Some of you have probably seen this before, but I wanted to share an excellent lecture by Feynman on the relationship between math and physics that I listened to yesterday. When I don't feel like listening to music I sometimes put these sorts of things on in the background while I work. If I internalize 10% of it I've still gained something. This was good enough that I replayed it after listening to it the first time and paid even closer attention.
I especially liked the discussion of the difference between (what he calls) Babylonian and Greek mathematics, and the fact that physicists are more like the Babylonians. It's something that I think can really be generalized to all science, including economics.
The idea is that Greek mathematicians did the math we do today: you take a few axioms that you assume are fundamental and build up a system of knowledge on top of it. The Babylonians did math differently. It was rule-based but it wasn't axiomatic. Different pieces of the puzzle could be used to develop a proof that was convincing, but it was not derived up from knowledge that was assumed to be any more fundamental than any other knowledge. Feynman describes Babylonian math as "efficient" in that sense, and I'd also add that it is robust.
Physics works that way too, according to Feynman - physics is Babylonian. There's no fundamental truth. Instead, we take bits of different things we know and try to construct theories that connect those dots. It's wrong, he says, to expect that you have all the axioms at your disposal. And if you don't have all the axioms at your disposal then reasoning from an incomplete list (this assumes you haven't made a mistake in your reasoning - a big assumption in itself for human beings), you're going to get wrong results. The whole nature of the scientific endeavor is to understand what we don't know about. If you don't fully understand a phenomenon, how are you going to be able to assert you have all the relevant axioms at your disposal?
Draw whatever conclusions you want to about the fatal conceit of Mises on this point. You all know I have, of course.
So is the Greek math we're taught wrong?
No - and Feynman is very adamant about this. He says towards the end that it's not a mathematician's job to do physics. If the mathematician isn't doing what you want him to do don't complain to him about it: do the work yourself! What the Greek approach provides is a collection of arguments and ways of thinking about the world that are derived using a particular algorithm in mind. It's a framework or a superstructure that we as human beings have found very useful. It may not be the efficient way to discover new properties about the world, but building up from axioms is a very efficient way to erect a stable edifice of a series of mathematical propositions, given a common denominator set of axioms. And such an edifice is very useful to have.
In a lot of ways, this is why I don't mind mainstream "microfounded" neoclassical economics. I recognize the problems with it. But it provides a framework that has proven to be very useful in understanding human society. I would not let that constrain me from doing Babylonian economics. The so-called "ad hoc", non-microfounded mathematical macroeconomics as well as the more pluralist methods of qualitative researchers and other heterodox economists ought not to be considered so heterodox. They have important contributions as well.