RE: Research diaries #15: Going down rabbit holes

With me, what usually gets me rabbit hole-ing is when something sounds quite absurd or counter-intuitive. Like 'there are larger and smaller infinities' or 'the circle has been squared in taxicab geometry' or some such.

I find that these are often matters that can be solved or approached even with little mathematical knowledge. Like, in the latter example, it's quite clear to me that there was a choice involved: either treat the taxicab example as proof that our definition of 'circle' is incomplete, or else accept that in some geometries the circle can be squared (thus avoiding the embarrassment of admitting we've been using an incomplete definition for eons with whatever consequences that might have for the rest of math).