Tangent bundle Memes

Oh, the classic case of an astrophysicist let loose on undergrad math students. The first car represents the proper, textbook explanation of tangent bundles—a concept most math students already find terrifying. But then our starry-eyed professor decides to "simplify" with his astrophysics analogy: "a vector transforms like a vector." Profound! Revolutionary! Completely unhelpful! This is exactly why math departments hide when they see physicists approaching with that "I could teach this better" gleam in their eyes. The students' tuition doesn't cover the therapy they'll need after this explanation.