The Science of Discworld IV Judgement Da - By Terry Pratchett, Ian Stewart Page 0,126

as the carbon resonance. In fact, because the star burns helium and beryllium fuel, the star’s nuclear reactions automatically home in on the temperature that makes the fuel burn. Isn’t it amazing that a coal fire burns at exactly the temperature that makes coal burn? No. If coal burns at all, then feedback ensures that the energy balance of the reaction automatically works out correctly. It may be amazing that our universe is so rich that coal can burn, or red giants shine, but that is a very different issue from fine-tuning. In a complex universe, however it may work, complex objects can arise, and they will be beautifully suited to the rules of that universe because that is how they came to be. But that does not imply that the universe was specially chosen or created to give rise to such objects. Or that those objects are improbable, or special.

The carbon resonance of a red giant, and the energetics of burning coal, are feedback systems. Like a thermostat, they automatically adjust themselves to keep going. This sort of feedback is extremely common and not at all remarkable. No more remarkable, in fact, than the amazing way that our legs are just long enough for our feet to meet the ground. Gravity pulls us down, the ground pushes us up, and the combination perches us in just the place where our feet and the ground are in exquisite alignment.

The issue of the physical constants is deeper. Today’s picture of fundamental physics depends on a series of mathematical equations, all fairly elegant and neat. However, these equations also involve about thirty special numbers: things like the speed of light; and the fine structure constant, which governs the forces holding atoms together. These numbers appear to be pretty much random, but they matter just as much as the equations. Different values of these fundamental constants lead to very different solutions of the equations – different kinds of universe.

The differences are not just the obvious ones: gravity being stronger or weaker, light travelling faster or slower. They can be more dramatic. Change the fine structure constant even a little, and atoms become unstable and fall apart. Make the gravitational constant smaller, and stars blow up, galaxies disappear. Make it larger, and everything collapses into a single gigantic black 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