a list compiled by Alex Kasman (College of Charleston)

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The Curve of the Snowflake (1956)
William Grey Walter
Note: This work of mathematical fiction is recommended by Alex for hardcore fans of science fiction.

A beautiful and brilliant woman organizes a team of scientists (and a mathematician) who together make fusion energy efficient and invent a flying submarine...and perhaps a time-machine as well. When one of the team members disappears and another seems to have found a manuscript written by him a hundred years in the future inside a "flying saucer" with a fractal surface, the truth becomes elusive.

As you can see from that description, math is not really central to this work. It is intriguing that the ship is described as having a surface based on the Von Koch snowflake curve since the book, written in 1956, predates the current interest in "fractals" (a word which had not yet even been coined when the book was written.) Although in more recent works, fractals are always presented as coming from chaos theory, it is presented in this book as a pathological example in topology that the character had previously sought to understand. The fact that the resulting surface area would be infinite (even though the volume finite) is used to explain unusual properties of the ship. Other mathematical aspects of the book include the claim that in "the future", language is mathematically analyzed ("an operational calculus of semantic probability") and reorganized so that all expressions are explicit and precise. Math is also frequently used as an analogy in the book:

  • There is an interesting analogy made using the snowflake curve describing science as a finite geometric object with infinite for everyone.
  • "Men and women can never be really happy together until we have worked out the algebra of love so that we can say exactly what we mean, and prove the equation of consummation."
  • "He had as much he would have had trying to teach a fifth-century Athenian differential calculus to stop him worrying about the paradox of the tortoise and the hare."
  • "Roughly, I think he went on to define Mentality as the rate of change of behaviour and this puts Mentality in the class of rational abstractions such as Velocity and Gravityl then if you like to use thw word Mind, remember it is just a handy abbreviation...just as Speed is for Velocity."
  • "All expression can be defined within this space of three dimensions. A mathematical expression is high in discipline but close to zero of ambiguity and may be anywhere on the scale of communication. Poetry and painting and music -- the arts in general -- may be at any point on a scale of discipline but are never at zero of ambiguity, though they may have limited value as communication..."

The author of the book was a famous physiologist working on electroencephalography. His predictions of the future are interesting both in how wrong they are as well as occasionally how prescient they were. For instance, he predicts the birth control pill and the fact that it helps prevent cancer (both science fiction when the book was written, even if not particularly far fetched) and he was also a bit ahead of the curve on "free love"...a topic which he seems to have felt very strongly about. However, I am surprised that a man with his training would not seem to understand the chromosomal aspects of sex determination in the male gametes, or that he would claim that "the degrees of living freedom [are] so few" that when we find life elsewhere in the universe it is almost certain to be exactly like us with "only trivial differences".

Contributed by Joel Schneider, Children's Television Workshop

"The artifact of the title is the Von Koch curve, which is well known now in the fractal business as the snowflake curve. A time machine figures in the story and is in the shape of a three-dimensional snowflake curve. I asked my eighth-grade teacher what that would look like. She suggested that I figure it out myself. Working on the problem off and on over several years, I solved it and that's what started me on the road to mathematics. I found a copy of the book a copy a few months ago thanks to a used book site on the web. Rereading it after all these years was fun. There's a moral in my story for teachers."

This book has also been published as Further Outlook.

Contributed by Prem

Maybe my ratings are little out as I read the book more than thirty years back. Anyway I enjoyed it and the curve is still in my memory and I realy drew it step by step till the pencil and paper could not do the job. Maybe I try on the computer now.

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Works Similar to The Curve of the Snowflake
According to my `secret formula', the following works of mathematical fiction are similar to this one:
  1. The Last Starship from Earth by John Boyd
  2. Star, Bright by Mark Clifton
  3. Strange Attractors by William Sleator
  4. Count to a Trillion by John C. Wright
  5. The Feeling of Power by Isaac Asimov
  6. Occam's Razor by David Duncan
  7. The Woman Who Shook the World-Tree by Michael Swanwick
  8. Paradox by John Meaney
  9. Luminous by Greg Egan
  10. Misfit by Robert A. Heinlein
Ratings for The Curve of the Snowflake:
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:
2.5/5 (2 votes)
Literary Quality:
4/5 (2 votes)

GenreScience Fiction,
MotifTime Travel,

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Exciting News: The 1,600th entry was recently added to this database of mathematical fiction! Also, for those of you interested in non-fictional math books let me (shamelessly) plug the recent release of the second edition of my soliton theory textbook.

(Maintained by Alex Kasman, College of Charleston)