MATHEMATICAL FICTION:

a list compiled by Alex Kasman (College of Charleston)

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The Island of Five Colors (1952)
Martin Gardner
(click on names to see more mathematical fiction by the same author)
Highly Rated!

In this sequel to The No-sided Professor, our heroes tackle the Four Color Theorem, which was unproved at the time. (See here for a brief summary of a recent proof.) Included are some historically accurate details about the prior attempts to prove the theorem, and a (fictional) counter-example in the form of an African island divided into five simply connected districts -- each of which borders the other and the ocean. Unfortunately, we do not get to hear Prof. Slapenarski's explanation of this phenomenon because he is pulled into the depths of a Klein bottle by what appears to be a giant insect.

Gardner apparently no longer likes to see this story in print. His recent collection The No-Sided Professor does not include it. He explains that "(1) It was based on a confusion between the four-color map theorem and a simpler theorem, easily proved, which says that five regions on the plane cannot be mutually contiguous, (2) the true four-color theorem, unproved when I wrote my story, has since been established by computer programs, though not very elegantly. As science fiction, the tale is now as dated as a story about Martians or about the twilight zone of Mercury." I don't know, I still like it!
Reprinted in Fantasia Mathematica.

Contributed by Paul Kainen

I'm writing since apparently Gardner doesn't know (or forgot) that there _is_ a way to have such a situation - even with an arbitrary finite number of such mutually bordering regions. It's a topological "pathology" refered to as "the lakes of Wada" (a Japanese name I guess but the pun is nice). The catch is that the regions cannot have boundaries of finite length.

If one has an island with n distinct lakes, first dig a canal from the first lake so that it gets within, say 1 km of every point on the boundary of the island and within 1 km of every point on the boundary of the other lakes. Now repeat this process for the second lake, etc. Each lake remains a simply connected region, albeit with a rather long boundary. Now repeat the whole process replacing 1 km by, e.g., 1/10 km, and keep going. As I vaguely recall, one can show that in the limit, the lakes remain simply connected and all of them share a common boundary.

Probably Gardner did know it (as he picked an island as a setting for his story).

My ratings are based on having read other stories by Gardner, though not this one, and on your description above.

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Works Similar to The Island of Five Colors
According to my `secret formula', the following works of mathematical fiction are similar to this one:
  1. No-Sided Professor by Martin Gardner
  2. The Four-Color Problem by Barrington J. Bayley
  3. Left or Right by Martin Gardner
  4. What Dead Men Tell by Theodore Sturgeon
  5. The Feeling of Power by Isaac Asimov
  6. The Library of Babel by Jorge Luis Borges
  7. The Sinister Researches of C.P. Ransom by Homer C. Nearing~Jr.
  8. Misfit by Robert A. Heinlein
  9. Vault of the Beast by Alfred Elton van Vogt
  10. The Mathenauts by Norman Kagan
Ratings for The Island of Five Colors:
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:
5/5 (4 votes)
.
Literary Quality:
3/5 (4 votes)
..

Categories:
GenreScience Fiction,
Motif
TopicGeometry/Topology/Trigonometry,
MediumShort Stories,

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