# Which mathematical operations leave the ontology invariant? [closed]

So usually one maps a math equation to an ontology in physics. Imagine me modelling a ball rolling up an inclined plane at an arbitrary angle. Now, the moment I make the inclined angle 90 degrees to the plane it collides with the plane and becomes a turning point. This can be modelled as an elastic collision (0 time duration and infinite force). This trick is known as renormalization.

Now, I can have an ontology that says all interactions must have finite durations the moment I choose the inclination angle to be 90 degrees this mapping is void. What happened? Well, we mapped force to a number in this ontology and the moment we let force be infinite we remember infinity is a concept not a number and thus we can arguably extended our ontology.

## Question

What all mathematical operations leave the ontology invariant for a physicist?

• Also does this suggest the math to be more fundamental than ontology? Commented Nov 1, 2023 at 10:31
• ???? A math theory assumes the existence of some specific objects and structures and it applies to models that satisfy the axioms of the theory. Commented Nov 1, 2023 at 11:25
• Yes. All my question is saying that physicists extend the ontology (set of axioms) by using a concept (renormalization) Commented Nov 1, 2023 at 11:31
• 90 degrees to what? What collides with what plane? What becomes a "turning point"? I cannot make head or tail of this question. Commented Nov 1, 2023 at 13:22
• What is the "mathematical operation" here? Physicists are constantly pushing the boundaries of their models to accommodate new effects, idealized situations (as in this case), etc. There is no telling out of context and ahead of time which model restrictions can be profitably relaxed or removed. This does not suggest that mathematics is "more fundamental" than ontology, it suggests that it is more flexible than the fragment of it that any particular model uses. Which should not be surprising because it is developed to be this way. The maxim is to maximize options, as Maddy puts it. Commented Nov 1, 2023 at 13:22