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[dougsweetser at gmail.com (Doug)]

> What would they [complex numbers] offer over existing methods?

You what they say, time is money.  When I think about a quaternion in
spacetime (t, x, y, z), it can be broken up into four subgroups: three
complex numbers that share the same real (tx, ty, and tz) and just the
real number t.  By using real numbers and only real numbers, one can
do an vast amount of real analysis.  It is what should be the primary
and secondary focus: time dominates not only financial markets, but
everyday physics.

There are two cases of physics/finances crossover I am aware of.
First is the calculation of the value of options, the Black-Scholes
equation.  That involves geometric Brownian motion, and no, I don't
really know what that means, I just read it on the web.  These kinds
of equations are near impossible to deal with, so folks use a tool
from physics, the Monte Carlo method, another thing I know by its name
only.  Second, less well known, has to do with the distribution of
wealth in societies, which looks like it has two populations, one that
behaves like a hot gas (the masses), and the other for the well off -
>200k/yr in the US - that is more logarithmic (sorry, no references).

Quantum mechanics done over the real numbers is dead dull.  All that
fun interference stuff with the two slits requires complex numbers.
It is complete speculation on my part, but there may be financial
systems that behave like quantum systems.  Quantum systems are those
where space and time have some organized structure, where both matter.
 I can imagine there are large blocks of capital - central government
banks, the fortune top 100 companies - where it does matter where
there money is when modeling the motion of money.  On Wall Street, you
can bet on anything, so if able to spot an interference pattern based
on the organized movement of large blocks of money, then you could bet
on its volatility.

Of course this could just be BS.
doug

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