What is the right mathematical language in which to talk about modularity, boundaries, etc?
I think this is an ill-posed question. Boundaries and modularity could be discussed in the context of different mathematical languages/frameworks: quantum mechanics, random dynamical systems formalism, neural network formalism, whatever. All these mathematical languages permit talking about information exchange, modularity, and boundaries. Cf. this comment.
Even if we reformulate the question as “Which mathematical language permits identifying boundaries [of a particular physical system, because asking this question in the abstract for any system also doesn’t make sense] most accurately?”, then the answer probably depends on the meta-theoretical (epistemological) framework that the scientist who asks this question applies to themselves.
I think this is an ill-posed question. Boundaries and modularity could be discussed in the context of different mathematical languages/frameworks: quantum mechanics, random dynamical systems formalism, neural network formalism, whatever. All these mathematical languages permit talking about information exchange, modularity, and boundaries. Cf. this comment.
Even if we reformulate the question as “Which mathematical language permits identifying boundaries [of a particular physical system, because asking this question in the abstract for any system also doesn’t make sense] most accurately?”, then the answer probably depends on the meta-theoretical (epistemological) framework that the scientist who asks this question applies to themselves.