The Mathematical Universe

This is a book about the mathematical nature of our Universe. Armed with no more than basic high school mathematics, Dr. Joel L. Schiff takes you on a foray through some of the most intriguing aspects of the world around us. Along the way, you will visit the bizarre world of subatomic particles, honey bees and ants, galaxies, black holes, infinity, and more. Included are such goodies as measuring the speed of light with your microwave oven, determining the size of the Earth with a stick in the ground and the age of the Solar System from meteorites, understanding how the Theory of Relativity makes your everyday GPS system possible, and so much more. These topics are easily accessible to anyone who has ever brushed up against the Pythagorean Theorem and the symbol p, with the lightest dusting of algebra. Through this book, science-curious readers will come to appreciate the patterns, seeming contradictions, and extraordinary mathematical beauty of our Universe.

Auteur
Joel Schiff has a PhD in Mathematics from the University of California Los Angeles and spent his academic career at the University of Auckland, New Zealand. He is the author of seven other books, four of which are mathematical in nature. He and his wife discovered the asteroid 12926 Brianmason from their own observatory. Schiff was also the publisher of the international quarterly, Meteorite, for many years.

Résumé
I first had a quick look, then I started reading it. I couldn't stop. -Gerard 't Hooft (Nobel Prize, in Physics 1999)
This is a book about the mathematical nature of our Universe. Armed with no more than basic high school mathematics, Dr. Joel L. Schiff takes you on a foray through some of the most intriguing aspects of the world around us. Along the way, you will visit the bizarre world of subatomic particles, honey bees and ants, galaxies, black holes, infinity, and more. Included are such goodies as measuring the speed of light with your microwave oven, determining the size of the Earth with a stick in the ground and the age of the Solar System from meteorites, understanding how the Theory of Relativity makes your everyday GPS system possible, and so much more. These topics are easily accessible to anyone who has ever brushed up against the Pythagorean Theorem and the symbol , with the lightest dusting of algebra. Through this book, science-curious readers will come to appreciate the patterns, seeming contradictions, and extraordinary mathematical beauty of our Universe.

Contenu

Dedication

Acknowledgements

About the Author

Prologue

Preface

1. The Mystery of Mathematics

   Let us be reasonable

   All set

   Where is Mathematics?

   Fine tuning

   A blast from the past: Euclid's geometry

   Taking the Fifth further

   Pi in the sky

   Off to Monte Carlo

   Smashed pi

   The divine Isoperimetric Inequality

2. From Here to Infinity

   Zeno's Paradox

   Summing Up

   In what Universe is this true?

   The power of e

   Fast money

   What is normal? Multiplying ad infinitum

3. Imaginary Worlds The Strange Case of

   The ' 's have it

   The God-like Euler identity

   Even more imaginaries - quaternions

   But wait, there is more - octonians

   The world's hardest problem - the Riemann Hypothesis

4. Random Universe

   Going steady

   Brownian Motion

   Life is a gamble

   The dating game The world of entropy - order to chaos

   Information entropy

5. Order from Chaos

   Cellular Automata

   Life as a game

   Infectious disease model - SIR

   Mimicking Darwin One-dimensional CA

   The whole is greater than the sum of its parts

   Bees and termites

   ... And ants

   Bacteria count

   A hive of Mathematics: Fibonacci

   Dynamical systems

   Messrs. Fatou, Julia and Mandelbrot

   The fractal Universe

6. Mathematics in Space Faster than a speeding bullet

   Down to Earth

   Heavens above

   Light-years

   The great recession

   The Universe is flat

   Measuring the invisible: Black holes

   A galaxy far, far away

   7. The Unreality of Reality

   Miniature Universe

   Quantum world

   Infinite space

   Qubits It is all relative, Albert

   That equation

   What time is it anyway?

   Matters of gravity

   Time in motion

   Radiation

   Symmetry and groups

7. The Unknowable Universe

   Gödel incompleteness

   Halting problem

   EMX

   Where is it, Dr. Heisenberg?

   Summing up

Appendix I: Being Reasonable

Appendix II: Hyperbolic Geometry and Minkowski Spacetime

Appendix III: The Uncountable Real Numbers

Appendix IV: c2 = c: Square and Line have Same Cardinality

Appendix V: Geometric Series

Appendix VI: Cesàro Sums

Appendix VII: Rotating a Vector via a Quaternion

Appendix VIII: Quaternions q2 = -1

Appendix IX: Riemann Zeta Function

Appendix X: Random Walk Code

Appendix XI: Age of the Solar System

Appendix XII: Chelyabinsk Meteoroid

Appendix XIII: Logic Gates

Appendix XIV: Galaxy Distance via Cepheids

Appendix XV: Time Dilation

Appendix XVI: Expansion of the Universe

Bibliography

Index