When asked what went through his mind while he was crouched in the rocket nose-cone, awaiting blast-off, he replied, ‘I was thinking that the rocket has 20,000 components, and each was made by the lowest bidder.’ Martin Rees Some dimensionally dependent phenomena seem reasonable. Take, for instance, the idea of a random walk. In one dimension this means that we start at the origin and move to the left or the right with equal probability; in two dimensions we have four equally probable directions in which we can walk; in both cases it can be shown that the probability of eventually returning to the origin is 1; we cannot, in theory, get lost. As the dimension increases, so we might reasonably think are the chances of getting lost, never to return to the origin, increase, and so they do. In three dimensions the probability of our return is only about 0.34 and in n dimensions, where n is large, that probability is about 1/2n. But it does not take much investigation into hyper-dimensions to cause our intuition to be confounded.
