We all ready have a well defined rigorous AGI[0] that would have god like intelligence. There are some approximations that played pacman [1] without knowing anything specific about pacman itself. i.e. it learned how to play by itself.
[0] http://wiki.lesswrong.com/wiki/AIXI [1] http://www.youtube.com/watch?v=yfsMHtmGDKE