Wednesday, November 01, 2006

still pondering a way to formulate the intuition regarding economics

Okay... one of the basic insights at play in what i want to talk about is that the assertion that \langle a | M | b \rangle can be interpreted as a probability amplitude was originally couched in a physical theory. If it had been couched strictly as a mathematical theory leading to a calculation of probability, then it would have been easier to spot the obvious question -- on what grounds do we have the right to interpret this calculation as a probability? In other words, how are we to interpret this calculation in terms of standard theories of probability? i will assert, here, that there are none -- that, in fact, this constitutes a third theory of probability -- neither frequentist nor Bayesian.

As such, it would seem to me to be one of the most highly tested theories of probability, ever. After all, people are verifying the correspondence between calculations -- grounded in this mathematics and with this probabilistic interpretation -- and physical predictions and observations out to 30+ decimal places.

If this is the case, could this mathematical engine be a better workhorse for other probabilistic calculations? For example, could we use this mathematics to model trading? Could we interpret price, for example, as the probability that when a trade is observed we will see a certain distribution of goods and services across the agents of the market place? Naively, is there a workable model of the following form?

|t \rangle -- information underlying a trader's ask
\langle s| -- information underlying a trader's bid
M -- observables associated with this trade
(\langle s | M | t \rangle)^2 -- price of the observed trade = probability that goods and services connected in this trade will be seen in a certain distribution given the information underlying the ask and bid.

(i acknowledge that i passed out putting the kids to bed and allowed midnight of Oct 31st to pass by before making this post.)


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