I've got a very non-statistics math background, but what you say suggests that there would be a nice way to visualize standard deviations two-dimensionally (sin

I've got a very non-statistics math background, but what you say suggests that there would be a nice way to visualize standard deviations two-dimensionally (since they arise from an L_2 norm), and that it's the one-dimensional "bell curve cross-section width" pictures that confuse people.