Is thinking computable?

[immortal]

I have been thinking about this question for quite a while and want opinions from mathematicians, programmers and others.

http://denninginstitute.com/pjd/PUBS/AmSci-1990-2-thinking.pdf

How, he(Penrose) asks, could an algorithm have discovered theorems like Turing’s and Gödel’s that tell us what algorithms cannot do?

I want to specifically discuss about this question. We know mathematicians prove theorems, for example Alan Turing proves that no algorithm exists to solve the halting problem and he arrives at an algorithm which shows what algorithms cannot do but my question is did he arrived at that algorithm in a computable way or to put it in an another way is there an algorithm which generates other algorithms or did he just discovered it in a non-computable way. Even programmers come up with new algorithms for various problems and when we are in the process of generating a new algorithm do our brains really invent them or do we directly access insights from some where?

In other words in order to show that machines can think does a machine need to come up with a new algorithm all by itself, an algorithm which generates new algorithms, is a neural network aware of what it is doing to acquire such an understanding of the problem and generate an algorithm to solve that problem?

 

What is thinking?

[Semjase]

All our brain is essentially an organic computer minus the experience

of real that us advanced life forms seem to enjoy. The brain is

no different than any other computer a massive super computer

could duplicate it's function. Our experince of real must have

technology behind it since a standard computer cannot

experience real. Can the experience of real impart an extra

intelligence that no computer can ever have, the answer

is yes since it is a feedback system, which constantly

corrects things.