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Chaos and dialectics

Tuesday 29 December 2009

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Chaos and Dialectics

in "Reason in Revolt: Marxism and Modern Science"

By Alan Woods and Ted Grant

Dialectical materialism, elaborated by Karl Marx and Frederick Engels, was concerned with much more than political economy: it was a world view. Nature, as Engels in particular sought to demonstrate in his writings, is proof of the correctness of both materialism and dialectics. "My recapitulation of mathematics and the natural sciences," he wrote, "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…" (16)

Since their day, every important new advance in scientific discovery has confirmed the Marxian outlook although scientists, because of the political implications of an association with Marxism, seldom acknowledge dialectical materialism. Now, the advent of chaos theory provides fresh backing for the fundamental ideas of the founders of scientific socialism. Up to now chaos has been largely ignored by scientists, except as a nuisance or something to be avoided. A tap drips, sometimes regularly, sometimes not; the movement of a fluid is either turbulent or not; the heart beats regularly but sometimes goes into a fibrillation; the weather blows hot or cold. Wherever there is motion that appears to be chaotic—and it is all around us—there is generally little attempt to come to terms with it from a strictly scientific point of view.

What then, are the general features of chaotic systems? Having described them in mathematical terms, what application does the mathematics have? One of the features given prominence by Gleick and others is what has been dubbed "the butterfly effect." Lorenz, had discovered on his computer-simulated weather a remarkable development. One of his simulations was based on twelve variables, including, as we said, non-linear relationships. He found that if he started his simulation with values that were only slightly different from the original—the difference being that one set were down to six decimal places and the second set down three places—then the "weather" produced by the computer soon veered wildly from the original. Where perhaps a slight perturbation might have been expected, there was, only after a brief period of recognisable similarity, a completely different pattern.

This means that in a complex, non-linear system, a small change in the input could produce a huge change in the output. In Lorenz’s computer world, it was equivalent to a butterfly’s wing-beat causing a hurricane in another part of the world; hence the expression. The conclusion that can be drawn from this is that, given the complexity of the forces and processes that go to determine the weather, it can never be predicted beyond a short period of time ahead. In fact, the biggest weather computer in the world, in the European centre for Medium-range Weather Forecasting, does as many as 400 million calculations every second. It is fed 100 million separate weather measurements from around the world every day, and it processes data in three hours of continuous running, to produce a ten day forecast. Yet beyond two or three days the forecasts are speculative, and beyond six or seven they are worthless. Chaos theory, then, sets definite limits to the predictability of complex non-linear systems.

It is strange, nevertheless, that Gleick and others have paid so much attention to the butterfly effect, as if it injects a strange mystique into chaos theory. It is surely well established (if not accurately modelled mathematically) that in other similarly complex systems a small input can produce a large output, that an accumulation of "quantity" can be transformed to "quality." There is only a difference of less than two per cent, for example, in the basic genetic make-up of human beings and chimpanzees—a difference that can be quantified in terms of molecular chemistry. Yet in the complex, non-linear processes that are involved in translating the genetic "code" into a living animal, this small dissimilarity means the difference between one species and another.

Marxism applies itself to perhaps the most complex of all non-linear systems—human society. With the colossal interaction of countless individuals, politics and economics constitute so complex a system that alongside it, the planet’s weather systems looks like clockwork. Nevertheless, as is the case with other "chaotic" systems, society can be treated scientifically—as long as the limits, like the weather, are understood. Unfortunately, Gleick’s book is not clear on the application of chaos theory to politics and economics. He cites an exercise by Mandelbrot, who fed his IBM computer with a hundred year’s worth of cotton prices from the New York exchange. "Each particular price change was random and unpredictable," he writes. "But the sequence of changes was independent of scale: curves for daily and monthly price changes matched…the degree of variation had remained constant over a tumultuous 60-year period that saw two world wars and a depression." (17)

This passage cannot be taken on face value. It may be true that within certain limits, it is possible to see the same mathematical patterns that have been identified in other models or chaotic systems. But given the almost limitless complexity of human society and economics, it is inconceivable that major events like wars would not disrupt these patterns. Marxists would argue that society does lend itself to scientific study. In contrast to those who see only formlessness, Marxists see human development from the starting point of material forces, and a scientific description of social categories like classes, and so on. If the development of chaos science leads to an acceptance that the scientific method is valid in politics and economics, then it is a valuable plus. However, as Marx and Engels have always understood, theirs is an inexact science, meaning that broad trends and developments could be traced, but detailed and intimate knowledge of all influences and conditions is not possible.

Cotton prices notwithstanding, the book gives no evidence that this Marxist view is wrong. In fact, there is no explanation as to why Mandelbrot apparently saw a pattern in only 60 years’ prices when he had over 100 years’ of data to play with. In addition, elsewhere in the book, Gleick adds that "economists have looked for strange attractors in stock market trends but so far had not found them." Despite the apparent limitations in the fields of economics and politics, however, it is clear that the mathematical "taming" of what were thought to be random or chaotic systems has profound implications for science as a whole. It opens up many vistas for the study of processes that were largely out of bounds in the past.


It is as yet too early to form a definitive view of chaos theory. However, what is clear is that these scientists are groping in the direction of a dialectical view of nature. For example, the dialectical law of the transformation of quantity into quality (and vice versa) plays a prominent sole in chaos theory:

"He (Von Neumann) recognised that a complicated dynamical system could have points of instability—critical points where a small push can have large consequences, as with a ball balanced at the top of a hill."

And again:

"In science as in life, it is well known that a chain of events can have a point of crisis that could magnify small changes. But chaos meant that such points were everywhere. They were pervasive." (24)

These and many other passages reveal a striking resemblance between certain aspects of chaos theory and dialectics. Yet the most incredible thing is that most of the pioneers of "chaos" seem to have not the slightest knowledge not only of the writings of Marx and Engels, but even of Hegel! In one sense, this provides even more striking confirmation of the correctness of dialectical materialism. But in another, it is a frustrating thought that the absence of an adequate philosophical framework and methodology has been denied to science needlessly and for such a long time.

For 300 years, physics was based on linear systems. The name linear refers to the fact that if you plot such an equation on a graph, it emerges as a straight line. Indeed, much of nature appears to work precisely in this way. This is why classical mechanics is able to describe it adequately. However, much of nature is not linear, and cannot be understood through linear systems. The brain certainly does not function in a linear manner, nor does the economy, with its chaotic cycle of booms and slumps. A non-linear equation is not expressed in a straight line, but takes into account the irregular, contradictory and frequently chaotic nature of reality.

"All this makes me feel very unhappy about cosmologists who tell us that they’ve got the origins of the Universe pretty well wrapped up, except for the first millisecond or so of the Big Bang. And with politicians who assure us that not only is a solid dose of monetarism going to be good for us, but they’re so certain about it that a few million unemployed must be just a minor hiccup. The mathematical ecologist Robert May voiced similar sentiments in 1976. ‘Not only in research, but in the everyday world of politics and economics, we would all be better off if more people realised that simple systems do not necessarily possess simple dynamical properties.’" (25)

The problems of modern science could be overcome far more easily by adopting a conscious (as opposed to an unconscious, haphazard, empirical) dialectical method. It is clear that the general philosophical implications of chaos theory are disputed by its scientists. Gleick quotes Ford, "a self-proclaimed evangelist of chaos" as saying that chaos means "systems liberated to randomly explore their every dynamic possibility…" Others refer to apparently random systems. Perhaps the best definition comes from Jensen, a theoretical physicist at Yale, who defines "chaos" as "the irregular, unpredictable behaviour of deterministic, non-linear dynamical systems."

Rather than elevate randomness to a principle of nature, as Ford seems to do, the new science does the opposite: it shows irrefutably that processes that were considered to be random (and may still be so considered, for everyday purposes) are nevertheless driven by an underlying determinism—not the crude mechanical determinism of the 18th century but dialectical determinism.

Some of the claims being made for the new science are very grand, and with the refinement and development of methods and techniques, may well prove true. Some of its exponents go so far as to say that the 20th century will be known for three things: relativity, quantum mechanics and chaos. Albert Einstein, although one of the founders of quantum theory, was never reconciled to the idea of a non-deterministic universe. In a letter to the physicist Neils Bohr, he insisted that "God does not play dice." Chaos theory has not only shown Einstein to be correct on this point, but even in its infancy, it is a brilliant confirmation of the fundamental world view put forward by Marx and Engels over a hundred years ago.

It is really astonishing that so many of the advocates of chaos theory, who are attempting to break with the stultifying "linear" methodology and work out a new "non-linear" mathematics, which is more in consonance with the turbulent reality of ever-changing nature, appear to be completely unaware of the only genuine revolution in logic in two millennia—the dialectical logic elaborated by Hegel, and subsequently perfected on a scientific and materialist basis by Marx and Engels. How many errors, blind alleys and crises in science could have been avoided if scientists had been equipped with a methodology which genuinely reflects the dynamic reality of nature, instead of conflicting with it at every turn!

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