Abstractions are vital, but like many living things, dangerous, because abstractions always leak. (“You’re very clever, young man, but it’s reductionism all the way down!”) This is in some sense the opposite of a mathematician: a mathematician tries to ‘see through’ a complex system’s accidental complexity up to a simpler more-abstract more-true version which can be understood & manipulated—but for the hacker, all complexity is essential, and they are instead trying to unsee the simple abstract system down to the more-complex less-abstract (but also more true) version. (A mathematician might try to transform a program up into successively more abstract representations to eventually show it is trivially correct; a hacker would prefer to compile a program down into its most concrete representation to brute force all execution paths & find an exploit trivially proving it incorrect. /// from Gwern’s excellent On Seeing Through and Unseeing: The Hacker Mindset)
Velocity is the first derivative of position, while acceleration is the second.