“Multi modal” system representation in graph format. You can represent an electric, hydraulic and mechanical system in one graph. Anything really by relating them to the substituent energy and power. Its representation allows you to easily extract the differential equation. Neat stuff.
My brain is tickling, thank's a lot for the reference!
For example, specific systems have fairly well understood corollaries like a compressed fluid behaving as a mechanical spring within a system. Further, mass is akin to capacitor (stores energy), a spring is akin to inductor (stores energy), a damper is akin to a resistor (dissipates energy) in terms of their representation on the differential equation of their response. You might find some control theory an interesting read but I don't know if it speaks to exactly what you're looking for in terms of the broadest applicability.
Much appreciated!
> 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)?
To what end though? How would you even begin measuring success in such a vast context?
Don't get me wrong, I appreciate the art for arts sake, just curious to hear more.
Well, so far it's just mindgames, so while these are very valid questions, I never thought of an exact goal... But I'd recognize it when I'd see it. The best answer I can come up with right now:
First, I'd want to understand what components are necessary and sufficient to make up "a system".
From there, these components and their relationships would need to be understood from a mathematical perspective (maybe graph theory, but I'm not 100% sure).
Then, one could look for patterns in nature that reflect such components, and rule out which of those patterns are valid components of such generic systems, and which not, based on heuristics that were developed/explored in the previous step.
The following step might be to investigate how the interplay of a given systems components is mapped in human language, and how similar or topologically identical systems differ in spoken representations with respect to the different parametrizations of the aforementioned scopes [...]
(Etc.) - is this a satisfying answer, or does it just lead to more open ends? Anyway, that's the process as far as I've mapped it so far.
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 :-)