a list compiled by Alex Kasman (College of Charleston)

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Milo and Sylvie (2000)
Eliot Fintushel
(click on names to see more mathematical fiction by the same author)

Contributed by "William E. Emba"

"Shapeshifting is treated as a form of Banach-Tarski equidecomposition. And part of a Zorn's Lemma proof is given explicitly."

This story appeared in the March 2000 issue of Asimov's Science Fiction. A sequel appeared in the same magazine almost three years later.

For those who may not know, the Banach-Tarski Theorem is a real, surprising, and somewhat disturbing theorem of geometry. What it says, essentially, is that any sphere can be broken apart into a finite number of pieces and then reassembled into another sphere of any desired volume. Certainly this is disturbing: one is inclined either to be impressed that mathematics has shown us that volume is not what we think it is, or perhaps one will conclude that mathematics doesn't make sense after all! [See Division by Zero]. When I learned about it as an undergraduate (back in the 20th century) we were told that this was an indication of possible problems with the Axiom of Choice (an axiom of set theory that is not universally popular), but that viewpoint seems to be out of date. This is now seen as just one of many indications that volume is a slipperier topic than one might expect. In particular, as this theorem and others like it show, the notion of volume is not "finitely additive"...and there is no alternative measure for arbitrary sets in dimensions 3 or higher which are! In other words, when it comes to volume, the whole may NOT be equal to the sum of its parts.

For more information about this funky theorem, check out this link or even this one.

Now, please forgive me for being too serious, but it annoyed me that the story misuses the theorem. If one were to ignore the atomist view of matter, and if one had a way to break matter (even your own body) up into pieces of arbitrary shape, then the Banach-Tarski theorem WOULD give you a way to reassemble those pieces into something of a different volume. However, this story makes it sound as if it is the theorem that gives them the power to break their body into pieces, and that's just silly. (Sorry.)

(Note: This is just one work of mathematical fiction from the list. To see the entire list or to see more works of mathematical fiction, return to the Homepage.)

Works Similar to Milo and Sylvie
According to my `secret formula', the following works of mathematical fiction are similar to this one:
  1. The Grass and Tree by Eliot Fintushel
  2. The Time Axis by Henry Kuttner
  3. Izzy at the Lucky Three by Eliot Fintushel
  4. Diamond Dogs by Alastair Reynolds
  5. Snow by Geoffrey A. Landis
  6. La formule: (A story of fourth dimension) by Jean Ray
  7. Axiom of Dreams by Arula Ratnakar
  8. The Cubist and the Madman by Robert Metzger
  9. The Exception by Alex Kasman
  10. Schild's Ladder by Greg Egan
Ratings for Milo and Sylvie:
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:
3/5 (1 votes)
Literary Quality:
3/5 (1 votes)

GenreScience Fiction,
TopicGeometry/Topology/Trigonometry, Real Mathematics,
MediumShort Stories,

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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)