Friday, January 13, 2012

Flatterland, a book review

Over the holidays, I read Flatterland by Ian Stewart. Stewart is an English mathematician and contributor to a branch of geometry called "catastrophe theory." Sounds fun, eh?

The subtitle of Flatterland is "Like Flatland, only more so." Stewart wrote it as a sequel to and extension of Edwin Abbott's 1884 geometrical satire, Flatland. One hundred years after the events of the first book, Victoria Line, great-great-granddaughter of the original A. Square, reads her ancestor's book (against her father's express prohibition) and finds in it a code for summoning a visitor from Spaceland.

Instead of a Sphere, Victoria receives a visit from a Space Hopper, a creature who helps her visit not just many dimensions higher than the third, but a number of other strange geometric worlds. In one she sees fractals everywhere. In another, parallel lines converge. In another she can see herself in the distance. Her investigation into curved space leads into a discussion of quantum physics and relativity, a theory the Space Hopper insists is poorly named, since it's based on the one thing that isn't relative - the speed of light.

So how's the book to read? My 8th grade son read it before me, and he found it mind-twisting and thought provoking - hard, but worth it. For me, with a year of college physics and no math beyond calculus, it was surprisingly accessible. Yes, it's difficult to visualize the worlds Stewart describes, but he assures us it's difficult for mathematicians, too. And its's fun to toss these ideas around lightly like oddly-shaped objects to juggle. The format consists mostly of dialogue between the Space Hopper, who is a little bit self-satisfied, and Victoria, who is by turns a stubborn teenager, a dense student, an independent reasoner, and an inspired explorer of new intellectual landscapes.

I wish the discussion of fractional dimensions were more thorough: I felt I almost had it when the story moved on. I enjoyed Moo-bius the Cow and the Klein bottles. Topology was fun to dip into, as was the discussion of infinity and parallel lines. The section on quantum physics and relativity took me back to the weirdest, most fun parts of physics. As for the story itself, while the plot is not enthralling, it's sufficient to carry the exploration of mathematics.

Who would like this book? Anyone who would like his or her mind stretched in weird ways. I'd recommend it especially for kids in grades 8-10 who like math even if they don't like calculation; people who like visual puzzles; and people like me who want their ideas of math and science tickled by new ways of thinking about and trying to visualize shape and space.

More than anything, Flatterland is valuable because it shares with us the freaky, imaginative side of mathematics and demonstrates that math is not just a matter of plodding through more and more difficult algebra and calculus. Instead, mathematics can become a great playground for the imagination.

Does anyone have another playful or challenging melding of math and literature to recommend?

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