The End of Time: The Next Revolution in Physics

The argument seems decisive because we instinctively feel that Lucy has (or, rather had, since sadly she was killed by a car) some unchanging identity. But is the cat that leaps the cat that lands? Except for the changes in her body shape, we do not notice any difference. However, if we could look closely we might begin to have doubts. The number of atoms in even the tiniest thing we can see is huge, and they are in a constant state of flux. Because large numbers play a vital role in my arguments, I shall give two illustrations. Have you ever tried to form a picture of the number of atoms in a pea?

Figure 5 Triangle Land is like an inverted pyramid, with frontiers formed by special triangles as explained in Figure 4. Platonias corresponding to configurations of more than three particles have not only frontiers but also analogous internal topographic features. This illustration, based on the parachute of a salsify seed (shown life-size on left) from my wife’s garden, is an attempt to give some idea of the rich structure of the frontiers of Platonia. No attempt is made to represent the even richer internal structure. Platonia’s Alpha is where the ribs converge. Because Platonia has no Omega, the salsify ribs should extend out from Alpha for ever. (The wind carries the actual seeds rather efficiently into our neighbours’ gardens, where the progeny flourish, but they are not always welcome, although salsify is an excellent vegetable.)

Imagine a row of dots a millimetre apart and a metre long. That will be one thousand dots (10³). (Actually, it will be 1001, but let us forget the last 1.) One thousand such rows next to one another, also a millimetre apart, gives a square metre of dots, one million (10⁶) in total. The number of dots in one or two squares like that is about the number of pounds or dollars ordinary mortals like me can hope to earn in a lifetime. Now stack one thousand such squares into a cube a metre high. That is already a billion (10⁹). So it is surprisingly easy to visualize a billion. Five such cubes are about the world’s human population. Yet we are nowhere remotely near the number of atoms in a pea.

We shall keep trying. We make another cube of these cubes. One thousand of them stretched out a kilometre long takes us up to a trillion (10¹²). A square kilometre of them will be 10¹⁵ (about the number of cells in the human body), and if we pile them a kilometre high we get to 10¹⁸. We still have a long way to go. Make another row of one thousand of these kilometre cubes, and we get to 10²¹. Finally, make that into a square, one thousand kilometres by one thousand kilometres and a kilometre high – it would comfortably cover the entire British Isles to that height. At last we are there: the number of dots we now have (10²⁴) is around the number of atoms in a pea. To get the number in a child’s body, we should have to go up to a cube a thousand kilometres high. It hardly bears thinking about.

Equally remarkable is the order and organized activity in our bodies. Consider this extract from Richard Dawkins’s The Selfish Gene:

The haemoglobin of our blood is a typical protein molecule. It is built up from chains of smaller molecules, amino acids, each containing a few dozen atoms arranged in a precise pattern. In the haemoglobin molecule there are 574 amino acid molecules. These are arranged in four chains, which twist around each other to form a globular three-dimensional structure of bewildering complexity. A model of a haemoglobin molecule looks rather like a dense thornbush. But unlike a real thornbush it is not a haphazard approximate pattern but a definite invariant structure, identically repeated, with not a twig nor a twist out of place, over six thousand million million million times in an average human body. The precise thornbush shape of a protein molecule such as haemoglobin is stable in the sense that two chains consisting of the same sequences of amino acids will tend, like two springs, to come to rest in exactly the same three-dimensional coiled pattern. Haemoglobin thornbushes are springing into their ‘preferred’ shape in your body at a rate of about four hundred million million per second and others are being destroyed at the same rate.