MATHEMATICAL FICTION:

a list compiled by Alex Kasman (College of Charleston)

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The Logic Pool (1997)
Stephen Baxter
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Contributed by Dave Renfro

The Logic Pool deals with an intelligence that is similar to the meme-minds in Gregory Benford's Foundations Fear. Meme-mind -- I think this means some sort of intelligence whose existence arises from abstract ideas, like beauty and morality (but maybe more complex than these). As the ideas evolve and become modified over time, the underlying meme-mind achieves consciousness analogous to ordinary intelligences (biological and machine) that achieve consciousness when certain matter/energy things evolve and become modified over time (e.g. consciousness from a human brain, consciousness from a Pentium 24 chip, etc.). Anyway, Baxter's lifeform is a tree--in the mathematical sense--that is a complex and evolving collection of axiomatic theories. Each chain in the tree is an axiomatic theory and each branch grows by continuously adding new axioms obtained by using Godel's technique to obtain statements that are [undecidable - ak] in the theory generated by the set of all statements preceding (in the lattice-order sense) the axiom being added.

Contributed by Kyle Ankeny

"'The Logic Pool' definitely focus's on mathematics. As I said, math isn't my favorite, so some of this was hard to grasp and understand for me. :) Here's some passages from 'The Logic Pool':

(quoted from The Logic Pool)

"Marsden's data stores contain a fragmented catalogue of mathematical variants. All founded on the postulates of arithmetic, but differing in their resolution of undecidable hypothesis."
"Undecidability. You're talking about the incompleteness theorems,"
"Right. No logical system rich enough to contain the axioms of simple arithmetic can ever be made complete. It is always possible to construct statements that can be neither disproved nor proved by deduction from the axioms; instead the logical system must be enriched by incorporating the truth or falsehood of such statements as additional axioms..."
The Continuum Hypothesis was an example.
There were several orders of infinity. There were 'more' real numbers, scattered like dust in the interval between zero and one, that there were integers. Was there an order of infinity between the reals and the integers. This was undecidable, within logically simpler systems like set theory; additional assumptions had to be made.
"So one can generate many versions of mathematics, by adding these true-false axioms."
"And then searching on, seeking out statements which are undecidable in the new system. Yes. Because of incompleteness, there is an infinite number of such mathematical variants, spreading like the branches of a tree...."

"Ok, don't get the wrong idea, it is not THAT dry. There is a plot wrapped around this math. Essentially, they find a dead researcher, and are trying to figure out how he died, this what he was working on. He had evidently created sentient creatures that used these axioms and such, they were like the 'tree'.


This story is just one of several related stories in the book Vacuum Diagrams.

Contributed by Kyle Ankeny

I think [Vacuum Diagrams] is an excellent Hard SF book. It spans 5 million years of human history, through wars with the Xeelee, the fall of civilization (sort of), and the final victory of Dark Matter life over Baryonic life. It is an epic book, and the physics in it sometimes make you just sit back and say 'wow'. It deals with all areas of science, from biology to mathematics. I highly recommend you try to get this book (I first read it from the library, and then bought it on EBay for $1.00!), I believe there was a few copies on EBay, and there may be more than when I got mine. So maybe the characterization in the book isn't the greatest, but the book isn't about character development, it's about epic ideas.

See also Godel's Sunflowers.

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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 The Logic Pool
According to my `secret formula', the following works of mathematical fiction are similar to this one:
  1. Gödel's Sunflowers by Stephen Baxter
  2. Gödel Numbers by J.W. Swanson
  3. Manifold: Time by Stephen Baxter
  4. Touching Centauri by Stephen Baxter
  5. Gödel's Doom by George Zebrowski
  6. The Light of Other Days by Arthur C. Clarke / Stephen Baxter
  7. The Planck Dive by Greg Egan
  8. Oracle by Greg Egan
  9. Herbrand's Conjecture and the White Sox Scandal by Eliot Fintushel
  10. Imaginary Numbers : An Anthology of Marvelous Mathematical Stories, Diversions, Poems, and Musings by William Frucht (editor)
Ratings for The Logic Pool:
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 (1 votes)
..
Literary Quality:
3/5 (1 votes)
..

Categories:
GenreScience Fiction,
MotifGödel,
TopicLogic/Set Theory,
MediumShort Stories,

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(Maintained by Alex Kasman, College of Charleston)