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### Summary

### Summary

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 mathematicsas 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 figurelarge 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 treatingzero 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 likedouble-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 speakonly 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 notonly 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. Thebeauty 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 toinfinity.

### Author Notes

Robert Kaplan has taught mathematics to people from six to sixty, most recently at Harvard University.

### Reviews 4

### Booklist Review

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

### Publisher's Weekly Review

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 algebraÄlet alone modern higher mathÄunthinkable. 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.) (c) Copyright PWxyz, LLC. All rights reserved

### Library Journal Review

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.ÄKristine Fowler, Mathematics Lib., Univ. of Minnesota, Minneapolis (c) Copyright 2010. Library Journals LLC, a wholly owned subsidiary of Media Source, Inc. No redistribution permitted.

### Choice Review

Kaplan (Harvard Univ.) surveys many of the meanings associated with the word "zero." He focuses primarily on mathematical conceptions of zero, but physical and psychological notions are also considered. He begins with Sumerian times, then moves to Greece and India to determine how the zero concept developed, and comments on the difficulty of multiplying large numbers, such as Roman numerals, without the zero. In India, about a thousand years ago, mathematicians began to treat zero as a number rather than as a symbol, thereby allowing certain types of computation that we take for granted today. In the Middle Ages, Arab traders gradually introduced the idea of the zero to Europe; little by little, zero became indispensable to bankers and merchants who developed bookkeeping. By the time the calculus was invented, zero was here to stay. Interwoven with factual material, particularly on the history of the numeral "0," are a host of the author's speculations and conjectures, historical, cultural, and poetical, about nothingness. Chapter titles, numbered from zero to 16, offer colorful reading, e.g., "The Lens"; "The Greeks Had No Word for It"; "A Mayan Interlude: The Dark Side of Counting"; "Almost Nothing"; and "The Unthinkable." Bibliography and notes (78 pages) are available on the publisher's Web site. General readers; undergraduates. M. Henle; Oberlin College

### Table of Contents

Acknowledgement | p. x |

A Note to the Reader | p. xii |

0 The Lens | p. 1 |

1 Mind Puts Its Stamp on Matter | p. 4 |

2 The Greeks had no Word for it | p. 14 |

3 Travelers' Tales | p. 28 |

4 Eastward | p. 36 |

5 Dust | p. 50 |

6 Into the Unknown | p. 57 |

7 A Paradigm Shifts | p. 68 |

8 A Mayan Interlude: The Dark Side of Counting | p. 80 |

9 Much Ado | p. 90 |

1 Envoys of Emptiness | p. 90 |

2 A Sypher in Augrim | p. 93 |

3 This Year, Next Year, Sometime, Never | p. 103 |

4 Still It Moves | p. 106 |

10 Entertaining Angels | p. 116 |

1 The Power of Nothing | p. 116 |

2 Knowing Squat | p. 120 |

3 The Fabric of This Vision | p. 129 |

4 Leaving No Wrack Behind | p. 137 |

11 Almost Nothing | p. 144 |

1 Slouching Toward Bethlehem | p. 144 |

2 Two Victories, a Defeat and Distant Thunder | p. 160 |

12 Is it out There? | p. 175 |

13 Bath-House with Spiders | p. 190 |

14 A Land Where it was Always Afternoon | p. 195 |

15 Was Lear Right? | p. 203 |

16 The Unthinkable | p. 216 |

Index | p. 220 |