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RE: maden semantic proposal Re: Math on the web

From: Kasday, Leonard R (Len), ALTEC <kasday@att.com>
Date: Thu, 19 Feb 1998 16:16:26 -0500
Message-ID: <c=US%a=_%p=ATT%l=NJC240PO04-980219211626Z-8819@njb140bh3.EMS.ATT.COM>
To: "'w3c-wai-ig@w3.org'" <w3c-wai-ig@w3.org>
I'm a newbie to audio renderings of math.

But I've got to say, in support of Chris Maden's proposal for a semantic
math markup, philosophically speaking,  it indeed splits content from
presentation.

Plus I find it more readable than the others.    (Although this may not
be completely fair; I'm looking at the screen, not listening to it; and
I've already worked with Maxwell's equations)

Furthermore, by using a  suitable stylesheet, this semantic markup could
be translated into either MathML markup for people who prefer those
representations.  I'm not speaking of CSS stylesheets of course: you'd
need something with the power of DSSSL
(http://csg.uwaterloo.ca/~dmg/dsssl/tutorial/tutorial.html); maybe XSL.

Len

All opinions expressed here are my own, not necessarily those of my
employer.
=============================================================
kasday@att.com         phone 732 949 2693

Leonard R. Kasday
Room 1J-316A
AT&T Laboratories
101 Crawfords Corner Rd.
Holmdel NJ 07733


Chris Maden wrote:

>----------
>From: 	Chris Maden[SMTP:crism@ora.com]
>Sent: 	Thursday, February 19, 1998 2:19 PM
>To: 	w3c-wai-ig@w3.org
>Subject: 	maden semantic proposal Re: Math on the web
>
>[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>
>
>
>
Received on Thursday, 19 February 1998 16:16:26 GMT

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