The Mathematical Universe
Description
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.
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Content
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 infinitum3. Imaginary Worlds
The Strange Case of The ' 's have itThe 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 chaosInformation entropy
5. Order from Chaos
Cellular Automata
Life as a game
Infectious disease model - SIR
Mimicking Darwin
One-dimensional CAThe 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 bulletDown 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 RealityMiniature Universe
Quantum world
Infinite space
Qubits
It is all relative, AlbertThat 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 q 2 = -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