3) There are physical limits to computation (http://en.wikipedia.org/wiki/Bremermann%27s_limit). Bremermann’s Limit is the maximum computational speed of a self-contained system in the material universe. According to this limit, a computer the size of the Earth would take 10^72 years to crack a 512 bit key. In other words, even an AI the size of the Earth would not manage to break modern human encryption by brute-force.
I don’t think that’s so obviously true. Here are some possible arguments against that theory:
1) There is a theoretical upper limit at which information can travel (speed of light). A very large “brain” will eventually be limited by that speed.
2) Some computational problems are so hard that even an extremely powerful “brain” would take very long to solve (http://en.wikipedia.org/wiki/Computational_complexity_theory#Intractability).
3) There are physical limits to computation (http://en.wikipedia.org/wiki/Bremermann%27s_limit). Bremermann’s Limit is the maximum computational speed of a self-contained system in the material universe. According to this limit, a computer the size of the Earth would take 10^72 years to crack a 512 bit key. In other words, even an AI the size of the Earth would not manage to break modern human encryption by brute-force.
More theoretical limits here: http://en.wikipedia.org/wiki/Limits_to_computation