Academic Mysticism

In thinking about evolution the other day, it occurred to me that I do not actually understand causality. Accordingly, I looked in at the Wikipedia monograph on Causality to see how much was already understood about that subject, and in so doing I came upon yet another infernal 'paradox':

The Paradox of the Grand Hotel

Consider a hypothetical hotel with countably infinitely many rooms, all of which are occupied – that is to say every room contains a guest. One might be tempted to think that the hotel would not be able to accommodate any newly arriving guests, as would be the case with a finite number of rooms. Etc., etc., etc.

Anticipated amusement turned to anger which soon became outrage. Why do academic mystics tie themselves into knots by making absurd assumptions and then marvelling at the paradoxical results?

The paradox is summarized in the monograph on Infinity as follows:

The paradoxical nature of infinity is illustrated by the idea of a grand hotel, with infinitely many rooms—all of which are occupied by guests—but can nevertheless manage to accommodate a new guest by moving each existing guest over, one by one, to other rooms.

A hotel with an infinitely large number of rooms, each large enough to contain a guest, would have to be infinitely large. But the only universe that we have ever experienced appears to be finite in size. It appears, therefore, that the paradoxical Grand Hotel could not exist because it could not fit inside the universe.

Infinity is a concept encountered in mathematical theory (1/0 = ∞) and in science fiction, but not in reality, or I'm very much mistaken.

Eugene Paul