From: Deane Yang (deane_yang_at_[hidden])
Date: 2006-06-08 10:11:07
Leland Brown wrote:
> I suspect (though someone may well correct me!) that fractional dimensions
> are never strictly necessary, in the sense that the formulas can probably
> be rewritten to avoid them.
In earlier discussions, there were a few examples of fractional
dimensions provided. The one I am familiar with is called "volatility"
in finance but probably has a name like "heat conductance" or "diffusion
coefficient" in physics. It is the coefficient c in the heat equation:
u_t = c^2 u_xx
You can see that c has units of length/sqrt(time). You can argue that
people should use c^2 directly instead of c (this is analogous to using
the variance of a Gaussian in place of the standard deviation), but it
*is* very useful to be able to work with c itself.