Since Richard Feynman died, Frank Wilczek has become my favourite living physicist. I base this on the quality not of their research (which I'm nowhere near fit to judge) but their words and thoughts (which are sublime).
I was therefore please to stumble across this the other day while searching for something else online. (It reminds me a lot of a piece that Wilczek wrote for Nature a few years ago.) It's basically about (i) the remarkable ability of numbers to explain the world and (ii) an extreme application of Occam's Razor by which scientists are trying to create theories of the universe that contain the minimum number of nonconceptual (i.e., apparently arbitrary) quantities. As so often, Einstein explained it best:
I would like to state a theorem which at present can not be based upon anything more than upon faith in the simplicity, i.e., intelligibility, if nature: there are no arbitrary constants... that is to say, nature is so constituted that it is possible logically to lay down such strongly determined laws that within these laws only rationally completely determined constants occur (not constants, therefore, whose numerical value could be changed without destroying the theory).
Wilczek takes us from the mystical Pythagorean Brotherhood for whom "All Things are Number" via Kepler's Zeroth Law (a bold but incorrect attempt to fit the solar system into a structure determined by the Platonic solids) and quantum electrodynamics (which has only two nonconceptual quantities, the mass of an electron and the fine-structure constant) to quantum chromodynamics (QCD), which takes us surprsingly close to the ultimate goal:
To the extent that we are willing to use the proton itself as a meterstick, and ignore the small corrections due to u and d quark masses, QCD becomes a theory with no nonconceptual elements whatsoever.
I also liked his mention in passing that our naming of the square root of 2 as being irrational stems from the, well, irrational anxiety thatn this number engendered the Pythagoreans. We might say the same about "imaginary" numbers (products of the square root of -1), which are really no more or less imaginary than any other numbers and, like other numbers, seem to have a lot to do with the world. The Special Theory of Relativity, for example, suggests that the relationship between space and time is the same as the relationship between "ordinaryreal" and "imaginary" numbers. Time is certanly mysterious compared to space (we can only directly exprience the time that we call "now" and can only remember the past, not the future) but not many people would consider space to be "real" and time to be "imaginary". We need better words to describe this relationship. Answers on a postcard (or in a comment) please...