When I wrote the last post, I didn't realize at the time that I was running about a 102 F temperature, and would end up spending the next three days in bed with alternating bouts of chills and sweating, talking in my sleep - it was not one of the more pleasant weekends I've ever spent. While the underlying concept of measuring complexity is sound, I erred on the definition of entropy. Entropy is not a measure of the number of states in a given system configuration, but rather a measure of the change in the number of states in a configuration over time - in a non-self organizing system, the potential number of states increases, consequently becoming more disorganized (or more properly, converting into heat).
The concept describing the log of the number of states itself is the multiplicity of a system. Multiplicity isn't of course the only measure of complexity, but its a pretty useful one. Think of the traditional model of chaos - the conversion of laminar flow to turbulance. Typically there the first state is simple laminar flow - each water molecule flows in a straight line. As the flow moves faster, interactions with the surrounding media become more prominant, causing first a split into two streams, then four, then eight, until eventually there are thousands of such substreams, and the water becomes turbulant (this is the typical model described by Lorentz equations, by the way).
I have to wonder, though, if in fact there is some underlying connectivity between language (whether human based or artificial, as in the case of XML) and chaos theory, by this same modelling. Specifically, as the multiplicity of a document schema increases, so does the turbulence induced by that schema. I'm not sure what that the interpretation of that turbulence might be, though informational noise would be an obvious candidate. A simple schema is unambiguous - the specific meaning of a given aspect (element content or attribute value) is clearly defined, within its own constraints. However, as the number of aspects increase, their potential for coupling increases, for two properties to both be dependent upon a third (potentially undeclared) property, or two elements may in fact describe the same property in different and potentially conflicting, ways. Ambiguity is a form of informational noise.
Keeping this short (for me) tonight. I will be migrating in the near future to a new website, though it should still be accessible via http://www.metaphoricalweb.com. Until next time ...