About peace of mind:
I was just thinking about the meaning of the verb "to mind" as in "Do you mind?" or "I don´t mind."
On a basic level what is happening if you "mind" - that is in the sense of being bothered by something - is that something is processed by your intellect (mind). From there it seems to cause a sort of negative emotion.
So as a consequence: if you don´t process things through your intellect, they cannot bother you. You are at peace. ;)