a list compiled by Alex Kasman (College of Charleston)

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The Extraordinary Hotel or the Thousand and First Journey of Ion the Quiet (1968)
Stanislaw Lem
(click on names to see more mathematical fiction by the same author)
Highly Rated!
Note: This work of mathematical fiction is recommended by Alex for math majors, math grad students (and maybe even math professors).

Here, the famous Polish 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.

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.
This story was published both in the book Stories About Sets (in which it is apparently the only work of fiction) and in the recent Imaginary Numbers.

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. Hilbert's Hotel by Ian Stewart
  4. The Gnome and the Pearl of Wisdom: A Fable by Richard Willmott
  5. Turing (A Novel About Computation) by Christos Papadimitriou
  6. Sphereland: A Fantasy About Curved Spaces and an Expanding Universe by Dionys Burger
  7. His Master's Voice by Stanislaw Lem
  8. Intoxicating Heights (Höhenrausch. Die Mathematik des XX. Jahrhunderts in zwanzig Gehirnen) by Dietmar Dath
  9. Infinities by John Barrow
  10. The Kissing Number by Ian Stewart
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,

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