XML and entropy, again

[Michael Champion <michaelc.champion@gmail.com>]

We had a  classically xml-devish thread back in October about the
implications of Shannon's information theory for XML.  I must say I
didn't understand  much of that thread, but Kurt Cagle has an
intriguing entry in his weblog
http://metaphoricalweb.blogspot.com/2004/12/xml-and-entropy.html that
puts forth some ideas that seem both interesting and somewhat
practical.

"Entropy is important because it can better clarify the domain at
which it is best to work with a given document. XQuery I think
provides a good case in point here. XQuery supports XPath, and so it
has some of the advantages that XSLT has, but it's not really all that
useful for dealing with documents -- converting a DocBook document
into WordML or vice versa would be impossible in XQuery, but for many
business schemas with comparatively low entropies, XSLT is definitely
overkill."

 I for one like the idea of his interpretation of the entropy of an
XML document in terms of the number of discrete states that its
(implicit or explicit?) schema allows.  I also like the idea that
certain tools are more or less appropriate depending on the entropy of
the documents being processed -- perhaps it's something like SAX and
DOM for low entropy, XQuery for medium entropy, and XSLT for high
entropy (very document-ish) documents.   I wonder, however, about the
assertions made for the appropriateness of XQuery and XSLT, e.g.
"converting a DocBook document into WordML or vice versa would be
impossible in XQuery".  It gets back into our XSLT vs XQuery
permathread -- do the two have radically different capabilities with
respect to handling recursive structures and/or recursive alorithms,
or are they more or less different syntaxes for the same capabilities?

Thoughts, anyone?   Sorry to reopen the permathread, but I think
Kurt's approach might lead to a more focused and possibly conclusive
discussion,  Maybe wwe can all can trade ideas about this with our
relatives over the holidays :-)