I just saw this blog post via Facebook, and it looks like an interesting mental exercise:
Check out this video:
I’ve never tried mirror writing, but used to practice writing upside down. It has practical uses when explaining things to people.
A related exercise that I thought was useful is studying Hebrew. Reading and writing from right-to-left is a challenging mental workout in the beginning. Arabic, Farsi or any right-to-left language would have the same effect for speakers of a left-to-right language.
In fact, writing with the other hand cannot strengthen your intelligence as a whole. This will stimulate the formation of new neural connections until it simply becomes a habit. But on the other hand, it really enhances your overall coordination. I am extremely interested in the development of ambidextria to improve my fight from both stances.