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Robert Kaplan

The Nothing that Is: A Natural History of Zero 1st Edition

by Robert Kaplan (Author), Ellen Kaplan (Illustrator)

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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.

ISBN-10

0195142373
ISBN-13

978-0195142372
Edition

1st
Publisher

Oxford University Press
Publication date

December 7, 2000
Language

English
Dimensions

7.73 x 4.68 x 0.6 inches
Print length

240 pages
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Editorial Reviews

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

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.

Product details

Publisher ‏ : ‎ Oxford University Press; 1st edition (December 7, 2000)
Language ‏ : ‎ English
Paperback ‏ : ‎ 240 pages
ISBN-10 ‏ : ‎ 0195142373
ISBN-13 ‏ : ‎ 978-0195142372
Item Weight ‏ : ‎ 8 ounces
Dimensions ‏ : ‎ 7.73 x 4.68 x 0.6 inches

Best Sellers Rank: #549,709 in Books (See Top 100 in Books)
- #225 in Math Games
- #382 in Mathematics History
- #2,295 in History & Philosophy of Science (Books)

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4.2 out of 5

108 global ratings

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dasilvam

At times giddy, but always interesting

Reviewed in the United States 🇺🇸 on December 25, 2009

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I wish I could share the writer's sense of excitement regarding the concepts discussed in this book or, barring that, I wish his enthusiasm was infectious. What keeps this book from being perfect is the ocassional lack of an editor's touch in its tone.

But this is by no means a disqualifying factor. The book is actually well-written overall and very thoroughly researched. There are some reviews that pout over the author's conclusions regarding the historical origin of the concept of zero but these conclusions are well-documented and the assessment comes honestly enough. If you truly disagree, then do your own research and write your own book! As this is much more than a simple historical review of the origins of the concept of nothing in mathematics, even if you disagree with the author's conclusions, there is still much to explore and learn.

Most of all, this book does and excellent idea of documenting why the very concept of zero was so hard to come by and gives the reading a reasonable understanding that this is no insignificant advancement in human understanding.

2 people found this helpful

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Dave_42

Much Ado About Nothing

Reviewed in the United States 🇺🇸 on August 22, 2010

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"The Nothing That Is: A Natural History of Zero" by Robert Kaplan is a look at what is perhaps the most significant creations and advances ever made in mathematics. Imagine trying to calculate using Roman Numerals or any system that did not have columns, and its significance doesn't end there as it is critical in dealing with negative numbers and calculus. Zero took a journey from indicating nothing, to being a number of value which then forced the creation of the idea of null to once again indicate nothing.

Kaplan's book looks at all the aspects of Zero, from what it meant, to the symbols used for it and where they might have come from, to its importance in mathematics and for that matter in philosophy. His note at the front of the book suggests that the reader need only have had high-school algebra and geometry, but to get the most out of this book it would be better to have had some higher math, as well as a full and well-rounded education as Kaplan makes references which hit on a number of areas.

The book itself almost defies being placed into a category. There are elements of history, philosophy, psychology, and of course math contained in its seventeen chapters (appropriately starting with chapter Zero). The first nine chapters have a great deal to do with the history of the number and the symbol used for it, and how it impacted Mesopotamia, Greece, India, and even a chapter on how it was perceived in Mayan culture.

The book then transitions from more of a history to more about how Zero is used in mathematics, covering issues such as what is the a number to the power of 0, and then by extension what is 0 to the power of 0. It also touches on Zero's important relative Infinity. Note that the chapters almost always offer a blend of history, math, and other subjects, and I am merely offering my perspective on where the greater focus is in each of these sections.

Later in the book, the focus becomes much wider, looking at Zero's impact on different areas of society, including everything from literature to technology with the coming of binary systems such as computers. Kaplan somehow manages to contain all this in a book of fewer than 220 pages, so the pages and chapters are packed with a lot to think about.

The weakness of the book is that it doesn't easily fit into any category. It is not a scholarly treatment of the subject, and in fact Kaplan admits that some of what he writes is based on weak evidence, or in his words he has "tried to bridge a chasm on the slenderest threads of evidence". At the same time, I would not think this is a good book for a novice to math, or history, or many other subjects. As a result, there is probably a rather limited audience for this type of book.

As much as I love the subject, I am going to round down to three stars overall, partially due to the issues with finding an audience for the book as it is written, and partially due to the huge number of references he makes, without providing notes and a bibliography. To be fair he does provide a link to these in his "Note to the Reader" at the front of the book, but one can only hope that the link remains there for as long as this book is available.

5 people found this helpful

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Gregory Brown

So much more than "a math lesson."

Reviewed in the United States 🇺🇸 on September 9, 2019

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The book is a wonderful recounting of competing theories and paradigms involved in the evolution of the concept, character, and use of zero. There are explanations of the development of math proofs, but they are laid out in careful steps for anyone who is comfortable with math reasoning and interested in the topic of the book. Recent experience and training in higher math are not required to enjoy and learn from this book.

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Alaturka

Should have been a great book

Reviewed in the United States 🇺🇸 on March 13, 2002

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It is on the surface a very interesting book. One wonders why much more was not written about it. Kaplan is obviously very knowledgeble about the topic but he exerts himself a little too much at times to show that he has a lot to say about many other tangential topics as well.
The history of zero, as a concept, as a math tool then beyond it, as a philosophy is covered well, not in great detail but enough to give a flavor of its adventures through our civilizations through ages. He falls on the side of Eastern Mediterranean and Middle Eastern roots of zero as a number rather than India, but the arguments are rather weak and evidence pale.
Kaplan's often very convoluted and meandering prose takes a great toll as you force yourself through the book. His philosophy dripping muses, which seem to have more personal origins than general, creates a fog around the real topic. He takes every opportunity to show off his considerable knowledge of Classics. A good amount of philosophy is to be expected given the topic, but his relentless contortions of language and side thoughts makes it an unpleasant read. Where was the editor?
His discussion of quantum fluctuations of empty space was a very relevant stop along the way, but it seems he has confused it with cosmic background radiation, which is a totally different physical phenomenon, and misses out on a great chapter by itself.
It is a great subject, and Kaplan certainly does not attempt to cover it in more traditional historical style, which is commended, but I wish it had less poetry and philosophical musings of personal nature and more zero in it.

23 people found this helpful

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Milt Johnson

Excellent

Reviewed in the United States 🇺🇸 on August 24, 2021

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Excellent

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R. Hoad

A great body of research in a readable format

Reviewed in the United Kingdom 🇬🇧 on January 4, 2020

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I bought this for myself and it was a brilliant piece of work rendered very readable but which kept ones interest.

Valter C.

Finalmente!

Reviewed in Italy 🇮🇹 on October 5, 2022

Verified Purchase

Per coloro che sono interessati alle origine mesopotamiche dello zero, in questo libro si trova una informazione che è veramente rara da trovare.

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Andrei

Ottimo titolo

Reviewed in Italy 🇮🇹 on March 26, 2017

Verified Purchase

Il libro si presenta in buone condizioni, come indicato dal venditore nella descrizione.
Per quanto riguarda il testo, esso risulta molto interessante: traccia la storia affascinante della "creazione" del numero zero. In alcuni punti può sembrare abbastanza tecnico/scientifico, ma resta comunque una lettura valida per tutti coloro che sono interessati a questo tipo di argomento.
Personalmente, ho scelto la versione in lingua inglese perché mi fido sempre delle edizione Penguin.

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Leonardo

Avaliação

Reviewed in Brazil 🇧🇷 on November 6, 2021

Verified Purchase

Leitura para ser feita aos poucos. Precisa ser lida e relida conforme avança. Recomendo.

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Julie Maslowski

Gift

Reviewed in the United Kingdom 🇬🇧 on March 10, 2013

Verified Purchase

Another book given to my husband, he loves books and we have alot of them so if it makes him happy, so be it

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