The Nothing that Is A Natural History of Zero

by Kaplan, Robert; Kaplan, Ellen

• ISBN13: 9780195142372
• ISBN10: 0195142373
• Format: Paperback
• Copyright: 2000-12-07
• Publisher: Oxford University Press

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 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.

Author Biography

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

Acknowledgements	x
A Note to the Reader	xii
The Lens	1	(3)
Mind Puts its Stamp on Matter	4	(10)
The Greeks had no Word For It	14	(14)
Travelers' Tales	28	(8)
Eastward	36	(14)
Dust	50	(7)
Into the Unknown	57	(11)
A Paradigm Shifts	68	(12)
A Mayan Interlude: The Dark Side of Counting	80	(10)
Much Ado	90	(26)
Envoys of Emptiness	90	(3)
A Sypher in Augrim	93	(10)
This Year, Next Year, Sometime, Never	103	(3)
Still It Moves	106	(10)
Entertaining Angels	116	(28)
The Power of Nothing	116	(4)
Knowing Squat	120	(9)
The Fabric of This Vision	129	(8)
Leaving No Wrack Behind	137	(7)
Almost Nothing	144	(31)
Slouching Toward Bethlehem	144	(16)
Two Victories, a Defeat and Distant Thunder	160	(15)
Is It Out There?	175	(15)
Bath-House with Spiders	190	(5)
A Land Where It was Always Afternoon	195	(8)
Was Lear Right?	203	(13)
The Unthinkable	216	(4)
Index	220