The Faber Book of Science (64 page)

Though the existence of deterministic chaos comes as a surprise, we should not forget that nature is not, in fact, deterministic anyway. The indeterminism associated with quantum effects will intrude into the dynamics of all systems, chaotic or otherwise, at the atomic level. It might be supposed that quantum uncertainty would combine with chaos to amplify the unpredictability of the Universe. Curiously, however, quantum mechanics seems to have a subduing effect on chaos. A number of model systems that are chaotic at the classical level are found to be non-chaotic when quantized. At this stage, the experts are divided about whether quantum chaos is possible, or how it would show itself if it did exist. Though the topic will undoubtedly prove important for atomic and molecular physics, it is of little relevance to the behaviour of macroscopic objects, or to the Universe as a whole.

What can we conclude about Laplace’s image of a clockwork universe? The physical world contains a wide range of both chaotic and non-chaotic systems. Those that are chaotic have severely limited predictability, and even one such system would rapidly exhaust the entire Universe’s capacity to compute its behaviour. It seems, then, that the Universe is incapable of digitally computing the future behaviour of even a small part of itself, let alone all of itself. Expressed more dramatically, the Universe is its own fastest simulator.

This conclusion is surely profound. It means that, even accepting a strictly deterministic account of nature, the future states of the Universe are in some sense ‘open’. Some people have seized on this openness to argue for the reality of human free will. Others claim that it bestows upon nature an element of creativity, an ability to bring forth that which is genuinely new, something not already implicit in earlier states of the Universe, save in the idealized fiction of the real numbers. Whatever the merits of such sweeping claims, it seems safe to conclude from the study
of chaos that the future of the Universe is not irredeemably fixed. The final chapter of the great cosmic book has yet to be written.

The unpredictable and the predetermined unfold together to make everything the way it is. It’s how nature creates itself, on every scale, the snowflake and the snowstorm. It makes me so happy. To be at the beginning again, knowing almost nothing. People were talking about the end of physics. Relativity and quantum looked as if they were going to clean out the whole problem between them. A theory of everything. But they only explained the very big and the very small. The universe, the elementary particles. The ordinary-sized stuff which is our lives, the things people write poetry about – clouds – daffodils – waterfalls – and what happens in a cup of coffee when the cream goes in – these things are full of mystery, as mysterious to us as the heavens were to the Greeks. We’re better at predicting events at the edge of the galaxy or inside the nucleus of an atom than whether it’ll rain on auntie’s garden party three Sundays from now. Because the problem turns out to be different. We can’t even predict the next drip from a dripping tap when it gets irregular. Each drip sets up the conditions for the next, the smallest variation blows prediction apart, and the weather is unpredictable the same way, will always be unpredictable. When you
push the numbers through the computer you can see it on the screen. The future is disorder. A door like this has cracked open five or six times since we got up on our hind legs. It’s the best possible time to be alive, when almost everything you thought you knew is wrong.

The vision given to us by Newton and by those who followed in the Age of Enlightenment is of an orderly and predictable world, governed by laws and rules – laws and rules which can best be expressed in mathematical form. If the circumstances are simple enough (for instance, a planet moving around a sun, bound by the inverse square law of gravitational attraction), then the system behaves in a simple and predictable way. Effectively unpredictable situations (for instance, a roulette ball whose fate – the winning number – is governed by a complex concatenation of croupier’s hand, spinning wheel, and so on) were thought to arise only because the rules were many and complicated.

Over the past 20 years or so, this Newtonian vision has splintered and blurred. It is now widely recognised that the simplest rules or algorithms or mathematical equations, containing no random
elements
whatsoever, can generate behaviour which is as complicated as anything we can imagine.

This mathematics which ‘is different’ is the mathematics of ‘deterministic chaos’. What it says is that a situation can be both deterministic
and
unpredictable; that is, unpredictable without being random (on the one hand) or (on the other hand) attributable to very complicated causes.

‘Simple’ as they may be in themselves, these chaos-generating equations have the property of being ‘nonlinear’. In a
linear
equation you can ‘guess ahead’. Imagine a road lined with telegraph poles in a perspective drawing. Given two or three poles, you can easily draw in the rest for yourself. But nature often draws itself differently, using
nonlinear
equations. Imagine a river running alongside the road. The water has flat bits and bumpy bits. But however many I draw in for you, there is no way for you to tell (with a real river) where the next flat bit or bumpy bit is going to be. This holds true on every scale.
Look down from a balloon and you’ll see that parts of the bumpy bits look relatively flat. Put your face close to the water and you’ll see that the flat bits contain relatively bumpy bits. The maths is the same for each case, and equally unpredictable.

In this sense, ‘nonlinear’ means two and two do not necessarily make four. Much of physics and other areas of science where so much progress has come, are linear (or at least decomposable into essentially linear bits). And so mathematical texts and courses have focused on linear problems. But increasingly it seems that most of what is interesting in the natural world, and especially in the biological world of living things, involves nonlinear mathematics. It was biologists – working on the ups and downs of animal population – who were among the first to see that not only can simple rules give rise to behaviour which looks very complicated, but the behaviour can be so sensitive to the starting conditions as to make long term prediction impossible (even when you know the rule).

There is a flip side to the chaos coin. Previously, if we saw complicated, irregular or fluctuating behaviour – weather patterns, marginal rates of Treasury Bonds, colour patterns of animals or shapes of leaves – we assumed the underlying causes were complicated. Now we realize that extraordinarily complex behaviour can be generated by the simplest of rules. It seems likely to me that much complexity and apparent irregularity seen in nature, from the development and behaviour of individual creatures to the structure of ecosystems, derives from simple – but chaotic – rules. (But, of course, a lot of what we see around us is very complicated because it is intrinsically so!)

I believe all this adds up to one of the real revolutions in the way we think about the world. Knowing the simple rule or equation that governs a system is not always sufficient to predict its behaviour. And, conversely, exceedingly complicated patterns or behaviour may derive not from exceedingly complex causes, but from the chaotic workings of some very simple algorithm. Ultimately, the mathematics of chaos offers new and deep insights into the structure of the world around us, and at the same time raises old questions about
why
abstract mathematics should be so unreasonably effective in describing this world.

The language of the genes has a simple alphabet, not with twenty-six letters, but just four. These are the four different DNA bases – adenine, guanine, cytosine and thymine (A, G, C and T for short). The bases are arranged in words of three letters such as CGA or TGG. Most of the words code for different amino acids, which themselves are joined together to make proteins, the building blocks of the body.

Just how economical the language of inheritance is can be illustrated with a rather odd quotation from a book called
Gadsby,
written in 1939 by one Ernest Wright: ‘I am going to show you how a bunch of bright young folks did find a champion, a man with boys and girls of his own, a man of so dominating and happy individuality that youth was drawn to him as a fly to a sugar bowl.’ This sounds rather peculiar, as does the rest of the fifty-thousand word book, and it is. The quotation, and the whole book, does not contain the letter ‘e’. It is possible to write a meaningful sentence with twenty-five letters instead of twenty-six, but only just. Life manages with a mere four.

Although the inherited vocabulary is simple its message is very long. Each cell in the body contains about six feet of DNA. A useless but amusing fact is that if all the DNA in all the cells in a single human being were stretched out it would reach to the moon and back eight thousand times. There is now a scheme, the Human Genome Project, to read the whole of its three thousand million letters and to publish what may be the most boring book ever written; the equivalent of a dozen or so copies of the
Encyclopaedia
Britannica.
There is much disagreement about how to set about reading the message and even about whether it is worth doing at all. It probably is. The Admiralty
sent the
Beagle
to South America with Darwin on board not because they were interested in evolution but because they knew that the first step to understanding (and, with luck, controlling) the world was to make a map of it. The same is true of the genes. To make this map will be expensive – about as much as a single Trident nuclear submarine. The task will be stupefyingly tedious for those who have to do the work, but, before the end of the century, someone will publish the inherited lexicon of a human being. To be more precise, there will be a map of a sort of Mr Average – the chart is, of course, of a male – as the information will come from short bits of DNA from dozens of different people …

Human genetics was for most of its history more or less restricted to studying pedigrees which stood out because they contained an abnormality. This limited its ability to trace patterns of descent to those few families – like the Hapsburgs – who appeared to deviate from the perfect form. Biology has now shown that this perfect form does not exist. Instead there is a huge amount of inherited variation. Thousands of inherited characters – perfectly normal diversity, not diseases – distinguish each person. There is so much variety that everyone alive today is different, not only from everyone else, but from everyone who ever has lived or ever will live. The mass of diversity can be used to look at patterns of shared ancestry in any family, aristocratic or plebeian; healthy or ill. Because all modern genes are copies of those in earlier generations each can be used as a message from the past. They bring clues from the beginnings of humanity more than a hundred thousand years ago and from the origin of life three thousand million years before that …

There have been claims that we may soon find the gene that makes us human. The ancestral message will then at last allow us to understand what we really are. The idea seems to me ridiculous.

Just how ridiculous it is can be seen by looking at the search for another important gene, one which I inherited from my father, and he from his and so on back to a distant ancestor that lived long before the birth of our own species. This is the gene that makes me male. The maleness gene was tracked down recently and its message spelt out in the four DNA letters, A, G, C and T. It starts like this: GAT AGA GTG AAG CGA. There are 240 of these letters altogether and, between them, they contain the whole tedious biological story of being a man. This brief ancestral bulletin does nothing to tell that half of the
population which is unfortunate enough not to have it what it is really like to be male rather than female. Being a man involves a lot more than a sequence of DNA bases; and the same is true for being a human.