You can know why the analogy holds without having enough detail to compute with it. Likewise you could have a picture that is truly part of you, but where not all of it is, so that you only get halfway there.
It is pretty easy to understand why the Doppler effect happens (at least, if you happen to be exactly my past self). You can easily have the ability to independently come up with the explanation without being able to derive the formula.
You can know why the analogy holds without having enough detail to compute with it. Likewise you could have a picture that is truly part of you, but where not all of it is, so that you only get halfway there.
It is pretty easy to understand why the Doppler effect happens (at least, if you happen to be exactly my past self). You can easily have the ability to independently come up with the explanation without being able to derive the formula.