Daytime TV: Random beauty

If you don't know what to do with yourself on a wet Saturday afternoon, why not make a human being? All you need, if you don't have a member of the opposite sex to hand, is some air, water, coal and chalk. Oh, and you will probably need a smidgen of iron, zinc, phosphorous and sulphur. You can probably get the whole lot for under a fiver. A bargain or what?

Of course, not being a scientist, I couldn't tell you what proportions to use or how to mix them or how long to cook them. You will just have to work that out. Alternatively, you could have watched The Secret Life of Chaos (BBC Four, Thursday 14 January, 9pm). Professor Jim Al-Khalili assembled these ingredients on a trestle table in a busy London street. How do the atoms of such ordinary materials, he asked, combine to produce living, feeling and sometimes thinking human beings?

Whoever thinks that science is dry, hard and factual has obviously never spent an hour in Jim's company. Any scientist who can describe the natural world as "one great big, blooming, buzzing confusion" has a poet's sense of "the drunkenness of things being various".

A few years ago I sat spellbound through his documentary on the atom. It was thrilling stuff. "If you dip a cup into the sea and extract a cupful of water, there are as many atoms in the cup as there are cups of water in all the oceans of the world." And that was just the start. Sex, intrigue, serendipity and sheer genius were all shown to be involved in unravelling the mystery of the atom, which is mostly empty space.

Now he was looking at how those sub-microscopic smudges combined to produce crinkled shorelines, creamy skies, slowly somersaulting galaxies and us. There is no need to go to a priest or philosopher to answer Paul Gauguin's famous questions: "Where do we come from? What are we? Where are we going?" Just ask a scientist. The answer, in all cases, is mathematics. It's a good job nature is better at the subject than I am, otherwise the world would look very different.

In one sense the answer is banal. Didn't Newton propose the very same idea? Yes, says Jim, but his laws do not explain how life itself arose. Ah well, I suppose he couldn't think of everything. I mean, what would there be left for the rest of us to do?

If Newton had a rival in the 20th century, it would be Alan Turing, the man who cracked the Enigma code, pioneered modern computing and then, obviously in need of a new challenge, turned his attention to morphogenesis, the biological process by which an organism takes shape. A picture of a glitter ball appeared on the screen but Jim said it was a fish embryo. Which is good enough for me.

Turing used equations to describe how a clump of identical cells began to turn into a heart, an eye or a brain. What might he have achieved if his sexuality had not fallen foul of the law? Jim was pretty worked up about the way Turing was treated - "one of the most shameful episodes in British science" - and rightly so. Turing's suicide is yet another stain on the British judiciary.

Boris Belousov's investigation of how bodies extract energy from sugars was another torch beam shone down into the cellar of nature's laws. He added a chemical to a clear solution. It changed colour. Nothing remarkable in that. Except it changed back to clear. Then to coloured, then to clear. Repeated. It was an example of self-organisation. The principle was illustrated with spinning circles and swirling lines. Either that or someone had popped something in my coffee.

And here we reached the nub of the matter. A system that is completely described by mathematical equations is more than capable of becoming unpredictable without any outside interference. And that, in a nutshell, is chaos theory. It received its most famous expression in Edward Lorenz's paper "Does the flap of a butterfly's wings in Brazil set off a tornado in Texas?" (1972), although there's a story that he did not provide the title.

Chaos is gently bubbling in the most serene mathematics, although it seems to have erupted everywhere else. Benoit B. Mandelbrot's "thumbprint of God" formula, which shows how all complexity stems from one simple equation, is the numerical equivalent of Apollo and Dionysus. It works on a loop. The tiniest variation feeds back into the system to create distortion, which then creates further variation, leading to greater feedback and even more distortion and so on. It sort of undermines the rationale for module evaluations when you think about it. But it does provide you with the perfect excuse for an untidy office.