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From: "Mark Lundquist" <no.spam@getalife.com>
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Subject: Re: Dimensionality Checking (Ada 20XX)
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"Stephen Leake" <stephen.a.leake.1@gsfc.nasa.gov> wrote in message
news:ulmg8jz7r.fsf@gsfc.nasa.gov...

Stephe, thanks to you and also to Wilhelm Spickermann for jogging my memory.
Yes, of course... there always has to be an arbitrary reference point, to
correspond with a quantity of zero in the logarithmic unit (log(1) = 0; 1
what?)

>
> Actually, Decibels are the log of a _ratio_ of sound pressure levels:
>
> Db = 10 log P/P_0
>
> where P_0 is a reference sound pressure. I don't have my physics book
> handy (it's at home so my daughter can use it; wow!), so I don't
> remember what the standard reference is.
>
> > The astronomical magnitude scale is logarithmic with respect to
> > brightness.
>
> Again, log of a ratio, relative to some standard brightness.
>
> > pH is the negative log of the moles/L of H+.
>
> Hmm, that sounds right, but my chemistry book is at home also.

i.e. log of concentration, which is also a ratio (molarity in a given
solvent can also be expressed in w/w, ppm or whatever, which makes it more
obvious)

I get it now :-)...

Unit-safety/conversions would still have to support logarithmic units, but
it would define Log only for "dimensionless" in the sense we've been using
it (the sense that Nick, et al, finally got me to understand).

Cheers,
Mark