a list compiled by Alex Kasman (College of Charleston)

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Luminous (1995)
Greg Egan
(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 hardcore fans of science fiction.

A truly wonderful story in which two math grad students discover that the things we consider to be "truths" in number theory are actually part of a dynamical system, subject to change over time and in competition with alternative "truths" that are equally valid at other "locations" in the number system.

I like the anecdote about the mathematician whose reputation is so great, that once a rumor spread that he has found a (secret) algorithm for factoring large numbers quickly, people around the world stopped using the RSA encryption algorithm. The story also has some clever science fiction elements, such as a microbe which you can put in your body which has the effect of making anyone who touches your blood instantly very ill. (It sounds weird, but hey, it saves one of the protagonists lives, so don't knock it!)

One thing I don't quite understand, and perhaps someone else can write in if they were able to make more sense of it than me, is where this "fractal boundary" between the different domains of mathematical truth was supposed to exist. It seems as if they mapped it out as part of the number theory of the integers...but I cannot quite imagine the integers having any sort of topology that would allow fractal submanifolds. The set is too discrete..or rather, too SMALL since it is countable. Was this boundary supposed to be part of the complex plane? Or am I not thinking of it in the right way altogether?

Anyway, I'm probably taking this too seriously as usual. It is definitely a way cool story, and it certainly makes you think about the foundations of mathematics...although it did not "convert" me to Platonism in the end.

Contributed by Arturo Magidin, UNAM, Mexico

Our heroes are trying to escape from `Industrial Algebra', an evil corporation that wants to use their mathematical discoveries (or perhaps supress them). Our heroes have discovered that arithmetic is inconsistent... but only when using numbers so large that no mathematician has encoutered the inconsistency (there is an undercurrent of constructivism/intuitionism running through the story). They use Luminous, a super fast computer made out of light, to verify the result, and discover an entirely different world co-existing with ours... using different rules of arithmetic."

Contributed by Henry Segerman, Stanford

This is the best math fiction I've read. The math is speculative, and most likely couldn't be fleshed out in reality, but it makes for a great story - lots of 'wow' factor."

Contributed by Matteo

"Really liked not only the mathematical background, but also writing-style of Egan. The incipit is really great. If only more sf writers write like him."

Originally published in Isaac Asimov's Science Fiction Magazine, September 1995, also appears in _The Year's Best Science Fiction: Thirteenth Annual Collection_, edited by Gardner Dozois. Note that this story was also reprinted in an anthology of the same title in 1999, which is unfortunately already out ot print.

Dark Integers, a sequel to Luminous was published in 2007.

BTW: Check out Egan's Home Page for more information about his fiction, his programming and the mathematics underlying them.

Contributed by BCP

[Spectacular site, btw. I'm very grateful for all the work you've put into it.]

In your review you mentioned not understanding what space the fractal border was in, because the integers are too discrete. I'm fairly sure that it's a curve in the logical space of arithmetic propositions, not in the numbers themselves: an enormous graph with each node a true assertion and each link an inference, or in the 3d form with distance as the number of inferential steps.

For instance, the computer plotting it makes "billions of inferential loops" (valid circular deductions), and "portrayed the network of statements as an intricate lattice in three dimensions (a crude representational convention)". "At the border, every theorem you test is getting contradictory advice. From one neighbor, x-1 = y-1 . . . but from another, x+1 = y+2. And the topology of the border is so complex that a near-side theorem can have more far-side neighbors than near-side ones-and vice versa."

Anyways, it's a great story. I don't know what to say for a review, except that I've spent much more time thinking about it afterwards than I spent actually reading it. I'm only a student, but the mathematical imagery of this gives me all kinds of actual math ideas to play with (what's the distribution of the inference-count of propositions in first order logic?) And I had exactly the opposite philosophical response to you. It sounds like you took the story to be arguing for Platonism because constructivism is so absurd - I'm a firm Platonist, but the details of how constructivism like this would work have too much fun math to resist!

Thank you again for your efforts with the site, and best of luck, Brady Pelkey

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Works Similar to Luminous
According to my `secret formula', the following works of mathematical fiction are similar to this one:
  1. Dark Integers by Greg Egan
  2. Planck Time by Michael Iwoleit
  3. Doctor Who: The Algebra of Ice by Lloyd Rose (pseudonym of Sarah Tonyn)
  4. Mathematica by John Russell Fearn
  5. Mathematica Plus by John Russell Fearn
  6. The Mathenauts by Norman Kagan
  7. Distances by Vandana Singh
  8. Mysterious Mysteries of the Aro Valley by Danyl McLauchlan
  9. The Living Equation by Nathan Schachner
  10. The Ultimate Analysis by John Russell Fearn
Ratings for Luminous:
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 (6 votes)
Literary Quality:
4.17/5 (6 votes)

GenreScience Fiction,
MotifCool/Heroic Mathematicians, Academia, Aliens, Female Mathematicians,
TopicAlgebra/Arithmetic/Number Theory, Fictional Mathematics, Chaos/Fractals, Logic/Set Theory,
MediumShort Stories,

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