Shifting the Earth: The Mathematical Quest to Understand the Motion of the Universe

323 Pages·2011·4.28 MB·English

by  Arthur Mazer

SHIFTING THE EARTH

SHIFTING THE EARTH
The Mathematical Quest to
Understand the Motion of the
Universe
ARTHUR MAZER
AJOHNWILEY&SONS,INC.,PUBLICATION
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LibraryofCongressCataloging-in-PublicationData:
Mazer,Arthur,1958–
ShiftingtheEarth:themathematicalquesttounderstandthemotionof
theuniverse/ArthurMazer.
p.cm.
Includesbibliographicalreferencesandindex.
ISBN978-1-118-02427-0 (pbk.)
1. Kepler’slaws.2. Motion.3. Celestialmechanics.I.Title.
QB355.3.M392012
521(cid:2).3–dc23
2011013592
PrintedintheUnitedStatesofAmerica
oBookISBN:978-1-118-10829-1
ePDFISBN:978-1-118-10832-1
ePubISBN:978-1-118-10831-4
10987654321
CONTENTS
PREFACE ix
ACKNOWLEDGMENTS xv
1 PERFECTION 1
2 PERFECTIONISTS 5
A Tour of Athens / 5
Plato’s Challenge / 8
Eudoxus’ Universe / 10
The Math (a mathematical presentation requiring
linear algebra) / 14
3 THE ICONOCLAST 24
Insanity / 24
A Disturbing Insight / 29
Aristarchus and Onthe Sizes andDistances of the Sun and Moon
(a mathematical presentation requiring trigonometry) / 29
4 INSTIGATORS 38
A Heavy Hand / 38
Patriarchs / 41
The Irony / 43
v
vi CONTENTS
Fun / 44
Apollonius’ Osculating Circle and the Ellipse (a mathematical pre-
sentation requiring calculus) / 46
Fun’s Harvest / 62
5 RETROGRADE 63
The Imperial Theocracy / 63
Ptolemy’s Universe / 67
Ptolemy and The Almagest (a mathematical presentation requiring
trigonometry) / 70
Inspiration / 91
6 REVOLUTIONARY 93
Possibilities / 93
Copernicus’ OnRevolutions, the Pursuit of Elegance / 103
The Model (a mathematical presentation requiring
trigonometry) / 106
An Elegant Result / 116
7 RENEGADES 117
Countering the Reformation / 117
The Trio: Tycho, Kepler, and Rudolf / 119
Meanwhile in Italy / 131
NewAstronomy, in Kepler’s Own Likeness / 134
A Path Strewn with Casualties / 136
The Physicist’s Law / 142
Tycho’s Gift / 145
Mars’ Bed / 147
Configuring the Ellipse: The Second Law (a mathematical presenta-
tion requiring trigonometry) / 149
The Mentor / 167
8 THE AUTHORITY 168
Louis XIV, the Sun King / 168
Newton, the Math King / 172
The Influential Principia / 181
Without Fluxions (a mathematical presentation of Newton’s laws of
motion and the ellipse requiring high school algebra) / 184
CONTENTS vii
Newton’s Laws, Kepler’sLaws, and Calculus (a calculus-basedpre-
sentation of Newton’s laws of motion and the ellipse) / 207
Newton’s Agenda / 224
9 RULE BREAKERS 225
Beginnings / 225
Debunking the Ether / 232
The Established and the Unknown / 240
Trouble / 246
Exiting the Quantum Universe / 249
Bending the Light / 251
An Ergodic Life / 252
Victory / 254
The Experiment / 259
The Famous and the Infamous / 260
Exodus / 264
The End / 267
Relativity / 268
SpecialRelativity(amathematicalpresentationrequiringhighschool
algebra) / 271
EPILOGUE 293
BIBLIOGRAPHY 295
INDEX 301

PREFACE
There is a comic of a skinny little kid who, while standing on a stool so that
he can look at himself in a mirror, views the image of a ripping, six-packed,
Shwartznegger-esque champ. It’s all too true to life and, like the best of comics,
begs a question. Suppose that the same skinny kid looks at the mirror 35 years
laterwhenheisapudgy,baldingman.Whatistheimagethathewillsee?Willhe
continuetoseethechamp,orwillhehavecometoacceptwhoheis,butindoing
soseemorepossibilitiesforhimselfthanthelittleboycouldhaveimagined?This
question is the topic of many novels and movies. It is intriguing because there
is no predestined path for the boy to follow and there is no definitive outcome.
ShiftingtheEarth relates the story of how humanity collectively dispossessed
itself of its geocentric fabrication and accepted a less prestigious position in the
universe.Itwasnotpreordainedthathumanitywouldtossoutitsself-image,pack
up what remained, and move to a new heliocentric earth. Psychological barriers
resisted the move. Vested interests battled to bound humanity on a geocentric
earth, and while they did not prevail, they put up a good fight. One can even
imagine a scenario where they might have prevailed. The mathematicians and
astronomers who contributed to the accomplishment did not live in a vacuum
and were very much affected by their cultural environment. Shifting the Earth
describes of the interplay between the forces tugging at the contributors in dif-
ferent directions and how the contributors ultimately created a prevailing force
of their own.
The question of a heliocentric versus geocentric structure was indisputably
resolved in the seventeenthcentury, a centurysteeped in the controversiesof the
Counter-Reformation.TheaccomplishmentwastheconduittotheEnlightenment
ix