For something I'm writing  I'm interested in examples of bad arguments which involve the application of mathematical theorems in nonmathematical contexts. E.G. folks who make theological arguments based on (what they take to be) Godel's theorem, or Bayesian arguments for creationism. (If necessary I'm willing to extend the net to physics, to include bad applications of the second law of thermodynamics or the Uncertainty Principle, if you know any really amusing ones.)

3$\begingroup$ Do you want examples where they use the theorem correctly, but the realworld context violates one of the assumptions (e.g., ignoring that the Earth is not thermodynamically a closed system), or that they just misunderstand the theorem itself? $\endgroup$ – Scott McKuen Apr 12 '11 at 14:59

45$\begingroup$ Does "applying the BanachTarski paradox to an orange" qualify? $\endgroup$ – Someone Apr 12 '11 at 15:14

11$\begingroup$ Rather than Gödel's incompleteness theorem applied to theological arguments, there is Gödel's ontological proof of the existence of God (en.wikipedia.org/wiki/Gödel's_ontological_proof), which is more likely to be misapplied... $\endgroup$ – godelian Apr 12 '11 at 15:19

19$\begingroup$ I feel like most people misapply Godel's incompleteness theorem. $\endgroup$ – Sean Tilson Apr 12 '11 at 15:25

9$\begingroup$ Perhaps it was my being ignorant of algebraic topology as a kid, but splitting my sandwich with my brother did not seem to be fair! $\endgroup$ – F Zaldivar Apr 13 '11 at 0:45
I just came across the paper BAKSNEPPEN MODELS FOR THE EVOLUTION OF STRUCTURED KNOWLEDGE in SOCIETY. INTEGRATION. EDUCATION Proceedings of the International Scientific Conference.
The abstract states:
Models of biological evolution can help to understand many social and economical phenomena where the search for optimality is hindered by voluntary or random competition. BakSneppen is one of the most significant models because it balances at best explication power and simplicity. Unlike cellular automata models, BakSneppen models join locality and globality. The authors try to reread these models in the framework of mathematics, where, despite its high developped structure, knowledge waves can hinder comprehension both of pupils and of scholars.