Wednesday, February 07, 2007

Pg. 69: "King of Infinite Space"

Siobhan Roberts is a Toronto freelance writer and journalist whose work focuses on reconciling what the British novelist and scientist C.P. Snow famously referred to as “the two cultures” of science and art.

According to her online biography:
In 2001 she met Donald Coxeter, then age 94, and was taken with his tremendous and enduring passion for geometry, as well as his stomach-curdling bedtime elixir — Kahlúa coffee liqueur, peach schnapps, sometimes a splash of vodka, all mixed with soymilk — and his lifelong habit of standing on his head every morning, to which he attributed his longevity. She followed Coxeter to the last geometry conference he would attend, in Budapest in the summer of 2002, where he gave the opening address, providing a new and elegant proof of a theorem relating to “four mutually tangent circles,” a subject which finds application in data-mining technology.
Her close study resulted in the book, King of Infinite Space: Donald Coxeter, The Man Who Saved Geometry.

I asked Siobhan to put her book to the "page 69 test," and here is what she reported:
Page 69 finds us in the summer of 1928, at a turning point in Donald Coxeter's career as a geometer.

Upon the recommendation of his father, Coxeter had spent that summer in Vienna, undergoing psychoanalysis with Dr. Wilhelm Stekel, a protégé-cum-dissident of Freud's. Stekel instructed Coxeter to keep a dream diary. His dreams recorded his anxieties about his romantic failings. But when Coxeter wasn't on Stekel's couch, he loitered in the readings rooms at the University of Vienna and there he discovered the work of Ludwig Schläfli (1814-1895). At the end of his life, Coxeter was asked which mathematician in all of history he would like to be able to talk to, and he chose Schläfli. So in that sense, page 69 is nicely representative of Coxeter's passion for geometry.

Schläfli was particularly known for his work with polytopes. And Coxeter, too, had a preoccupation with polytopes — a species of shapes that reside in any number of dimensions (including two-dimensional polygons and three-dimensional polyhedra, like the five Platonic solids). Coxeter was drawn to higher-dimensional polytopes, and the fourth dimension he said was his favorite (the fourth dimension is traditionally thought of as time, but dimensions can be thought of simply as extra coordinates that quantify existence — say, interest rates, or President Bush's poll numbers; geometers often prefer to think of the fourth dimension in terms of space).

Coxeter was so entranced with the fourth dimension in grade school that he was dismally behind on the mathematical basics. To compensate, when he was cramming for the entrance exams to Cambridge, his tutor forbade him from thinking in four dimensions — except on Sundays.

Today Coxeter's work on symmetries is applied in pretty much every realm of science — in everything from telecommunications and data-mining technology to a recent cosmological hypothesis that the universe is shaped like a dodecahedron. His "Coxeter groups"— tools for investigating symmetries of polytopes — are being used by string theorists in conjunction with Einstein's gravity equations in the search for supersymmetry. Of course, these applications were inadvertent as far as Coxeter was concerned, and beyond his ken. He was a huge fan of the rational nonsense of Alice in Wonderland, explaining: "It's like reading about a part of mathematics that you know is beautiful but that you don't quite understand. Like string theory. That's as much a mystery to me as it is to anyone who can't make head nor tail of the 11th or 16th dimension."
Many thanks to Siobhan for the input.

Among the considerable praise for King of Infinite Space:
“Siobhan Roberts has achieved something extraordinary in this book, a paean to a geometer and all geometry. It tells a brave, compelling story. It comprehends a whole universe — our universe — of kaleidoscopes and crystals, groups and symmetry, bicycles and snowflakes, music and movement. It is lucid, beautiful, and exalting.”
—James Gleick, author of Isaac Newton, Faster, and Chaos

"King of Infinite Space is exhaustive and definitive. Roberts's painstaking research, documented by 73 pages of endnotes, turns up many gems. Especially notable is Roberts's access to Coxeter's diaries, which inject the book with anecdotes of rather startling candor…Invaluable...[F]or the devotee of geometry, there is no substitute for Coxeter, and no substitute for this long-overdue treatment of his life."
—Jordan Ellenberg, Washington Post

“A biography of Donald Coxeter has long been overdue. Now Siobhan Roberts has provided one, and a marvelous book it is. King of Infinite Space covers all of Coxeter’s major achievements, and in words any reader can understand. Her beautifully written tribute is rich in details about Coxeter’s long life, and his colorful interactions with the world’s top mathematicians. I found it impossible to stop reading.”
—Martin Gardner, longtime "Mathematical Games" columnist in Scientific American, and author of numerous books including The Ambidextrous Universe and most recently Are Universes Thicker Than Blackberries?

“What emerges loud and clear in King of Infinite Space is that Siobhan Roberts understands Coxeter’s spirit very deeply. She understands what drove him, and she knows just how to put into words the fire that always inhabits a great mathematician’s soul. I hope that King of Infinite Space will bring to many people not only a sense for the beauty of mathematics itself, but also a sense for how the very human love of hidden patterns and symmetries can result in a hundred years of exultant exploration.”
—Douglas Hofstadter, author of Gödel, Escher, Bach, from the Foreword of King of Infinite Space

King of Infinite Space gives us a lively view of the history of mathematics while weaving the story of Donald Coxeter, a broad-minded genius who built an important bridge between two opposite extremes of mathematical creation—the pictorial world of classical geometry, and the ideal world of abstract algebra.”
—Freeman Dyson, Professor of Physics at the Institute for Advanced Study, Princeton University, and author of Disturbing the Universe
Visit Siobhan Roberts' other writing and check out these interesting links.

About the book's title:
“I could be bounded in a nutshell and count myself a king of infinite space.”
—William Shakespeare, Hamlet, Act II, Scene 2
(as cited by Coxeter regarding “The Finiteness of Triangles,” Introduction to Geometry)
Visit -- home of a supplement to the book, with enhanced content including photographs, archives, papers, and links.

On May 2, 2007, there will be a night of talks focused around the book hosted by the City University of New York Graduate Center.

Read (if the New York Times permits access) an article by Siobhan about the study of the brains of Einstein, Coxeter, and others. She also has an article at the Boston Globe on Coxeter.

Discover "Why ‘rithmetic shouldn’t make you cringe."

Visit Siobhan Roberts' website.

Previous "page 69 tests:"
Erin McKean, That's Amore!
Michael Lowenthal, Charity Girl
Niraj Kapur, Heaven's Delight
Keith Dixon, The Art of Losing
David Edgerton, The Shock of the Old
Mary Sharratt, The Vanishing Point
David Fulmer, The Dying Crapshooter's Blues
Anya Ulinich, Petropolis
Jagdish Bhagwati, In Defense of Globalization
Olen Steinhauer, Liberation Movements
Andrei Markovits, Uncouth Nation
Julie Kistler, Scandal
Robert Ward, Four Kinds of Rain
Tim Harford, The Undercover Economist
William Landay, The Strangler
Kate Holden, In My Skin
Brian Wansick, Mindless Eating
Noria Jablonski, Human Oddities
Ruth Scurr, Fatal Purity
Neal Pollack, Alternadad
Bella DePaulo, Singled Out
Steve Hamilton, A Stolen Season
Eric Klinenberg, Fighting for Air
Donna Moore, ...Go to Helena Handbasket
Louis Bayard, The Pale Blue Eye
Neal Thompson, Riding with the Devil
Sherry Argov, Why Men Marry Bitches
P.J. Parrish, An Unquiet Grave
Tyler Knox, Kockroach
Andrew Rehfeld, The Concept of Constituency
Laura Wiess, Such a Pretty Girl
Jeremy Blachman, Anonymous Lawyer
Andrew Pyper, The Wildfire Season
Wendy Werris, An Alphabetical Life
Laura Lippman, What the Dead Know
Meghan Daum, The Quality of Life Report
Scott Reynolds Nelson, Steel Drivin' Man
Richard Aleas, Little Girl Lost
Paul Collins, The Trouble With Tom
John McFetridge, Dirty Sweet
Michael Kazin, A Godly Hero
Bill Crider, Murder Among the OWLS
Zachary Shore, Breeding Bin Ladens
Rolf Potts, Vagabonding
Matt Haig, The Dead Fathers Club
Lawrence Light, Fear & Greed
Simon Read, In The Dark
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Henry Ansgar Kelly, Satan: A Biography
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Jim Lehrer, The Phony Marine
Julie Phillips, James Tiptree, Jr.
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Sarah Katherine Lewis, Indecent
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William Easterly, The White Man's Burden
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Andrew Blechman, Pigeons
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Michael Lewis, The Blind Side
David A. Bell, The First Total War
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Rosanna Hertz, Single by Chance, Mothers by Choice
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Robert Vitalis, America's Kingdom
Stephen Elliott, My Girlfriend Comes To The City And Beats Me Up
Colin McGinn, The Power of Movies
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--Marshal Zeringue