A physicist once blew my mind with the following observation. "Mathematicians always get it wrong when you talk about the relationship between position and velocity. You say that velocity is the derivative of position, acceleration the derivative of velocity, etc. And that's all fine, down to 16 decimal places, give or take. Past that, quantum effects become significant. You don't have a clean mathematical identity: perhaps velocity is approximately the derivative of position, acceleration is approximately the derivative of velocity, but below the Planck scale, these quantities aren't even continuous!"