Since fellow member hackenslash sent me away to read Sir Roger Penrose's The Emperor's New Mind, I've discovered some new things. (I am now an avid Penrose fan and went on to read Shadows of the Mind! I plan to read all of his books ) I read material similar to the two books and found out about something I didn't know about before: Hypercomputers.

Basically put: Hypercomputers can compute things which a normal Turing Machine can not - things which are usually called 'non-computable' such as the Halting Problem.

Here are some links to interested users to scientific papers on the things:

http://pdfcast.org/pdf/hypercomputation

http://pdfcast.org/pdf/coins-quantum-me ... -s-barrier

http://pdfcast.org/pdf/quantum-hyper-co ... omputation

http://pdfcast.org/pdf/arrn

http://pdfcast.org/pdf/a-new-godelian-a ... ting-minds

http://pdfcast.org/pdf/modal-argument-f ... ting-minds

At the moment they are just abstract mathematical constructs however this lady proved that her new model of computation could hypercompute. (See ARRN)
Hypercomputation obviously poses interesting questions for consciousness and the universe in general.
Enjoy reading!