On Wed, May 13, 2015 Bruno Marchal <[email protected]> wrote: > Why would Turing machine obeys the laws of physics? >
Because a Turing Machine like all machines involves change. A clockwork must read a cell on a tape made of matter and determine if it is white or black, and a clockwork must determine if it should change the color of that cell or not, and a clockwork must determine if it should move the tape one space to the right or one space to the left or just stop. And nobody knows how to make clockwork without using matter that obeys the laws of physics. Nobody, absolutely nobody. > > You can implement Turing machine in Lambda calculus > No you can not! The word "implement" means to put a plan into effect and Lambda calculus or any other type of ink on paper can not do that. You can find books about Lambda calculus that describe how Turing Machines operate but it's just a description, to actually make a Turing Machine as opposed to just talking about one, you'll need matter and the laws of physics. A book about Lambda calculus or about anything else can't calculate diddly squat. > > You can implement them in Fortran, in Algol, > Not unless you have a computer made of matter that obeys the laws of physics to run those Fortran or Algol programs on. >> nearly all numbers are non computable > > > > I told you that by numbers I mean integers, what you call number here > are non computable functions. > And what you call non computable functions Turing himself called non computable numbers in the very 1936 paper that introduced the concept that would later be called a "Turing Machine". > If we are machine, reality is not a machine, and with comp physics is an > important part of that reality > > > If by mathematics you mean tha arithmetical truth, then mathematics > knows the arithmetical truth. > Nothing can divide all arithmetical truth from all arithmetical falsehoods. Nothing can do it including arithmetic. > > At this stage, a plea for intuitionism is inadequate. It implies > non-comp (strictly speaking). > I don't care, I'm not interested in "comp". >> 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. > > > > Grave confusion of level. > Maybe on some level our entire universe is just a simulation program written in Fortran, but if it is as far as we know that program is running on a computer made of matter that obeys the laws of physics, > <sigh> > <burp> >> In other words those computer textbooks provide simplified and > approximated descriptions of how real computers operate. > > They described fundamental mathematical object which have been > discovered by mathematician working in the foundation of mathematics > Yes exactly, those textbooks DESCRIBE a Turing Machine, and the blueprints of a 747 DESCRIBE that airplane, but you can't fly to Tokyo on a description. > > physical computation is defined by the ability by nature to emulate > (approximatively) those mathematical objects. > Mathematical computational "objects" are defined by their ability to approximate physical computational objects. > >>> 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. > > > > Only if computationalism is false, > Sounding rather theological you just said that physical reality is needed for some manifestations, so physics must have something mathematics does not. QED. >> Godel said there are an infinite number of statements that are true (so >> you can never find a counterexample to prove it wrong) > > > > ? > ! > >> 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. > > > But I am pretty sure, to tell you my opinion, that the conjecture is > either true or false. > I accept that Goldbach is either true or false, Godel and Turing did too, but the question is does anything, ANYTHING, know if it is true or not. Godel and Turing say not necessarily, and even if Goldbach is provable or unprovable there are an infinite number of similar statements that are not. > > mathematicians have studied the difference between truth and proofs, > The difference is not all true statements have a proof, and in general there is no way to determine which statements it is possible to prove to be right or wrong and which statements you can not. > comp uses only the arithmetical realism, > I don't care, I'm not interested in "comp". > >>> 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, > > > > They don't talk about reality. > But you just did. > > with comp, Gödel's theorem is an argument in favor of arithmetical > realism. > I don't care, I'm not interested in "comp". 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