MathML woes

[Ross Goeres]

[snip]
> I think Barbie summed it up best: "Math is hard."
>
> Even most people who are good with computers find math hard.  There are
> many programmers who have trouble thinking in recursive/dynamic
> programming terms, or who have trouble with the sort of simple 3D vector
> math found in games.  As such, searching for exponentials, or putting
> them on the web, just doesn't come up that often.  If it did, it would
> be a bigger part of HTML/wiki/whatever.
[snip]

The lack of a consistent mathematical representation for search engines
recently has hampered my ability to find references to the fact that taking the
arithmetic mean of ratios is a bad idea.  In turn, someone trying to
independently find references that support my theories of which of the infinite
number of means is applicable in a given situation is going to run into the
same problem.  This is only one example of the aggravation I experience from
the growing gap between computation and mathematics.

The separation of computer ?science? from mathematics is what prompted Norbert
Weiner to remark that computation is about insight, not numbers.  The
ASCII-only entry into this e-mail limits how I can represent the following
examples:

It is unfortunate that the factorial function is used as an example of
recursion because the integer stopping condition leads many (if not most)
computer scientists to labor under the misconception that the argument must be
an integer; e.g. some so-called ?scientific? calculators issue an error message
for 5.3! because the designers/programmers/engineers did not know that n! =
Gamma(n+1), so 5.3! = Gamma(6.3).  Many of these same ?scientific? calculators
issue error messages instead of calculating sqrt(-1)^sqrt(-1) -? a ?real?
number, BTW.

I suppose that there may be too few of us for whom a lack of MathML makes a
difference to constitute a ?market? to be worth ubiquitous implementation.  How
does www.backspaces.net handle mathematical representations?

--Ross


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[Owen Densmore]

> I suppose that there may be too few of us for whom a lack of MathML  
> makes a
> difference to constitute a ?market? to be worth ubiquitous  
> implementation.  How
> does www.backspaces.net handle mathematical representations?

Hi Ross, good to hear an interesting struggle on this topic.  Maybe  
we should start an archive on the "Math as a second class citizen on  
the Web" topic!  :)

I don't have mathematical notation on backspaces.net yet.  We've been  
discussing how to do it and naturally MathML is one of the candidates.

MathML does require users to soup up their browsers by adding a plug-
in and/or getting get a set of new fonts.  There are some annoyances  
as well, such as FireFox complaining that CMSY10 CMEX10 are not  
installed when the Mathematica suite from MIT *is* installed (and  
handles all the characters needed, I think!).  So getting MathML  
working, even if your browser supports it, can be tricky.

And naturaly, some browsers do not handle MathML yet.  Safari, and  
WebKit upon which it is built, apparently does not.
   http://lists.apple.com/archives/webcore-dev/2005/Jun/msg00010.html

Wikipedia, which has an extensive mathematics section, does not use  
MathML, alas.  It uses images instead, a common practice:
   http://en.wikipedia.org/wiki/Combinatorics

Here's an interesting article on Math support in HTML and includes a  
fairly complete overview of the problem space:
   http://www.cs.tut.fi/~jkorpela/math/
Note that MathML is only one of many and is considered weak.  The  
author says, for example:
   "If you ask me, the language hopelessly mixes structure and  
appearance."
He does, however, point to a good pro-MathML article:
   http://www.irt.org/articles/js081/index.htm

Carl pointed me to an excellent site, The N-Category Cafe, which  
makes good use of MathML:
   http://golem.ph.utexas.edu/category/

There are a few sites that do not use MathML, but do a reasonable job  
of building equations via HTML features like tables, sub, super,  
font, and so on.

Here's a stunt that uses fixed pitch fonts with LaTeX inspired syntax:
   http://www.w3.org/MarkUp/html3/maths.html
This is fairly old and presumably uses a preprocessor to implement  
the <MATH></MATH> tag, converting the LaTeX to <pre></pre> fixed  
pitch font usage.  Here is a similar discussion on ASCII Math notation:
   http://mathforum.org/typesetting/code.example.html
Finally, Karl's Calculus uses an interesting set of HTML and email  
stunts:
   http://www.karlscalculus.org/notation.html

     -- Owen

Owen Densmore   http://backspaces.net


On Dec 27, 2006, at 7:14 AM, Ross Goeres wrote:

>
> [snip]
>> I think Barbie summed it up best: "Math is hard."
>>
>> Even most people who are good with computers find math hard.  
>> There are
>> many programmers who have trouble thinking in recursive/dynamic
>> programming terms, or who have trouble with the sort of simple 3D  
>> vector
>> math found in games.  As such, searching for exponentials, or putting
>> them on the web, just doesn't come up that often.  If it did, it  
>> would
>> be a bigger part of HTML/wiki/whatever.
> [snip]
>
> The lack of a consistent mathematical representation for search  
> engines
> recently has hampered my ability to find references to the fact  
> that taking the
> arithmetic mean of ratios is a bad idea.  In turn, someone trying to
> independently find references that support my theories of which of  
> the infinite
> number of means is applicable in a given situation is going to run  
> into the
> same problem.  This is only one example of the aggravation I  
> experience from
> the growing gap between computation and mathematics.
>
> The separation of computer ?science? from mathematics is what  
> prompted Norbert
> Weiner to remark that computation is about insight, not numbers.  The
> ASCII-only entry into this e-mail limits how I can represent the  
> following
> examples:
>
> It is unfortunate that the factorial function is used as an example of
> recursion because the integer stopping condition leads many (if not  
> most)
> computer scientists to labor under the misconception that the  
> argument must be
> an integer; e.g. some so-called ?scientific? calculators issue an  
> error message
> for 5.3! because the designers/programmers/engineers did not know  
> that n! =
> Gamma(n+1), so 5.3! = Gamma(6.3).  Many of these same ?scientific?  
> calculators
> issue error messages instead of calculating sqrt(-1)^sqrt(-1) -? a  
> ?real?
> number, BTW.
>
> I suppose that there may be too few of us for whom a lack of MathML  
> makes a
> difference to constitute a ?market? to be worth ubiquitous  
> implementation.  How
> does www.backspaces.net handle mathematical representations?
>
> --Ross
>
>
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[Owen Densmore]

Oops .. I forgot another interesting stunt, ASCIIMathML, a JavaScript  
solution.

ASCIIMathML.js uses JavaScript to input a stylized (LaTeX) math  
stream which the browser then changes into math notation on the fly:
   http://www1.chapman.edu/~jipsen/mathml/asciimath.html

I'm pretty impressed with this.  It uses the de-facto standard,  
LaTeX, and converts it to reasonable math notation.  It could be made  
searchable, as long as you don't mind searching for LaTeX!  I've been  
wanting to learn TeX and this could be the 2-fer I'm looking for.

I'd like to know the downside of this notation .. otherwise, I'd say  
its a good candidate.

     -- Owen

Owen Densmore   http://backspaces.net

[Marcus G. Daniels-3]

Owen Densmore wrote:

>There are a few sites that do not use MathML, but do a reasonable job  
>of building equations via HTML features like tables, sub, super,  
>font, and so on.
>  
>
There's also the option of  LaTeX on the server side, generating bitmaps
in inline HTML.   Not a beautiful solution from a web technology point
of view, but the output would be portable, the feature set would be
robust, and, most importantly, it would look right.  MathML or
Mathematica source code, etc. could be provided as separate downloads.