alcolade's comments

Thanks for clarifying. It was unclear to me what they meant by "topologically equivalent". In other words, I didn't see what the problem was...

Another human analogy could be: you take a photo from every art show and museum, and use those for reference as you paint.

I'm not an expert, but in my experience working with CUDA/OpenCL/OpenGL, GPU latency usually comes down to data transfer and reduction operations (like max or sum). If you are okay with some kind of double-buffering, you can usually "hide" those latencies.

I see, yes I usually resort to this when I can't build it myself.

Thank you for your suggestions

Can you suggest where those artifacts should be stored?

I often have projects that require third party libraries, and perhaps I change or upgrade the version of the library I use during the history of my project. I would like to have everything versioned together so if I check out a certain commit, I know that everything will work.

The downside of this is that my git repo will get bloated over time if I keep changing large dlls. I've sometimes made submodules to mitigate this problem. Git lfs also seemed like a good solution, but your comment makes me feel like I'm doing something bad here...

You need to also count "points at infinity" in the "projective" plane. So the "projectivized" equations are actually X^2 + Y^2 = 1Z, and X^2 + Y^2 = 4Z. The intuition is similar to how 2 parallel lines will meet at the horizion (infinity).

I was thinking of the Riemann curvature tensor which is just some measure of curvature at each point. If the bug were at some point of S^2 he would notice the curvature.

Of course, this is assuming S^2 is getting its geometry from a certain embedding into R^3 that comes to mind. You could define different Riemann curvature tensors over S^2 that may have zero curvature in certain places, like squishing a balloon against a flat table for example.

I guess my point was that topology and curvature are different things (like you pointed out with your comment about RP^2), and saying that "a sphere looks flat locally" is missing the point!

Also, it didn't occur to me that this notion of curvature doesn't make sense in 1d, i.e. for S^1 like you said.

If the bug were truly mathematical, he would notice the curvature of S^1 and S^2 without walking around (since curvature is defined at each point), but that is obviously very pedantic of me and shows why I wouldn't write an article nearly as interesting as this one.