On Wed, Dec 19, 2018 at 8:16 AM John Clark <[email protected]> wrote:
> On Tue, Dec 18, 2018 at 7:02 PM Jason Resch <[email protected]> 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. > What is special about the equations of the physical universe? > > >> 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. > > The output of a computation is not the computation, and we make use of non-halting programs all the time. For example, Operating Systems, Web Servers, Virtual Machines, etc. Ideally, these programs never halt, and usually they never output anything, unless they crash. Would a program that simulates John Clock's brain need to halt in order for that simulation to realize John Clock's consciousness? Jason -- 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.
