Saturday, January 08, 2005
Proofs Over the Edge
The Edge espouses the thesis that providing a forum for smart people discussing profound ideas is far more important than having a decently designed web site. Its latest contribution to mankind is very long, thought provoking, (mostly) accessible and unlike much of the stuff on the Internet, worthy of careful attention: They asked 120 notable thinkers the question, "What do you believe is true even though you cannot prove it?" A sampling of quotes can't really do it justice, but here's an attempt anyway.
What I believe but cannot prove is that quantum physics teaches us to abandon the distinction between information and reality.
I am convinced that quantum mechanics is not a final theory. I believe this because I have never encountered an interpretation of the present formulation of quantum mechanics that makes sense to me...I believe that the hidden variables represent relationships between the particles we do see, which are hidden because they are non-local and connect widely separated particles.
If I were to flip a coin a million times I'd be damn sure I wasn't going to get all heads. I'm not a betting man but I'd be so sure that I'd bet my life or my soul. I'd even go the whole way and bet a year's salary. I'm absolutely certain the laws of large numbers—probability theory—will work and protect me. All of science is based on it. But, I can't prove it and I don't really know why it works. That may be the reason why Einstein said, "God doesn't play dice." It probably is.
Since I am a mathematician, I give a precise answer to this question. Thanks to Kurt Gödel, we know that there are true mathematical statements that cannot be proved. But I want a little more than this. I want a statement that is true, unprovable, and simple enough to be understood by people who are not mathematicians. Here it is. [...] [I]t never happens that the reverse of a power of two is a power of five [...]
(I thought Goldbach's Conjecture met this criteria as well, but Dyson also provides a simple method for generating easy to grasp, non-provable probable mathematical truths)
The Atom, the nucleus and the proton, each in its own time, were considered elementary and indivisible, only to be replaced later by smaller objects as the fundamental building blocks. How can we be so arrogant as to exclude the possibility that this will happen again?