I cannot see how Newton could calculate $\dot x$ without thinking of $x$ as $x(t)$, though he never wrote something like $x=x(t)$. In fact, that is why I added that comment, because the separation you have made would be only possible after having the modern definition of function.

@AliTaghavi I don't know about other countries, what I know is that it applies in all Iranian universities, at least, as far as mathematics is concerned.

@AliTaghavi You know better than me that MO is not a right place to discuss such longstanding national dispute.

@FedorPetrov More strange is that most students don't see such a very strange something :)

To be honest, I heard that about fifteen years ago when I was a math student and I've never had any professional reason to get back to it. I've just mentioned it here to help the question to be better understood. However, the mere fact that I remembered it after fifteen years perhaps says something about the importance of your question.

Does "you can't comb a hairy ball flat without creating a cowlick" or "you can't comb the hair on a coconut" count as an answer? Hairy Ball Theorem

With the level of analogy that you have asked for, this question can be mapped into Thurston's question, "Thinking and Explaining", of course, missing some key details :)

@PietroMajer what a beautiful bit of history :)