W3C home > Mailing lists > Public > w3c-wai-ig@w3.org > January to March 1998

Re: Math on the web

From: David Poehlman <poehlman@clark.net>
Date: Thu, 19 Feb 1998 14:38:33 -0500 (EST)
To: Chris Maden <crism@ora.com>
cc: w3c-wai-ig@w3.org
Message-ID: <Pine.GSO.3.96.980219143806.1207C-100000@shell.clark.net>
lynx had fun with this see below.

   &nabla;  E = &rho; &epsilon; 0 &nabla;  E = - &part; &ApplyFunction;
   B &part; &ApplyFunction; t c 2 &InvisibleTimes; &nabla;  B = &part;
   &ApplyFunction; E &part; &ApplyFunction; t + j &epsilon; 0 &nabla;  B
   = 0 &nabla; E rho ep 0 &nabla;  E 0 B t c 2 &nabla;  B E t j ep 0
   &nabla;  B 0 E &rho; &epsilon; 0 E B t c 2 B E t j &epsilon; 0 B 0


On Thu, 19 Feb 1998, Chris Maden wrote:

> [T. V. Raman]
> > MathML has everything you need to do good audio renderings. I've
> > been part of the MathML working group since its inception and was an
> > active participant in the initial design phase--and have been a
> > passive observer since to make sure that the representation was
> > adequate for producing multiple presentations.
> 
> While I appreciate the effort that's gone into MathML, I think a
> static math document type is a mistake.  Moreover, MathML is
> schizophrenic about whether it wants to be presentational or
> semantic.
> 
> MathML's presentational markup can be accessible by voice or touch,
> but with a certain amount of ambiguity.  You know that something is
> superscripted, or that numbers are positioned one over the other, but
> you don't know if the superscript is an exponent or an isotope, or if
> the \over is a division or a combinatorial.  (Justify <mphantom> from
> an accessibility point of view.)
> 
> On the other hand, any static semantic DTD will be ignored by the
> scientific and mathematical communities, because new notation is often
> introduced to express new ideas.  Moreover, MathML's semantic elements
> are infix operators - Knuth thought the \over infix was a bad idea
> twenty years ago, and only justified it by technological limitations
> that no longer hold.
> 
> A better idea, IMO, is to promulgate a markup *methodology* instead of
> a DTD, whereby expressions and elements are homologous, and
> presentation is in the stylesheet where it belongs.  My markup method
> is similar to MathML's semantic <apply> and <relation> elements, but
> attempting to enumerate all applications and relations is doomed.
> Instead, authors can choose appropriate element type names; even
> without a stylesheet, the markup is readable, and the author can
> provide a stylesheet that allows for whatever new markup he wishes to
> introduce.
> 
> As an example, here are Maxwell's equations, in presentational MathML,
> semantic MathML, and my own proposal
> (<URL:http://www.oreilly.com/people/staff/crism/math/>):
> 
> <!-- presentational MathML -->
> <mrow>
>   <mrow>
>     <mi fontslant="plain">&nabla;</mi>
>     <mo>&middot;</mo>
>     <mi fontweight="bold" fontslant="plain">E</mi>
>   </mrow>
>   <mo>=</mo>
>   <mfrac>
>     <mi>&rho;</mi>
>     <msub>
>       <mi>&epsilon;</mi>
>       <mn>0</mn>
>     </msub>
>   </mfrac>
> </mrow>
> <mrow>
>   <mrow>
>     <mi fontslant="plain">&nabla;</mi>
>     <mo>&times;</mo>
>     <mi fontweight="bold" fontslant="plain">E</mi>
>   </mrow>
>   <mo>=</mo>
>   <mrow>
>     <mo>-</mo>
>     <mfrac>
>       <mrow>
>         <mi>&part;</mi>
>         <mo>&ApplyFunction;</mo>
>         <mi fontweight="bold" fontslant="plain">B</mi>
>       </mrow>
>       <mrow>
>         <mi>&part;</mi>
>         <mo>&ApplyFunction;</mo>
>         <mi>t</mi>
>       </mrow>
>     </mfrac>
>   </mrow>
> </mrow>
> <mrow>
>   <mrow>
>     <msup>
>       <mi>c</mi>
>       <mn>2</mn>
>     </msup>
>     <mo>&InvisibleTimes;</mo>
>     <mrow>
>       <mi fontslant="plain">&nabla;</mi>
>       <mo>&times;</mo>
>       <mi fontweight="bold" fontslant="plain">B</mi>
>     </mrow>
>   </mrow>
>   <mo>=</mo>
>   <mrow>
>     <mfrac>
>       <mrow>
>         <mi>&part;</mi>
>         <mo>&ApplyFunction;</mo>
>         <mi fontweight="bold" fontslant="plain">E</mi>
>       </mrow>
>       <mrow>
>         <mi>&part;</mi>
>         <mo>&ApplyFunction;</mo>
>         <mi>t</mi>
>       </mrow>
>     </mfrac>
>     <mo>+</mo>
>     <mfrac>
>       <mi>j</mi>
>       <msub>
>         <mi>&epsilon;</mi>
>         <mn>0</mn>
>       </msub>
>     </mfrac>
>   </mrow>
> </mrow>
> <mrow>
>   <mrow>
>     <mi fontslant="plain">&nabla;</mi>
>     <mo>&middot;</mo>
>     <mi fontweight="bold" fontslant="plain">B</mi>
>   </mrow>
>   <mo>=</mo>
>   <mn>0</mn>
> </mrow>
> 
> <!-- semantic MathML -->
> <!-- This is impure, as semantic MathML is lacking vector functions
>      for the inner or dot product, cross product, divergence, and
>      curl.  It also appears to lack a simple negation, in the
>      negative-number (as apposed to functional inverse) sense. -->
> <relation>
>   <eq/>
>   <mrow>
>     <ci type="vector">&nabla;</ci>
>     <mo>&middot;</mo?
>     <ci type="vector">E</ci>
>   </mrow>
>   <apply>
>     <divide/>
>     <ci>rho</ci>
>     <ci>
>       <msub>
>         <mi>ep</mi>
>         <mn>0</mn>
>       </msub>
>     </ci>
>   </apply>
> </relation>
> <relation>
>   <eq/>
>   <mrow>
>     <ci type="vector">&nabla;</ci>
>     <mo>&times;</mo>
>     <ci type="vector">E</ci>
>   </mrow>
>   <apply>
>     <minus/>
>     <cn>0</cn>
>     <apply>
>       <partialdiff/>
>       <ci type="vector">B</ci>
>       <bvar>
>         <ci>t</ci>
>       </bvar>
>     </apply>
>   </apply>
> </relation>
> <relation>
>   <eq/>
>   <apply>
>     <times/>
>     <apply>
>       <power/>
>       <ci>c</ci>
>       <cn>2</cn>
>     </apply>
>     <mrow>
>       <ci type="vector">&nabla;</ci>
>       <mo>&times;</mo>
>       <ci type="vector">B</ci>
>     </mrow>
>   </apply>
>   <apply>
>     <plus/>
>     <apply>
>       <partialdiff/>
>       <ci type="vector">E</ci>
>       <bvar>
>         <ci>t</ci>
>       </bvar>
>     </apply>
>     <apply>
>       <divide/>
>       <ci>j</ci>
>       <ci>
>         <msub>
>           <mi>ep</mi>
>           <mn>0</mn>
>         </msub>
>       </ci>
>     </apply>
>   </apply>
> </relation>
> <relation>
>   <eq/>
>   <mrow>
>     <ci type="vector">&nabla;</ci>
>     <mo>&middot;</mo>
>     <ci type="vector">B</ci>
>   </mrow>
>   <cn>0</cn>
> </relation>
> 
> <!-- my proposal -->
> <equations>
>   <equation> <!-- equation sets its children equal to each other -->
>     <divergence>
>       <vector>E</vector>
>     </divergence>
>     <divide> <!-- divide divides its first child by its second -->
>       <variable>&rho;</variable>
>       <indexed-variable>
> 	<variable>&epsilon;</variable>
> 	<constant>0</constant>
>       </indexed-variable>
>     </divide>
>   </equation>
>   <equation>
>     <curl>
>       <vector>E</vector>
>     </curl>
>     <negation>
>       <partial-differential> <!-- partial-differential is of the first
>                                   child with respect to the second -->
> 	<vector>B</vector>
> 	<variable>t</variable>
>       </partial-diffential>
>     </negation>
>   </equation>
>   <equation>
>     <multiply>
>       <exponent> <!-- exponent is first child to the power of the
>                       second -->
> 	<variable>c</variable>
> 	<constant>2</constant>
>       </exponent>
>       <curl>
> 	<vector>B</vector>
>       </curl>
>     </multiply>
>     <add>
>       <partial-differential>
> 	<vector>E</vector>
> 	<variable>t</variable>
>       </partial-differential>
>       <divide>
> 	<vector>j</vector>
> 	<indexed-variable>
> 	  <variable>&epsilon;</variable>
> 	  <constant>0</constant>
> 	</indexed-variable>
>       </divide>
>     </add>
>   </equation>
>   <equation>
>     <divergence>
>       <vector>B</vector>
>     </divergence>
>     <constant>0</constant>
>   </equation>
> </equations>
> 

Hands-On-Technolog(eye)s
touching the internet
voice: 1-(301) 949-7599
poehlman@clark.net
ftp://ftp.clark.net/pub/poehlman
http://www.clark.net/pub/poehlman
Received on Thursday, 19 February 1998 14:38:50 GMT

This archive was generated by hypermail 2.2.0+W3C-0.50 : Tuesday, 19 July 2011 18:13:39 GMT