Is God a Mathematician_ - Mario Livio [0]
The Equation That Couldn’t Be Solved: How Mathematical Genius Discovered the Language of Symmetry
The Golden Ratio: The Story of Phi, the World’s Most Astonishing Number
The Accelerating Universe: Infinite Expansion, the Cosmological Constant, and the Beauty of the Cosmos
Simon & Schuster
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Copyright © 2009 by Mario Livio
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Library of Congress Cataloging-in-Publication Data
Livio, Mario.
Is God a mathematician? / Mario Livio.
p. cm.
Includes bibliographical references and index.
1. Mathematics—Philosophy. 2. Logic, symbolic and mathematical.
3. Mathematicians—Psychology. 4. Discoveries in science. I. Title.
QA8.4.L586 2009
510—dc22 2008045850
ISBN-13: 978-1-4165-9443-7
ISBN-10: 1-4165-9443-4
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To Sofie
CONTENTS
Preface
1. A Mystery
2. Mystics: The Numerologist and the Philosopher
3. Magicians: The Master and the Heretic
4. Magicians: The Skeptic and the Giant
5. Statisticians and Probabilists: The Science of Uncertainty
6. Geometers: Future Shock
7. Logicians: Thinking About Reasoning
8. Unreasonable Effectiveness?
9. On the Human Mind, Mathematics, and the Universe
Notes
Bibliography
Credits
PREFACE
When you work in cosmology—the study of the cosmos at large—one of the facts of life becomes the weekly letter, e-mail, or fax from someone who wants to describe to you his own theory of the universe (yes, they are invariably men). The biggest mistake you can make is to politely answer that you would like to learn more. This immediately results in an endless barrage of messages. So how can you prevent the assault? A particular tactic that I found to be quite effective (short of the impolite act of not answering at all) is to point out the true fact that as long as the theory is not precisely formulated in the language of mathematics, it is impossible to assess its relevance. This response stops most amateur cosmologists in their tracks. The reality is that without mathematics, modern-day cosmologists could not have progressed even one step in attempting to understand the laws of nature. Mathematics provides the solid scaffolding that holds together any theory of the universe. This may not sound so surprising until you realize that the nature of mathematics itself is not entirely clear. As the British philosopher Sir Michael Dummett once put it: “The two most abstract of the intellectual disciplines, philosophy and mathematics, give rise to the same perplexity: what are they about? The perplexity does not arise solely out of ignorance: even the practitioners of these subjects may find it difficult to answer the question.”
In this book I humbly try to clarify both some aspects of the essence of mathematics and, in particular, the nature of the relation between mathematics and the world we observe. The book is definitely not meant to represent a comprehensive history of mathematics. Rather, I chronologically follow the evolution of some concepts that have direct implications for understanding the role of mathematics in our grasp of the cosmos.
Many people have contributed, directly and indirectly, over a long period of time, to the ideas presented in this book. I would like to thank Sir Michael Atiyah, Gia Dvali, Freeman Dyson, Hillel Gauchman, David Gross, Sir Roger Penrose, Lord Martin Rees, Raman Sundrum, Max Tegmark, Steven Weinberg, and Stephen Wolfram for very helpful exchanges. I am indebted to Dorothy Morgenstern Thomas for allowing me to use the complete text of Oscar Morgenstern’s account of Kurt Gödel’s experience with the U.S. Immigration