Book contents
- Frontmatter
- Contents
- Preface and acknowledgements
- Part I Einstein's revolution
- Part II Philosophical progress
- 8 Who invented space?
- 9 Zeno's paradoxes: is motion impossible?
- 10 Philosophers at war: Newton vs. Leibniz
- 11 The philosophy of left and right
- 12 The unreality of time
- 13 General relativity: is space curved?
- 14 The fall of geometry: is mathematics certain?
- 15 The resurrection of absolutes
- 16 The resilience of space
- Part III Frontiers
- Appendix A Spacetime diagrams
- Appendix B Symmetry and Lorentz's minority interpretation
- Appendix C Simple formulas for special relativity
- Appendix D Websites
- Appendix E Guide to further reading
- Index
14 - The fall of geometry: is mathematics certain?
from Part II - Philosophical progress
- Frontmatter
- Contents
- Preface and acknowledgements
- Part I Einstein's revolution
- Part II Philosophical progress
- 8 Who invented space?
- 9 Zeno's paradoxes: is motion impossible?
- 10 Philosophers at war: Newton vs. Leibniz
- 11 The philosophy of left and right
- 12 The unreality of time
- 13 General relativity: is space curved?
- 14 The fall of geometry: is mathematics certain?
- 15 The resurrection of absolutes
- 16 The resilience of space
- Part III Frontiers
- Appendix A Spacetime diagrams
- Appendix B Symmetry and Lorentz's minority interpretation
- Appendix C Simple formulas for special relativity
- Appendix D Websites
- Appendix E Guide to further reading
- Index
Summary
We reverence ancient Greece as the cradle of western science. Here for the first time the world witnessed the miracle of a logical system which proceeded from step to step with such precision that every single one of its propositions was absolutely indubitable – I refer to Euclid's geometry. This admirable triumph of reasoning gave the human intellect the necessary confidence in itself for its subsequent achievements.
(Einstein, 1933)Some seek truth and some doubt it. Some are dedicated to seeking progress in our knowledge of reality, and some find it all too absurd. In the European tradition, the battles between these two warring tribes took place in the shadow of a great fortress. Defenders of truth could raise their fingers over the heads of the sceptics and point upwards to mathematics: a shining crystal palace of certainty surrounded by thick walls of deductions and demonstrations. But the revolution in theories of space and time during the twentieth century finally levelled this fortress. Sceptics have overrun even mathematics. Much of the fashionable relativism that has flourished during the past 30 years took heart from this downfall of mathematics, and with good reason.
Euclid and his Elements
Geometry was the glory of ancient Greece. Building on its beginnings in Egypt and Babylon, the ancient Greeks pursued geometry with extraordinary passion and precision for a thousand years, and first built up the fortress of mathematics on firm foundations.
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- Information
- Space, Time and EinsteinAn Introduction, pp. 149 - 158Publisher: Acumen PublishingPrint publication year: 2002