In physics, we do model. We describe the world in terms of mathematics. We make reasoned predictions and decisions.

But this description still doesn’t feel satisfactory. Yes, it’s all true. But it’s missing something.

I think it’s because we don’t start and we don’t stop with the mathematics. We have some toy model, some very oversimplified model, that still works. Chad Orzel does a great job of describing that here -> https://www.forbes.com/sites/chadorzel/2016/10/12/the-surprising-power-of-really-simple-physics/#1612e1197dab

Sometimes, as physicists, we try to get a handle on how, if one measurable property of a situation is changed, how another measurable property will change. We will manipulate our data until we get a straight line and then figure out what that relationship is. (I’m still miffed that Desmos won’t let me linearize the way a physicist would linearize.) That’s when we don’t have a model.

But, along with the mathematical formalism, I often find physicists using some sort of overarching model of the world, often a visual representation. The AMTA (American Modeling Teachers Association) was started by physics teachers thinking about how can we model the world. They focus constantly on drawing a representation of what’s going on in the situation.

When we have a model, we use it. Even if we think it oversimplifies the situation. And then we apply the model, using mathematical reasoning if not mathematical techniques. And we see if it gives a good enough prediction to be an applicable model.