
Boost : 
From: Matt Calabrese (rivorus_at_[hidden])
Date: 20051011 19:54:25
On 10/11/05, Deane Yang <deane_yang_at_[hidden]> 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 nonderived unit classifications raised to a noninteger powers
makes sense and have even talked about such situations with mathematicians.
Looking back to the archives, I see people talking about fractionalpowered
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
fractionalpowered 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
hypervolume in Ndimensional space, where N is the value of the exponent.
Continuing with "length" as an example, your_meters^2 represents a
hypervolume in 2 dimensional space (area), and your_meters^3 represents a
hypervolume 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 derivedclassifications are still
perfectly fine, just so long as the resultant unit type does not have
fractional powered base units in its makeup. Considering you apparently
have an example where fractionalpowered 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 fractionalpowered 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
Boost list run by bdawes at acm.org, gregod at cs.rpi.edu, cpdaniel at pacbell.net, john at johnmaddock.co.uk