There's a formalism that we manipulate to reason, but we're always aided by geometric and spatial analogies. The Monster is a permutation group, which means it

There's a formalism that we manipulate to reason, but we're always aided by geometric and spatial analogies. The Monster is a permutation group, which means it moves things around, and we visualise 11 dimensions by considering 3 dimensional analogues or by projecting the shadow of 11-dimensional objects onto 2 or 3 dimensions.