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 CreditsPREFACE
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. Sohow 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 abstractof 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 betweenmathematics 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 thisbook. 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 and Naturalization Service. William Christens-Barry, Keith Knox, Roger Easton, and in particular Will Noel were kind enough to give me detailed explanations of their efforts to decipher the Archimedes Palimpsest. Special thanks are due to Laura Garbolino for providing me with crucial materials and rare files regarding the history of mathematics. I also thank the special collections departmentsof the Johns Hopkins University, the University of Chicago, and the Bibliothèque nationale de France, Paris, for finding some rare manuscripts for me. 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 SharonToolan 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...
Leer documento completo
Regístrate para leer el documento completo.