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polymathwannabe comments on Open Thread - Aug 24 - Aug 30 - Less Wrong
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There is a difference between things that are impossible per se and things we think are impossible. Logical impossibilities are impossible regardless of anyone's opinion. Good luck with that square circle survey.
Square circles exist in the Manhattan metric.
It is not really interesting that a circle can be X if you first change the definition of circle.
It's not arbitrary redefinition, though. like the old joke about "calling a tail a leg doesn't make it one"; it's actually a consistent geometry.