That analogy does not really work. To use a modern car for transport, its power source can usually be treated as a black box, but if you don't know the math of

That analogy does not really work. To use a modern car for transport, its power source can usually be treated as a black box, but if you don't know the math of Big-O, you don't understand it, and if you don't understand it, you may be unable to apply it in a situation where you have not rote-learned the answer, or, worse, misapply it without noticing. I have seen enough of this to know that it is a real problem.