Matt Calabrese wrote:
On 10/11/05, Deane Yang <deane_yang@yahoo.com> wrote:
What I'm more interested in learning is how you handle "composite quantities", which are obtained by multiplying and dividing existing units (like "meters/second"), as well as raising to a rational power (like the standard unit of volatility in finance, "1/square_root(years)".
Rational powers are handled with power functions and metafunctions, as I showed in later replies. However, I would like much more information regarding "volatility in finance." Up until now, I have seen absolutely no cases where non-derived unit classifications raised to a non-integer powers makes sense and have even talked about such situations with mathematicians. Looking back to the archives, I see people talking about fractional-powered base units being possible and speak of examples from other threads, but I can't seem to find such examples. An exact link would be very helpful. Right now I support fractional powers, but not when the operation yields fractional-powered base units.
sqrt(Hz) arises occasionally; the unit of noise is seconds^{1/2} = 1/sqrt(Hz), the unit of magnetic field noise is Tesla per sqrt(Hz), and so on. In fact, this sounds entirely analagous to the financial application Deane mentioned (but do they really define the volatility as the reciprocal of the noise, or is it something different?). But it only occurs in a very narrow specialization. I have never seen fractional base units occur anywhere else. Links seem surprisingly hard to come by, but if you look at the Wikipedia article for SQUID (the superconducting version, not the animal ;), you will see the noise level mentioned in units of femto-Tesla/sqrt(Hz). http://en.wikipedia.org/wiki/SQUID HTH, Ian