> It's not really a "wrong" interpretation of calculus, but it has limitations. Eventually the geometric intuition breaks down. As long as you realise it's an

> It's not really a "wrong" interpretation of calculus, but it has limitations. Eventually the geometric intuition breaks down. As long as you realise it's an analogy, it's not the actual thing, I don't see the problem. So for example gradient descent in neural networks is partial differentiation along 100s or 1000s of dimensions, and I wouldn't try to visualise that directly; I might use an analogy of a marble rolling down a 3-dimensional landscape to find a local minimum, but that's clearly an analogy.