Abstract
I will use the simple case of a harmonic oscillator to introduce and resolve three novel puzzles about physical symmetries. One puzzle is that the fact that boosts are symmetries of Newtonian mechanics is not particularly important for explaining why a spring inside a ship remains invariant under constant boosts of the ship. A second puzzle is that, in many cases, both the connection between symmetries and representation and the one between symmetries and observations seem trivial. And the third puzzle is that there are symmetries discussed by physicists where the connection between symmetries, representation and observations are broken.
