Euclid's Window: The Story of Geometry from Parallel Lines to Hyperspace

Through Euclid's Window Leonard Mlodinow brilliantly and delightfully leads us on a journey through five revolutions in geometry, from the Greek concept of parallel lines to the latest notions of hyperspace. Here is an altogether new, refreshing, alternative history of math revealing how simple questions anyone might ask about space — in the living room or in some other galaxy — have been the hidden engine of the highest achievements in science and technology.

Based on Mlodinow's extensive historical research; his studies alongside colleagues such as Richard Feynman and Kip Thorne; and interviews with leading physicists and mathematicians such as Murray Gell-Mann, Edward Witten, and Brian Greene, Euclid's Window is an extraordinary blend of rigorous, authoritative investigation and accessible, good-humored storytelling that makes a stunningly original argument asserting the primacy of geometry. For those who have looked through Euclid's Window, no space, no thing, and no time will ever be quite the same.

Leonard Mlodinow, Ph.D., was a member of the faculty of the California Institute of Technology before moving to Hollywood to become a writer for numerous television shows ranging from Star Trek: The Next Generation to Night Court. He has also developed many bestselling and award-winning educational CD-ROMs, and delivered technical and general lectures in ten countries. He is currently Vice President, Emerging Technologies and R&D, at Scholastic Inc. He lives in New York City.

Contents

Introduction

I THE STORY OF EUCLID

1. The First Revolution

2. The Geometry of Taxation

3. Among the Seven Sages

4. The Secret Society

5. Euclid's Manifesto

6. A Beautiful Woman, a Library, and the End of Civilization

II THE STORY OF DESCARTES

7. The Revolution in Place

8. The Origin of Latitude and Longitude

9. The Legacy of the Rotten Romans

10. The Discreet Charm of the Graph

11. A Soldier's Story

12. Iced by the Snow Queen

III THE STORY OF GAUSS

13. The Curved Space Revolution

14. The Trouble with Ptolemy

15. A Napoleonic Hero

16. The Fall of the Fifth Postulate

17. Lost in Hyperbolic Space

18. Some Insects Called the Human Race

19. A Tale of Two Aliens

20. After 2,000 Years, a Face-lift

IV THE STORY OF EINSTEIN

21. Revolution at the Speed of Light

22. Relativity's Other Albert

23. The Stuff of Space

24. Probationary Technical Expert, Third Class

25. A Relatively Euclidean Approach

26. Einstein's Apple

27. From Inspiration to Perspiration

28. Blue Hair Triumphs

V THE STORY OF WITTEN

29. The Weird Revolution

30. Ten Things I Hate About Your Theory

31. The Necessary Uncertainty of Being

32. Clash of the Titans

33. A Message in a Kaluza-Klein Bottle

34. The Birth of Strings

35. Particles, Schmarticles!

36. The Trouble with Strings

37. The Theory Formerly Known As Strings

Epilogue

Notes

Acknowledgments

Index