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From: Ian McCulloch (ianmcc_at_[hidden])
Date: 2005-10-11 20:18:11

Matt Calabrese wrote:

> 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 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).


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