> On 3 May 2018, at 14:42, John Clark <johnkcl...@gmail.com> wrote: > > On Thu, May 3, 2018 at 4:40 AM, Bruno Marchal <marc...@ulb.ac.be > <mailto:marc...@ulb.ac.be>> wrote: > > >>I don't have a main dogma but if I did it would be information not matter. > > > That contradicts you argument where you were to matter needed for a > computation to just exist. > > I don't think so. A random collection of atoms is unlikely to be able to > perform a calculation and a random collection of mathematical symbols is > unlikely to be a proof of anything. In both cases the interesting part is not > the individual atoms or the individual mathematical symbols, it is the way > they are organized. That's why I said information is as close as you can get > to the traditional religious concept of the soul and still remain within the > scientific method. > > > > If not, where is the problem to accept the facts that not only the > arithmetical reality contains all computations, > > All correct arithmetical mathematical calculations may exist in some mystical > Platonic universe and all possible books may too, but you need matter to sort > out the correct calculations from the incorrect ones and the good books from > the gibberish; matter in the form of a calculating machine in one case and > the author Jorge Luis Borges in the other.
The arithmetical relations are not random, and indeed,, they are Turing universal. Ypiu don’t need any “mystical platonic universe”, you need only to believe in the arithmetical reality, and actually only the sigma_1 reality, which is that if a number are some verifiable property it exist a program capable of finding it. The set of partial recursive functions is the basic of computer science. The mechanist hypothesis makes impossible for any universal machine to distinguish any computations, below their substitiution level, making any use of an ontological physical universe similar to the use of particles by Bohm to eliminate the other branches of the wave. Peano Arithmetic (PA) can already prove the existence of all computation. PA proves its own incompleteness relatively to its most probable computations/continuations, and the fact that below its level of substitution it can see only the map of its undistinguishable continuations, a bit like an electronic orbital gives you the place where you can find an electron, and the orbital distinguish only the position relevant to first person conservation. It is not a matter of choice. Everett use mechanism, one we have the quantum, phase randomisation explains the white rabbit away, but with mechanism, we have to to justify the quantum from the sum on all computations, not just the quantum one. Study the first chapter of Martin Davis, to get the fact that the notion of computation is an arithmetical notion. Like you say, it is the relation which counts, and it happens that the (sigma_1) relations can mimic exactly all computations, in all programming language, or computer, or universal/machine/number/coombiantor... Sometimes I have the feeling that you take for granted a physical ontology, but that is automatically doubtful once you understand that the notion of computation does not require any physical assumption. In fact K, S and the combination (x y): (K K) …(S S), ((K K) K) ((K K) S), … with only the two laws ((K x) y) = x (((S x) y) z) = ((x z)(y z)) Is enough. Don’t add metaphysics where nothing more is asked that the belief that (3^3) + (4^3) + (5^3) = (6^3) is either true or false independently of you verifying this or not. You seem also to have a problem to distinguish a description of computation, which also exist in arithmetic, and the fact that participating to some true arithmetical relations, a computation is truly emulated. That confuse syntax and semantic, and is well explained in mathematical logic textbooks. Bruno > > 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 > <mailto:everything-list+unsubscr...@googlegroups.com>. > To post to this group, send email to everything-list@googlegroups.com > <mailto:everything-list@googlegroups.com>. > Visit this group at https://groups.google.com/group/everything-list > <https://groups.google.com/group/everything-list>. > For more options, visit https://groups.google.com/d/optout > <https://groups.google.com/d/optout>. -- 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.
