Or even the famous question "Can you hear the shape of a drum?", to which we have a constructive proof (under some mathematical idealizations) that the answer is " No".
That's been simplified enough to distort the question. Real listeners are not limited to simple observation of frequencies they can move there ears around to get a more 3d picture.
*their
That's why I keep telling people there's no such thing as a perfect lie. People have no idea just how much information leak there is in every action they make; the only question is whether someone is dedicated enough to find the right side channel. And doing that is only getting cheaper thanks to progress of technology.