Re: Article in Scientific American

Chris Smith wrote:
Stephen Montgomery-Smith <stephen@xxxxxxxxxxxxxxxxx> wrote:

Proofs are also "run." They are fed into a computer called a human brain, and it outputs the answer "correct" or "not correct."


Perhaps I should have been clearer about what I meant. I wasn't at all talking about "checking" a proof or a program for correctness. I was instead looking at the average use case. That is, perhaps for the first few years after something is produced, people are skeptical of it. After it's stood the test of time for a while, though, it gradually passes into the category of things that everyone expects to be correct. With the computer program, there's only a certain limited class of problems -- those that cause the program to abort or produce obviously incorrect output -- that are still amenable to being detected once that happens, because people who are not interested in verification don't generally read the code for computer programs. But people do still read proofs, and even when they expect them to be 100% correct, they still do so with the intent of understanding why the result is necessary, which means that if anything is wrong, it's feasible they will find it.


To be fully checked, you also need to disect the brains and analyse them for correct functioning (which is not so easily done).


I think it's safe to define that problem out of existence on the grounds of futility. If the consensus logical reasoning of all of humanity is somehow flawed because of inherent faults in our brains that prevent us from seeing certain contradictions, then all of mathematics is hopeless anyway. It's very tedious, though, to prefix every theorem in mathematics with this condition: "unless there's a flaw in the human brain that prevents logically consistent reasoning for everyone,
c^2 = a^2 + b^2" Therefore, I plan to vote against the idea.


Yes, but the probability of the computer program being correct does increase it if it is run on different computers with different compilers, operating systems, etc.


Only if the problem leads to obviously or verifiably incorrect results. Claiming this as a standard of proof equates "provable" with "not disprovable", which we all (hopefully) know would be incorrect. Perhaps I should have said that the probability increases, but doesn't converge toward 1.

My broad claim is that you are creating a much higher standard of what is required to check a computer program for correctness than that for a proof.

If you stick to an absolute certainty of correctness, then proofs can be flawed in the same ways as computer programs. If you allow a certain reasonable uncertainty, then I would find a well checked computer program as equally believable as a well checked proof.
.

Relevant Pages

  • Re: Free Will
    ... Clearly humans are complex, and also humans have this feature (self vs. ... but how it is produced in brain is another matter. ... I can make a computer program that has a model of external world, ... qualia - the experience of pain. ...
    (comp.ai.philosophy)
  • Re: OUTGOEDELING A HUMAN?
    ... 'LauLuna will never believe this sentence' ... I insert probes into your brain at various ... The computer program works in the ... Well, if it is a true claim, then it's a true ...
    (sci.logic)
  • Re: Does Searles "Chinese Room" argument imply that consciousness is non-scientific?
    ... I feel the problem is within a computer program ... symbols certainly do accrue meaning, ... ascription of syntax or symbolic operations of a brain is a ... matter of that brains interpretation... ...
    (comp.ai.philosophy)
  • Re: Article in Scientific American
    ... Someone seeking to understand the four-color theorem is unlikely to read the entire bit of code that generated the evidence for its truth; they are even less likely to read the code for the compiler, or examine the implementation of the CPU. ... brain, and it outputs the answer "correct" or "not correct." ... Yes, but the probability of the computer program being correct does increase it if it is run on different computers with different compilers, operating systems, etc. ...
    (sci.math)
  • Re: Article in Scientific American
    ... With the computer program, there's only a certain limited class of ... somehow flawed because of inherent faults in our brains that prevent us ... then all of mathematics is hopeless ... Only if the problem leads to obviously or verifiably incorrect results. ...
    (sci.math)