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 :-)
“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.
What we are selling on the market as a fabrication shop is our ability to absorb variance and to build things that have never been built before (and will never be built again). Our whole business is built around variance. However, variance is not the same as randomness. If I look at the productivity of one worker, it has a certain rhythm and falls within a certain range, and what makes it chaotic is that no matter what scale I look at (worker, team, dept, shop), the variance is consistent.
Just getting into this line of work and trying to make predictions about it has blown apart a lot of the ways I used to look at the world. The systems I study and work with are beautiful because they're chaotic, and just predictable enough to be relatively stable, but unpredictable enough to stay challenging and interesting.
This is generally what people mean when they talk about "economies of scale": The more of a thing you make, the faster and cheaper you can make it. Moore's law (indirectly) names the constants on this curve for a integrated electronics, which is a field where the exponential relationship is more pronounced and continues over many more orders of magnitude than in most disciplines.
Just looking at learning curves per industry, do you think its possible to make educated guesses as to which would stand to benefit more from improvement?
Duhigg's The Power of Habit, and some of his other books also do a good job at applying one principle across many fields.
What I noticed is that every discipline invents their own lingo to describe the systems in play at the ethos of their discipline and they often manifest as some sort of law, principle or concept.
What I'm really curious about learning is to see if there's some sort of overarching discipline that focuses on these sort of systems as a meta and finds improvement points or market opportunities based on a given principle.
Take Moore's law for instance. It essentially describes a relationship between the most atomic component of {system} and the price of the commodity that is offered by that {system}. (system=hardware)
Now apply that to any other field. How about energy production? Is there a correlation between amount of cells in a solar panel and the price of energy at large available to consumers? This is still in the field of engineering so I'm guessing there will be some sort of relationship, but I wonder what taking it further into business and design for instance would look like.
I don't know how that would look like but to clarify I don't expect any of these laws to illustrate a similar pattern, but I do expect them to define how further along or behind any given "system" is, assuming that they are somehow comparable.