MATHEMATICAL FICTION:

a list compiled by Alex Kasman (College of Charleston)

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Occam's Razor (1956)
David Duncan
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Contributed by Vijay Fafat

This story involves the concept of discontinuous time embedded in a sort of “Meta-Time”. Essentially, Duncan proposes the idea that True Reality evolves along Meta-Time which is broken up into smaller fragments. A chain of such non-consecutive intervals forms the timeline which we perceive and there are potentially infinitely many such chains which govern other realities. In that sense, we are like a movie film where the characters exist only on the frames and not in the gaps between them. We ourselves do not feel the discontinuity because we do not experience the interstitial Meta-Time intervals. True Reality consists of all these intertwined movies running at the same (Meta)Time. Duncan couples this idea with a second, intriguing - if far-fetched idea – that extremely thin, mathematically minimal surfaces like surfaces of soap bubbles, under suitable topologies, can arc across the time-gaps and act as doorways to these other, interspersed realities (the effect when two separate timelines synchronize for a brief interval and its name - “Tib’s crossing” – are very aptly described).

He spends a considerable amount of time discussing how soap bubbles give a convenient way of visualizing minimal-surface solutions to a number of closed-curve constructions in 3-D. “Occam’s Razor” or the “Principle of Parsimony” gets its fair time for discussion as well, though the author has extrapolated the original principle to the observation that Nature seems to prefer extremal solutions (“Minimal surfaces, minimal distances, minimal time and minimal energy. All are included under one general principle which in honor of William of Occam I’ll call the principle of universal parsimony”).

It would have been a fabulous short story about big-ideas but Duncan decided to launch into a novel-length exposition where it does not work at all. The novel is written tautly enough, with some very good passages, but the plot is extremely thin and makes absolutely no sense. On a military island, against the backdrop of a race to the moon amongst many nations, a topologist playing around with soap films ends up creating an opening to an alternate reality. From there, a man resembling the devil and an Eve cross over to our space. After a convoluted chase, the devil is shot and Eve returned to her reality. The soap-bubble machine is now slated to be used as a regular gate to all those other universes (“This is the topology of the future. Gentlemen, we are about to short-circuit the universe!”)

The story-line fails on many fronts and has too many holes to list here (why should you find biped humanoids or even “green” grass in another reality at all??.) But I would still recommend this book because I enjoyed most of his writing and it does a decent enough job of arousing interest in the mathematical theory of minimal surfaces. Some notable quotes:

(quoted from Occam's Razor)

“Ensign Waters: I work with mathematical formulas, not soap film. When I compute the minimal path of a guided missile, I want to know what I’m doing!
Prof. Staghorn: I assure you that anyone who computes the path of a guided missile can’t possibly know what he’s doing.”

“Prof. Staghorn: Any solution you reached by mathematical computation would be nothing except an abstraction of what you see before you in reality. I’m trying to impress upon you that all mathematical abstractions, if valid, must relate to reality. But if you have the reality, why must you also have the abstraction?”

“There are certain minimal surfaces or minimal distances, connecting an infinite number of points, where mathematics based upon the calculus of variations is helpless […] And yet the solution exists in reality and can be demonstrated visually in soap film”

[while naming the effect when two separate time-lines synchronize for a brief interval] “There’s no Saint Tib. So there’s no Tib’s eve either. It’s a time that never was and never will be – or it’s a period removed from time altogether. So I called this thing ‘Tib’s passing’ “

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Works Similar to Occam's Razor
According to my `secret formula', the following works of mathematical fiction are similar to this one:
  1. The Curve of the Snowflake by William Grey Walter
  2. Star, Bright by Mark Clifton
  3. The Einstein See-Saw by Miles J. Breuer
  4. The Feeling of Power by Isaac Asimov
  5. Schild's Ladder by Greg Egan
  6. Border Guards by Greg Egan
  7. Turnabout by Gordon R. Dickson
  8. Starman Jones by Robert A. Heinlein
  9. Into the Comet by Arthur C. Clarke
  10. A Subway Named Moebius by A.J. Deutsch
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Categories:
GenreScience Fiction,
MotifTime Travel,
TopicGeometry/Topology/Trigonometry, Mathematical Physics,
MediumNovels,

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(Maintained by Alex Kasman, College of Charleston)