> On 17 Dec 2018, at 17:03, John Clark <[email protected]> wrote: > > > On Mon, Dec 17, 2018 at 8:30 AM Bruno Marchal <[email protected] > <mailto:[email protected]>> wrote: >> On Sat, Dec 15, 2018 at 11:44 AM Jason Resch <[email protected] >> <mailto:[email protected]>> wrote: > >> >>> Pure numbers may not correspond to point in time and space, but their >> >>> relationships do. >> >> >> Where and when did 2+2=4 happen? > > That is a category mistake. > > I agree, but I didn't say it, Jason is the one who said "Pure numbers may > not correspond to point in time and space, but their relationships do”.
Their relationship can explain (and have to explain with mechanism) the origin of the belief in time in the mind of the number. Elementary arithmetic ===> computations ====> matter (internal statistics on computations). Numbers exists out of time and space, but can reappear (and should) in the emerging space-time structure. > > > Events happens, in physical realities. “2+2=4” can be said to be true, not > > that it happens. The truth of 2+2=4 is just not a physical truth. It is an > > arithmetical truth. > > OK I think that's pretty much correct, it's dumb to ask where and when 2+2=4 > happened because the relationships between numbers have nothing to do with > the fundamental properties of time and space and so can not generate them. OK. > And therefore Physics has something Arithmetic doesn’t. Assuming Physics (with a big P). But with Mechanism, Physics is explained in the phenomenology of numbers, and that one is imposed by incompleteness. You can say that physics has something that Arithmetic does not, but not in a different sense that prime numbers and digital machine/numbers have properties that simple numbers do not have. Physics emerges from inside arithmetic, for purely logic-arithmetical reason (logic is not enough, some Turing universal system must be assumed, like elementary arithmetic). > > >> Does that relationship between 2 and 4 ever change? > > > Same remark. We can’t say that it changes, nor that it does not change, as > > change does not apply. > > Then numbers and their relationships are insufficient to produce a mind, more > is required because change is essential for a mind, even a rudimentary one. Here is the rudimentary one we need: the change given by the successor function. The change from 0, to s(0), to s(s(0))), etc. That change is enough thanks to the fact that a computation is a digital notion, and it involves only discrete steps, well manage by the “s(x)” function. > > > If something physical needs to be added, how could a universal machine > > detect it > > Obviously it couldn't detect it if it only had numbers to work with. But it can live it. Of course you need to see that “computation” can be defined using only classical first order logic and the symbols 0, s, + and *. It is easy if you allow the use of the primitive recursive function, like exponentiation, then Gödel used the Chinese lemma in Number theory to discharge the use of the exponential function, and get the Turing universality (implicitly as Gödel missed Church’s thesis) of elementary arithmetic. > But I'm not sure what you mean by "universal machine", a machine must have > the ability to change and you just said and I agreed that it's silly to talk > about a number or its relationship with another number occurring at a time or > at a place, so a "machine" made of nothing but numbers is self contradictory. > A digital machine is not made of anything. It is implemented, in Turing sense, through additive/multiplicative number relation. Gödel did this in 46 steps in his 1931 paper, from the definition of divisibility and prime to the definition of provability. Or see Davis’s Dover for the same step toward computability. By a later theorem of Kleene, all computability notion can be transformed into some “beweisbar” predicate of a Turing-complete theory. > > > and how would that physical primary thing interfere with the computations > > in arithmetic > > Interfere? Physics doesn't interfere with computations it produces them, Not when we assume mechanism, and even without mechanism, the digital-machine/number do have a physics that we can compare with our physics, and indeed that match well and explain the quantum observable weirdness, the "many-world”, which here becomes the many-computations (a constructive notion like the Universal Dovetailer illustrates). > and Turing showed exactly how it does so when reduced to its simplest most > fundamental level. > > > It is bad philosophy/religion. > > If it's bad philosophy/religion then logically that implies there must be > something good about it. Th search of truth. Science. > > > If you agree that 2+2=4 independently of you, > > If I was the sum total of physical reality I would disagree, but I'm not so I > don't. > > > then it follows that all computations exists independently of you. > > OK, in platonic heaven all computations exist, and I mean all of them, the > incorrect ones as well as the correct ones, and only a physical Turing > Machine can seperate the correct from the incorrect computations. The universal dovetailer run all computation. The notion of correct or not does not apply to computation, which is just a digital (arithmetic) process. When we use a computation for some goal, a notion of bugs makes sense, but the universal dovetailer, or the sigma_1 proposition does not refer to such kinds of bugs, which are notion relative to goal, which of course is not in the universal dovetailing. You can look at the annexe of “conscience et mécanisme” for a universal dovetailer illustrated in the language LISP, or, if you have follow the combinators thread, you get all computation by applying the two S and K laws on all combinators: K, S, KK, KS, SK, SS, K(KK), KKK, K(KS), KKS, … The laws are Kxy = x Sxyz = xz(yz) For example SKKK = KK(KK) = K. That will give all computations, including the one responsible for you consciousness state here and now. But that is only a tiny part of the explanation, as physics as o be retrieved from the first person indeterminacy on all computations going through your state in the universal dovetailing (aka the sigma_2 arithmetical true sentences). > In the same way when Michelangelo carved his huge statue of David he started > with a single colossal block of marble and used his chisel to seperate the > parts of the block that were correctly part of David from the parts of the > block that were incorrectly part of David. There were an infinite number of > incorrect Davids inside that block of marble and only one correct one, and > Michelangelo used his brain and his chisel to get to the correct one, and > both are made of matter that obeys the laws of physics. We don’t have that problem here. Programs have a grammatical structure which is checkable, so we can run them all, and dovetail on their executions, and so emulate all computations. > > > Today we know that not only all computations are emulated in arithmetic, > > but we know that they are already emulated by just one degree 4 diophantine > > polynomial. > > Degree 4 diophantine polynomials aren't going to be DOING any emulating or > DOING anything else either until something changes, and numbers can't change > and neither can their relationships, so they can't DO anything. The change are relative, like in block-universe, and defined only through the use of s, + and *, and 0. The computation is in the semantic of those symbols. As you seem to be OK with digital mechanism, and with the fact that 2+2=4 is independent of you, you are forced to accept that the computation which brought your actual state here and now is implemented, with infinitely many variants, in the same independent of you manner. > But matter/energy can change and its the only thing that can, so it's the > only thing that can DO stuff. > > > The problem is that you don’t study the proofs given. > > The problem is after less than half a page it's painfully obvious your > "proof" does not deserve more study because you are unable to answer even the > most elementary questions about it, such as "who does that personal pronoun > refer to?”. That is weird. I have answered that question each time you asked me. In Helsinki, it refers to the guy in Helsinki, and thus after the duplication, it refers to both copies. But as no-one can be aware of their copies in the first person way, the guy in Helsinki can predict with probability one that after push-hing the button he will feel to be in one city, but cannot know which one in advance. We always talk about the same guy, and we know who is is. After duplication, he has survived in both copies. He has become two person, but BOTH can only access their local memories and environment, and so both will live the 1p breaking of the 3-1 symmetries. Nobody has any problem with this, even my most ultra-dogmatic-materialist opponents. Step 3 seems to be problematic only for just you. To be sure, some people took some time to get this, but eventually, it is because they were forgetting that the question is about a prediction on a first person experience. > > >If Mechanism is correct, the universe cannot be computable. > If Mechanism is false, the universe cannot be computable. > > If Mechanism is correct then complex objects including intelligent conscious > ones can best be understood by examining the interactions of its parts. But > Mechanism does NOT demand everything about a complex object be understandable > (that would be Materialism not Mechanism) and Turing proved that in general > we can not understand what a physical purely mechanical MACHINE will do, it > might stop and it might not, all we can do is watch it and wait, and we might > be waiting forever. Turing proved this for the arithmetical computation too. He use an “apparent physical machine” just for pedagogical purpose. The halting problem concern all sigma_1/pi_1 arithmetical problem. Arithmetic emulates all machine searching a Riemann critical zero, and we still don’t know if such computation are halting or not, in arithmetic. Bruno > > > you need to asses step 3 > > You need to fix step 3. > > > you beg the question in the same recurrent manner of the creationists, and > > people having dogma. > > Wow, calling a guy known for disliking religion religious, never heard that > one before, at least I never heard it before I was 12. > > 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] > <mailto:[email protected]>. > To post to this group, send email to [email protected] > <mailto:[email protected]>. > 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. 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