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.

MODELS, TOYS AND LIFE-FORMS

There’s a lot of loose talk of ‘truth’ in on-line discussion, so why not try to understand what we’re talking about when we use the word? To lay one persistent myth right away: truth cannot be final. To believe that it can, is a dangerous delusion.

Truth is a function of a model that a creature makes of its environment. What does this mean? It means that every living creature is a centre of action, an agent; and the action in question, the behaviour, is structured by systems of selection, ‘intentions’ if you like, related to the survival of the particular creature. So the agent, be it never so simple, has, as it were, a set of ‘values’ according to which it operates. This set of values is closely related to a picture of the world in which the creature lives moves and has its being. So we can quite legitimately talk of the world of the bacterium, the world of the slug, the world of the mackerel, the world of the eagle, that of the whale, the chimpanzee or the human being. All of these ‘worlds’ are of course limited ‘interpretations’ of the world as such, what we call the ‘real world’;  and the behaviour of the various creatures makes real contact with it. But to suppose that this contact is in any case exhaustive is unjustified.  Every agent, in the sense in which the word is used here, possesses knowledge of the world; and knowledge and truth are closely related concepts. But knowledge and truth are never final.

The bacterium, for example, may have a fairly basic sort of existence, structured only by its ability to detect nutrient-rich areas of the medium in which it lives. Its values will have to do with ‘choosing’ to move up the gradient away from the nutrient-poor areas to those that are richer in its particular food-source. Nevertheless, this basic sort of existence is still that of an agent, and its agency is connected both to the rudimentary sense-organs of the bacterium and to the extent to which these give a ‘picture’ of the world. Even though it may be merely reacting to stimuli, we can consider the bacterium as having a simple sensory-cognitive apparatus, as constructing from its experience a view of its world and as acting according to principles of choice based upon its experience of that world. Such a set of responses to its environment could be referred to as the bacterium’s ‘model’ of reality. When the bacterium discovers the food-source, it clearly possesses a kind of ‘truth’.

As behaviour and sensory experience become more complex, a creature’s ‘world’ becomes more complex, too. The slug’s world is far more complex and richer in experience than that of a bacterium. The mackerel’s world is by many degrees of freedom more complex than that of a slug; and so on up through the levels of complexity of the creatures that inhabit this planet. At every level of complexity, there are centres of agency, systems of choice, sensory-cognitive systems and thus at every level, we can talk of values and models of the world. The slug and the mackerel have models of the world that we can hardly imagine, but that we can conceive, by analogy with our own, as involving a complex picture of the environment in which the creature lives, plus a set of biased responses to that environment related to the life-needs of the creature. If we can talk of a bacterium’s model of reality, then we can also talk of a mackerel’s model, a chimp’s model and so on. The only thing that prevents us from using the concept of truth with reference to animals is that they possess no language. But they clearly possess a non-linguistic analogue of truth. It goes without saying that we are incapable of assessing their degree of consciousness.

Now each of these creatures – and by extrapolation, all other creatures – can be understood as using their particular model of the world to interact with their environment without reflecting on whether it ‘really’ corresponds to the real world as it is in itself. Indeed (to indulge in a bit more anthropomorphism), we must assume that bacteria, slugs and all the other non-human creatures use their models  entirely ‘uncritically’  and don’t bother to ask any questions about their fundamental assumptions. To that extent, each of these creatures can, in a sense, be considered as regarding their particular model of the world as final and definitive. And that is indeed the case, not because their models are actually definitive, but because no other model is needed for their purposes.

As far as human beings are concerned, the picture with respect to these matters is both different and similar. It is similar in that human beings, too, operate as centres of agency, interacting with and choosing elements in an environment of which they have an internal model. The difference is in the extent to which human creatures are able to think abstractly and critically about their model. It is language that allows human beings to perform this particular feat and as far as we know, it is unique among the creatures of this planet. Nevertheless, this difference is probably one of degree rather than one of essence; and our ability to reflect upon our model of reality is clearly constrained by our set of sensory-cognitive abilities that also sets limits to our freedom to be aware of the usefulness or otherwise of our model. We are clearly limited in ways that are analogous to those in which the other creatures so far mentioned, bacteria included, are limited to a distinct range of access to the world and a distinct manner of interacting with it.

So these questions arise:  Why have we humans generally considered our particular access to the world as somehow privileged? Why have we traditionally thought that our senses, and our language give us a completely representative picture of the world as such. Why have we believed that our knowledge is not just of our particular world – similar, in that sense to the bacterium’s world, the slug’s world, the chimp’s world or whatever –  but of the world tout court? Why have we told ourselves that our knowledge and our truth concern the world as it is in itself, the ‘real’ world, the entire and unrestricted world? The reason for this is probably to be found in the uncritical acceptance of the sensory-cognitive apparatus with which we are born; and we share this uncritical acceptance with non-human creatures. It is what is called ‘naive realism’ by philosophers. When we use our gift of language to describe that world to each other, we seem to be talking about things that exist in themselves, not just elements of our particular human experience. Nevertheless, it is certain that in doing this, we over-value both the power of our senses and our ability to describe our world in abstract terms. This latter over-valuation is what Wittgenstein called, ‘the bewitchment of our minds by language’. The fact that we continue to believe that our sensory-cognitive approach to the world, allied to our language, gives us complete and exhaustive access to ‘reality in itself’ is surprising enough; that members of the scientific community continue to believe this thousands of years after philosophers first drew attention to the delusion is little short of miraculous.  Language is a wonderful trick, to be sure, but it is just a human trick and as such related to all the other strategies for coping that other creatures on this planet have evolved. To believe that it gives us a representation of the world as it is in itself, a definitive and totally faithful picture, a final account, is simply foolish. Why should evolution suddenly equip humans with the ability to construct a completely exhaustive picture of reality?

Let us enunciate a basic principle to restore to our species some salutary humility: our access to the world and thus our model of the world, though more complex, is in essence no more definitive, no more final, no more complete or exhaustive than that of a bacterium or a slug. Why should it be? Our best science is no more than an elaboration through language of a model of the world that arises from our sensory-cognitive apparatus. Evolution tinkered this apparatus together as it did the slug’s and the chimp’s. To think that that apparatus is godlike in its potential omniscience is at best over-optimistic, at worst almost psychotic. Common sense and science provide models of the world; and they are the best things we have; but they constitute knowledge of our world. How the world is IN ITSELF, we don’t know and cannot say. Maybe in evolving higher sensory-cognitive abilities and a more sophisticated language we could hoist ourselves a little further up the cognitive ladder and understand a bit more about the universe. But for that we would have to turn into different creatures.

Those scientists who think that the scientific method, as practised since the Enlightenment, gives us complete and exhaustive access to the world are simply deluded. Science itself has moved closer to humility; and quantum physics has taken us to the very limits of what we are equipped to grasp. But the continued use in the biological sciences of outmoded nineteenth-century science, as if it were final ‘truth’ about the world, is not only regrettable but also unconscionably ideological. The presence of ideology in science always distorts theory into ‘final truth’, even if it is admitted that some detail remains to be filled in. Let us be quite clear on this point: our science gives us access to reality, just as the bacterium has access to reality, but this access is always limited by our particular models.  All knowledge is relative to a particular frame of reference; and all demonstrable truth likewise. Thus knowledge and truth are relative concepts. We cannot operate without a model of reality; but at least let us operate with a model that is not a child’s toy and a model that we do not naively confuse with reality as such. 

The real world, the world as such, the world in itself, is unknown to us. It may well be unknowable. But let us avoid strutting around pontificating on final truth like a child with a toy weapon thinking he’s a mighty warrior. Our technology makes contact with reality, because it works; but this proves nothing final about the world as such; and our models and theories, as useful intellectual machines, prove nothing final about it either. They give us limited access to reality and nothing more. Reality in itself is the unknown, the mystery; and in nibbling away at that mystery, though we have made progress, we are quite unable to say how far we have got – in principle unable, because we can never compare our models of reality with reality itself. We approach reality through our models, and no other way; and we are stuck with the model we have, until we create a better one. Paradigm-shifts happen in this way; and there is one in the making.

So to conclude, talk of ‘truth’ in science certainly means something, but it doesn’t mean what some people think it means. It means a particular, limited degree of access to the world; it does not mean perfect and final access. So let’s have a bit more cautious humility. If some people believe in God, this is probably because the word represents to them the broadest possible notion of reality in ways that other basic terms such as ‘matter’ or ‘energy’ do not. Since every theory - Darwinism and M-theory included – is a limited theory, and since we are in principle unable to say just how limited, because we don’t yet know what we’ve left out, we do well to hold our truths lightly and avoid absolute declarations of the ‘there-is-no-room-for God’ variety.

Live your model and let models live. Types of discourse were referred to by Wittgenstein as ‘language-games’ (and the connection with toys is obvious here) or later as ‘forms of life’. Our science is merely one form of life of one particular life-form. It would be absurd for a slug to regard its knowledge as definitive and final truth. Ditto for us.