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The Extraordinary Hotel or the Thousand and First Journey of Ion the Quiet (1968)
Naum Ya. Vilenkin
Highly Rated!
Note: This work of mathematical fiction is recommended by Alex for math majors, math grad students (and maybe even math professors).

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 context.

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.

Contributed by Suguna

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.

Contributed by Anonymous

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.

Contributed by Lapo Fanciullo

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!

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Works Similar to The Extraordinary Hotel or the Thousand and First Journey of Ion the Quiet
According to my `secret formula', the following works of mathematical fiction are similar to this one:
  1. The Infinite Assassin by Greg Egan
  2. The Cat in Numberland by Ivar Ekeland (author) / John O'Brien (illustrator)
  3. The Monkey in Hilbert's Hotel by K. B. Basant
  4. Hilbert's Hotel by Ian Stewart
  5. The Gnome and the Pearl of Wisdom: A Fable by Richard Willmott
  6. Turing (A Novel About Computation) by Christos Papadimitriou
  7. Sphereland: A Fantasy About Curved Spaces and an Expanding Universe by Dionys Burger
  8. His Master's Voice by Stanislaw Lem
  9. Intoxicating Heights (Höhenrausch. Die Mathematik des XX. Jahrhunderts in zwanzig Gehirnen) by Dietmar Dath
  10. Puzzles from Other Worlds by Martin Gardner
Ratings for The Extraordinary Hotel or the Thousand and First Journey of Ion the Quiet:
RatingsHave you seen/read this work of mathematical fiction? Then click here to enter your own votes on its mathematical content and literary quality or send me comments to post on this Webpage.
Mathematical Content:
4.5/5 (4 votes)
Literary Quality:
3.5/5 (4 votes)

GenreScience Fiction, Didactic,
TopicInfinity, Real Mathematics, Logic/Set Theory,
MediumShort Stories, Available Free Online,

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Exciting News: The 1,600th entry was recently added to this database of mathematical fiction! Also, for those of you interested in non-fictional math books let me (shamelessly) plug the recent release of the second edition of my soliton theory textbook.

(Maintained by Alex Kasman, College of Charleston)