I've thought about this a lot, it's my goto "one day I'll write a book about this".
I frame the problem slightly different (heh):
Different disciplines, branching out, will (or so says my hypothesis) discover the same topologies, but express them differently due to different scopes (perspective, dimensionality, DSLs [...]).
What I'm thinking about is: how can we parametrize the manifestations of these scopes, and, ubiquitously, reverse-engineer them, thus linking all the systems?
Then: which systems are topologically identical? If there are classes, how many? How do they differ? Are they (the systems OR the classes of systems) related?
If so, is there a hierarchy (or are there multiple hierarchies)?
My urge for this came from the intricate geometric representations for arithmetic problems; different scientific disciplines and industries just appear to fall into the same pattern.
If someone knows a book that touches on this topic, please let me know about it, this thought is haunting me for years now :-)
I frame the problem slightly different (heh):
Different disciplines, branching out, will (or so says my hypothesis) discover the same topologies, but express them differently due to different scopes (perspective, dimensionality, DSLs [...]).
What I'm thinking about is: how can we parametrize the manifestations of these scopes, and, ubiquitously, reverse-engineer them, thus linking all the systems?
Then: which systems are topologically identical? If there are classes, how many? How do they differ? Are they (the systems OR the classes of systems) related?
If so, is there a hierarchy (or are there multiple hierarchies)?
My urge for this came from the intricate geometric representations for arithmetic problems; different scientific disciplines and industries just appear to fall into the same pattern.
If someone knows a book that touches on this topic, please let me know about it, this thought is haunting me for years now :-)