[om] MathML draft Notes available for review

[Andreas Strotmann]

Thanks, Stan!

A few things I noticed:

-- Aren't there a few Unicode code points for unit symbols? It might be 
useful to mention them eventually.

 -- one important distinction you missed when discussing possible 
sources of ambiguity of a unit or a dimension is that between absolute 
and relative uses. This is a fundamental distinction, namely that 
between the designation of a specific point in a continuum and the 
description of a relation between two such points.  A particular case in 
point is absolute temperature vs. temperature difference, where it is 
decisive, for example, in determining whether or not a conversion factor 
of 1/1.8 is an appropriate annotation for a Fahrenheit temperature.

 -- a matter of taste, certainly, but I'd much prefer the full 
lower-case name (kilo, micro(!)...) of the unit prefix used in a URI. In 
my cultural background, (ab-)using the roman letter 'u' to stand for the 
greek letter 'mu' makes very little sense, and the requirement of 
(multi-)capitalization is inconsistent with the all-lowercase stance of 
(much of) the rest of MathML. Besides, those URI's get long anyway, so I 
really don't see what you gain by using the  abbreviated form.

 -- in a related issue, is it possible to use your "own" unit prefixes 
('dozen', 'score', 'half' come to mind)?

 -- you write that a primary use of units is to annotate numbers. 
However, units are often used to annotate whole mathematical formulas,  
especially in physics, where a 'dimensions check' is routinely used as a 
useful sanity check for formulas (I think physicists use a complex 
dimension added in square brackets as a notation).

 -- In K-14 education, financial maths is proabably just as important as 
physics when it comes to providing practical examples. Monetary units 
play a fundamental role there, and they should be discussed either here 
or in an accompanying document.  For such units, however, the URI 
mechanism is probably woefully inadequate (try annotating the numbers in 
the recently published UN Human Development Index report).

 -- in particular the prefixes are used differently in this context 
(millions/Mio) -- and inconsistently cross-culturally to boot (billions 
vs. milliards)

 -- similar things are probably true of dates and times, with rather 
arcane distinctions between UTC and GMT being (perhaps literally) the 
smallest problem. Even today, there is any number of calendars being in 
active use in a large population, some of them lunar, some solar, some a 
mixture of both...

-- I'd like to see an example giving the correct MML representation of 
the position of the W3C headquarters at MIT in standard coordinates 
(degrees...seconds... latitude and longitude), both presentation and 
content markup.

-- dto. for the date and time of the opening ceremony for that august 
body :-)

-- another example of a unit that changed over time (I heard) is that of 
Mach (=speed of sound), which apparently was measured with an error at 
an embarassingly small digit early on, and which was corrected only 
embarassingly recently.

In summary, I'm not sure if a URI mechanism is really appropriate for 
capturing the potentially intricate way that units of all kinds are used 
and specified in mathematics. To me, it would make more sense to 
represent such a potentially complex concept as a compound MathML 
element, where separate ingredients are treated in separate 
sub-elements, and specifications can be arbitrarily vague ("Dollar") or 
specific ("annual average buying-power-equivalent of a constant 
1990-average Australian Dollar as determined from statistics collected 
by xyz based on a standardized shopping portfolio defined by zyx," for 
example -- again, try the UN HDI statistics...).

However, this again seems to be a case where a second edition cannot do 
anything more appropriate, because that would almost certainly involve 
the introduction of new MathML symbols (perhaps <unit/>, <dimension/>, 
<meter/>, <kilo/>...) and a description of their use along the lines of 
your essay.

 -- Andreas

Stan Devitt wrote:

> The following may be of interest to people
> on on this list:
>
> There has been a number of questions on the www-math at w3.org
> list over the last while on handling Units in MathML.
> Earlier, there has been questions on types, bound variables,
> and on the interaction with graphics.
>
> As part of its activities, the working group has been
> putting together "Notes" on several such topics including
> web services. These are really part of the on-going exercise
> of understanding how MathML can be used for certain
> activities and while these are not in their final form, we
> felt that they could benefit substantially at this point
> from the discussions that might arise from a wider review.
>
> For access to the draft copies of these notes, please go to
>
> http://www.w3.org/Math/Documents/Notes.
>
> The notes are all presented as  XHTML+MathML+SVG documents
> and use the universal style sheet. In particular, this may
> mean that parts of them do not show well in older browsers.
> Translations to other formats may occur later once they are
> closer to completion.
>
> Please mail comments and questions  to  www-math at w3.org
>
> Thanks  in advance for your assistance.
>
> Stan Devitt
> W3C Math Working Group
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