The Mathematical Universe: From Pythagoras to Planck

ISBN-13: 9783030506513 / Angielski / Miękka / 2020 / 303 str.

Joel L. Schiff

Spis treści

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

8. 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

 

O autorze

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.

  

Blurb

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 π, 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.