FOR THE LAST five years the 'new sciencé' of chaos has been the subject of intense controversy. Whole sections of bookshops are devoted to it, Douglas Adams says he's seen the light, and Living Marxism denounces it as bourgeois pessimism. What exactly is it, and is it compatible with Marxism? PAUL CLARKE investigates. CHAOS theory has been applied to such a variety of phenomena that it is difficult to sum it up in a few simple propositions. But at the most general level the proponents of chaos say the following.
First, all events and systems in the real world have determinate causes and are law governed. But there are phenomena governed by particular mathematical laws which despite being determined and law-governed have unpredictable, apparently random and chaotic outcomes.
Randomness
Second, within the apparent randomness laotic phenomena are general paterne ane cmic irec that ineer pin the apparent randomness of chaotic events, and give them Anyone in the least familiar with the basic propositions of dialectical materialism will instantly see how the ideas of chaos parallel some basic Marxist ideas about the world.
To see what the real interest and application of chaos theory is, it is necessary to look at how it arose. Chaos theory grew up within separate and apparently Page 10 May 18, 1991 No. 2 diverse disciplines - meteorology, fluid dynamics, and of course pure mathematics.
Weather forecasting and predicting the behaviour of liqula nows regulary come up against a similar problem. At a certain point regular and ordered events suddenly go 'chaotic.
Models
Building mathematical models of these events is incredibly complex, because the number ovariables involved is so large. In other words, the mathematical equations which ›overn oitcomes ate non 111e01 eyond a certain point develop ments in the weather or liquid flows seem random and unpre dictable, by definition.
Marx's closest collaborator, Frederick Engels, made a striking remark about the historical process which can be taken as summing up his concept of dialectical materialism. Events, he said, are governed by parallelogram of forces' In other words, there can be thousands of individual determinants of a single event, but in principle, if you knew all the different determinants you could trace the course of a particular event with absolute certainty and predictability.
Chaos theory says something different. It says you can know all the determinants, and not know the outcome.
złomc ozc cvr has known this f for a long time. In a particle accelerator you can repeat a particular experiment over and'over again, in exactly the same conditions, and never get the same result.
You may be able to predict the range of results over, say, 100 experiments. You may in certain cases be able to predict the average result over a large number of experiments. But the resultof a particular experiment you cannot predict.
Many physical events can be: modelled in terms of linear equations - i.e. those with few variables. Their progress is more-or-less orderly and pre dictable. But at the heart of İterat on of naaiens eginations (the repeated multiplication of these equations by a constant).
Progress in this branch of mathematics has been celerated by the progress in computers, enabling huge numnere oi erz on o non ne equations to take place in a short period. The results are striking.
Instead of the regular progression of results you get with linear equations, nonlinear equations seem produce random results, with no pattern at all.
Strange attractors But then something peculiar happens. Periodically, the same results occur over and over again; the result often settles down around three or four standard outcomes. In the heart of chaos there is order. In the parlance of chaos theory these repeated results are known as 'strange attractors'.
The rapid advances in computers have enabled strange attractors to be depicted visually. Every equation can be repre sented by a graph - a picture Benoit Mandelbrot, a scientist working for the computer giant IBM. pioneered the computer graphing of huge numbers of terations of non-linear equations.
The results have been spectacular - patterns of infinite complexity, and numerous levels, which at different levels of magnification never repeat themselves, but throw up the same images over and over again.
Startling
These images ('Mandelbrot sets') are startling because they appear to show pictures of phenomena in the natural horses, valleys. They powerfully suggest that a wide range of natural systems are governed by non-linear equations.
Now why should any of this be of interest to Marxists? Apart from the trite answer that Marxists should after all be interested in the world which they seek to cnange, lt is because oI the light which chaos theory sheds on our notion of determ1n1sm. Marxism is a determinism. More precisely, historical materialism socio-economic determinism. Marxists assert that phenomena, natural or social, have specific causes, and are thus not random or accidental, but law-governed.
Contradictions
All Marxist theory has been particularly concerned with the notions of contradiction and rupture. In other words, Marxist theory seeks to explain how, at a certain point, systems _ natural or social.- go into crisis, decay and are reborn as something else.
Chaos theory, strictly speaking, deals with the physical world - the behaviour of noninear dynamical systems. Bu nany people, not least the U Defence Department, have been quick to try to find parallels in he social and political world, for example crowd control.
Might not a rioting crowd be considered a 'non-linear dynamical system'? Might there not be a hidden lawfulness in its apparently random xists, of course, know there is.
Narrow
However, at the present state of our knowledge, it is far too early to start to claim that chaos represents a new magical key that will reshape the whole of human knowledge and every scientific discipline - its proved applicability is so far too narrow.
But the insights of chaos are broadly in line with Marxism, and have been even anticipated by Marxist theory. Chaos shows us that reality is law governed, even if particular events, in principle, cannot be predicted.
It shows that extremely complex systems, involving many variables, are extremely sensitive to initial conditions - ie as they develop, initial errors and deviations become magnified in a dramatic way (apply that to socialist organisations and you get some interesting results!). It shows that although science cannot 'explain everything' - ie ore leerer even-ica ce he parameters that give rise to apparent disorder.
All this of course is death to a particular kind of mechanical, non-dialectical, determinism. Marxists should not worry about that. Reality can be looked at as ordered chaos or chaotic order. Whichever way, it is subiect to intervention and change.
Is chaos compatible with Marxism? Yes. Is it a major step forward in human knowledge? Wait and see.
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