Humans and Mother Nature don't always act the same.

Under topics such as ThereAreNoTypes there seems to be a recurring issue of applying math concepts to non-math concepts - RealWorldEntities.  For example, in "traditional" math you can safely say things like "x will always be a subset of y" and rely on that assumption forever and ever. One does not have to consider the cost of changing that assumption later. But with real-world things that is not always the case. Marketers, managers, lawyers, law-makers, ''etc.'' can get pretty creative (in a good and bad sense) and turn the tables on previously-established concepts. 

Of itself that doesn't mean math is out of luck on such things, see NonMonotonicLogic for one example of a system designed to deal with such things. There aren't inherent limits on what can be analyzed by mathematics, because it is just a way of formalizing how we think, in a way that allows rigorous conclusions to be drawn.

Further, there are often multiple ways to model something with math. A given approach may make an interesting mental exercise, but not necessarily be the final word.

Changing technology is another monkey-wrench: before we had PDA's as one device and a cell-phone as another. Now a given device can be both. If there were laws governing cell-phones before, now the issue of whether cell-phone laws should cover a dual device pops up. An actual case of this type of thing is Canada courts trying to make a distinction between voice phone lines and data phone lines. The lines are so blurred now that Canada is thinking about overhauling huge chunks of its telephone laws.

A similar thing is happening in the US; the traditional telcos are arguing that various VoiceOverIp services are in fact telephone companies, and should be taxed and regulated as such.  The VoiceOverIp companies disagree, of course.

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See ClassificationProblem
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CategoryMath