In investigating laws of science, one has first of all to decide what depends on what. Does the dynamics of a material body depend on its color or temperature? Does it depend on the place or the time at which the experiment is performed and so on? If one has decided that the outcome is independent of some parameters, new and deep insights on the expected laws can be obtained. The entire theory of special relativity could be deduced from the experimental fact that the velocity of light is the same for all observers who are moving relative to one another with constant velocity, and the requirement that the laws of mechanics should be the same for all such observers.

Now, if we take the equations describing these laws for one observer and transform them into the equations for any other one, we will obtain formally new equations, depending upon the relative velocity of the two observers. But the equations must be the same, by our requirement. Thus, all admissible equations of the theory must be unchanged under such a transformation. This demand of invariance puts a great restriction on all possible equations of the theory.

Laws of invariance are an important guide if we enter an unknown field of knowledge. The simplest applications go back to classical antiquity. Indeed, the simplest transformation which occurs in science is reflection. When Archimedes studied the law of the lever, he used this concept, demanding symmetry between left and right.