Another weird one...just about everything in this category will be.
Jordan Ellenberg ends his Slate article, Does Gödel Matter?, with this:
His work was revolutionary, yes, but it was a revolution of the most unusual kind: one that abolished the constitution while leaving the material circumstances of the citizens more or less unchanged.
If you know what the incompleteness theorem says:
Given any system of axioms that produces no paradoxes, there exist statements about numbers which are true, but which cannot be proved using the given axioms.
you'll immediately understand its appeal to non-mathematicians of a mystical bent.
What is it about Gödel's theorem that so captures the imagination? Probably that its oversimplified plain-English form "There are true things which cannot be proved" is naturally appealing to anyone with a remotely romantic sensibility. Call it "the curse of the slogan": Any scientific result that can be approximated by an aphorism is ripe for misappropriation. The precise mathematical formulation that is Gödel's theorem doesn't really say "there are true things which cannot be proved" any more than Einstein's theory means "everything is relative, dude, it just depends on your point of view." And it certainly doesn't say anything directly about the world outside mathematics, though the physicist Roger Penrose does use the incompleteness theorem in making his controversial case for the role of quantum mechanics in human consciousness. Yet, Gödel is routinely deployed by people with antirationalist agendas as a stick to whack any offending piece of science that happens by. A typical recent article, "Why Evolutionary Theories Are Unbelievable," claims, "Basically, Gödel's theorems prove the Doctrine of Original Sin, the need for the sacrament of penance, and that there is a future eternity." If Gödel's theorems could prove that, he'd be even more important than Einstein and Heisenberg!
This is what happens when you take an approximation of an idea, apply it to your pet thesis and consider that proof enough. It's not proof at all.
Yes, I play in mathematical mode but I understand it as metaphor, as I do when dealing in physics mode. It gives you a pattern to direct your explorations, but if you knew how many of those patterns don't pan out, lead to unexpected destinations or are beyond human computability you'd feel awfully stupid trying to justify your mysticism with mathematics (Pythagoras not withstanding...he didn't justify his mysticism with mathematics, he expressed it that way...he recognized his mysticism in the math).
