alt Hacker NewsSuch a bad (AI written?) article. These kind of introduction to advanced topics feels like how to draw an owl tutorial where they spent so much time diving into what group is.
> The group of all rotations of a ball in space, known to mathematicians as SO(3), is a six-dimensional tangle of spheres and circles.
This is wrong. It's 3D, not 6D. In fact SO(3) is simple to visualize as movement of north pole to any point on the ball + rotation along that.
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That is very strange. It's certainly not an academic level explanation, but that's not what the magazine is for. But the blatant incorrect statement is beyond the pale. Dim(SO(N)) = N(N-1)/2. Thus SO(4) has dimension 6.
The “tangle of spheres and circles” is probably a reference to the Hopf fibration.
The quality of this article is par for the course for Quanta Magazine, sadly. I do not need to accuse the author of using AI to explain the data I'm seeing here. It feels like every submission on HN from Quanta garners the exact same discussion: The article is almost worthless because it presents complex ideas in such a cheap, dumbed-down, and imprecise way that it ceases to communicate anything interesting. (Interested readers can fare much better by reading other sources.) It's been this way for years. The phenomenon is almost Wolfram-Derangement-Syndrome-like.