Science, SETI, and Mathematics

Science, SETI, and Mathematics
Carl L. DeVito
Publisher: Berghahn Books
ISBN No: 978-1-78238-070-2
Release at: 2014
Pages: 221
First Edition
File Size: 1 MB
File Type: pdf
Language: English

Description of Science, SETI, and Mathematics

This book is intended for my colleagues in the humanistic and natural sciences who share my interest in the search for extraterrestrial intelligence (SETI). It is about the role mathematics might play in this endeavor. Since I am writing for a wide audience, an audience of people with very diverse backgrounds, I have focused on ideas and avoided mathematical symbolism and technical jargon. No prior knowledge of mathematics is assumed and, since this subject may be new to many of my readers, I also present the history of, and the science behind, this search. My goal is to stimulate a discussion, among scientists interested in this area, of the ideas presented here.

Content of Science, SETI, and Mathematics

Chapter 1. Where Are We? 1

Remark: Natural Numbers, Sets, and Subsets 5

Chapter 2. Naïve Questions 7

Remark: Infinite Sets, Correspondences, Unions, and Intersections 15

Chapter 3. Are We Special? 17

Remark: Systems of Enumeration, Powers of Ten, Positional Notation, and Casting Out Nines 23

Chapter 4. Stories—Part One 26

Remark: Human Perception of Motion, and Mathematical Description of Physical Fields 32

Chapter 5. Measuring Our Solar Neighborhood 36

Remark: Euclid’s Fifth Postulate, Non-Euclidean Geometries, and How Choice of Geometry Affects Physics 43

Chapter 6. The Scotsman 47

Remark: The Fundamental Wave Equation, Partial Differential Equations, Equations of Mathematical Physics, and the Function Concept 51

Chapter 7. The Birth of SETI 54

Remark: Two Functions and Why They Are Special, the Power of Trigonometry, and Fourier Series 60

Chapter 8. The Conference at Green Bank 64

Remark: The Drake Equation, Drake’s Postcard, and Prime Numbers 69

Chapter 9. Stories—Part Two 73

Remark: Development of Calculus, Models for Time, Differential Calculus and the Science of Motion, and Derivatives and Partial Derivatives 84

Chapter 10. Talking to E.T. 89

Remark: Continuity of Space, Area, Integral Calculus and the Founding of Carthage, Line Integrals and the CAT Scan 94

Chapter 11. Languages 99

Remark: Real Numbers as the Basis for Calculus, Complex Numbers and the Calculus of Complex Functions, Complex Integration, and Whether Mathematical Objects Are Real 109

Chapter 12. Paradoxes 113

Remark: Group Theory in Algebra and Geometry 115

Chapter 13. The Universal Science 119

Remark: Atomic Weights and the Avogadro Number 127

Chapter 14. The Special Theory of Relativity 129

Remark: Space-Time, Higher Dimensional Spaces, and Hilbert Space 138

Chapter 15. The General Theory of Relativity 143

Remark: The Geometry of Minkowski’s 4-World, and Why Points Are Zero Dimensional 149

Chapter 16. The University of Colorado Study 152

Remark: Space as Multi-Dimensional, the Dimension of Sets, and General Topology and Functional Analysis 160

Chapter 17. Surprise! 163

Remark: Fibonacci Numbers and the Golden Ratio, Logarithms, Exponentials, and the Number e, Connections to the Complex Numbers 165

Chapter 18. Epilogue 169

Remark: Ramanujan 176

Appendix I. Infinite Sets 177

Appendix II. Mars 182

Appendix III. The DeVito-Oehrle Language 185

Bibliography 198

Index 203

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