254 Are the Androids Dreaming Yet?
chaotic equation so complex that the only way to see it is to run the program and watch the output: no form of program analysis will give you any clue as to what it produces. There is only one stipulation. The answer to problem Y MUST be held within the program as a computable algorithm. Put another way, the computer must already be ‘programmed’ to answer the question.
Could a human mathematician be pre-programmed from birth? Yes, there is no fundamental objection to this. Mathematicians could be born to solve the problems they solve. But this would present a couple of issues. Where is this program stored? And who, or what, programmed the mathematician? Could we perhaps find an experiment to determine whether mathematicians are pre-programmed?
One view held by philosophers is that the Universe programmed the mathematician. They believe we live in an entirely determined Universe with no free will. There is then no mystery as to how Andrew Wiles came up with his proof. He was destined to do it from the dawn of time. The ink that fell from his pen to the paper was always going to fall in just that way. We live in a clockwork Universe and although we might feel we have free will, this is an illusion. I simply don’t believe this. If I am right and humans do exercise free will, Andrew Wiles cannot be a computer. And because Andrew is not alone in discovering proofs, those mathematicians cannot be computers either. Humans are, therefore, not computers.
The Chance Objection
I said there was no automatic way to solve any problem above the logic limit, but this is not quite true. There is one automatic method you could deploy to generate a non-computable proof, the infamous ‘monkeys and typewriters’ idea where we use random chance to generate information. Many people have suggested it is possible to write a play such as Shakespeare's Hamlet by simply typing random characters until we happened upon the play. The argument is flawed.
The first flaw is the process would take a super-astronomically long time. Even if every atom in the Universe were a monkey with a typewriter, it would take orders of magnitude longer than the age of the known Universe to come up with the script to a play or a mathematical proof.
The probability of finding a solution to Fermat’s Last Theorem by chance is about 1 in 10°°. That’s 1 with 50,000 zeros after it. For a comparison, there are only 10’ atoms in the known Universe. To be, or
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