The Universe in Zero Words

by Mackenzie, Dana

• ISBN13: 9780691152820
• ISBN10: 0691152829
• Format: Hardcover
• Copyright: 2012-04-09
• Publisher: Princeton Univ Pr

Summary

Most popular books about science, and even about mathematics, tiptoe around equations as if they were something to be hidden from the reader's tender eyes. Dana Mackenzie starts from the opposite premise: He celebrates equations. No history of art would be complete without pictures. Why, then, should a history of mathematics--the universal language of science--keep the masterpieces of the subject hidden behind a veil? The Universe in Zero Wordstells the history of twenty-four great and beautiful equations that have shaped mathematics, science, and society--from the elementary (1+1=2) to the sophisticated (the Black-Scholes formula for financial derivatives), and from the famous (E=mc2) to the arcane (Hamilton's quaternion equations). Mackenzie, who has been called "a popular-science ace" by Booklistmagazine, lucidly explains what each equation means, who discovered it (and how), and how it has affected our lives. Illustrated in color throughout, the book tells the human and often-surprising stories behind the invention or discovery of the equations, from how a bad cigar changed the course of quantum mechanics to why whales (if they could communicate with us) would teach us a totally different concept of geometry. At the same time, the book shows why these equations have something timeless to say about the universe, and how they do it with an economy (zero words) that no other form of human expression can match. The Universe in Zero Wordsis the ultimate introduction and guide to equations that have changed the world.

Table of Contents

preface	p. 6
introduction: the abacist versus the algorist	p. 10
equations of antiquity	p. 16
Why we believe in arithmetic: the world's simplest equation	p. 20
Resisting a new concept: the discovery of zero	p. 26
The square of the hypotenuse: the Pythagorean theorem	p. 30
The circle game: the discovery of ¿	p. 40
From Zeno's paradoxes to the idea of infinity	p. 46
A matter of leverage: laws of levers	p. 52
equations in the age of exploration	p. 56
The stammerer's secret: Cardano's formula	p. 60
Order in the heavens: Kepler's laws of planetary motion	p. 68
Writing for eternity: Fermat's Last Theorem	p. 74
An unexplored continent: the fundamental theorem of calculus	p. 80
Of apples, legends... and comets: Newton's laws	p. 90
The great explorer: Euler's theorems	p. 96
equations in a promethean age	p. 104
The new algebra: Hamilton and quaternions	p. 108
Two shooting stars: group theory	p. 114
The geometry of whales and ants: non-Euclidean geometry	p. 122
In primes we trust: the prime number theorem	p. 128
The idea of spectra: Fourier series	p. 134
A god's-eye view of light: Maxwell's equations	p. 142
equations in our own time	p. 150
The photoelectric effect: quanta and relativity	p. 154
From a bad cigar to Westminster Abbey: Dirac's formula	p. 164
The empire-builder: the Chern-Gauss-Bonnet equation	p. 174
A little bit infinite: the Continuum Hypothesis	p. 182
Theories of chaos: Lorenz equations	p. 194
Taming the tiger: the Black-Scholes equation	p. 204
conclusion: what of the future?	p. 214
acknowledgments	p. 218
bibliography	p. 219
index	p. 222ÿþ
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