[Right Wing Professor]

Well jeepers Professor, wherever did you get the idea that we human beings live "in" a "formal system?" I thought we all lived in a "real" system. Sorry to be such a P.I.T.A.

If ya want to think about life, the universe and everything, there are just some things ya gotta pay forward. Group theory is well worth the effort, it's beautiful and much less demanding than calculus. And you'll never look at a tesselation on the wall of the Alhambra the same way again.

[betty boop]

...you'll never look at a tesselation on the wall of the Alhambra the same way again.

The tesselation on the wall of the Alhambra is a real system; group theory a formal system that gives a plausible description of it. The two are distinct: You conflate the two only at your peril.