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. For instance, I allow the expression power< 1, 2 >( your_meters_quantity * your_meters_quantity ) // where power< 1,2 > denotes a power of 1/2 However, I have chosen to disallow: power< 1, 2 >( your_meters ) since it does not seem to ever make sense -- for any base classification type, not just length. In an attempt to rationalize why this was the case, I noticed that a base classification raised to a power could be looked at as a hyper-volume in N-dimensional space, where N is the value of the exponent. Continuing with "length" as an example, your_meters^2 represents a hyper-volume in 2 dimensional space (area), and your_meters^3 represents a hyper-volume in 3 dimensional space (volume), and your_meters^-3 could be looked at as units per volume, etc. This model makes sense for all integer powers, yet not for rational powers for base units, as it would imply a concept of fractions of a dimension, which intuitively I do not believe exist, though I am admittedly not a mathematician and my model could be too specific. Keep in mind that rational powered derived-classifications are still perfectly fine, just so long as the resultant unit type does not have fractional powered base units in its make-up. Considering you apparently have an example where fractional-powered years is used (years being a base unit of time), I suppose my logic could be flawed, though I haven't heard of your example and googling around doesn't appear to be helping either. If you can, would you link to information regarding such fractional-powered base classifications? It's easy to go back and allow them in my library, as my restriction is mostly just superficial, but I won't do so until I see a place in practice where such operations actually make sense. Thanks in advance. -- -Matt Calabrese