> Systems theory
I'm confused. Is it a law or a theory? And no, it can't be both. Laws are proved. Theories are unproven.
"Systems Theory" in above refers to a field of study, not a name for the idea they were discussing.
And your assertion about Laws and theories is incorrect.
It may be useful, also, for you to read these two pages:
https://en.wikipedia.org/wiki/Scientific_law
https://en.wikipedia.org/wiki/Scientific_theory
The difference between Law and Theory (in scientific discourse) is not what you believe it to be.
ELI5?
1. A law gives you a relationship with no mechanism. It almost always appears as a mathematical formula. You know how the pieces change with respect to another, but not why.
2. A theory gives you a mechanism. It tells you why. On rare occasions, it will not provide quantifiable predictions, in which case it is a qualitative theory.
> Laws are proved. Theories are unproven.
This is not what is used to identify something as either a law or a theory in scientific discourse.
First, "laws" may be disproven, or falsified: Newton's Law of Gravity could actually be considered disproven as it is not accurate at all scales, but it's accurate enough within its scope to continue using it. It's considered a law in the sense that it matches empirical, observed data (within certain bounds). See [0] for details on that. So that, right there, is a flaw in your understanding.
Second, laws do not attempt to offer an explanation of the phenomenon they describe, they offer predictive value like "a ball dropped from 50 meters will, at time t, have velocity ...". Again, Newton's Laws do not explain why gravity works, only offering a model to calculate the effect of it. This brings us to theories.
Theories are, again, falsifiable via empirical evidence (like laws), but they offer an attempt at explanation. A Theory of Gravity would try to explain why objects are attracted to each other and why the mass effects the amount of attraction. The theory can be shown as false, but like a law it can only be shown to match empirical data. This is not the same as proven.
TLDR: The distinguishing characteristic is that both attempt to predict, but theories attempt to explain. Both are falsifiable, and neither are considered proven only to match empirical data (possibly within some constraints).
[0] https://en.wikipedia.org/wiki/Newton%27s_law_of_universal_gr...
“Hypothesis. Theory. Law. These scientific words get bandied about regularly, yet the general public usually gets their meaning wrong.”
https://www.scientificamerican.com/article/just-a-theory-7-m...
Systems theory has the concepts of "gain margin" and "phase margin" -- how much you can amplify feedback or delay feedback, respectively, before your self-adjusting feedback mechanism fails to find equilibrium and turns into an oscillator.
Even though most non-engineering systems don't fit the mathematical theory, the idea that only a finite amount of gain + delay is available, and that the two are somewhat inter-convertible, generalizes astoundingly well.