as it occurs in natural objects-­in clouds, trees, mountain ranges, or snow crystals. The shapes of all these are dynamical processes jelled into physical forms ...." (Gleick, 117) (So too the fractal maps I'm showing you represent dynamic systems jelled into visual forms.)

Mitchell Feigenbaum (mathematician):
"In a way, art is a theory about the way the world looks to human beings. It's abundantly obvious that one doesn't know the world around us in detail.
"Somehow the wondrous promise of the earth is that there are things beautiful in it, things wondrous and alluring, and by the virtue of your trade, you want to understand them" (Gleick, 186­
187) . Scientists involved with chaos theory are critical of
"reductionism, the analysis of systems in terms of their component parts. . . . They believe they are looking for the Whole" (Gleick, 5), and in fractal math, the whole does not equal the sum of its parts. The new math abandons axioms that Western humanism (along with science) has taken as gospel. For chaos scientists, the axiom "the whole equals the sum of its parts" insidiously promotes the reductionism and limitations much of contemporary science. In fractal math, any part can itself be infinite and thus as large as
(or larger than) the whole. In another sense, a part does not exist without its whole and is in itself immeasurable. If the whole does NOT equal the sum of its parts, then logical analyses that examine each part and add them up will not reach an understanding of the whole. So you see an entirely different mode of analysis is mandated by chaos theory.
It is both philosophically and mathematically significant that Benoit Mandelbrot, the father of fractal geometry, states (after venturing a few definitions of "fractal") that he would rather leave fractal undefined! He writes," "I continue to believe that one would do better without a definition [of the term fractal]." (Mandelbrot, 361.) This may sound confusing and vague, but what it means is, Mandelbrot does not want to close the door of possibility by rigid definition. It's a radically new way of thinking.
As greater and greater complexities in dimension are revealed, they are found to correspond to complexities in nature, and the ideas of Mandelbrot, applied to the human body, are meeting with
spectacular success. For example, in the study of arrhythmias of the heart. There are hundreds of thousands of deaths each year in the United States from ventricular fibrillation. These occur when all of the parts seem to be working well, yet the whole system goes into fatal chaos. Dr. Ary L. Goldberger of Harvard Medical School encouraged collaborative work among mathematicians, physiologists, and physicists to deal with heart fibrillation. "When we see bifurcations, abrupt changes in behavior," he said, "there is nothing in conventional linear models to account for that ....In 1986 you won't find the word fractals in a physiology book. think in 1996 you won't be able to find a physiology book without it." According to chaos experts, "fibrillation is a disorder of a complex system, just as mental disorders--whether or not they have chemical roots--are disorders of a complex system" (Gleick, 281­284). While Goldberger found linear analyses inadequate for understanding heart fibrillation, Arnold Mandell, a San Diego psychiatrist, also found in 1977 that "' peculiar behavior' in certain enzymes in the brain ...could only be accounted for by the new methods of nonlinear mathematics" (Gleick, 298). Before chaos theory, "there were no tools for analyzing irregularity as a building block of life. Now those tools exist" (Gleick, 300). The intellectual map of the world is permanently changing, and we today find ourselves immersed in this great adventure.
As I have been speaking, I'm certain a number of your minds have been churning away calling up examples of fractal reality that
we constantly encounter. That is, some of you are already prepared to join me in my foolish journey into chaos theory and to call it not foolish but wise. Perhaps you saw the recent PBS program on "Healing and the Mind." The human body, of course, has enough branching structures to entertain the most fervid of fractal scientists. And although, as I recall, neither Moyers or any of his guests mentioned fractals or chaos, the entire series implicitly questioned the linear thinking of modern medicine and pointed out its difficulties in addressing the body as a whole organism.
The Moyers series showed how the kind of linear thinking ingrained in each of us held back the exciting discoveries of neuroscientist Candace Pert. Dr. Pert and her co-workers had collected fifteen years of data on neuropeptides, which are "biochemical units of emotion," before they were willing finally to accept their data and acknowledge its significance--namely that "the mind is not just in the brain but...is part of a communication network throughout the brain and body" (Moyers, 181). (This explains, does it not, why physical exercise improves mind function.) Usually fifteen years of such unequivocally corroborating data are not necessary to verify a thesis. Pert and her colleagues were inhibited from thinking clearly by their traditional training. That mental and physical were blended in peptides was difficult for them to accept because they were indoctrinated to believe that mind and body are separate and distinct. Pert amusingly attributed their reluctance to credit their evidence to what she called "a turf deal that Descartes made with the Roman Catholic Church. He got to study science, as we know it, and left the soul, the mind, the emotions, and consciousness to the realm of the church.... What's happening now may have to do with the integration of mind and matter" (Moyers, 179-180). The separation of body and soul, of course, predates Descartes. It probably came into Western thinking from the East with Orphic theology in the 7th and 6th centuries B.C. in Greece, and from there into ascetic philosophy and Christianity, which swallowed both the mysticism and the dualism of Orphism whole.
The new scientific insistence on the fallacies of dualism and reductionism, and the new scientific emphasis on the roles of integration and intuition represent a cataclysmic change in scientific method that, I contend, will thoroughly change modes of thought in the 21st century. The patterns of thought we currently use come largely from the great discoveries of science in the past and I doubt that will change. That is, the great discoveries of contemporary science will dictate paradigms of thought in the century to come.
Chaos science's focus on interconnection and its concerted attack on Euclidean tools and linear thinking already has parallels in the humanities. Both feminists and multiculturalists have been highly critical of linear thinking, which has centered narrowly on the ideas and achievements of white European males, excluding most
of the world's populations. Feminist emphasis on inclusion and on
the dignity and importance of every human being is fully in harmony with the new science. Currently there are scholars in all the humanities (from philosophy to literary studies to art criticism) attending chaos institutes and applying chaos theory to their work. Of course some academic disciplines have for decades been teaching holistic rather than reductionist approaches. Architectural design, nursing, home economics, and nutrition, for example, have generally taken whole environments into account, and certainly the 21st century will afford them greater respect than has the 20th.
In our intellectual history, most people recognize a paradigm shift only after it has occurred. Today, if we look attentively (or even half-heartedly), we can see the shift in progress, and it is enormously exciting. We are actually watching new forms of thought being brought into being! Never has the intellectual world been at a more fertile stage! Never have thinkers been more highly privileged than we!
Let me say, however, that the new value assigned to nonlinear forms of thought does not mean we abandon linear thought entirely, but only where it has proven inadequate. Let us not forget that linear thinking (whatever its limitations) and our attempts to be objective (however flawed) have led to valuable insights as well as to misdirections. And let us also be aware that linear analysis has played a role in creating chaos theory itself. Both modes of thinking--linear and complex--co-exist now and they should also in
the next century--with greater awareness, to be sure, of the limitations of each. I am not arguing that linear thinking will be abandoned but rather that nonlinear thinking will become dominant.
New modes of thought will take into account the huge disorderly world previously ignored. The shift will emphasize inclusion rather than exclusion, in history as well as geology, in politics as well as in physics, and it will look suspiciously at disciplines that seek to remain pure and separate, just as it will question decisions by, for example, 4th century scholars who choose to study St. Jerome while excluding Jovinianus. Such decisions were and are personal, subjective, and highly biased rather than objective, as formerly asserted.
Contemporary science enforces and deepens critiques of objectivity by showing it as based upon a duality of body vs. mind that does not exist. In being objective, we were told, we reject our feelings and use our minds. But now science shows that feelings embody mind and that mind embodies feelings. To say they are separate is to delude ourselves.
In the 21st century, new tools of science will bring fractal mathematics and complexity theory to our understanding of thought­process, and that will affect all studies at the university. The insistence of scientists upon the connection of thought with all other forces and dynamical systems will be so widely accepted that holism will be axiomatic. Whereas in the 20th century we have been teaching students to separate into components, to analyze, to
exclude, in the 21st we'll be teaching them to appreciate branching connections, to harmonize, to include everything they can because everything is relevant. Computers and fractal math give us tools of inclusion previously lacking--magical and consequential tools.
To say that everything relates to everything else, that in effect every fact, every action, every raindrop is significant or consequential, puts a newly enormous burden on us* as collectors of information and as thinkers trying to understand ourselves, our world, and our universe. One of the most exciting ideas going is David Shapiro's concept of "group mind." Shapiro contends that the world is too complex to be understood by a single person, and that many individuals are contributing to a group mind that in part exists and in part is being brought into existence by new insights. Subsections of group mind exist, and there is also a world group mind.
Shapiro's idea is a new-century concept that disallows the competition and arrogance of twentieth century university scholarship. Willy nilly, in the 21st century, the university will no longer to able to separate itself from the world it studies and it will have a healthier as well as more realistic sense of its citizenship in a community for which it bears increasing respect.
(That is to say, other universities will begin to resemble IUSB.)
*Questions about what to include and what exclude in our courses raise questions about pedagogical morality.
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Competition in the 21st century will be looked upon as comparable to the foot's quarreling with the hand--as utterly self­defeating and senseless. Rather, awards will be given for outstanding collaboration and cooperation. At IUSB and elsewhere, many of us have been experimenting with collaborative learning, so we are already taking tiny steps toward our challenging future. I can't imagine what devices there will be to stimulate our individual -and collective intuition, but because of the new validation of intuition by science, I look forward to seeing a text in the year 2000 entitled 101 Types of Intuition and their Applications. Intuition will not be the amorphous concept it is today. It will be carefully studied, and it will have meaning in many specific senses that students will be asked to master.
Humor will be one of the devices used to stimulate intuition, because humor makes fractal sense. Physiologists have shown that humor affects our entire system--chemically, dynamically, psychically and in every other way. Similarly, fractal science explains why Dr. Whitaker's exercising led to productive thought. It stimulated his total being, in which thought is embodied. Fractally seen exercise stimulates mind as much as muscle.
New theories of chaos validate all kinds of information that
traditional studies have excluded. They lead to a new respect for
nature, for people, and for all of being--a respect that has been
notably absent in many prominent Weste:i;-n thinkers. With the
development of global consciousness and ideas analogous to
Shapiro's group mind, a new sense of interconnection and interdependence must lead to a new spirit of toleration. Leslie Kanes Weisman suggests that chaos theory mandates universal respect for all human beings, disallowing hatreds~ sed upon raaism-+an~all 't-be ether isms. , because to hate others is to hate ourselves.
Although my time is just about up, I haven't begun to suggest the vast territories that the new ideas of chaos embrace. I wanted to show how chaos theory applies to music, how Mandelbrot planted :the-already germinating seeds of a new aesthetics base l:l}?OB f.-t:a.G't;a--: s·e-a-les ,[!iow David Shapiro's idea that memory is process not data makes fractal sens~ and how positive and powerful chaos theory is when we apply it to our personal lives. I wanted to show at even greater length how feminism and multiculturalism stress values that chaos theory promotes and depends upon.
So I end, in the cherished foolish way of the ancient, the medieval, the renaissance scholar--wanting to explain everything-­and in only 60 minutes. And I end also, as I promised, contending with what I hope you now look upon as newly WISE foolishness, contending that Sharon Pollock's Native Americans, in their whimsical, chaotic, spontaneous meeting, exhibited a more productive form of thought than you or I might have achieved by writing an analytical essay. Their unstructured, free-wheeling meeting was effective because it was consistent with natural thought process and with chaotic reality. The Natives understood that everything about their being and their lives was somehow
• involved in the question of guns and self-defense. Their successful method is fully harmonious with chaos theory--and the Natives, believe it or not, needed no instruction from Benoit Mandelbrot. In response to my foolishness and chaos, you have shown wise patience and orderly forbearance, for which I am deeply grateful. Thank you .
•

WORKS CITED
Gleick, James. Chaos: Making a New Science. Penguin Books, 1987. Mandelbrot, Benoit. The Fractal Geometry of Nature. NY: W.H. Freeman and Co., updated and augmented 1983. Moyers, Bill. Healing and the Mind. NY: Doubleday, 1993. Peitgen, Heinz-Otto and Dietmar Saupe, eds. The Science of Fractal Images. NY: Springer Verlag, 1988. Petgen, Heinz-Otto and Peter H. Richter. The Beauty of Fractals. NY: Springer Verlag, 1986. Reed, Stephen K. Cognition, 2nd edition. Brooks/Cole, 1988. Spark, Muriel. The Mandelbaum Gate. NY: Avon Books, 1992. Whitaker, James. Health and Healing (Nov. 1992), Vol. 2, No. 12.