Rants: August 2008 Archives

I knew about MathML for some time now, but I never thought it was this bad. See, MathML is an XML based markup language used to describe in a standards compliant manner mathematical notations. In principle this is a cool thing, until I saw a real world example from Wolfram Research:

<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <msqrt> <mi> z </mi> </msqrt> <mo> &#10869; </mo> <mrow> <munderover> <mo> &#8721; </mo> <mrow> <mi> k </mi> <mo> = </mo> <mn> 0 </mn> </mrow> <mi> &#8734; </mi> </munderover> <mrow> <semantics> <msub> <mrow> <mo> ( </mo> <mrow> <mo> - </mo> <mfrac> <mn> 1 </mn> <mn> 2 </mn> </mfrac> </mrow> <mo> ) </mo> </mrow> <mi> k </mi> </msub> <annotation encoding='Mathematica'> TagBox[SubscriptBox[RowBox[List[&quot;(&quot;, RowBox[List[&quot;-&quot;, FractionBox[&quot;1&quot;, &quot;2&quot;]]], &quot;)&quot;]], &quot;k&quot;], Pochhammer] </annotation> </semantics> <mo> &#8290; </mo> <mfrac> <msup> <mrow> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> - </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mi> k </mi> </msup> <mrow> <mi> k </mi> <mo> ! </mo> </mrow> </mfrac> </mrow> </mrow> </mrow> <mo> /; </mo> <mrow> <mrow> <semantics> <mo> &#10072; </mo> <annotation encoding='Mathematica'> &quot;\[LeftBracketingBar]&quot; </annotation> </semantics> <mrow> <mi> z </mi> <mo> - </mo> <mn> 1 </mn> </mrow> <semantics> <mo> &#10072; </mo> <annotation encoding='Mathematica'> &quot;\[RightBracketingBar]&quot; </annotation> </semantics> </mrow> <mo> &lt; </mo> <mn> 1 </mn> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <eq /> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <sum /> <bvar> <ci> k </ci> </bvar> <lowlimit> <cn type='integer'> 0 </cn> </lowlimit> <uplimit> <infinity /> </uplimit> <apply> <times /> <apply> <ci> Pochhammer </ci> <apply> <times /> <cn type='integer'> -1 </cn> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <ci> k </ci> </apply> <apply> <times /> <apply> <power /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> z </ci> </apply> </apply> <ci> k </ci> </apply> <apply> <power /> <apply> <factorial /> <ci> k </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> <apply> <lt /> <apply> <abs /> <apply> <plus /> <ci> z </ci> <cn type='integer'> -1 </cn> </apply> </apply> <cn type='integer'> 1 </cn> </apply> </apply> </annotation-xml> </semantics> </math>

It is awfully complex and verbose! This just reiterates what I held to be true for a long time now - XML is being abused. It is great for moving hierarchical data between disparate systems - even non-hierarchical data if you focus on the interoperability and compatibility it facilitates, however using it as RDBMS storage solutions or this kind of hyper verbose markup is down right a waste of space and time. When will people learn that efficiency is important?

Look at this well known equation (all from the Wikipedia entry):

In LaTeX it looks like this:

x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}

Terse, huh?

Look at MathML:

<math xmlns="http://www.w3.org/1998/Math/MathML">
 <mi>x</mi>
 <mo>=</mo>
 <mfrac>
  <mrow>
   <mrow>
    <mo>-</mo>
    <mi>b</mi>
   </mrow>
   <mo>&PlusMinus;</mo>
   <msqrt>
    <msup>
     <mi>b</mi>
     <mn>2</mn>
    </msup>
    <mo>-</mo>
    <mrow>
     <mn>4</mn>
     <mo>&InvisibleTimes;</mo>
     <mi>a</mi>
     <mo>&InvisibleTimes;</mo>
     <mi>c</mi>
    </mrow>
   </msqrt>
  </mrow>
  <mrow>
   <mn>2</mn>
   <mo>&InvisibleTimes;</mo>
   <mi>a</mi>
  </mrow>
 </mfrac>
</math>

It is disgusting...