I think it's becoming obvious we need better metaphors for high-dimensional spaces than "it's like geometry except not at all". At the end of it all, we have

I think it's becoming obvious we need better metaphors for high-dimensional spaces than "it's like geometry except not at all". At the end of it all, we have a big list of numbers (a vector) where each position in the list (component/dimension) implies a specific "meaning" that we don't know. We also have a variety of well-known mathematical operations we can do on those lists, the effects of which may depend on the number of positions present (the dimensionality of the vector space). The challenge would be to find a good intuitive model to explain those effects (and ideally a way to visualise the lists that preserves the effects). Saying "it's an 1800 dimensional sphere" satisfies neither of those properties: You cannot visualise it and even if you want to think about it theoretically, it has none of the intuitive properties of a 2D or 3D sphere.