Synopses & Reviews
A symbol for what is not there, an emptiness that increases any number it's added to, an inexhaustible and indispensable paradox. As we enter the year 2000, zero is once again making its presence felt. Nothing itself, it makes possible a myriad of calculations. Indeed, without zero mathematics as we know it would not exist. And without mathematics our understanding of the universe would be vastly impoverished. But where did this nothing, this hollow circle, come from? Who created it? And what, exactly, does it mean?
Robert Kaplan's The Nothing That Is: A Natural History of Zero begins as a mystery story, taking us back to Sumerian times, and then to Greece and India, piecing together the way the idea of a symbol for nothing evolved. Kaplan shows us just how handicapped our ancestors were in trying to figure large sums without the aid of the zero. (Try multiplying CLXIV by XXIV). Remarkably, even the Greeks, mathematically brilliant as they were, didn't have a zero--or did they? We follow the trail to the East where, a millennium or two ago, Indian mathematicians took another crucial step. By treating zero for the first time like any other number, instead of a unique symbol, they allowed huge new leaps forward in computation, and also in our understanding of how mathematics itself works.
In the Middle Ages, this mathematical knowledge swept across western Europe via Arab traders. At first it was called "dangerous Saracen magic" and considered the Devil's work, but it wasn't long before merchants and bankers saw how handy this magic was, and used it to develop tools like double-entry bookkeeping. Zero quickly became an essential part of increasingly sophisticated equations, and with the invention of calculus, one could say it was a linchpin of the scientific revolution. And now even deeper layers of this thing that is nothing are coming to light: our computers speak only in zeros and ones, and modern mathematics shows that zero alone can be made to generate everything.
Robert Kaplan serves up all this history with immense zest and humor; his writing is full of anecdotes and asides, and quotations from Shakespeare to Wallace Stevens extend the book's context far beyond the scope of scientific specialists. For Kaplan, the history of zero is a lens for looking not only into the evolution of mathematics but into very nature of human thought. He points out how the history of mathematics is a process of recursive abstraction: how once a symbol is created to represent an idea, that symbol itself gives rise to new operations that in turn lead to new ideas. The beauty of mathematics is that even though we invent it, we seem to be discovering something that already exists.
The joy of that discovery shines from Kaplan's pages, as he ranges from Archimedes to Einstein, making fascinating connections between mathematical insights from every age and culture. A tour de force of science history, The Nothing That Is takes us through the hollow circle that leads to infinity.
Review
"For my money, the best popular mathematics book ever written."--Margaret Wertheim, Los Angeles Times Book Review
"Get this book. Read it. Think long and hard and sweetly about what the human mind is for: The gift of thinking, the joy and fulfillment of searching for the truth."--Michael Pakenham, The Baltimore Sun
"Deeply informed, lucidly written, this engaging work is a thought-provoking inquiry into a significant topic in the history of human thought."--Frederick Pratter, Christian Science Monitor
"Elegant, discursive, and littered with quotes and allusions from Aquinas via Gershwin to Woolf.... A book that will give a lot of readers pleasure and inform them, by stealth, at the same time. A fine holiday present for any mathematically inclined friend or relative."--Ian Stewart, The Times (London)
"Philosophy, poetry, astronomy, linguistics--readers will marvel at what Kaplan draws out of nothing.... Written in a wonderfully eclectic and unpredictable style.... Kaplan leavens his mathematics with piquant illustrations and lively humor, thus extending his audience even to readers generally indifferent to numbers."--Booklist
"Where did the familiar hollow circle that we use to denote zero come from? That's a story fraught with mystery, and Mr. Kaplan tells it well.... Kaplan, a popularizer of mathematics who has taught at Harvard, is an erudite and often witty writer."--Jim Holt, Wall Street Journal
"It is a true delight to read Robert Kaplan's The Nothing That Is. Full of remarkable historical facts about zero, it is both illuminating and entertaining, touching deeper issues of mathematics and philosophy in a very accessible way."--Sir Roger Penrose, Rouse Ball Professor of Mathematics at the University of Oxford, and the author of The Emperor's New Mind
"An attempt to do for Zero what Dava Sobel did for Longitude.... Kaplan has a light touch.... The effect is of a knowledgeable uncle suddenly prompted on a summer's afternoon to tell you all he knows on his favorite subject."--Jeremy Gray, The Sunday Times
"It is hard to imagine that an entertaining, informative book could be written about nothing, but Robert Kaplan has done it brilliantly. Starting with the great invention of zero as a place holder, Kaplan takes you through the use of zero in algebra, and in calculus where equating a derivative to zero magically calculates maxima and minima, to the importance of the null set. His book closes with that unthinkable question, `Why is there something rather than nohting?' on which one cannot long meditate without fear of going mad."--Martin Gardner, former columnist for Scientific American and author of Relativity Simply Explained
Review
"Get this book. Read it. Think long and hard and sweetly about what the human mind is for: The gift of thinking, the joy and fulfillment of searching for the truth."--Michael Pakenham, The Baltimore Sun
"An attempt to do for Zero what Dava Sobel did for Longitude.... Kaplan has a light touch.... The effect is of a knowledgeable uncle suddenly prompted on a summer's afternoon to tell you all he knows on his favorite subject."--Jeremy Gray, The Sunday Times
"Where did the familiar hollow circle that we use to denote zero come from? That's a story fraught with mystery, and Mr. Kaplan tells it well.... Mr. Kaplan, a popularizer of mathematics who has taught at Harvard, is an erudite and often witty writer."--Jim Holt, Wall Street Journal
"Robert Kaplan's The Nothing That Is is a magnificent meditation on the concept of zero, and, therefore, on everything. His passionate writing brings us to the Mayans, the Babylonians, the Greeks, the Indians, the Arabs, and the early moderns as they worked towards, or from, an understanding of zero. Reading Kaplan, we experience that striving, and its glory, for ourselves."--Barry Mazur, Professor of Mathematics, Harvard University
"It is hard to imagine that an entertaining, informative book could be written about nothing, but Robert Kaplan has done it brilliantly. Starting with the great invention of zero as a place holder, Kaplan takes you through the use of zero in algebra, and in calculus where equating a derivative to zero magically calculates maxima and minima, to the importance of the null set. His book closes with that unthinkable question, `Why is there something rather than nohting?' on which one cannot long meditate without fear of going mad."--Martin Gardner, former columnist for Scientific American and author of Relativity Simply Explained
Synopsis
For math professor Kaplan, the history of zero is a lens for looking not only into the evolution of mathematics but into very nature of human thought. "Where did the familiar hollow circle that we use to denote zero come from? That's a story fraught with mystery, and Mr. Kaplan tells it well".--"Wall Street Journal". 38 illustrations.
Synopsis
A symbol for what is not there, an emptiness that increases any number it's added to, an inexhaustible and indispensable paradox. As we welcome the new millennium, zero is once again making its presence felt. Nothing itself, it makes possible a myriad of calculations. Indeed, without zero mathematics as we know it would not exist. And without mathematics our understanding of the universe would be vastly impoverished. But where did this nothing, this hollow circle, come from? Who created it? And what, exactly, does it mean?
Robert Kaplan's The Nothing That Is: A Natural History of Zero begins as a mystery story, taking us back to Sumerian times, then to Greece and India, piecing together the way the idea of a symbol for nothing evolved. For Kaplan, the history of zero is a lens for looking not only into the evolution of mathematics but into very nature of human thought. He points out how the history of mathematics is a process of recursive abstraction: how once a symbol is created to represent an idea, that symbol itself gives rise to new operations that in turn lead to new ideas. The beauty of mathematics is that even though we invent it, we seem to be discovering something that already exists.
The joy of that discovery shines from Kaplan's pages, as he ranges from Archimedes to Einstein, making fascinating connections between mathematical insights from every age and culture.
About the Author
Robert Kaplan has taught mathematics to people from six to sixty, most recently at Harvard University. In 1994, with his wife Ellen, he founded The Math Circle, a program, open to the public, for the enjoyment of pure mathematics. He has also taught Philosophy, Greek, German, Sanskrit, and Inspired Guessing. Robert Kaplan lives in Cambridge, MA.
Table of Contents
Acknowledgments
A Note to the Reader
0. The Lens
1. Mind Puts Its Stamp on Matter
2. The Greeks Had No Word for It
3. Travelers' Tales
4. Eastward
5. Dust
6. Into the Unknown
7. A Paradigm Shifts
8. A Mayan Interlude: The Dark Side of Counting
9. Much Ado: 1. Envoys of Emptiness, 2. A Sypher in Augrim, 3. This Year, Next Year, Sometime, Never, 4. StillIt Moves
10. Entertaining Angels: 1. The Power of Nothing, 2. Knowing Squat, 3. The Fabric of This Vision, 4. Leaving No Wrack Behind
11. Almost Nothing: 1. Slouching Toward Bethlehem, 2. Two Victories, a Defeat and Distant Thunder
12. Is It Out There?
13. Bath-house with Spiders
14. A Land Where It Was Always Afternoon
15. Was Lear Right?
16. The Unthinkable
Index