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You can also convert your logic model into something that can be viewed as an image completion problem, eg, by translating categorical diagrams into a adjacency
by zmgsabst 5y ago
You can also convert your logic model into something that can be viewed as an image completion problem, eg, by translating categorical diagrams into a adjacency matrix and “completing” a partial one. (Hopefully, but preliminary results are encouraging.)
So far, we’ve started publishing about shape types encoded that way and are hoping to get to Zn group models by the end of the year. (Work is done, but I’m a slow writer.)
https://www.zmgsabstract.com/whitepapers/shapes-have-operations https://www.zmgsabstract.com/whitepapers/shapes-have-operati...
- zozbot234 5y agoVery interesting work. Visual and diagrammatic reasoning are part of this problem, yes. It might turn out that some proofs that might be generally thought of as hard are actually "visually" justified, in a way that could even perhaps increase our power to justify mathematical statements. The extended paper Gowers links in his blogpost discusses one such case in depth, namely the well-known problem of whether a chessboard with two opposite corners removed can be tiled by two-square dominoes.