I am a little late to this party but Arnold asks for a popularization of the Impossibility Theorem. Mine is as follows

You can have a government that is

  1. Rational
  2. Democratic
  3. Free

Choose two.

I like to say it that way because it sounds cute and is therefore more easily remembered. Indeed, you can’t really have a government that is rational and democratic unless you are willing to accept some really weird forms of democracy.

Moreover, it doesn’t just apply to governments but groups in general.

I used to say that this proved that groups were fundamentally different than individuals, because unlike an individual a group can’t really be said to “want” anything. It depends on how you ask the question.

Well, it turns out that it depends on how you ask individuals the question as well. Which shouldn’t come as a surprise given, what looks to me like, increasing evidence that the mind really is a bunch of independent modules.