Wednesday, July 20, 2005

Deep Thought II

OK, so it was kind of nasty of me to make fun of Lumo's Deep Thoughts, even if he did ask for it by bringing in all sorts of irrelevant prejudices. So it's only fair that I give any readers an opportunity to return the favor by providing my own "deep thoughts."

To be counted as "deep," I consider that an idea needs to be both non-obvious (deep in the sense of hidden) and foundational, i.e. it must unify and provide the foundation for explanation of many phenomena. I will cheat by giving very well established examples:

1) The atomic hypothesis. Feynman said that if only one scientific idea could be saved, this was the one. It was formulated by the ancient Greeks, more than two millenia before anyone could devise any ways to test it.

2) Mathematics as "the" tool for explaining nature. Pythagoras was the first, but only a little further progress occurred before Kepler.

3) The method of postulate and proof in Geometry. This third gigantic Greek idea was influential immediately. It's power has grown over the centuries.

4) Analytic geometry. Combining geometry with algebra and arithmetic created modern mathematics.

5) Solar system dynamics as explained by Kepler, Galileo, and Newton. The first and greatest scientific success story.

6) Natural selection and the Origin of Species. Makes biology and human nature explicable.

Those, I think, are the real biggies, but there are a few more almost as important.

7) Atoms in chemistry - the Greek idea finally applied to real scientific predictions and phenomena.

8) The Electromagnetic Field. Foundational to the explanation of the behavior of ordinary matter as well as relativity, quantum theory, and modern field theories of matter. Probably the most important technological development since fire.

9) Thermodynamics and Statistical Mechanics - two beautiful ideas now seen as one.

10) Relativity

11) Quantum Mechanics

and one to take us almost up to the 21st century.

12) Gauge Field Theories - It seems so odd that redundancy of description should prove so fundamental to our current understanding of nature. It would be nice if some smart guy like Lumo could explain this.

Their are other deep ideas of course, but these 12, and especially the first six, are the prototypical examples.

Are there deep ideas in string theory? I can think of some candidates - the Kaluza-Klein idea (which of course predates strings), supersymmetry (also independent of strings) and maybe holography. LM doubtless has better candidates.

So what about Lubos's favorite whipping boy, Loop Quantum Gravity? The idea of making the holonomies the dynamical entities might fit (of course it predates LQG), and spin foams, if real, would surely qualify.

Needless to say, none of these latter two groups of ideas can be considered deep until they prove to describe reality, and on that, the jury is still out.