Are people silly for not having coherent, non-contradictory beliefs, or is it silly to expect intelligent people to have global, universal, coherent beliefs about messy reality?
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The classical example in the first image there: What's the square root of a complex number? Note that for real numbers, there are two choices, eg sqrt(4) could = 2 or -2, but we have a convention of choosing the positive root.
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It turns out that if you try to extend that choice consistently to the complex plane, and travel around the origin, extending your definition locally in a consistent way, when you get back to the positive reals you get sqrt(4) = -2. This issue motivates like half of all math now.
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. Banned in Sweden. SubGenius, Zhuangist, white-hat troll. Defrocked mathematician. Brain problems. I/me.