I am reading a book on algebraic geometry and I google some keywords, eventually come up with this post in terry tao blog:
I think I got good intuition on the different thoughts on a group, but not this one:
(6) Dynamic: A group represents the passage of time (or of some other variable(s) of motion or action) on a (reversible) dynamical system.
Can anyone explain to me how a group represents the passage of time? I can only think of Noether's theorem on conservation law when combining the concept of time and algebra.