The Science of Discworld IV

hole. In fact – so the story goes – if you change any one of those constants by more than a very tiny amount, the resulting universe is so different from ours that it could not possibly support the organised complexity of life. Having lots of constants compounds this; it is like winning the lottery thirty times in a row. Our existence is not only balanced on a knife edge: it is a very sharp knife.
    It’s a striking tale, but it’s riddled with holes.
Pan narrans
just can’t stop itself.
    One basic, and fatal, flaw in a large portion of the literature is to consider varying the constants only one at a time, and only by a small amount. Mathematically, this procedure explores only a tiny region of ‘parameter space’, the overall range of possible combinations of constants. What you find in this limited region is unlikely to be representative.
    Here’s an analogy. If you take a car, and change any single aspect even a little bit, the odds are that the car will no longer work. Change the size of the nuts
just a little
, and they don’t fit the bolts and the car falls apart. Change the fuel
just a little
, and the engine doesn’t fire and the car won’t start. But this does not mean that only one size of nut or bolt is possible in a working car, or only one type of fuel. It tells us that when you change one feature, it has knock-on effects on the others, and those must also change. So parochial issues about what happens to little bits and pieces of our own universe when some constant is changed by a very small amount and the rest are left fixed are not terribly relevant to the question of that universe’s suitability for life.
    Some additional sloppy thinking parlays this fundamental blunder into a gross misrepresentation of what the calculations concerned actually show. Suppose, for the sake of argument, that each of the thirty parameters has to be individually fine-tuned so that the probability of a randomly chosen parameter being in the right range is 1/10. Change any parameter (alone) by more than that, and life becomes impossible. It is then argued that the probability of all thirty parameters being in the right range is 1/10 raised to the power 30. This is 10 -30 , one part in a nonillion (ten billion billion billion). It is so ridiculously small that there is absolutely no serious prospect of it happening by chance. This calculation is the origin of the ‘knife edge’ image.
    It is also complete nonsense.
    It’s like starting at Centrepoint, in the middle of London, and going a few metres westwards along New Oxford Street, a few metres northwards up Tottenham Court Road, and imagining you’ve covered the whole of London. You haven’t even explored a few metres in a north-westerly direction, let alone anything further away. Mathematically, what is being explored by each change to a
single
parameter is a tiny interval along an axis in parameter space. When you multiply the associated probabilities together, you are exploringa tiny box whose sides correspond to the changes made to individual parameters – without considering changing any of the others. The car example shows how silly this type of calculation is.
    Even using the constants for
this
universe, we can’t deduce the structure of something as apparently simple as a helium atom from the laws of physics, let alone a bacterium or a human being. Our understanding of everything more complex than hydrogen relies on clever approximations, refined by comparison with actual observations. But when we start thinking about other universes, we don’t have any observations to compare with; we must rely on the mathematical consequences of our equations. For anything interesting, even helium, we can’t do the sums. So we take short cuts, and rule out particular structures, such as stars or atoms, on various debatable grounds.
    However, what such calculations actually rule out (even when they’re correct) are stars just like those in this universe and atoms just like those in this universe. Which isn’t quite the point when we’re discussing a different universe. What other structures could exist? Could they be complex enough to constitute a form of life? The mathematics of complex systems shows that simple rules can lead to astonishingly complex behaviour. Such systems typically behave in many different interesting ways, but not in just
one
interesting way. They don’t just sit there being dull and boring, except for one special ‘finely tuned’