I guess what bothers me is that visualizations are supposed to leverage our intuition and gut feeling. Like in Geometry, the teacher tell you that when the line

I guess what bothers me is that visualizations are supposed to leverage our intuition and gut feeling. Like in Geometry, the teacher tell you that when the lines are parallel, the angels on on a bisecting line are the same. You "see" it on the image and it immediately makes sense. When you have a weird new operation that doesn't behave in any relatable way then the visualization is effectively useless. I explained a bit further here how you can completely skip this pseduo-2D stuff and things remain very clear: https://news.ycombinator.com/item?id=27246386 https://news.ycombinator.com/item?id=27246386 Maybe the 2D plane is useful in other contexts and it's an analogy that's worth internalizing - I don't wanna knock it entirely - but in the case of Fourier Transform it's a high cognitive load for something that's actually not that important and easy demonstrated from the roots of unity. And the net effect is that the stuff that can't be visualized, and that is arguably more important, is glossed over b/c it's not pretty enough