Dialectical materialism, elaborated by Karl Marx and Frederick Engels, was concerned with much more than political economy: it was a worldview. 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, 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 and concluded:

Each particular price change was random and unpredictable 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.

  1. Engels, F. Anti-Dühring, p. 16.

  2. Gleick, J. op. cit., p. 86.