In principle, we could do the
> same computations we do with electronic computers using lines on sand
> or with sticks or stones. Well, provided space, time, the mechanics
> of doing so many computations weren't constraints. Math is language
> (which is to say, a lot of congealed human labor) but incredibly
> economized. So, math is power. The more math we talk (to ourselves
> and with others), the more streamlined in form and enriched in content
> of people's communication become. If it were up to me to design the
> curriculum of kindergartens and elementary schools, game theory and
> other abstract math tools would be built in from the get-go.
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Two quickies:
First, there's been a substantive backlash on the triviality argument regarding computation that you allude to above*
Second, as Michael Mandel pointed out a few years ago in a piece in Business Week in 2005 which sort of stuck in my craw, all kinds of differently envisaged outcomes to the same event could be rendered rationally consistent using game theory:
http://www.businessweek.com/bwdaily/dnflash/oct2005/nf20051011_3028_db084.htm
There's been quite a bit of discussion about game theory's limits/problems by epistemologists, especially with respect to the issues pointed out by Edmund Gettier and Jaako Hintikka. The behavioral economics crowd has also pointed out lots of interesting stuff.
*If interested, see "Godel, Putnam and Functionalism" by Jeff Buechner, esp. chapter 3. Devastating counterarguments to in principle arguments regarding computation are also taken up by Brian Rotman in "Ad Infinitum."
Ian