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The Nothing That Is: A Natural History of Zero

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Robert Kaplan, «The Nothing That Is: A Natural History of Zero»
Oxford Univ. Press | ISBN 0195128427 | (Oct. 15, 1999) | PDF | 8.3 Mb | 240 Pages



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The publisher says The Nothing That Is is "in the tradition" of Dava Sobel's bestselling Longitude, presumably because it is both lyrically written and underillustrated. It's more accurate to describe it as in the tradition of something old enough to have a tradition: the cabinet of curios, a natural history in the old sense.

Robert Kaplan is a mathematics teacher, and he organizes his cabinet around–nothing. How did we come to have a symbol for zero? Who used it first? Usually the invention (or discovery) of zero is given as occurring in India in about the year 600 CE. Kaplan gives much more shrift to Sumerian, Babylonian, and Greek experiments with abacuses, counting boards, positional notation, and abstract thought. He acknowledges that his approach will be controversial:

Haven't all our dots funneled back to India? Were zero and the variable not truly born here, twin offspring of sunya and what seems the singularly Indian understanding of vacancy as receptive? But like an hour-glass, the funnel opens out again and the dots stream down to ancient Greece.

Kaplan's meditations on zero are not confined to its origin. He muses on the "zero of self," on infinitesimals, on the Mayan zero, and on the nothingness of suicide. Throughout, he shows "a sensuous delight in syllables," a love of words as well as numbers, that makes the book a feast for both halves of the brain. –Mary Ellen Curtin

From Publishers Weekly
We know how useful it is to call nothing a number, but our ancestors didn't: without the idea of zero, complicated arithmetic was hard enough, and algebraAlet alone modern higher mathAunthinkable. Kaplan elucidates expertly the history and uses of the symbol for nothing at all not only in math, and the history of math and science, but also in historical linguistics, medieval metaphysics, accounting, pedagogy and literary interpretation. Among the questions he poses: What psychological and symbolic meanings did zero have for medieval mystics? Sumerians invented positional notation (the convention that lets the 8 in 283 mean 80, not 8); ancient Greeks had to conquer the Babylonians even to learn that. It was in India that the idea arose of treating no-thing as a number just like one-thing or two-things. (Kaplan suggests that the circular symbol arose from the depression left by a counting stone removed from sand.) The zero idea spread through the Arab world to Europe and China. A cast of mathematical thinkers, among them Archimedes, Aryabhata and John von Neumann, join less likely figures in Kaplan's bevy of anecdotes, among the latter Meister Eckhart, Dostoevsky, Sylvia Plath and Wallace Stevens (the source of the book's title). Kaplan's eloquence can blur the line between metaphor and consequence: the "fluidity of position" that zero brought to European arithmetic indeed helped cause Renaissance social "fluidity," but only through a very long chain of effects. More often, Kaplan is entertaining, clear and to the (decimal) point. Who knew there was so much to say about nothing? 40,000 first printing; author tour; foreign rights sold in Italy, the Netherlands, the U.K., Germany, Brazil. (Oct.)
Copyright 1999 Reed Business Information, Inc.

From Library Journal
Kaplan presents a fascinating discussion of the intertwining development of the name, symbol, and concept of zero from ancient through surprisingly recent times. His investigative approach intriguingly combines historical, etymological, and mathematical perspectives. (Not coincidentally, Kaplan is an educator in mathematics, philosophy, and languages.) While the breadth of the author's reasoning is impressive, several controversial arguments cry out for documentation, so it is unfortunate that the notes and references are to be published only on the related web site. Little mathematical background is assumed, and the general reader will appreciate the lyrical and literate writing style. The final chapters on the "psychological embodiment" of zero are fuzzy and dispensable, but previous tangents ranging from calculus to the Mayan calendars are well worthwhile. Overall, a thought-provoking and entertaining look at an idea too likely to be taken for granted. Recommended for public and academic libraries.AKristine Fowler, Mathematics Lib., Univ. of Minnesota, Minneapolis
Copyright 1999 Reed Business Information, Inc.

Jim Holt, The Wall Street Journal
So 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, blending rival historical accounts with his own conjectures….Mr. Kaplan, a popularizer of mathematics who has taught at Harvard, is an erudite and often witty writer.

Washington Post Book World, November 26, 1999
An expert elucidation of the history and uses of the symbol for nothing, ranging from those in math and science to historical linguistics, medieval metaphysics, accounting, pedagogy and literary interpretation.

From Booklist
Philosophy, poetry, astronomy, linguistics–readers will marvel at what Kaplan draws out of nothing. Or, rather out of the symbolic representation of nothing: the zero. Written in a wonderfully eclectic and unpredictable style, this history takes us back to ancient Greece to show the limits of ingenuity among mathematicians lacking a zero. The scene then shifts to India, where the zero emerges shrouded in mystery. When this strange and powerful cipher becomes the property of Arab traders, the tale takes on an aura of magic and intrigue, as medieval Europeans recoil from what they see as a mark of infidel sorcery–only to later embrace it as a symbol of God's power to make all things out of nothing. Theology aside, the zero rapidly demonstrates its astonishing powers to amplify human intelligence not only in pure mathematics (where it helps to create logarithms) but also in practical fields such as banking (where it proves its worth in double-entry bookkeeping). Kaplan leavens his mathematics with piquant illustrations and lively humor, thus extending his audience even to readers generally indifferent to numbers. Bryce Christensen

From Kirkus Reviews
Part history, part philosophy, with some story problems thrown in for good measure: a wandering tale of the origins and uses of the number zero. Remember learning the Roman numerals in grade school? Kaplan is quick to point out that their system of counting used different letters for 1, 5, 10, 100 (I, V, X, C). This leads to problems when you want to represent the very large, millions or billions. A number system that uses place as an indicator of size was clearly needed, but this creates a need for a placeholder. Otherwise, 207 would be indistinguishable from 27, and chaos would ensue. Kaplan opens with a history of counting systems even more confusing than the Roman, Sumerians counting in base 60 or the Buddha counting by hundreds. Kaplan proposes several theories about the origin of the shape of the zero. Is it the impression left on a sand-covered counting board by the removal of a stone, signifying a placeholder with nothing in it? Or is it perhaps the crescent shape of a writing stylus pressed twice into the clay? Was zero ``discovered'' by more than one culture independently? From the origins of zero we discover what zero represented for different cultures. To the Mayans, zero was an angry god, periodically represented by a human who would be beaten to death. On the mathematics side, we learn how zero is used in algebra (solving quadratic equations), calculus (maxima and minima occur where the slope of a function is zero), physics (conservation laws), and set theory (generating the integers from the empty set). Finally, the author discusses the larger meaning of nothing. Perhaps it is ``the salaryman of Japanese society'' or more generally ``anonymity, mirroring our fear of making no difference to others.'' Full of ideas but going nowhere in particular, which is perhaps what the author intended all along. (First printing of 40,000; author tour) – Copyright ©1999, Kirkus Associates, LP. All rights reserved.

John Derbyshire, The New Criterion, October 1999
The Nothing That Is ably documetns humanity's long and weary groping toward the domestication of zero, with many curious and illuminating asides drawn from the author's wide field of interest.

Review
"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
"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
"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
"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
"A fascinating discussion of the intertwining development of the name, symbol, and concept of zero from ancient through suprisingly recent times. His investigative approach intriguingly combines historical, etymological, and mathematical perspectives…. A thought-provoking and entertaining look at an idea too likely to be taken for granted."–Library Journal (starred review)
"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)
The Nothing That Is ably documents humanity's long and weary groping toward the domestication of zero, with many curious and illuminating asides drawn from the author's wide field of interest."–The New Criterion

Frederick Pratter, Christian Science Monitor, November 4, 1999
The charm of this volume is that the reader can never again dismiss "nothing" as unimportant. Deeply informed, lucidly written, this engaging work is a though-provoking inquiry into a significant topic in the history of human thought.

Carlin Romano, The Philadelphia Inquirer, December 19, 1999
The peculiar pleasures of The Nothing That Is require following Kaplan's exquisite explanations and descriptions slowly, even dutifully….he's both enormously accessible and routinely challenging. Just when it seems that Kaplan has nothing more to say about a topic, he takes down - or is that puts up? - the "No Vacancy" sign, and shows there's another room of though he can open up.

Book Description
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.

Book Info
Discusses how mathematics develops in a process of recursive abstraction, as illustrated by the development of the concept of zero. DLC: Zero (The number).

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.