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> But surely there is a lot of interesting math that is concerned with the connectedness of the input and output spaces themselves, in context of there still ex
by zmgsabst 3y ago
> But surely there is a lot of interesting math that is concerned with the connectedness of the input and output spaces themselves, in context of there still existing a mapping between the input and output.
Topology.
Topology studies neighborhoods in your space and how they relate to things like functions, limits, etc.
Since you brought up images:
https://en.wikipedia.org/wiki/Digital_topology https://en.wikipedia.org/wiki/Digital_topology
And data science:
https://en.wikipedia.org/wiki/Topological_data_analysis https://en.wikipedia.org/wiki/Topological_data_analysis
- GolDDranks 3y agoYeah, topology seems to have a lot to do with it! However, I hesitated to jump into that conclusion, because my impression of topology is that it's concerned of "whether" something is connected (and often about the directedness of surfaces/spaces), because topology allows "stretchiness" of its study matter. The connections between things are then kind of binary things - either something is connected or not. However, in the world of "connected dimensions", there seems to be degrees of connectedness. Linear correlation being from the simplest end, but more generally, shared entropy. So it feels like just "topology" doesn't quite catch the field and its pecularities. Thanks for the links!! Much appreciated.