On Tue, Dec 18, 2018 at 7:02 PM Jason Resch <jasonre...@gmail.com> wrote:
>> Arithmetical computations don't change so there can't be a correspondence >> between >> them and the evolution of spacetime or with anything else that can >> change. >> > > *"y = 2x+1" defines the arithmetical relation of "oddness".* > Definitions can't compute anymore than the English word "cow" can produce milk. > *Solutions to this equation yield (compute) for y all possible odd > numbers. * > Correct computations can do that, incorrect computations can not, and no computation can happen without matter/energy and the laws of physics. So equations can't even compute incorrect solutions to themselves let alone correct ones. > *y* changes with respect to increasing values of *x*, > In this context x and y are words in the language of mathematics that represent the physical process a Turing Machine would undergo if it were running the y = 2x+1 program. Mathematics is a excellent language but x and y are still just words and they don't change anymore than the English word "calf" changes to "cow" as time passes. > *Similar equations (arithmetical relations) exist in arithmetic which can > compute, the Fibonacci numbers, the primes, the moves made by Deep Blue, > the outputs of LISP programs, and the time evolution of the Schrodinger > Equation for the Hubble Volume we find ourselves in.* > Equations are sentences in the language of mathematics and no sentence in any language can compute, because like words sentences don't change, but fortunately physical turing machines do. >> A functioning Turing Machine does not take its marching orders from the >> Peano Postulates or from the numbers they define, a functioning Turing >> Machine only does what its program orders it to do and even then only if >> that order does not violate physical law. Depending on the program you >> could have the functioning Turing Machine output that 2+3 is 4,5,6,-17, >> 6.02*10^23. or an infinity of other things, but only one of those programs >> treats numbers the way Peano said they should be treated, and thus out of >> an infinite of possible programs only one will produce an output >> consistent with arithmetic. >> > > *> I think I see the problem with our failure to communicate or reach > agreement on this. You appear to be equating "all computations" with "all > descriptions of all computations" or "all outputs of any computation > interpreted as true statements". * > A computation is the output of a Turing Machine after it has worked on data X with program Y and halted. Programers never want their programs to make arithmetical errors but this isn't always easy because there are an infinite number of programs that halt and contain no grammatical errors in the very very simple Turing Machine language but are nevertheless not compatible with the Peano Postulates and so do make arithmetical errors. > > *When I say all computations, I am referring to the executions of each > Turing machine initiated with each possible starting program, allowed to > run forever or halt, whichever that may be.* > If it goes on forever then it's not a computation it's just a Turing Machine moving around, but there is still a infinite number of programs that will halt and of those almost all of them will not be compatible with the Peano Postulates which dictates how numbers should behave. And only the Peano Postulates are harmonious with physical law; if the hand calculator you use to design a bridge is running a typical program it will not be based on Peano and so will make arithmetic errors and thus the bridge you're designing will fall down. That's why calculator manufactures make sure the program is not typical and is one of the very rare programs that is Peano friendly and will tell you that 2+2 is 4 and not 5. 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.
