[om] Re: [om-a] critique of OpenMath

David Carlisle davidc at nag.co.uk
Fri Jan 19 11:38:45 CET 2001

> Since it is done without reference to any pre-existing CDs, I assume it
> would not be acceptable to OMS. 

Not at all. OM is not a purely formal system in which it is planned to
build the whole of Mathematics from the ground up. It is possible to
model the logical frameworks that are needed for such a project in
OpenMath, and some are doing that. But if you want to work in a
particular area, you don't need to "build up" to that area from the
existing CD collection. Just make a CD that details the list of symbols
you are going to use, and their definitions (which might just be
reference to some text book, or your lecture notes, or whatever)

> and implicit references to the GR formulas on the other. Calling this
> semantics is a stretch.

yes I know (but that's what I mean't). But the point of an OpenMath CD
isn't (necessarily) to supply full semantics in the sense of a formal
system, but just a mechanism of recording what the function is, so it
may just say that the symbol "K" is K-theory. (rather than some other
variable that just happened to have got the letter K today). That's
pretty much all it need say. (It might be helpful to say more, eg to
give a reference to exactly what definition is being used etc, but it
doesn't have to).

> Zwillinger does not in his pseudoCD try to define
> cos() via a series expansion etc. 

All a CD need do is say that the symbol named "cos" really does denote
the cos function. It doesn't need to give any formal definition.
(although again it may or may not be helpful to do so)

> You may think so, but <emphasis> the syntax is so offensive that it
> is hard to believe anyone would ever use it </emphasis>.
> And I know that there are x,y,z tools to make it unnecessary to use
> it. So why is it thrust in our face all the time? 

Because at the current stage of the game it's mainly tool writers or
people with an interest in influencing such people, who are going to be
reading this stuff.  Currently people using OpenMath and MathML (and to
a lesser degree, XML in general) are currently people with an interest
in the issues surrounding such languages. But I don't think that that is
a reflection of the fact that we are using XML syntax.  I wouldn't be
any happier thrusting lisp in people's face.

> So far as I can tell the reason to use XML is to prevent anyone from 
> doing interesting things.

It's a point of view, and I have a lot of sympathy with your championing
of lisp as a language. But if you take a look at the current explosion
of internet use, would you really want to say that XML prevents
interesting things being done, and all the interesting stuff is
happening in lisp?

> How to attack the hard problem?  I don't know for sure, but I'm looking
> at MINSE and glyphd.  The author of this stuff (Ka-Ping Yee) is now
> a grad student at UC Berkeley.  He did this quite impressive stuff while
> an undergrad at Waterloo, and it seems to have been totally ignored.
> I ignored it myself, but then I was already somewhat disillusioned!
> Not as disillusioned as Ping, though.

Minse shares some of the problems with TeX, in that it it leads
Mathematics into a ghetto (even if it it seems like a nice cosy
environment). I want the Mathematics markup to be part of the mainstream
document markup not some arcane black box. Document markup today (at
least) means XML. the fact that there are 1001 valid complaints one may
make against XML don't particularly concern me. There are 100000001
complaints one could make against English as a language, but it still
serves its purpose if the people I'm communicating with speak that

I grew up with TeX. Everyone I know: my friends, my wife, everyone; they
all use TeX. However it has dawned on me that there are in fact people
out there who have mathematical documents that I might want to share and
that they will never use TeX (or any batch formatter with an explicit
markup language). A plugin to use TeX, or minse or any other non
standard language wouldn't help bridge this divide. But in using XML,
MathML and OpenMath do at least offer a hope. The MathML WG includes
old TeX hackers like myself, but also representatives from Microsoft
(and design science who make the equation editor used by Word) and
assorted other companies and institutions somewhere in the middle of
that spectrum. XML may be verbose, and apparently lacking in features
but if it is something on which everyone can agree then that agreement
is worthwhile I think. You can write mathematics in Microsoft Word
(MathType) save it as MathML, display it (natively, without any extra
plugin) in Mozilla or Amaya browsers, or typeset it (directly, without
using a conversion program) in TeX. I believe this is progress, and I
don't believe that much progress would have been made if a syntax other
than XML had been used. Given a browser with embedded XSL (Internet Explorer
and some builds of Mozilla) the benefits of MathML rendering apply
equally to OpenMath.

> I assume that's not really true if you can set a table with arrow
> symbols in it.

Depends on your diagrams. If they are highly rectangular, perhaps, but
if you end up having to curve long arrows round the back from one node
to another, MathML isn't really going to help.

> The approval process itself seems to be hidden.
There's a web page for it on the site.  
> One could post the CD under the "extra" category, which is currently
> empty suggesting that this is not a hot activity.

?? extra currently is everything we have.
The empty one is "public" as currently nothing has been "approved"
although hopefully the mathML CDs will be approved soon.

> I may be expressing my exasperation that this
> activity has taken so long to achieve what appears to
> me to be relatively little, while several other projects
> gallop past.

Perhaps it's a case of the hare and the tortoise....


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