Wednesday, August 20, 2008

Super String: Vortex Theory?

In the 19th-century the was something called the vortex theory of atoms. It maintained that atoms are not pointlike but are incredibly tiny loops of energy that vibrate at different frequencies. They are minute whirlpools in the ether, a rigid, frictionless substance then believed to permeate all space. The atoms have the structure of knots and links, their shapes and vibrations generating the properties of all the elements.

Eminent physicists, including Lord Kelvin and James Clerk Maxwell, suggested that vortex theory was far too beautiful not to be true. Papers on the topic proliferated, books about it were published. Scottish mathematician Peter Tait's work on vortex atoms led to advances in knot theory. Tait predicted it would take several generations to develop the theory's mathematical foundations. Beautiful though it seemed, the vortex theory proved to be a glorious road that led nowhere.

Clearly there's an analogue with string theory, but I think lots of economics gets a pass because it is beautiful, meaning it is full of results that are surprisingly consistent and rigorous. I'm thinking Debreu's Theory of Value, Continuous time finance, Bellman's equations, Value functions. These fields take a lot of time to get really up to speed, but I don't see any results here that can't be found using simpler methods, and they mainly just confirmed intuitions, as opposed to generating results that are now used elsewhere. Many think such results can only indicate there's a deep truth there, because these things don't happen by accident. But I think a bunch of really smart people, given a set of things to explain, can invent a set of assumptions that generate these things a lot more easily than they imagine. This is why it's essential to have some experimental results that corroborate these forays, otherwise, it's can be like vortex theory.

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