Jan 5, 2010

Random thoughts on AI

I'm always pessimistic about AI.

Our current computation model is deterministic. Do you remember how Dijkstra 'proves' goto statement is harmful? He use one (or serveral) natural number(s) to represent the state of your process. We can map serveral natural numbers to a rational number, so in fact we can represent any state of any process as a rational number. A Turing Machine program has only two possible results: either terminate in finite time, like finite numbers, or trap in a infinite loop, like repeating decimals. Lambda calculus is proven to be a equivalence of Turing Machine.

But our brain is non-deterministic. I have a strong feeling that you can't describe the state of brain by a rational number, but a irrational number. You can predict what's the n-th digit of a rational number, while you can't predict the n-th digit of a irrational number, you won't know it until your computation reached that point.

The problem is that rational numbers live in a closure. You can't get an irrational number by applying basic arithmetic on rational number. If we can't get irrational number from rational number, can we get a brain from Turing machine? Maybe, if we find which state does PI represent of in a program.

The foundation of our world is non-deterministic. It seems easy to build deterministic base on non-deterministic, but hard in reverse. So I guess it will be hard to build a brain base on Turing Machine. Fortunately we have a new hope at our age, named Quantum Computing, which is based on non-deterministic mechanism. I know little about how it works, but it looks totally different from old fashion computation models.