Is God a Mathematician_ - Mario Livio [1]
I am grateful to Stefano Casertano for his help with difficult translations from Latin, and to Elizabeth Fraser and Jill Lagerstrom for their invaluable bibliographic and linguistic support (always with a smile).
Special thanks are due to Sharon Toolan for her professional help in the preparation of the manuscript for print, and to Ann Feild, Krista Wildt, and Stacey Benn for drawing some of the figures.
Every author should consider herself or himself fortunate to receive from their spouse the type of continuous support and patience that I have received from my wife, Sofie, during the long period of the writing of this book.
Finally, I would like to thank my agent, Susan Rabiner, without whose encouragement this book would have never happened. I am also deeply indebted to my editor, Bob Bender, for his careful reading of the manuscript and his insightful comments, to Johanna Li for her invaluable support with the production of the book, to Loretta Denner and Amy Ryan for copyediting, to Victoria Meyer and Katie Grinch for promoting the book, and to the entire production and marketing team at Simon & Schuster for all their hard work.
IS GOD A
MATHEMATICIAN?
CHAPTER 1
A MYSTERY
A few years ago, I was giving a talk at Cornell University. One of my PowerPoint slides read: “Is God a mathematician?” As soon as that slide appeared, I heard a student in the front row gasp: “Oh God, I hope not!”
My rhetorical question was neither a philosophical attempt to define God for my audience nor a shrewd scheme to intimidate the math phobics. Rather, I was simply presenting a mystery with which some of the most original minds have struggled for centuries—the apparent omnipresence and omnipotent powers of mathematics. These are the type of characteristics one normally associates only with a deity. As the British physicist James Jeans (1877–1946) once put it: “The universe appears to have been designed by a pure mathematician.” Mathematics appears to be almost too effective in describing and explaining not only the cosmos at large, but even some of the most chaotic of human enterprises.
Whether physicists are attempting to formulate theories of the universe, stock market analysts are scratching their heads to predict the next market crash, neurobiologists are constructing models of brain function, or military intelligence statisticians are trying to optimize resource allocation, they are all using mathematics. Furthermore, even though they may be applying formalisms developed in different branches of mathematics, they are still referring to the same global, coherent mathematics. What is it that gives mathematics such incredible powers? Or, as Einstein once wondered: “How is it possible that mathematics, a product of human thought that is independent of experience [the emphasis is mine], fits so excellently the objects of physical reality?”
This sense of utter bewilderment is not new. Some of the philosophers in ancient Greece, Pythagoras and Plato in particular, were already in awe of the apparent ability of mathematics to shape and guide the universe, while existing, as it seemed, above the powers of humans to alter, direct, or influence it. The English political philosopher Thomas Hobbes (1588–1679) could not hide his admiration either. In Leviathan, Hobbes’s impressive exposition of what he regarded as the foundation of society and government, he singled out geometry as the paradigm of rational argument:
Seeing then that truth consisteth in the right ordering of names in our