DO DICE PLAY GOD?

Ian Stewart

Mathematics Institute University of Warwick Coventry CV4 7AL M@CAW

Albert Einstein believed that God does not play dice with the Universe; that the world in which we live is governed by precise laws rather than chance. The branch of mathematics popularly known as Chaos Theory clarifies the question through a new paradox: precise laws may offer the appearance of randomness. As a result our cherished beliefs about determinism, predictability, and complexity are back in the melting-pot.

When Einstein's Theory of Relativity achieved public recognition, most people interpreted it as saying that 'everything is relative', a comfortable philosophy that, for example, justifies the rich ignoring the poor on the grounds that others are yet poorer. Actually, that's not what Einstein was saying at all: he was telling us that the speed of light is not relative, but absolute. Really, it should have been named the Theory of Nonrelativity. I think something similar has happened to Chaos Theory in the public mind. People are taking it to mean that 'everything is random', and some are using that to justify economic or ecological mismanagement. How unfair, for example, to blame the Chancellor of the Exchequer for not controlling inflation or unemployment, when 'everyone knows' that these are subject to random influences out of the Chancellor's control! But Chaos Theory doesn't offer that sort of excuse at all, because its message is far more complex than the popular image: some things behave predictably, some don't; some things that we think we understand may behave in very funny ways; some things that appear random may obey laws we haven't yet spotted; and most things don't fit into any of these categories at all!

I'd like to put the question the other way around, hence my title. To what extent is our world determined by chance events? Can the organised structures in the universe protect themselves against random destruction, and if so, how? For that matter, how do organised structures arise in the first place, in a universe of chaos?

A timely example is evolution. Until recently, most people who accept that evolution takes place at all have tended to view it as a process of increasing diversity, with the human race perched at the pinnacle of creation. The purpose of evolution is to produce us. This attitude is largely subconscious, but it shows up again and again, as Stephen Jay Gould argues in his book Wonderful Life. There he describes the bizarre fossils of the Burgess shale, which between them encompass more biological diversity than exists anywhere on Earth today. He draws the lesson that evolution is a contingent process: at key stages, what happens depends entirely on chance.

He concludes that if evolution were to be run again, the chance of any intelligent lifeform developing is minute.

That may be true: certainly we can't perform the experiment to make sure. But Gould's argument ignores an important feature of the evolutionary process: convergence. Evolution tends to attain similar ends by different means. The marsupials of Australia bear remarkable resemblances to placental mammals elsewhere. Pterosaurs, birds, bats, insects, and fish have all developed some form of flight; so for that matter have dandelion seeds. Senses such as vision or hearing are other examples. And so, perhaps, are brains.

Convergence shows that processes are not affected just by chance: they are also bound by hidden constraints. In evolution, the constraints include Darwinian 'survival of the fittest', which eliminates vast numbers of imaginable structures, and the laws of physics and chemistry, which preclude even vaster numbers of structures from being possible even in principle.

The picture of evolution that we thereby obtain is more subtle: neither goal-directed determinism nor pure contingency, but a mixture. Against a background of random variation, the process takes place within some body of constraints and stabilising influences. It is neither pure order nor pure chaos, but a kind of competitive game played between the two. How do recognisable structures arise from such a game? Why does neither player win?

According to the second law of thermodynamics, the entropy of the universe - its degree of disorder - continually increases. Our ultimate fate, from this point of view, is Heat Death, a state in which all temperature variations have evened out as heat is transferred from hot bodies to cool ones. Nothing interesting happens and everywhere looks just like everywhere else. Tourism is having a similar effect on human culture. Life appears to contradict the second law of thermodynamics. It seems to me that if it really does do this, then there's something wrong with the law! But there are so many legal loopholes in the second law that we need not worry too much that it may rule out our own existence. Comforting as that may be, it doesn't explain why the chaos in the universe doesn't just wipe us out, or why we don't organise our world so successfully that nothing unpredictable ever happens.

I need a word to capture what I have in mind. Out of deference to the second law, let me call it a negentrope. A negentrope is a 'negative disorderer': any structure that tends towards self-organisation, self-propagation, and self-modification. It has inherent stability of structure, but not so stable that it can't change at all. Negentropes exist, for we are negentropes. Every living creature on Earth is a negentrope. So are cultural tricks like language, evolutionary tricks like intelligence, and technological tricks like metalworking. Negentropes do not occur easily or often, but they occur fairly regularly, and once they've arisen they explode. One of the earliest negentropes was what Richard Dawkins calls 'the replicator'. This is a chemical molecule with the capacity to reproduce itself. It may take millions of years for such a molecule to arise by random association of atoms; but by golly, once it does, it's soon going to be found everywhere! In the same way, once metalworking is discovered, it will spread throughout human culture, and it will engender all kinds of new gadgets, from swords to spoons to satellites. Negentropes are enablers, they open up new realms of the possible.

Negentropes cannot appear on their own, however. They rely for their existence on a rich environment, a context. The replicator can only arise in a vast sea of chemicals; metalworking can only be developed within a culture that transmits ideas. The context affects the development, and makes some aspects of it virtually inevitable. In a warrior culture, the discovery of metalworking will lead inevitable to knives and swords. In a hunting culture it will lead to spears and arrowheads. In a fishing culture, to fishhooks. The arrival of a new negentrope is a major event, because - in its context - it triggers a whole sequence of changes. Moreover, these changes are stable in the sense that the new realms of the possible are implicit in the context, 'waiting' to be triggered. Transistors trigger television, but they don't give us a new breed of wheat.

Do dice play god? Does chaos reign supreme? No, because within a chaotic context it may be possible for negentropes to emerge. If they do, then by their nature they will not go away again, and once they exist they will tend to become more complex and more organised. Conversely, a population of negentropes, however organised it may be, can in turn become the context for a new kind of chaos: that's classic Chaos Theory, determinism implies randomness! Neither order nor chaos can win the game once and for all, because by doing so it would change the game to favour its opponent.

We are negentropes in a context of biochemical contingency. Our intelligence is a negentrope in a context of cell biology. Our culture is a negentrope in a context of interacting individuals, and so is our technology. Negentropes are defences against chaos.

But they can also create it. Because of our success in constructing negentropes, new sources of chaos and confusion beset our world. Too many of our negentropes have been developed within too limited a context. Fire protects us against cold, but its by-product, greenhouse gases, threatens global warming. One man's picnic-table is another's ravaged rainforest. Nuclear weapons may suppress the chaos of war, but they also open up the chasm of total self-destruction. Religions stabilise individual cultures but wreak intercultural havoc. The road to Hell is paved with flawed negentropes.

The problem with negentropes is that, flawed or not, it's very hard to get rid of them. Our technological and cultural negentropes have become so widespread that they are forming a new chaotic context in their own right. The future of our world may well depend upon finding a new set of negentropes, functioning within that context, for the control of culture and technology; negentropes that do not contain the seeds of their own - and our - destruction.