> I'm not enough of a cultural relativist to believe there's a civilization that cares more about the shape ∞ than the shape ◯.

Maybe these are "logarithmic" beings, as opposed to us "linear" beings? The lemniscate is based on geometric mean, which is basically multiplicative mean and/or mean in log-space -- as opposed to the additive mean in linear space.

If we assume we are linear beings good at intuitive addition but somewhat bad at intuitive multiplication, there could exist beings which live in log-space and whose minds are based on multiplication. Their circle would be the lemniscate.