The twinkle should become a bright LED flashlight at the very least.
If you dig out the paper I submitted to AGI-2016, you see a extremely terse outline of reasoning leading to a geometrical object as a limit form of assumptions described in earlier AGI-20xx and BICA-20xx papers. That manifold has been well studied by the mathematical community. Its how you think the hypergraphs are organized that I believe is the key. A couple of years ago, I mentioned the use of algebraic topology in this AGI context to my old dissertation advisor, who promptly went to NYU's Bobst library to check out the techniques I was suggesting. At our next meeting, he was saying "that stuff is unintelligible". Meanwhile, WS would like to see a chapter of the book. Cheers, Gene On 3/16/2017 6:11 AM, Ben Goertzel wrote:
Just for general bemusement ... here are some recent rough outlines I wrote indicating what I think are some interesting research directions related to hypergraphs, category theory and AI ... https://arxiv.org/abs/1703.04361 https://arxiv.org/abs/1703.04382 https://arxiv.org/abs/1703.04368 I am also musing on this paper http://geometry.caltech.edu/pubs/DKT05.pdf and wondering if we can somehow use it to do some interesting differential geometry on hypergraphs. A weighted hypergraph is sort of like a field on a simplicial complex, right? A weighted, typed hypergraph is sort of like a vector field on a simplicial complex. So maybe differential geometry and algebraic topology etc. on simplicial complexes can tell us something about weighted labeled hypergraphs, which in OpenCog are used as the core cognitive representation. But this is just a twinkle in my eye at the moment... -- Ben
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