On Mon, May 14, 2018 at 11:41:34AM -0400, John Clark wrote: > On Sun, May 13, 2018 at 9:06 PM, Russell Standish <[email protected]> > 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.
Hopefully you said independently implemented programs, on independently implemented hardware. If all computers ran the same buggy program, it wouldn't tell you much... > 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 At 100 degrees? That's a pretty average IQ! Maybe water boils at a different temperature in your country... Perhaps you're from Atlantis. Or perhaps you were referring to 373 Kelvin, in which case I'd be quite happy with an icy IQ. > 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. I love 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. > That was actually my point :). > > > > > > > > *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. > How do you establish that the proof has no error? Why are we supposing that the ZFC axiom correctly describes the mathematical system? How do you establish that the computers haven't made an error? (independent implementations do help, of course). It really underscores Chaitin's point that at some level of complexity, mathematics becomes an empirical subject, perhaps not all that different from physics. -- ---------------------------------------------------------------------------- Dr Russell Standish Phone 0425 253119 (mobile) Principal, High Performance Coders Visiting Senior Research Fellow [email protected] Economics, Kingston University http://www.hpcoders.com.au ---------------------------------------------------------------------------- -- 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 [email protected]. To post to this group, send email to [email protected]. Visit this group at https://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/d/optout.
