INDETERMINATE ORDER

 

Indeterminism requires us to understand that order is a process not a state. Order means having structure; but it does not mean some frozen symmetry that persists for time and eternity. A frozen symmetry if it persists for all time, has the power to persist for eternity since it is immune to change. But belief in the existence of such is almost certainly derived from our taste for abstraction; i.e., it exists only in our intellect. If structure is subject to unpredictable change, then, however well we think we understand it, its order is not yet detected, for the principle according to which the frozen symmetry mutates into something else has to be factored into the definition of the nature of the frozen state. It seems that nothing in the universe and indeed the universe itself can ever be a matter of frozen symmetry, for this reason. Since this is the case, we do well to look for ordering principles that are not mechanical. The only obvious candidate for such a principle is intelligence, or disguised intelligence in such notions as ‘emergence’, ‘complexity’ and suchlike.

Bohm has an interesting approach to chaos theory and to the relations between order and randomness. In his view, random order can be defined as a special case of chaotic order. He gives three characteristics of random order:

It is of infinite degree. It has no significant correlations or stretches of suborder of low degree. It has fairly constant average behaviour and tends to vary within limited domains. The domain within which it varies remains more or less constant, or else it changes slowly.

The notion of randomness is context dependent. To illustrate this, he gives the example of a fixed gun shooting bullets and the distribution-pattern of hits on the target in two cases, 1) where no details about the gun or the wind or the variations of ammunition etc are known and 2) where these details are known. In 1) the shots are random, in 2) they become more nearly determined. Thus the randomness is dependent upon the amount of information known about the system. It is therefore not objective nor subjective, but rather a combination of both. Randomness is a special case of a more general notion of order, i.e. orders of infinite degree. Chance and randomness are not equal to total disorder. Total lack of order is a concept without meaning.

The random number generator in a computer consists of a deterministic sequence of instructions but it is frequently linked to the computer’s clock, so that the same sequence is not generated each time it is used. The sequence starts from a different point each time. In the context of the computer, these sequences are non random and completely determined. Outside of this context, no determination of their order can be given. This shows how the concept of randomness is context-dependent. Despite the remark above, randomness, moreover, is not the same as an order of infinite degree. There are orders of infinite degree that are clearly not random. Language is such an order. The meanings, the dimensions of meaning of a language are infinite but these meanings are not random. The meanings arise within the context of human life and if this context is lacking, if the ‘forms of life’ (to borrow from Wittgenstein) reflected in the language concerned are missing – as in a person who understands nothing of the culture in question and does not speak the language, then the meaning is lacking; all such a person hears or reads is a rhythm of sounds or a collection of symbolic marks. This context-dependent fund of meaning is the whole order of the language and the order belongs both – i.e. at one and the same time – to the language itself and to the person who uses it.

“By treating randomness as a limiting case of order,” says Bohm, “it is possible to bring together the notions of strict determinism and chance (i.e. randomness) as processes that are opposite ends of the general spectrum of order.”

There is a continuum of order from complete determinism to complete chaos with an infinity of gradations in between. Deterministic systems possess order of low degree, reducible to a maximally compressible algorithm, while chaotic systems possess order of a degree approaching infinity; but the difference between the two is far from absolute. It consists of our understanding of the action of the variables as related to the context in which we view them. The concept of a completely disordered system is, as already mentioned, nonsensical: there will always be order of some sort. The chaotic system possesses order of very high degree and the so-called ‘totally random’ system possess order of infinite degree, but the latter is only random on account of our ignorance. Pollen grains in water will move chaotically under the influence of the Brownian motion of the water molecules. If all the details of all the molecular collisions were taken into account, the system would be strictly deterministic and the degree of order low. If this is not the case, then the degree of order is infinite and the movement of the pollen grains random. The randomness of the system is therefore a feature of knowledge of the system, not the result of something intervening from outside. Depending upon our measurements, randomness could turn into necessity. So randomness is necessity in a different guise: the degree of order depends upon the context in which the measure is made.

But since no system can be regarded as strictly isolated or self-contained, it may be affected by even weak external interactions. And anyway, no particular statement of the laws of nature will be completely and universally valid, because, as already remarked, whatever we SAY a thing is, it isn’t: it is something more and something different. If chance is a particular form of necessity, we can reverse the image and say that necessity is a particular form of chance. To illustrate this one only has to think of the statistical properties of temperature and pressure of a gas which can be treated mechanistically, but which are functions of the ‘random’ motions of the molecules. No notions of temperature and pressure are possible if all the motions of the molecules are known. It is precisely ignorance of those motions that permits quantification of temperature and pressure, quantities that can then be used in strictly deterministic calculations even though they depend upon ‘chance’ events.

What is randomness in one context may reveal itself as simple orders of necessity in another broader context; and vice versa, what is a simple order of necessity in one context may reveal itself as chance in another broader context. But in a still broader context, both are to be seen as extremes in the rich spectrum of orders of varying degrees that lie between them. We don’t have to fall into the assumption that either chance or necessity rules absolutely or that both rule absolutely: both could be correct abstractions and approximations in their contexts. No matter which system of law may be appropriate in the context under investigation, there will always be room for something more and something different – something more subtle, something that has the potential to be a manifestation of indeterminate creativity. It would be no exaggeration to declare that the universe has been a process of perpetual innovation from the Big Bang onwards, innovation, moreover, that at all points we cannot predict from our knowledge of the laws of nature despite the fact that, with hindsight, we can see that in all of these innovations (including life, self-conscious life and history) no known physical law is violated.