 On the above approach, the equations or expressions of physical interest are already given, and the strategy is to study their symmetry properties. There is, however, an alternative way of proceeding, namely the reverse one: start with specific symmetries and search for dynamical equations with such properties. In other words, we postulate that certain symmetries are physically significant, rather than deriving them from prior dynamical equations. The assumption of certain symmetries in nature is not, of course, a novelty. Although not explicitly expressed as symmetry principles, the homogeneity and isotropy of physical space, and the uniformity of time (forming together with the invariance under Galilean boosts “the older principles of invariance” — see Wigner  1967,[6]  pp. 4–5), have been assumed as prerequisites in the physical description of the world since the beginning of modern science. Perhaps the most famous early example of the deliberate use of this type of symmetry principle is Galileo’s discussion of whether the Earth moves in his Dialogue concerning the two chief world systems of 1632. Galileo sought to neutralize the standard arguments purporting to show that, simply by looking around us at how things behave locally on Earth — how stones fall, how birds fly — we can conclude that the Earth is at rest rather than rotating, arguing instead that these observations do not enable us to determine the state of motion of the Earth. His approach was to use an analogy with a ship: he urges us to consider the behaviour of objects, both animate and inanimate, inside the cabin of a ship, and claims that no experiments carried out inside the cabin, without reference to anything outside the ship, would enable us to tell whether the ship is at rest or moving smoothly across the surface of the Earth. The assumption of a symmetry between rest and a certain kind of motion leads to the prediction of this result, without the need to know the details of the laws governing the experiments on the ship. The “Galilean principle of relativity” (according to which the laws of physics are invariant under Galilean boosts, where the states of motion considered are now those of uniform velocity) was quickly adopted as an axiom and widely used in the seventeenth century, notably by Huygens in his solution to the problem of colliding bodies and by Newton in his early work on motion. Huygens took the relativity principle as his 3rd hypothesis or axiom, but in Newton’s Principia it is demoted to a corollary to the laws of motion, its status in Newtonian physics therefore being that of a consequence of the laws, even though it remains, in fact, an independent assumption.