TITLE: What processes are used to enumerate stable operating regimes and testable hypotheses?
QUESTION [1 upvotes]: It seems that in physics there are two key processes,

Phenomenology: Constructing a qualitative description of the phenomenology through experiment, observation, and explanation
Synthesizing: Taking all of the quantitative explanations for a cluster of phenomena and producing a minimal set of formulas or relationships

However, oftentimes the most useful effects follow from a process that I can only call:

"breaking down the kinds of behavior into well-characterized components"

To provide some examples,

in a free-body diagram the separation between forces, bodies, constraints
in heat conduction, broadly the separation between conducting medium and material
in materials, cross-tabulating phases and enumerating permissible transitions, sublimating, melting, vaporizing, ionizing
in an electrical circuit the sources, resistance, inductance, capacitance as well as many other circuit elements characterize an incredibly broad set of constructions.
in optics, rays, junctions, polarizers are all idealizations that provide a good mode of description.

Has any writing been done on the calculus behind these types of toys, and how generally to synthesize new ones, and verify that all permissible configurations have been enumerated? This strikes me as important due to apparent longer-term oversights in the scientific community such as the memristor. Also, is there a better name for this process?
Edit 1: I should clarify that this isn't necessarily about pedagogy or good teleology where increasingly fine regimes are introduced via the most basic understandable description of the prior, but rather my focus is on the processes by which testable hypotheses can be generated, such as cross-tabulating physical quantities.
Edit 2: Rephrased in the form of a question, to further focus the issue.
Edit 3: I have become aware that this may simply be called "interpretation," but specifically of experiments rather than of theory.

REPLY [0 votes]: Physics does rely on those two key processes- the capacity to collect measurements and then to invent a mathematical framework which successfully accounts for those measurements, based on certain fundamental principles (conservation laws, etc.).
But in the case of your second set of examples, what you are describing there is not physics but engineering, which is the practice of solving everyday problems using settled results from the world of physics.
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