|The author toys with the counter-intuitive nature
of the countably-infinite by postulating the existence of an
intergalactic hotel with rooms indexed by the positive integers. For
instance, the narrator of the story arrives at the hotel to find that
there are no vacancies. However, as a favor, the management makes
room for him by simply asking each of the other guests to move to the
next room. It goes on from there, discussing ideas which we have all
encountered before, but perhaps not in such an entertaining
Note: This story has frequently been misattributed to the famous Polish author Stanislaw Lem. This mistake was made in the collection Imaginary Numbers and was repeated here from that source. However, thanks to Fred Galvin and his suggestion that I look at a discussion about the authorship of this story, I am now (August 2015) correcting that mistake. It seems that the story was actually written by the mathematician Naum Ya. Vilenkin.
It apparently first appeared in Vilenkin's 1968 "Stories About Sets". Moreover, this story can be read for free starting on page 39 of this translation of Vilenkin's "In Search of Infinity".
In any case, the idea of using a hotel to discuss infinity is certainly not original to this short story.
George Gamow (in One, Two, Three...Infinity) attributes this hotel analogy to David Hilbert and Allyn Jackson points out to
me that the article ``Hilbert's Hotel," by Ian Stewart (New Scientist,
19/26 December 1998 - 2 January 1999, pages 59-61) also presents this analogy in the form of a story. 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.
I read this book long ago, in 1972, and
liked it enough to copy some excerpts,
which I no longer have. But the fact
that I still remember the main story
means it made quite an impression on
me. I found the story fascinating.
I remember reading this story as a kid (sometime in the 80s, I guess), well before running into the concept of countable infinity. I only remembered it again late in my university years, after reading up on Cantor and Turing. I suppose that this story made the ideas easier to understand later. I still think highly of this one.
I already knew the solutions on "how to host an additional guest" and "how to host an additional infinity of guests", but I had long wondered how to host an infinity of infinities of guests... Until I read this tale and found three answers. Thank you, Lem!