Another thought-provoking thread, Fr. Apollo.

To most Masons around the world (such as myself who was i,p and r'd in Tel Aviv), the letter G means nothing and it is not included as a symbol. The true mystery of the Compass/Square is actually the true mystery of "1, 2, 3, 4" and explains other Masonic symbolism as well. This is an esoteric meaning that is not talked about much. But since we're in the mood for sharing secrets, here goes. It's very simple:

Take regular polygons starting with a circle (has one side and has the value of "1") and layer them on top of each other. Next would be the vessica pisces. Then the Equilateral triangle. Then the square. Look at what you've got.

The All-Seeing Eye surrounded by the Compass & Square. The "G" is a stand-in for the All-Seeing eye because they represent the same thing--deity.