Professor Planck, of Berlin, the famous originator of the Quantum Theory, once remarked to me that in early life he had thought of studying economics, but had found it too difficult! Professor Planck could easily master the whole corpus of mathematical economics in a few days. He did not mean that! But the amalgam of logic and intuition and the wide knowledge of facts, most of which are not precise, which is required for economic interpretation in its highest form is, quite truly, overwhelmingly difficult for those whose gift mainly consists in the power to imagine and pursue to their furthest points the implications and prior conditions of comparatively simple facts which are known with a high degree of precision.(Keynes, Essays in Biography 1951 158n)It's true: powerful mathematical minds are not necessarily comfortable with the messiness of the real world. This observation might be applied as well to string (or more formal or mathematical) theorists vs theorists who are more data- or intuition-driven (often called phenomenologists, in a terrible use of terminology). Of course, some people (like Feynman, although he wasn't very mathematical by today's standards) are good at everything...
"We know a lot more than we can prove" -- Feynman
7 comments:
3 cheers for Professor Planck! None of those arrogant remarks that theoretical physicists could do everything.
PS: Could Feynman have excelled in the more mathematical end of string theory (as in contrast to say the Polchinski end)?
I doubt Feynman would have had sufficient interest in the purely formal work to have excelled. He would have probably found other, more exciting problems to work on ;-)
Interesting. It reminds me of a comment I often heard back in my fac, which trained both economists and mathematicians: that lousy mathematicians can make good economists. At the time I thought the comment implied that economics was easier than math; now I wonder if some skills required for excelling at the first may actually prevent someone from excelling in the second. Alas, Nash and von Neumann seem to disprove the point.
v.N. was probably a universal genius, and navigated the corridors of power in Washington, so probably also had the right kind of intuition and integrative intelligence to be a good economist. Nash, although he made an important contribution, doesn't seem the kind of guy you would want as chairman of the Federal Reserve. The anecdotes about his investing prowess are not positive :-)
http://www.geniusdenied.com/articles/Record.aspx?NavID=13_12&rid=11431
An article describing the verbally versus mathematically precocious cognitive profile.
http://web.mit.edu/krugman/www/culture.html
As Krugman famously puts it "This should sound familiar. More than 40 years ago, the scientist-turned-novelist C.P. Snow wrote his famous essay about the war between the "two cultures," between the essentially literary sensibility that we expect of a card-carrying intellectual and the scientific/mathematical outlook that is arguably the true glory of our civilization. That war goes on; and economics is on the front line. Or to be more precise, it is territory that the literati definitively lost to the nerds only about 30 years ago--and they want it back." There is plenty of room for the quantitative amongst us in the field of economics (to make a big impact).
It is trivially obvious that different areas require different set of talents: a great phenomenologist (I think of Sam Treiman for example) may not make a good string theorist, and vice versa. As Steve said, there is also the interest factor. By spending a year at the RIAS I am in fact, using myself as at test subject, experimenting with crossing over from the quantitative to the verbal.
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