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rtolsma

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Another cute way I thought for deriving e^ax as the derivative operator eigenfunctions, after seeing the Functions as Vectors post today

strongly recommend you check out the built in Swift APIs for screen capture and OCR. They’re heavily optimized for energy usage, and allow much finer grained controls on what apps are white/blacklisted for privacy

Yea I think one reason to restrict to spheres is because the voting function takes as input the relative preferences (like in [0,1]^n how does all 0s differ from all 1s), which implies the vectors should be normalized

Yes, I saw that! Inspired me to look at the original paper.

The video takes a slightly different approach from the paper and uses a retraction on the möbius strip to its boundary as a contradiction.

That particular argument doesn’t generalize as well in higher dimensions (in particular, the symmetric product won't always have a boundary to retract to), so I followed the original paper’s one instead. I'll add a link to that video as well

The High Dimensional Probability textbook is one of my all time favorites. The elegant mix of probability, geometry, and linear algebra can generate some really non-intuitive insights. The intuitions developed are also pretty useful for reasoning about modeling in a lot of applications