A few years ago, I read a thread on twitter or bluesky from a PhD mathematician working as a professor. It went something like this:
"I was playing fetch with my dog the other day, and it occurred to me that the dog knows with a high degree of precision where the ball will end up with no more information that seeing it come out of my hand--sometimes he can grab it mid-air without looking. Of course, the world functions in a regular and observable way, so the description of the ball's trajectory is determined by calculus. My dog must in some way be able to do the calculus necessary to find the ball. Therefore, my dog must be smarter than I'd previously thought."
Flawless logic, and wrong. Calculus describes how the ball moves, but the ball being thrown and the dog running to get it are natural processes that happen regardless of whether anyone knows the math. And a good thing, too: if you count from Euclid to Leibniz or Newton, that would be 2000+ years the world would have had to go not knowing where balls were going to land. Nor does knowing the math really help you, either: if an outfielder needed to do a differential to catch a fly ball, we could just give up on sports altogether; no one can do the math that fast, and it's not clear how it would help even if you could.
(It also says something about something that it took 2000 years to accurately describe what a puppy or a toddler can learn to do in an hour, or less.)
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