__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 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.

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Schiff, Joel L.

Springer International Publishing AG

Springer Nature ; Praxis Publishing

Springer Nature Switzerland AG

Springer-Praxis books in popular science, Cham, Switzerland, Chichester, UK, 2020

Popular Science, 1st ed. 2020, Cham, 2020

Springer Nature, Cham, Switzerland, 2020

Switzerland, Switzerland

1st ed. 2020, US, 2020

1st ed, S.l, 2020

Sep 10, 2020

1, 20201118

sm84855989

producers:
Adobe PDF Library 10.0.1

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类型: 图书

出版日期: 2020

出版社: Springer International Publishing; Imprint: Springer

Source title: The Mathematical Universe: From Pythagoras to Planck (Springer Praxis Books)

Contents 6
Acknowledgements 11
About the Author 12
Foreword 13
Prologue 15
A Brief Tale 15
Preface 18
1: The Mystery of Mathematics 20
Let us Be Reasonable 22
All Set 26
Where Is Mathematics? 28
Fine Tuning 31
A Blast from the Past: Euclid’s Geometry 36
Taking the Fifth Further 39
Pi in the Sky 47
Off to Monte Carlo 49
Smashed Pi 51
The Divine Isoperimetric Inequality 54
2: From Here to Infinity 58
Zeno’s Paradox 60
Summing Up 71
In What Universe Is this True? 79
The Power of e 86
Fast Money 90
What Is Normal? 91
Multiplying AD Infinitum 93
3: Imaginary Worlds 95
The Strange Case of x2 + 1 = 0 96
The ‘i’s Have It 99
The God-Like Euler Identity 101
Even More Imaginaries – Quaternions 105
But Wait, There Is More – Octonians 108
The World’s Hardest Problem – The Riemann Hypothesis 110
4: Random Universe 118
Going Steady 118
Brownian Motion 122
Life Is a Gamble 122
Exponential Decay 124
The Dating Game 125
Empowering Laws 128
The World of Entropy – Order to Chaos 132
Information Entropy 135
5: Order from Chaos 139
Cellular Automata 139
Life as a Game 146
Infectious Disease Model – SIR 150
Mimicking Darwin 151
One-Dimensional CA 156
The Whole Is Greater Than Sum of Its Parts 161
Bees and Termites 162
... and Ants 163
Bacteria Count 166
A Hive of Mathematics: Fibonacci 168
Dynamical Systems 171
Messrs. Fatou, Julia, and Mandelbrot 176
The Fractal Universe 181
6: Mathematics in Space 187
Faster Than a Speeding Bullet 187
Down to Earth 192
Heavens Above 194
Light-Years 197
The Great Recession 199
The Universe Is Flat 204
Measuring the Invisible: Black Holes 207
A Galaxy Far, Far, Away 211
7: The Unreality of Reality 213
Miniature Universe 214
Quantum World 218
Infinite Space 225
Qubits 228
It Is All Relative, Albert 232
That Equation 236
What Time Is It Anyway? 237
Matters of Gravity 238
Time in Motion 247
Radiation 253
Symmetry and Groups 255
8: The Unknowable Universe 264
Gödel Incompleteness 264
Halting Problem 265
EMX 266
Where Is It, Dr. Heisenberg? 267
Summing Up 269
Appendix I 272
Being Reasonable 272
Appendix II 275
Hyperbolic Geometry and Minkowski Spacetime 275
Appendix III 278
The Uncountable Real Numbers 278
Appendix IV 280
c2 = c: Square and Line Have Same Cardinality 280
Appendix V 282
Geometric Series 282
Appendix VI 284
Cesàro Sums 284
Appendix VII 285
Rotating a Vector Via a Quaternion 285
Appendix VIII 288
Quaternions: q2 = − 1 288
Appendix IX 289
Riemann Zeta Function 289
Appendix X 293
Random Walk Code 293
Appendix XI 295
Age of the Solar System 295
Appendix XII 298
Chelyabinsk Meteoroid 298
Appendix XIII 299
Logic Gates 299
Appendix XIV 302
Galaxy Distance Via Cepheids 302
Appendix XV 305
Time Dilation 305
Appendix XVI 308
Expansion of the Universe 308
Bibliography 310
Index 313

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 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

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. -- Provided by publisher

Front Matter ....Pages i-xviii
The Mystery of Mathematics (Joel L. Schiff)....Pages 1-38
From Here to Infinity (Joel L. Schiff)....Pages 39-75
Imaginary Worlds (Joel L. Schiff)....Pages 76-98
Random Universe (Joel L. Schiff)....Pages 99-119
Order from Chaos (Joel L. Schiff)....Pages 120-167
Mathematics in Space (Joel L. Schiff)....Pages 168-193
The Unreality of Reality (Joel L. Schiff)....Pages 194-244
The Unknowable Universe (Joel L. Schiff)....Pages 245-252
Back Matter ....Pages 253-303

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Erscheinungsdatum: 07.12.2020

2020-11-21