[om] Units example usage ?

Andreas Strotmann Strotmann at rrz.uni-koeln.de
Wed Apr 23 15:49:31 CEST 2003

```Well - that's indeed a difficult question.

I once requested unit symbols for MathML, and was refused with the
argument that multiplication with the meter symbol was all that was
needed, so that person favoured that one of your solutions.

However, zero meters is not the same as zero degrees Fahrenheit nor the
same as zero Kelvin, but multiplying anything with zero gives zero.
Using multiplicaton by units is therefore questionable.

Note also that frequently, dimensions can be either absolute or relative
(e.g. time and temperature -- Jan. 1, 2001, 00:00:01.001 GMT vs. 5
seconds; or 20 Kelvin as absolute temperature vs a temperature
difference of 20K), determining the operations that can legally be
performed on them (e.g. in a sum, at most one unit may be absolute).

Not just for this reason it is always good to use both the unit and the
dimension.

Note also that units are not just physical in nature.  The monetary
units are actually notoriously complicated to calculate with and
represent, and to specify: consider the 'old' Englisch system of pounds,
pence, shillings...; consider the need to specify time and date, and
sometimes the place, along with a monetary unit (e.g. 'in adjusted 1861
US-Dollars in the Northern states.')  Historians and economists use
these all the time and are used to it, but physicists need to consider
these aspects as well when considering historical findings (I believe I
heard that the actual length of an 'inch' was redefined to a metrically
exact number in fairly recent history, for example, and that the speed
of sound (and hence, the unit Mach) had to be corrected significantly
quite recently, too).  Which brings us to an even more complex problem
of calendars and 'absolute times'...

Personally, I would therefore prefer two possible solutions that you did
not mention.

a) Consider units as type specifications (0 of unit meters of dimension

b) use a generic function "unit" as follows (for example)

unit(0, meter)
unit(2.5,
dimension(quotient(Kelvin,second),
quotient(relative(temperature),relative(time)))

Both solutions (as far as I recall) still require an additional CD to be
introduced that contains the generic symbols (attribute names in a,
'unit' and 'dimension' in b) required for the solution.

A CD of the latter type should also include constructors for compound
units and dimensions (multiplication, integer powering, log, exp,
division, absolute, relative, absolute_with_named_zero, addition). Since
these obey special laws (e.g., the dimension length+length=length), they
should be available as distinct symbols.

(Just some quick thoughts.)

-- Andreas Strotmann

Paul Libbrecht wrote:
>
> Hi OpenMathers,
>
> We were about to use the units symbols until... I faced the fact that I
> wouldn't know how to use, say, the "meter" symbol.
>
> Should the be a predicate applied to (probably a number) the length
> amount ?
> Should I use a multiplication (not really elegant) ?
>
> Thanks.
>
> Paul
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