I agree with what you and the parent are saying here, and I suppose I didn’t well enough communicate my meaning. To clarify, I am focusing on the naive represen

I agree with what you and the parent are saying here, and I suppose I didn’t well enough communicate my meaning. To clarify, I am focusing on the naive representations, which I find people rely on too much. It is easy to learn lower dimensions naively and feel like they make sense, but you won’t bridge that understanding to higher dimensions as seamlessly as going from a point to a line to a circle to a sphere, etc. And for the pictorial representations which do exist, implicit in understanding them is the symbolic information. Conversely, you can understand common naive representations without an implicit understanding of the formalism. For example, we all know what a circle is before we know about irrational numbers, but it’s silly to try and understand a 5-cell or a tesseract without a broader understanding of k-dimensional space. It’s precisely that naive intuition that doesn’t generalize well. In other words, my point more simply was caution: use pictures, but don’t replace symbolic formalism with them, just use them augment your understanding once you’ve at least sort of got it.