On Sun, May 13, 2018 at 9:06 PM, Russell Standish <li...@hpcoders.com.au> wrote:
> > you already said, quite wisely, that if you had correctly used the ZFC >> > axioms to produce a proof the Goldbach Conjecture was true but then a >> > computer found a number that violated Goldbach you would place the >> blame on >> > the ZFC axioms and not on the laws of physics the computer operates >> under. >> > So like me you are saying it is physics and not axioms that is the >> ultimate >> > judge >> t >> hat >> >> decides what it true and what is not > > > > > *That is probably putting a little too much faith in computers, and the > possibility of bug-free programs.* In the thought experiment I specifically said numerous computers had made the calculation and they all agree that there is a huge even number that is not the sum of 2 primes. > > ** > > *There is a certain amount of scepticism of the proof of the 4 colour > theorem, which is only available as an enormous computer generated proof.* That proof was first demonstrated in 1976 and today I don't think there is anybody who thinks it is untrue, they just grumble that it doesn't advance human understanding of why it is true. As far as mathematical rigor is concerned you have to be far more literal in a computer program than in a mathematical proof because the computer will not fill in even the simplest logical gaps and will not tolerate the slightest amount of hand waving. And anyway, this sort of thing is not limited to computer proofs. In 2012 Shinichi Mochizuki came up with a proof of the ABC conjecture, but its 500 pages long and to this day about half of the world's mathematicians think the proof is valid and the other half think it is not. Recently the fans of it held a workshop to streamline the proof, but its still 400 pages long. To read and understand this thing you still need to have a boiling water IQ and you have to be prepared to devote the better part of a decade studying it. Its a gamble, after devoting years of your life to it when you could have been doing other things you may decide that Mochizuki's proof is all bullshit, or maybe you'll decide its a work of genius. To a lesser degree this happened with Andrew Wiles 's proof of Fermat's Last Theorem , it took about a year for the mathematical community to decide that Wiles got it right. It's things like this that make me think that maybe P really is equal to NP. I think most people intuitively feel that P is not equal to NP because that would sorta imply what we see in our everyday life, its harder to write a book than to read a book, its harder to write a symphony than to listen to one and appreciate its beauty, and it should be harder to discover a new mathematical proof than it is to follow a step by step argument. But it seems that that last thing may not be true, if I have a valid proof of the Riemann Hypothesis but it would take you as much brainpower to understand it as it would for you to find a proof on your own then there would be no point in you reading it. > >* * > > > *If the computer came up with a counter example to the Goldbach > conjecture, and lots of mathematicians independently verified the result by > hand,* By hand? The even number in question probably has about a hundred digits, so first of all you're going to have to find every prime number less than that super colossal number by long division and paper and pencil, and then show that no two of them add up to that number, and then you're going to have to do the same thing again and again to make sure you haven't made a mistake. And nobody is EVER going to do that by hand. > > > > *what you say would be correct, and people would look to find the error in > the ZFC proof* In the thought experiment I specifically said there was no error in the proof and the ZFC axioms do indeed imply that Goldbach is true, but the computers disagree. > >* * > *or reject the ZFC axiom.* So like me, and to my surprise like Bruno, if the ZFC axioms or ANY set of axioms say one thing but a computer whose ultimate operating system is the very laws of physics say the opposite then you reject the axioms and believe the physics. John K Clark -- You received this message because you are subscribed to the Google Groups "Everything List" group. To unsubscribe from this group and stop receiving emails from it, send an email to everything-list+unsubscr...@googlegroups.com. To post to this group, send email to everything-list@googlegroups.com. Visit this group at https://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/d/optout.
