The Beginning of Infinity: Explanations That Transform the World

by David Deutsch

For although any one constant is unlikely to be near the edge of its range, the more constants there are, the more likely it is that at least one of them will be. This can be illustrated pictorially as follows, with our bull’s-eye replaced by a line segment, a square, a cube…and we can imagine this sequence continuing for as many dimensions as there are fine-tuned constants in nature. Arbitrarily define ‘near the edge’ as meaning ‘within 10 per cent of the whole range from it’. Then in the case of one constant, as shown in the diagram, 20 per cent of its possible values are near one of the two edges of the range, and 80 per cent are ‘away from the edge’. But with two constants a pair of values has to satisfy two constraints in order to be ‘away from the edge’. Only 64 per cent of them do so. Hence 36 per cent are near the edge. With three constants, nearly half the possible choices are near the edge. With 100 constants, over 99.9999999 per cent of them are.