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
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.
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.