Wednesday, December 14, 2005

Love, Sex, and Death (no, just kidding. More math).

Sam:
"'Math types'...have a tendency to think math is THE expression, that it gets at some deeper truth than other expressions can. I once argued for hours with my friend Mark, who swears that if a = b and b = c then a = c IS TRUE. IS TRUE, not as a property of western logic, but simply as a fact of the universe. I've read way too much Heidegger to buy that."

I find it interesting, and yet also a source of my own enormous personal smug-itude, that most people who think that math is cool think it's cool roughly for the reason that Sam states: Math is The Expression of Truth, God is a Mathematician, all of scientific knowledge is intrinsically written in Mathematical language. That kind of thing--basically that Math is different or pure or something. They believe this in spite of the that fact that it's been PROVEN USING ITS OWN AXIOMS that it isn't.

If you're not interested in more philosophy of Mathematics, you can stop reading, because I've given you the punchline. Math may appear to be different than, say, language or Philosophy, and immune from the freaky things that happen when you start using language to talk about language or Philosophy to talk about Philosophy. It's not. Kurt Gödel proved that this was the case. He did it using math.

There was a movement in mathematics over the 250 years or so prior to Gödel's proof to logically formalize pretty much everything in math--that is, to formally derive it from first principles. The zenith of this effort was probably Whitehead & Russel's Pricipia Mathematica. This is a book which everyone claims is brilliant and groundbreaking, and which no one has actually read. It's several hundred pages long, and proves such things as, given the well defined concepts of addition, one, and two, that 1 + 1 = 2. No, really. And it proves them only if you take a couple of things, one of which being that meta- is not allowed to occur, to be axioms. Anyway, this movement pretty much died with Gödel. The idea that "Math is different" seems to have not died at all.

The Incompleteness Theorem is generally listed, with Relativity and Quantuum Theory, as one of the most profound theoretical advances of the 20th century. But whereas you almost cannot get through a high school physics class without learning Special Relativity, and the first thing you learn in chemistry class is the Bohr Atom, I have a BA in Mathematics and my classroom time with the Incompleteness Theorem was about ten minutes, it was a sidelight in the midst of learning about the rigorous formalization of the foundations of calculus, and it was presented like, "well, isn't that whacky. Anyway, back to what we were doing...." Apparently the idea that Mathematics isn't the language of truth any more than anything else is is too hard to grok, even for the Mathematicians.

3 comments:

Donnacha said...

It could be there's always a political consequence to truth and so with mathematics an incredible and definitely life altering human language..there will be a tendency to cloak it in absolutism as it muscles it's way into our superstitious constructs.that rule large areas of our lives......D

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Rebecca said...

I must say that it was precisely the moment when math turned into philosophy that I bailed. I liked the concreteness of numbers, the idea that the world could somehow be encapsulated in formulae (hence my earlier Chemistry interests) and once some professor proved that all numbers are in fact equivalent (or something equally mind-blowing) I decided that that was it, and I was off to something more "real," like art.

Transient Gadfly said...

Yeah, but you haven't really had your brain screwed with until somebody shows you the universe in which 1 + 1 = 0.