On Tue, May 12, 2015 Bruno Marchal <[email protected]> wrote: >> No, what they proved is that physical reality can emulate arithmetic; > > > > False. Just read the original paper of Church, Post, Turing, Kleene, > please. They don't mention physics at all. >
Please explain how to build a Turing Machine, or a machine of any sort, without using matter that obeys the laws of physics. > > BTW, they prove that the arithmetical reality is NOT emulable by > anything. the computable is only a quite tiny part of arithmetic. > I know, nearly all numbers are non computable so physics doesn't know what they are, but mathematics doesn't know what they are either, they aren't the solution to any polynomial equation and no function can produce them, an infinite series can't even approximate one. >> and one sort of physical reality, like a electronic computer, can >> emulate another sort of physical reality, like a galaxy, but we have no >> evidence that arithmetic can emulate anything. > > > > The proof is in all textbooks > Ink on paper is in those textbooks, there is no evidence that any book has ever been able to calculate anything, not even 1+1. You want to fly across the Pacific Ocean on the blueprints of a 747 and it just doesn't work. > > The sigma_1 arithmetical reality is Turing universal. Robinson > arithmetic is Turing universal. > Then I suggest you start the Sigma_1 Arithmetical Reality Computer Company with a Robinson Arithmetic subdivision and become the world's first trillionaire. > > No, the reason is that they want buy physical computer, to enacted the > computation relatively to our physical reality. > In other words those computer textbooks provide simplified and approximated descriptions of how real computers operate. > > But the physical reality is used only for that relative manifestation, > If so then physics can do something mathematics can not, make a calculation that has a relationship with our world. Physics must have some secret sauce that mathematics does not. > >>> (once you agree that 2+2=4 is a simpole truth on which we can agree >> on). >> > > >> We may agree on that but Godel and Turing tell us that there are an > infinite number of mathematical statements we will NEVER agree on, > > > They don't say that. They say that for all consistent machine there are > statement that they cannot prove. > Godel said there are an infinite number of statements that are true (so you can never find a counterexample to prove it wrong) but that have no proof (so you can't demonstrate its truth in a finite number of steps). If there were a way to put statements into two categories, the statements that can be proven true or false into one category and the statements that are either false or true but have no proof into another category we could concentrate our efforts on the first category and just ignore the second, but Turing proved that in general you can't even do that. If Goldbach's conjecture is in that second category (and if it isn't there are an infinite number of similar statements that are) then mathematicians could spend eternity looking (unsuccessfully) for a way to prove that Goldbach's conjecture is true, and spend an infinite number of years building ever faster computers looking (unsuccessfully) for an even integer that is not the sum of two prime numbers to prove that Goldbach's conjecture is false. So after an infinite amount of work you'd be no wiser about the truth or falsehood of Goldbach's Conjecture than you are right now. >> mathematical statements that even mathematics doesn't know if they are >> true or not. > > > > By definition, math "knows" the truth of the statement. > 90 years ago every good mathematician would have agreed with you, even Godel would have agreed with you, he was as surprised as anyone with what he discovered in his 1930 proof, but today no good mathematician would agree with you. > > You confuse again the mathematical reality and the mathematical theories. > Godel and Turing proved that there is no way even in theory to totally separate mathematical reality from mathematical non-reality, nothing can do it, not physics and not even mathematics itself can, therefore it is not valid to speak about a perfect land that contains nothing but truth. So you're the one who is confused not me. > <sigh> > <burp> 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 [email protected]. To post to this group, send email to [email protected]. Visit this group at http://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/d/optout.
