MATH

Let Me Count the Ways

Sunday, November 25, 2007

PERFECT FIGURES

The Lore of Numbers

And How We Learned to Count

By Bunny Crumpacker

Thomas Dunne/St. Martin's.

271 pp. $24.95

Some fishing boats trawl weighted nets across the seabed, hauling up everything they can possibly find, dumping the odd catch onto the deck for sorting. Perfect Figures does something like this with number lore. Were it not for Bunny Crumpacker's poetic asides, one might mistake this text for the output of a Web-crawling search engine.

Let's start with a nice sample of the rhapsodic prose, taken from the very first paragraph: "One is the beginning, the single starting place. It's the universe at the big bang. . . . It became a billion million stars, galaxies after galaxies of stars, stars with planets and moons and meteors and asteroids, each one containing everything again, atoms and molecules, charm and quark, and each thing -- each atom, each galaxy -- was still one, one again. One after one to infinity."

One briefly wonders: Is it wrong to say "a billion million" instead of "a million billion," "a thousand trillion," or "a quadrillion?" But Crumpacker's choice seems the correct one. She has a good ear. And her haul of facts makes for a tasty bouillabaisse of the numbers found in language, math, love, literature and everyday life. For example, she tells us that, in the 18th century, the English Royal Treasury maintained their numerical accounts in the form of marks on wooden sticks called tallies. Having ported their system to paper, they began burning the vast number of outdated tally sticks in the furnaces beneath the Parliament buildings -- which set fire to the paneling and burned down both Houses!

Although Crumpacker divides her chapters into sections in a way that is hard to follow, the breadth of her net produces pleasant surprises. A mere mathematician might not think of discussing collective names for groups of things, but Crumpacker is a generalist who has also written books on food and jazz, and the following excursus is perfect for a book on numbering: "a bed of clams or oysters, a flight of birds, a host of angels, a flood of tears, a bouquet of flowers, a bed of roses, a flight of stairs . . . a brood of chickens, a murder of crows, a sounder of swine . . . a chain of islands, a range of mountains, a stand of trees."

The author brings a frankly sexual charge to some discussions: "I like thinking of nine -- that masculine number, with its ball atop its straight line, a perfect outline, or a perfect sperm -- as a word buried in femi nine." Many passages have to do with linguistic and social aspects of numbers. We learn that "quintessence," which contains the Latin for "five," was used by the Pythagoreans to mean an ethereal fifth type of matter beyond earth, air, water and fire. Some modern-day cosmologists are in fact using this word to stand for a form of mysterious dark energy. And I've always wondered how we ended up patterning our lives by weeks -- Perfect Figures suggests it's because each phase of the moon lasts about seven days.

Sadly, the book includes no illustrations; instead, the text is broken up with boxed quotes that have the feel of Google-generated info-dredging. Numbers are many things: spoken names, written symbols, cultural talismans, magnitudes and thought forms. But they're also geometric patterns; indeed, that's how the Pythagoreans thought of them. Four calls out for a drawing of a tetrahedron (that is, a triangle-based pyramid), nine for a picture of the mystic star-shape called the enneagram, and when Crumpacker mentions the fortune-telling toy known as the Magic Eight Ball, she should show us an image of the 20-sided solid that bobbles within this black ball to reveal one triangular face at a time through its porthole. Numbers are more than words.

Nevertheless, taken on its own terms, Perfect Figures is a perfectly browsable, richly poetic compendium of number facts.

Let's close with a soaring quote, where the author imagines writing out googolplex, a number represented by a one followed by an astronomical number of zeroes: "When you were there, at the end of all your zeroes, zero after zero after zero, you could still add one more -- to make googolplex plus one -- to the line of numbers that you drew through the stars, connecting them zero by zero, to home, to one, to nothing, to all." ¿

--Rudy Rucker is a mathematician and author.


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