F. David Peat

As a result of the popular books and magazine articles that have appeared over the last few years the topic of chaos theory has become familiar to many people. While some psychologists may not be comfortable with the mathematical details of the theory they are probably acquainted with its broad outlines and general concepts. Thus, for example, the image of “butterfly effect” is often applied to systems so extraordinary sensitive that a perturbation as small as the flapping of a butterfly’s wings produces a large scale change of behavior. While chaos theory holds that such systems remain strictly deterministic they are, nevertheless, so enormously complex that the exact details of their behavior are, in practice, unpredictable even with the aid of the largest computers.

On the other hand, since such systems remain within the grip of their strange attractor while the details of their fluctuations appear to be random, nevertheless, their chaos is contained within a particular range of all possible behaviors. Their dynamics may, for example, exhibit a fractal structure in which similar patterns are repeated at smaller and smaller scales of space and intervals of time. As an example, while it is impossible to predict the exact value of a particular share on the stock market at an arbitrary date in the future one may be able to say something about its general pattern of fluctuation over a month, day or even an hour.

In a sense, therefore, chaos theory is something of a misnomer for it is not so much the study of systems in which all order has broken down in favour of pure chance but rather of those which exhibit extremely high degrees of order involving very subtle and sensitive behavior. The full description of such systems would require an enormous, potentially an infinite, amount of information. On the other hand, highly complex behavior can sometimes be simulated in very simple ways through the constant repetition of an iterative processes such as Prigogine’s baker’s transformation or the non-linear feedback associated with the changing size of insect populations.

While chaos theory and fractal descriptions are capable of simulating a wide variety of natural processes it remains an open question as to the extent to which such theories actually offer a full account of the inner workings of nature and society. For example, while repeated iterations can generate complex results this does not necessarily mean that such iterations are part of the actual generative processes of nature itself. Another pertinent question is to what extend dues absolute randomness and chaos occurs within the universe. While chaos theory is purely deterministic may there exist certain natural processes that are essentially chaotic, indeterministic and random? Quantum theory would be an obvious choice, for the time at which a radioactive nucleus disintegrates is, according to the theory, absolutely indeterministic – it is a matter of pure chance. David Bohm, however, has produced a deterministic version of quantum theory which perfectly accounts for all the empirical findings and predictions of the theory without invoking the assumption of absolute chance.

Another area in which intrinsic randomness occurs is in the sequence of digits of an irrational number. But what is the ontological basis of such numbers in nature? Are they a manifestation of intrinsic randomness in the universe or do they represent the abstract limits of processes that involve an infinite amount of information? At present there seems to be no way of deciding whether pure chance and randomness plays a role in the cosmos or if all systems are essentially deterministic in nature.

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