1. Yes, it’s a great video, but it’s [unfortunately] not me! It’s from 3Blue1Brown.com

2. You can make neat computer vision algorithm with tauquernions.

-m

]]>In a recent work of mine I described something very similar to the amodal / modal divide. I just called it “world-sheet” and “texture”. The world-sheet is the depth-map that results from network of subjective measurements of distance that we entertain in our mind. Texture is the modal-specific qualia patterns (e.g. in visual experience these would be mongrels) that enrich the information content and experiential quality of the models we hold in the world-sheet.

(If you are interested, here is the article in which I talked about this: https://qualiacomputing.com/2016/12/12/the-hyperbolic-geometry-of-dmt-experiences/)

]]>There are plenty of other areas of math out there, say topology, number theory, probability, category theory, to name a few broad fields. You seem to say that mathematics is about discovering the structure of our mental representations. Does that mean category theory is not ‘true’ math? If so, then what you mean by math is not what anyone else means by math.

And furthermore we can write down plenty of perfectly self-consistent geometrical theory that doesn’t necessarily correspond to either the physical world or to perception. You present some theory about some particular projections that you think match our visual perception, but you could easily write other projections (say, replace the sphere with an ellipsoid). And at most one of them would truly represent perception. Would you say the other one wasn’t ‘true’?

It makes much more sense to think of all the theories as ‘true’ math, and say that the question you’re interested in is a scientific question about what math describes the structure of your thoughts, rather than being in any sense about which math is ‘true’.

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