| Another take on the idea (attributed to lectures by David Hilbert) that the bizarre properties of the countably infinite can best be presented through the analogy of a hotel. Here, Mr. and Mrs. Smith get lost: instead of the Hilton Hotel in Tenerife they wind up at Hilbert's Hotel in Tenner Reef. Since the hotel has as many rooms as there are positive integers, there is no trouble in making room for them even though all of the rooms are already taken...each occupant merely moves up to the next room leaving room number 1 empty for the Smiths. With Stewart being a real mathematician and all, he pushes things a bit farther than does Stanislaw Lem in his version. And so, by the end, not only do we see how there is room for an infinite busload of new guests, but we see how there isn't room (or that there is a paradox, depending on how you want to look at it) for all of the clubs that could meet in each room. (In particular, the "Absentees' Club" of people who don't belong to the club that meets in their room has trouble finding a place to meet.)
Published in the 19/26 December 1998 issue of New Scientist.
(And, if you like this idea, you should also check out Welcome to the Hotel Infinity, a story by Nancy Casey available on her Webpage.) |
