Mathematics and the Laws of Nature: Developing the Language of Science (History of Mathematics)

241 Pages·2004·1.28 MB·English

by  John Tabak

mathematics and
the laws of nature
developing the language of science
THE HISTORY OF
M AT H E M AT IC S

TT HH EE HH II SS TT OO RR YY OO FF
mathematics and
the laws of nature
developing the language of science
John Tabak, Ph.D.
MATHEMATICS AND THE LAWS OF NATURE: Developing the Language
of Science
Copyright © 2004 by John Tabak, Ph.D.
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Library of Congress Cataloging-in-Publication Data
Tabak, John.
Mathematics and the laws of nature: developing the language of science / John Tabak.
p. cm. — (History of mathematics)
Includes bibliographical references and index.
ISBN 0-8160-4957-2 (acid-free paper)
1. Mathematics—History. 2. Science—History. I. Title.
QA21.T22 2004
510'.9—dc222003016961
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To George Baker. He is a law unto himself.

C O N T E N T S
Acknowledgments ix
Introduction: Natural Laws xi
1 Nature as Geometry 1
The Ancient Sky 2
Recording the Stars to Predict the Future 6
The Astronomical Calculations 9
The Tablets 12
2 Mathematics and Science in Ancient Greece 15
Ratios and the Measure of the Universe 15
A Geometry of the Universe 22
A Rotating Earth 27
Archimedes: Fusing Physics with Mathematics 28
The Law of the Lever 32
Archimedes’ Measurement of a Circle 34
The Siege of Syracuse 34
3 A Period of Transition 40
Nicholas Oresme 41
Nicolaus Copernicus 46
Johannes Kepler 51
Platonic Solids 57
Leonardo da Vinci and the Equation of Continuity 59
Proving Leonardo’s Equation of Continuity 64
4 New Sciences 66
Simon Stevin 68
Stevin and Music 72
Galileo Galilei 75
Fermat, Descartes, and Wallis 80
5 Mathematics and the Law of Conservation 88
of Momentum
The Laws of Motion 93
The Discovery of Neptune 98
6 Mathematics and the Law of Conservation 103
of Mass
Leonhard Euler and the Science of Fluid Dynamics 107
The Mathematics of Combustion 109
7 Mathematics and the Laws of 112
Thermodynamics
Sadi Carnot 118
Calculating the Efficiency of a Carnot Engine 124
James Prescott Joule 126
The First Law of Thermodynamics 128
The Second Law of Thermodynamics 133
Entropy 139
8 Modern Ideas about Conservation Laws 142
Olga Oleinik 147
9 Natural Laws and Randomness 153
Population Genetics 161
The Limits of Predictability 169
Genetic Counseling 174
Chronology 177
Glossary 195
Further Reading 201
Index 211
A C K N O W L E D G M E N T S
The author is deeply appreciative of Frank K. Darmstadt,
Executive Editor, for his many helpful suggestions and of Dorothy
Cummings, Project Editor, for the insightful work that she did
editing this volume.
Special thanks to Penelope Pillsbury and the staff of the
Brownell Library, Essex Junction, Vermont, for their extraordi-
nary help with the many difficult research questions that arose
during the preparation of this book.
ix