Re: Dimensionality Checking (Ada 20XX)

[Wilhelm Spickermann <wilhelm.spickermann@t-online.de>]

--On Mittwoch, Dezember 12, 2001 00:58:38 +0000 Mark Lundquist 
<mlundquist2@attbi.com> wrote:

>
> "Thomas Koenig" <Thomas.Koenig@online.de> wrote in message
> news:9v5pmr$ftq$1@mvmap66.ciw.uni-karlsruhe.de...
>>
>> The logarithm of a unit does not have significance.
>
> Decibels are the logarithm of something (actually, a multiple
> of a logarithm), and that something has units, e.g.
> (typically) sound pressure in micropascals (a pascal is 1
> N/m**2).

That something is a ratio of for instance currents or powers - a 
number without unit.

>
> The astronomical magnitude scale is logarithmic with respect
> to brightness.

It's a scaled logarithm of a *ratio* of brightnesses. The 
argument of the logarithm is a pure number.

>
> pH is the negative log of the moles/L of H+.

pH is the negative logarithm of the concentration of H+ divided 
by the concentration of H20 -- a pure number again.

>
> The Richter magnitude scale is logarithmic.

Logarithm of an energy ratio IIRC.

>
> Optical transmission density is logarithmic (don't know the
> units though).

I know nothing about that one... But there is no way to define 
taking the logarithm of something with a unit other than 1. Note 
that requiring the unit of something to be something predefined 
is just the obsolete way of taking a ratio.

Wilhelm