MATHEMATICAL FICTION:

a list compiled by Alex Kasman (College of Charleston)

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Gödel's Doom (1985)
George Zebrowski
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What if Gödel was wrong? That is the question asked in this well written but very confused short story. The characters in this story decide to test Gödel's theorem by running a computer program to check logical completeness and consistency. When they find that he was wrong, the universe changes accordingly.
Just as Heisenberg's Uncertainty principle is misused and mythologized by people who think it means something more than it does, Gödel's incompeteness theorem is often misused in popular writing. The author of this story clearly suffers a great many of these confusions all at once! To set the record straight, let me state that
  • The theorem does not say that there would only be a finite number of true statements in a complete system. It merely defines a complete logical system as one in which every statement can either be proved to be true or false. Obviously, in any non-trivial system there would be infinitely many of these statements whether it is complete or not!
  • Gödel's theorem does not address the question of whether the universe is deterministic. The question is whether something can be proved in a finite number of steps in a symbolic logic, not how the universe decides what will happen next!
  • The theorem also has nothing to say about the existence of "free will". This story repeats a mistake I have heard many times before -- that of confusing questions of determinism with those of "free will". The mistake works like this: First suppose the universe was deterministic and then prove that this contradicts some definition of "free will". Then act as if this somehow shows that in a non-deterministic universe there is free will. (In fact, the arguments against free will in a deterministic universe always seem to apply in a non-deterministic universe as well. The truth is that free will is a very slippery term, but that this has nothing to do with determinism.)

I also really object to the characters claim that pure mathematical research has never had any consequences in the real world. (They state explicitly that this experiment they are doing might be the first time.) I think that mathematics does not get much credit because it is rarely the last step in the process. However, we ought to recognize that steps earlier in the process of invention/discovery are also necessary, and without pure mathematical research I do not think we would have airplanes, televisions, computers, reliable cryptography, JPEG standard, global positioning satellites, etc.
First published in Popular Computing (1985) and reprinted in Mathenauts.

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(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 Gödel's Doom
According to my `secret formula', the following works of mathematical fiction are similar to this one:
  1. Gödel's Sunflowers by Stephen Baxter
  2. Not a Chance by Peter Haff
  3. Division by Zero by Ted Chiang
  4. The Logic Pool by Stephen Baxter
  5. The Planck Dive by Greg Egan
  6. Eye of the Beholder by Alex Kasman
  7. Turing (A Novel About Computation) by Christos Papadimitriou
  8. Silicon Muse by Hilbert Schenck
  9. Herbrand's Conjecture and the White Sox Scandal by Eliot Fintushel
  10. The Atrocity Archives by Charles Stross
Ratings for Gödel's Doom:
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 (2 votes)
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Literary Quality:
2/5 (2 votes)
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Categories:
GenreScience Fiction,
MotifGödel,
TopicComputers/Cryptography, Logic/Set Theory,
MediumShort Stories,

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