What is purity? June 14, 2008Posted by Ben Webster in math life.
So, maybe I’m a little late to this party, but I wanted to comment on a recent XCKD (yes, Isabel blogged it first, though I added it to our del.icio.us before she blogged it). This arranged several scientific fields, by order of purity. Of course, the mathematician is standing at the far end of the scale (saying “Oh hey, I didn’t see you guys all the way over there”). The same point has circulated in saying form as
“Biologists defer to chemists. Chemists defer to physicists. Physicists defer to mathematicians. Mathematicians defer only to God”
(does anyone have an attribution for this quote? My Google-fu was insufficient).
Now, I think it’s clear that I love XKCD (one of these days, I’ll get my shit together and drive out to the Boston meet-up. Who knows, maybe next Saturday), but I can’t help but disagree a bit with the premise of this comic. I think it misses something pretty important about mathematics.
I spend a reasonable amount of time thinking about what mathematics is, and how to explain this other people. You see, unlike (I believe) all my other co-bloggers, I’m single, which leads to me periodically dating, and thus having to explain to women who are not mathematicians, but rather, say, journalists or librarians or public-health types what mathematics is and why it is an endeavor a reasonable person would undertake. (One might suggest that even romantically-attached mathematicians have non-mathematical friends that they need to explain this stuff to. I would reply that there’s a bit less, ahem, biological imperative involved there).
And I think one of the key points here is this: mathematics is not science. Mathematics is often lumped in with science, and is often used by scientists. Mathematicians often know more science than normal people, and certainly scientists know more mathematics. But mathematics and science are fundamentally different activities, as different as making a gun and fighting in a battle. I mean, no one would claim there are no links between those occupations, or that gun-makers don’t pay a lot of attention to how guns are used, but not even a child would mistake one for the other. Putting mathematics on a continuum of purity with sciences is like putting it on a continuum with disciplines of art ordered by “highbrow-ness” (actually, I would argue that the latter captures the nature of mathematics better).
Consider the inane saying I quote above; anyone mathematician who’s met a physicist doesn’t really believe that. Physicists don’t defer to mathematicians, they defer to data. As do chemists, biologists, psychologists and sociologists, irrespective of their social relations with each other. Mathematicians, on the other hand, have escaped the tyranny of data. We are often guided in what we do by examples from other fields, but mathematics by definition is universal, rather than science, which is constrained by actual observations of the world. Now, of course, scientists would argue that the actual important questions about this universe, the one we live in, the world around us, we need data, and of course, they are right. You will never here me putting down science. But that’s not what I do, and personally I find that liberating. Not everybody agrees, and that’s fine, they can spend years hunched over a lab bench, or anxiously awaiting the results of terrifying expensive experiments at CERN. I’ll be happy staring at my chalkboard, scratching my head.