Fantasia Mathematica

So… Martin Gardner died Saturday.

Folks far more eloquent than I have expressed their thoughts on his life and legacy, but I want to focus on a magnificent book that — well — everyone should read.  It’s called Fantasia Mathematica, compiled and edited by Clifton Fadiman — in 1958.  Gardner has two short stories in there, and that was one of two places where I first learned his name.

(The other place was Asimov’s Science Fiction magazine, where he wrote monthly puzzles — apparently to hurt our brains.)

I first came across this gem of a book when I was around eight or nine years old.  Sometime around 1980, in other words.  My head was full of Star Trek, Star Wars, Dr. Who, and things like that.  And this book opened up parts of my brain I didn’t know existed.

It’s made up of three sections – the first section, Odd Numbers, consists of excerpts from larger works by famous authors (Aldous Huxley, H.G. Wells, Plato…) that just happen to include mathematics in them.  The third section, Fractions, is mostly made up of cute math poems and brief tales that don’t take up more than a page or two…

There was a young lady named Bright,

Who traveled much faster than light.

She started one day,

In the relative way,

And returned on the previous night.

But the middle section, Imaginaries, captured my fancy as a child and continues to do so now.  Seventeen short stories, averaging around 12 pages each, that find their basis in mathematics and tell wonderfully entertaining tales.  Some even come with certain names attached to them…  Clarke, Heinlein…

Cover of the Third Edition (1964)

  • There’s the story of the man who built a house in the shape of an unfolded tesseract.  An earthquake in the night folds the tesseract through the fourth dimension into its more natural shape, and once the architect and his companions enter, they find it difficult to leave.
  • There’s the story of the man who challenges Satan to solve Fermat’s Last Theorem.
  • There’s the story of subway that becomes a topological anomaly when a new branch line is opened – and a train disappears.
  • There’s the story of the man who rotates a piece of fourspace into our three-dimensional universe – and captures a cross-section of some fourth-dimensional creature.

…and then there are Martin Gardner’s tales.  Both rely heavily on topology for their mathematics (as do many in this section).

In the first of his that Fadiman included in the collection, called “No-Sided Professor”, Gardner extends on the concept of the one-sided Moebius Strip, and spins a tale where Dr. Stanislaw Slapenarski figures out how to go one step further than Moebius and create a no-sided surface.  What do you suppose that would look like?

The second tale, “The Island of Five Colors”, describes another apparent topological impossibility – an island with five tribes on it where they all share common borders.  Dr. Slapenarski returns to explain how he arranged the tribes after disproving the four-color theorem, and the narrator paints the territories before flying up in a plane to take photographic proof to bring back to civilization.

Cover of the New Edition (1997)

I remember not having a clue about a lot of what I was reading as I read it in 1980, but more so than any other book, it made me want to learn what these stories were talking about.  Plus, many of these stories paint the mathematicians as the heroes – they solve the puzzles, they save the day.

The only rough part to deal with is that these stories are old.  I mean, obviously they are, since the book was published in 1958, but some were even old back then.  The earliest (excluding Plato’s work) is from 1873, and many of the rest are from the early 1900′s.  To that end, well, they’re not particularly progressive.  In the 1929 work “The Captured Cross-Section”, by Miles J. Breuer, M.D., the first paragraph establishes that the protagonist’s fiancée, Sheila, is the “daughter of the Head of the Mathematics Department” who has “published some original papers.”  So she’s quite intelligent.  And yet, on the second page, her fiancé, Heagey…  Well, just read for yourself…

“But there are other quantities here,” Sheila interrupted, studying the paper intently, “that do not belong in equations for the rotation of coordinates.  They look like the integrals in electromagnetic equations.”

“Good for you!” Heagey cried enthusiastically.  ”That pretty little head has something on the inside, too.”

Now, maybe he was just needling her…  Or maybe it was 1929.

But honestly, set that stuff aside, read right past it, and you’ll find some wonderful stories.  I think it’s time for the Little Skeptic Girl to poke around in the Imaginaries section…

And in researching this article, I discovered that a book exists with all of Martin Gardner’s short stories – are there more adventures of Dr. Slapenarski??  I hope so!

So even though Gardner is remembered for much more than his fiction, tonight I’m taking my 3rd edition hardcover to bed with me to visit with Dr. Slapenarski again.

Rest in peace, Martin.  Count me among the many who you reached with your work.

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