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

Discover how mathematics and science have propelled history

From Ancient Greece to the Enlightenment and then on to moderntimes, Shifting the Earth: The Mathematical Quest to Understand theMotion of the Universe takes readers on a journey motivated by thedesire to understand the universe and the motion of the heavens.The author presents a thought–provoking depiction of thesociopolitical environment in which some of the most prominentscientists in history lived and then provides a mathematicalaccount of their contributions.

From Eudoxus to Einstein, this fascinating book describes how,beginning in ancient times, pioneers in the sciences andmathematics have dramatically changed our vision of who we are aswell as our place in the universe. Readers will discover howPtolemy′s geocentric model evolved into Kepler′s heliocentricmodel, with Copernicus as the critical intermediary. The authorexplains how one scientific breakthrough set the stage for the nextone, and he also places the scientists and their discoveries withinthe context of history, including:

Archimedes, Apollonius, and the Punic Wars

Ptolemy and the rise of Christianity

Copernicus and the Renaissance

Kepler and the Counter–Reformation

Newton and the Enlightenment

Einstein and the detonation of the atom bomb

Each chapter presents the work of a single scientist ormathematician, building on the previous chapters to demonstrate theevolutionary process of discovery. Chapters begin with a narrativesection and conclude with a mathematical presentation of one of thescientist′s original works. Most of these mathematicalpresentations, including the section on Einstein′s specialrelativity, are accessible using only basic mathematics; however,readers can skip the mathematical sections and still follow theevolution of science and mathematics.

Shifting the Earth is an excellent book for anyone interested inthe history of mathematics and how the quest to understand themotion of the heavens has influenced the broader history ofhumankind.

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 On the Sizes and Distances of the Sun andMoon (a mathematical presentation requiring trigonometry)/ 29

4 INSTIGATORS 38

A Heavy Hand / 38

Patriarchs / 41

The Irony / 43

Fun / 44

Apollonius Osculating Circle and the Ellipse (amathematical presentation requiring calculus) / 46

Fun s Harvest / 62

5 RETROGRADE 63

The Imperial Theocracy / 63

Ptolemy s Universe / 67

Ptolemy and The Almagest (a mathematical presentationrequiring trigonometry) / 70

Inspiration / 91

6 REVOLUTIONARY 93

Possibilities / 93

Copernicus On Revolutions, 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

New Astronomy, 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 mathematicalpresentation 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 slaws of motion and the ellipse requiring high school algebra)/ 184

Newton s Laws, Kepler s Laws, and Calculus (acalculus–based presentation of Newton s laws of motion andthe 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

Special Relativity (a mathematical presentation requiring highschool algebra) / 271

EPILOGUE 293

BIBLIOGRAPHY 295

INDEX 301

ARTHUR MAZER, PhD, is Manager of Quantitative Analytics at Southern California Edison, where he oversees the risk assessment of the company′s power and gas portfolio. Throughout his career, he has held various academic positions as well as analyst positions at Electrabel, Progress Energy, and Energy Power Marketing Corporation. Dr. Mazer is the author of Electric Power Planning for Regulated and Deregulated Markets and The Ellipse: A Historical and Mathematical Journey, both published by Wiley.

Summing Up: Recommended.  Upper–divisionundergraduates through researchers/faculty; generalreaders.   (Choice, 1 June 2012)