Illustrations may be useful even when imperfect, and therefore I have slurred over two points, which affect the illustration rather than the application which we are about to make. It was scarcely true to say that the shuffling cannot be undone. You can sort out the cards into their original order if you like. But in considering the shuffling which occurs in the physical world we are not troubled by a deus ex machina like you. I am not prepared to say how far the human mind is bound by the conclusions we shall reach. So I exclude you—at least I exclude that activity of your mind which you employ in [Pg 64] sorting the cards. I allow you to shuffle them because you can do that absent-mindedly. Secondly, it is not quite true that the original order never comes back. There is a ghost of a chance that some day a thoroughly shuffled pack will be found to have come back to the original order. That is because of the comparatively small number of cards in the pack. In our applications the units are so numerous that this kind of contingency can be disregarded. We shall put forward the contention that— Whenever anything happens which cannot be undone, it is always reducible to the introduction of a random element analogous to that introduced by shuffling. Shuffling is the only thing which Nature cannot undo. When Humpty Dumpty had a great fall— All the king’s horses and all the king’s men Cannot put Humpty Dumpty together again. Something had happened which could not be undone. The fall could have been undone. It is not necessary to invoke the king’s horses and the king’s men; if there had been a perfectly elastic mat underneath, that would have sufficed. At the end of his fall Humpty Dumpty had kinetic energy which, properly directed, was just sufficient to bounce him back on to the wall again. But, the elastic mat being absent, an irrevocable event happened at the end of the fall—namely, the introduction of a random element into Humpty Dumpty. But why should we suppose that shuffling is the only process that cannot be undone? The Moving Finger writes; and, having writ, Moves on: nor all thy Piety and Wit Can lure it back to cancel half a Line. [Pg 65]