1. The Unreasonable Effectiveness of Mathematics Bram Boroson, Clayton State University, 3/20/2013

2. Fox and Hedgehog “The fox knows many things, but the hedgehog knows one BIG thing.” Far-out ideas and amusing stories to tell But also one BIG thing to communicate

3. Quantum Physicist Eugene Wigner (1902-1995): Mathematics is “Unreasonably Effective”

4. E=mc 2, c is speed of light, a large number So there is LOTS of Energy in Mass But nobody trying to release energy would START by inventing equations or multiplication table

5. The Big Problem Math WORKS in science NOT like a hammer works in hitting nails Over and over math was invented “for kicks and giggles” and yet proved useful Something about math? Or our world?

6. Imaginary Friends Little could seem more useless than “imaginary numbers” We start learning math with counting Then fractions, negative numbers Irrational numbers Every equation has a solution

7. Quantum mechanics, time

8. Quarternions, Spin 1/2

9. Math: appeal of the General? Maybe math works because it’s abstract By talking about “2 plus 2” instead of apples, oranges, you can use it for apples OR oranges To me this doesn’t seem to be good enough

10. Max Tegmark’s MUH Mathematical Universe Hypothesis: our world IS mathematics Seems strange, radical! “Mathematical Platonism”: math exists apart from us in its own world We “discover” math truth using our minds instead of senses Occam’s razor: isn’t it simpler if LESS exists?

11. Our world’s math, but which Math? Do all mathematical systems describe possible worlds? Max Tegmark: only computable worlds If our world is a mathematical world “pulled at random out of a hat”, what’s in the hat? Alan Turing

12. Leibniz: Principle of Sufficient Reason One approach: the world is a special mathematical OBJECT What we can say about it only approximates what it is It’s singled out among other possible objects Nature never makes an arbitrary choice

13. Principle of Sufficient Reason Example in physics: infinite line charge Much of modern physics is written in terms of maximizing/minimizing an “action” Light bending (refracting) when passing through glass or water: minimizes the time it takes to go from A to B

14. Principle of Sufficient Reason Einstein’s General Relativity Problem of rotating spheres, centrifugal forces, and bulges Another example of Unreasonable Effectiveness: Tensor Calculus Principle of Sufficient Reason FAIL: Quantum Mechanics (Stern-Gerlach Experiment)

15. Approach 2: (early) Wittgenstein “The world is made of facts, not things; each fact could be different and all the others the same” 1, 2 prove 3… or 1, 3 prove 2? But then WHY is our world so special that there are ANY laws?

16. My own approach Symbols of mathematics are “formal” Geometry could be about “points, lines, planes” or “tables, chairs, desks” The symbols may be reinterpreted This property naturally allows for “axiom schema” “Facts” don’t stay put: allow symbols to be re- interpreted