Chapter 16, Infinity, part 2

Well, that depends on two things: the size of the cake, and the share which each child eats. If the cake weighs two pounds, and each child eats two ounces, it will be all eaten up when sixteen children have gone through the room. If the cake weighs only one pound, it will be eaten up when eight children have gone through the room. But if each child eats only one ounce, then again sixteen children will have to go through the room before the cake is eaten up, and so on. Many questions could be asked, all depending on the size of the cake and the size of each child's share. All this time you are tied to an hypothesis that the children eat cake (more or less). But now suppose we are freed from that hypothesis. Suppose no cake is given to the children. How many can pass through the room before it is all eaten up? The answer to that is: “An infinite number.” Infinity does not mean any particular number, or a very large number. It means a loosened chain, a discarded hypothesis, escape from the rule we were working under. Something else, not the size of the cake, determines the number of children. Infinity does not mean that there are enough children in the world now to go on passing through the room for ever, but that the number of children who pass through the room, now that the share of each child is 0 (zero), will have to be determined by the number of children that there are in the school, or the parish, or wherever it is that the children are supposed to come from; and not by the size of the cake. The size of the cake has no longer anything to do with answering the question: “How many children can pass through the room before the cake is all eaten?”