0

To clarify the question, by "systems of laws" I mean something like the collection of physical laws that govern nature, rules of a game like soccer or chess, or a power system that governs what fictional characters can do in a novel/video game.

Basically, it's a set of statements about an entity that are always true, and from which every possible event that could happen in the entity can be deduced; if it helps, think of them as a logic analogue of a Cartesian coordinate system. I think the concept of axioms comes close to what I'm going for, but I don't know what the branch of math they belong to is called, or if there are any other branches or theories that detail what I need better.

Chidi
  • 39
  • 5
  • To a certain extent I would suggest looking at the field of mathematical logic, and in particular the subfield model theory (and perhaps the subfield proof theory as well). However the scope suggested by your examples is extremely broad and I'm not sure that it's entirely well-defined. – Noah Schweber Oct 15 '21 at 04:34
  • The process of abstracting a real-life situation to a system of (usually simplified) mathematical "rules", performing deductions based on these rules, and expressing your conclusions in terms of the original real-life situation is commonly known as "applied mathematics". – Theo Bendit Oct 15 '21 at 04:40
  • Theres lots of subbranches of maths so there is no one 'ultimate' list of axioms or something. – Aaa Lol_dude Oct 15 '21 at 05:08
  • Thank you, I will look into mathematical logic, model theory and applied mathematics as well. – Chidi Oct 15 '21 at 05:09
  • @AaaLol_dude I'm not looking for an ultimate list of axioms, just mathematical branches that deal with the study of the kinds of systems mentioned in the question, if there are any. – Chidi Oct 15 '21 at 05:10
  • Then I would probablyrecommend Game Theory and combinatorics.

    If you are looking for True rules governing the physical world, you can look at Physics.

     – Aaa Lol_dude Oct 15 '21 at 05:13
  • @Aaa Lol-dude Physics is just an example of the kind of system I'm talking of. But yeah, the answer to the question recommends game theory as well. Will look into it. – Chidi Oct 15 '21 at 05:17

1 Answers1

1

A few candidates:

  1. Abstract algebra: If the "operations" satisfy certain laws (e.g. commutative, associative, has identity/inverses, etc), then what? E.g. The Rubik's Cube is governed by its symmetric group.

  2. Dynamical System: If we know the current status of the system, and its trend (derivative or infinitesimal change), then what? E.g. chaos theory, Poincaré recurrence theorem, ergodicity, etc.

  3. Game Theory: E.g. Zermelo's theorem can be applied to chess or any finite combinatorial game.

  4. Computer Science: What a Turing machine (which is set up by just a few rules) can/cannot do (in polynomial time)? What about qubits?

In fact, I would argue the axiomatic method is about to understand the behavior of systems under certain laws: I don't care what kind of "materials" your system is made of (it can be atoms as in physics, or texts/proofs as in mathematical logic), but as long as it satisfies this and that rule, I can tell you it must also ...

This question also reminds me of the constructo theory, but I really have no idea what it it.

Just a user
  • 14,899
  • Just read the article on constructor theory, and it looks really interesting, thank you for sharing it. While it sounds like a fresh perspective on physical laws, i think it's still too new for any real use. – Chidi Oct 15 '21 at 05:52