The great British physicist Ernest Rutherford once said “In science, there is only physics; all the rest is stamp collecting.” This is kind of the ultimate example of the arrogance of physicists, given a lovely ironic twist by the fact that when Rutherford won a Nobel Prize, it was in Chemistry. (He won for discovering that radioactive decays lead to transmutation of elements, causing one contemporary to quip that the most remarkable transmutation ever was Rutherford’s change from a physicist to a chemist for the Nobel.)

Of course, there’s a little truth to the statement– not the part about the inferiority of other sciences, but the fact that there are very different ways of doing science in different subdivisions of the subject. I had a bit of a Rutherford Moment yesterday, when I ran across Brian Switek’s review of The Calculus Diaries, specifically this comment:

There is nothing so ugly as an equation in a scientific paper. As a friend once told me, an equation in a paper looks like a dog turd on the lawn – the only reason you want to look at it is to know how to go around it.

This is almost completely inconceivable to me (at the risk of leaving myself open to the Vizzini joke). In my part of science, a paper *without* an equation is suspect, and I’m not exactly the world’s most mathematically inclined physicist. Physics is so intimately connected to math, and the business of doing physics is so inherently mathematical that its difficult to imagine a scientific paper about physics that doesn’t contain at least one equation. A press release or popular article, sure, but to a physicist, the equations aren’t some offal to be avoided en route to the science. The equations *are* the science. Objecting to the presence of an equation in a scientific paper is like objecting to the presence of meat in a steak sandwich.

This is not a knock on Brian, who writes a very good blog, and has a pop-science book of his own that you should check out. It’s just a general comment about the different operating modes of different sciences. I’m so immersed in physics at this point in my career that it’s always a little surprising to be reminded that there are areas of science where math doesn’t play the same central role that it does in physics. That’s so counter to the way physics operates, that it’s not hard to see how somebody within physics could dismiss less mathematical branches of science as mere stamp collecting.

(Of course, the Nobel in Chemistry isn’t the only irony to the Ruthford comment, at least in this context. Rutherford was an experimentalist to the core, and always distrustful of theory (he made an exception for Niels Bohr, because he was a good soccer player), preferring direct measurements to mathematical predictions (as is right and proper). And even the theorists of Rutherford’s day were relatively unsophisticated mathematically. Einstein needed ten years to develop General Relativity after he published the papers on Special Relativity in 1905, mostly because he had to learn a whole new branch of mathematics (and almost got scoopd by Hilbert, who knew the math but not how to apply it to physics). Heisenberg expended a great deal of effort working out his formulation of quantum mechanics because he had to independently develop matrix algebra that was already well known to mathematicians, and then had a great deal of trouble getting physicists to accept his theory, because they didn’t know matrix math either. Physics became dramatically more mathematically sophisticated after WWII. Prior to that, it was probably closer to the “stamp collecting” sciences of today.)