From The Blind Spot: Why Science Cannot Ignore Human Experience

“We can see from these examples that the laws of mathematical physics refer to idealized objects and their properties—free-falling bodies, frictionless planes, hypothetical ideal gases, perfectly elastic collisions, and so on. These idealized objects and properties aren’t physically real. They don’t actually exist in space and time, and they don’t participate in causal interactions. So they do not and cannot constitute the real world of nature. They’re fictional entities that we use as tools. They’re conceptual instruments necessary for us to formulate exact mathematical statements that we can apply to the real world through a series of increasingly accurate approximations. This is how we gain predictive knowledge of things and control over them.

Mathematical idealization and approximation constitute a method for knowing how things will behave under various conditions. But the method doesn’t tell us what things are and why they behave as they do. Hence, to think that the idealized laws of mathematical physics describe the inherent being of nature is fundamentally mistaken. To think this way is to confuse the map—an idealized and limited representation of the terrain—with the territory. As Husserl says, to think this way is to “take for true being what is actually a method.” This is the surreptitious substitution—the substitution of a tool to describe phenomena for nature itself, or confusing an instrument of prediction for how things are in themselves. It’s a kind of category mistake.