A trivial example is this: Newton found the law of gravity,
which goes like one over the square of the distance between the things gravitated.
Coulomb, in France, found the same law for electric charges.
Here's an example of this similarity.
You look at gravity, you see a certain law.
Then you look at electricity. Sure enough. The same rule.
It's a very simple example.
There are lots of more sophisticated examples.
Symmetry is very important in this discussion.
You know what it means. A circle, for example,
is symmetric under rotations about the center of the circle.
You rotate around the center of the circle, the circle remains unchanged.
You take a sphere, in three dimensions, you rotate around the center of the sphere,
and all those rotations leave the sphere alone.
They are symmetries of the sphere.
So we say, in general, that there's a symmetry
under certain operations if those operations leave the phenomenon,
or its description, unchanged.
