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.