On Tue, Jan 7, 2014 at 9:08 AM, Bruno Marchal <marc...@ulb.ac.be> wrote: > > On 06 Jan 2014, at 20:05, Telmo Menezes wrote: > >> On Mon, Jan 6, 2014 at 6:31 PM, Bruno Marchal <marc...@ulb.ac.be> wrote: >>> >>> Dear Stephen, >>> >>> >>> On 03 Jan 2014, at 20:21, Stephen Paul King wrote: >>> >>> Dear Bruno, >>> >>> I do not understand something. >>> >>> >>> >>> OK. (good!) >>> >>> >>> >>> Your idea >>> >>> >>> It is not an idea, but a result in an hypothetical context (or >>> theoretical >>> context). >>> >>> >>> >>> seems to me to be a very sophisticated and yat sneaky way of >>> reintroducing >>> Newton/Laplacean absolute time and/or Leibnitz' Pre-established Harmony. >>> >>> >>> It is only a remind of elementary arithmetic. The music 0, s0, ss0, sss0, >>> ssss0, sssss0, ssssss0, sssssss0, ... >>> You can see it as an elementary block digital time. If you want. And then >>> all other times are relative indexicals, including the physical and >>> subjective times. >> >> >> Bruno, >> >> I think I (perhaps naively) understand what you mean. My understanding >> is that, if comp is true, then the relationship between comp and the >> physical laws we observe is not a simple one. Even QM would be at a >> high level of abstraction in relation to raw reality. In this case, >> the recursive definition of integers would be the simplest possible >> expression of a fundamental building block that is responsible for >> time -- although the time we experience is a much more complex >> phenomena. >> >> It makes sense to me that time is strongly related to recursivity >> (maybe because of a CS background). I imagine moments being "copied >> forward" and changed in some fashion. >> >> Would you agree with these intuitions? > > > Yes. But recursivity relies on the ordering 0, s0, ss0, ... which is > admitted in the axioms, and so is a notion of time more primitive than the > recursive definition by themselves.

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Ok, I follow you up to here... > Another notion of time, which is still rather primitive is the time step of > the computations implemented by the UD (or arithmetic) like the > phi_344(76)^1, phi_344(76)^2, phi_344(76)^3, phi_344(76)^4, phi_344(76)^5, > phi_344(76)^6, phi_344(76)^7, ... (with phi_i(j)-n = the nth step of the > computation of program i on input j. It is different from the UD steps, > because the UD dovetails, and can execute billions of steps between > phi_344(76)^6 and phi_344(76)^7 for example. > But those times have no direct link with the "observed time" from inside, > which emerges from the logic of the first person points of view. The logic > of Bp & p, and Bp & Dt & p, have some canonical temporal significations. > Your time is eventually defined by the set of your continuation. It can > happen that phi_i(j)^n is lived by you statistically after some phi_i(j)^m > with m < n, a priori. ...but this is more mysterious to me. What should I read to understand this "phi" business? Telmo. > Bruno > > > > > > >> >>> >>> >>> >>> >>> >>> I recall reading how much Einstein himself loved the idea and was loath >>> to >>> give it up, thus motivating his quest for a classical grand unified field >>> theory. Physics has moved on... >>> >>> >>> After Aristotle Physics has also moved on ... I think Einstein was right >>> on >>> QM, and wrong on GR, in the sense that GR has to be justified by the >>> quantum, before, perhaps justifying the quantum by the "digital seen from >>> inside". >>> >>> >>> >>> >>> >>> You recently wrote: >>> >>> "The only "time" needed for the notion of computation is the successor >>> relation on the non negative integers. It is not a physical time, as it >>> is >>> only the standard ordering of the natural numbers: 0, 1, 2, 3, etc. >>> >>> So, the 3p "outer structure" is very simple, conceptually, as it is given >>> by >>> the standard structure, known to be very complex, mathematically, of the >>> additive/multiplicative (and hybrids of course) structure of the numbers >>> (or >>> any object-of-talk of a universal numbers). >>> >>> That is indeed a quite "static" structure (and usually we don't attribute >>> consciousness to that type of thing, but salvia makes some (1p alas) >>> point >>> against this)." >>> >>> >>> Let me try to clarify how I am confused by this claim. >>> >>> >>> OK. >>> >>> >>> >>> How many different versions of the integers "exist"? >>> >>> AFAIK, there can be only One and it is this *One* that acts as the "time" >>> (maybe) in your argument for all other "strings" of integers. >>> >>> >>> ? >>> >>> I have no clue what you are talking about. I am talking about the usual, >>> standard, finite and non negative integers, also known as natural >>> numbers. >>> I am not doing philosophy, so any problem you might have with this might >>> comes from unecessary over-interpretation you make, over what you have >>> been >>> supposed to have learned in high school. >>> >>> >>> >>> >>> >>> Are the "strings" distorted and/or incomplete "shadows" of the One? >>> >>> Are we permitted to use the allegory of the cave here? :-) >>> >>> >>> >>> Yes, but you need to do the work to understand the "real thing". We start >>> from arithmetic, that is: >>> >>> 0 ≠ s(x) >>> s(x) = s(y) -> x = y >>> x+0 = x >>> x+s(y) = s(x+y) >>> x*0=0 >>> x*s(y)=(x*y)+x >>> >>> or even just >>> >>> Kxy = x >>> Sxyz = xz(yz) >>> >>> ((K x) y) = x >>> (((S x) y) z) = ((x z) (y z)) >>> >>> And we stay in that theory. >>> >>> In that theory we define the observer by a believer in the axioms: >>> >>> >>> 0 ≠ s(x) >>> s(x) = s(y) -> x = y >>> x+0 = x >>> x+s(y) = s(x+y) >>> x*0=0 >>> x*s(y)=(x*y)+x >>> >>> together with the infinity of beliefs in the following induction axioms >>> (with F any formula in logic + {0, s, +, *}): >>> >>> (F(0) & Ax(F(x) -> F(s(x))) -> AxF(x) >>> >>> Just that is already very long to do, but that is done in the literature >>> and >>> is basically the "known" arithmetization of meta-arithmetic. >>> >>> Then incompleteness entails the nuances between proof and truth, and >>> consistency, and the double completeness theorem of Solovay provides the >>> 8 >>> hypostases, and we see that the classical introspecting machines can >>> understand by herself that what she observe might be only the shadow of >>> the >>> truth. >>> Indeed. >>> >>> >>> >>> >>> >>> How many "shadows" are there and how are they "distinguished" from each >>> other such that the notion of a computation is not lost? >>> >>> >>> By the study of the degrees of unsolvability. Notably. >>> >>> >>> >>> >>> In my work I have found that theoreticians in computer science >>> completely >>> take for granted that a computation is a process that can only occur in >>> the >>> absence of randomness. >>> >>> >>> That is well studied. It is computability relativized to oracles. >>> Computability on random oracle has been studied. >>> >>> >>> >>> >>> >>> Imagine if the atoms making up the CPU of your computer where to suddenly >>> start changing their positions and states due to outside interactions in >>> a >>> random/uncontrolled way? >>> >>> >>> That happens when I smoke a psychotropic plant, if not when I breath the >>> polluted air. >>> >>> >>> >>> No computation would occur! >>> >>> >>> Let us not exaggerate. No need to smoke the grass of Fukushima. >>> >>> >>> >>> >>> In fact, this is the situation that we find when, for instance, the >>> cooler >>> fan fails and the CPU overheats. >>> >>> >>> >>> Yes. The hypostases might be used to study the 1p associated to such >>> extreme >>> events. Would this give a NDE? Difficult questions, which needs some >>> technical progresses. >>> >>> >>> >>> >>> My point here is that the string of states that is a von Neumann >>> computation >>> >>> >>> von Neumann, Babbage, Turing, Church, Conway, Post, McCarthy, etc. OK. >>> >>> >>> >>> is something that has to be separable and/or isolated to be able to be >>> said >>> to "occur" or -to use the Platonic metaphor- "exist". >>> >>> >>> We start from the "E" interpreted in the usual way, like in "16 has a >>> successor". >>> And gives 8 different notion of existences, in the eight hypostases >>> (which >>> are each a mathematics with an intensional arithmetical interpretation). >>> >>> You get physics when you restrict the arithmetical interpretation on the >>> sigma_1 sentences, on the material hypostases. >>> >>> >>> >>> >>> So, what exactly is separating the "strings of integers" from each other >>> and >>> the One, such that we can coherently discuss them as actually being >>> computations and not just "representations of computations"? >>> >>> >>> The trueness of their relative association, together with their >>> redundancies. At the bottom, what do the separation are the additions and >>> multiplication, they separate the computations which halt from those who >>> does not halt, the first person views do the rest. >>> >>> Hope this helps. >>> >>> Best, >>> >>> Bruno >>> >>> >>> >>> >>> -- >>> >>> Kindest Regards, >>> >>> Stephen Paul King >>> >>> >>> >>> -- >>> 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 http://groups.google.com/group/everything-list. >>> For more options, visit https://groups.google.com/groups/opt_out. >>> >>> >>> http://iridia.ulb.ac.be/~marchal/ >>> >>> >>> >>> -- >>> 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 http://groups.google.com/group/everything-list. >>> For more options, visit https://groups.google.com/groups/opt_out. >> >> >> -- >> 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 http://groups.google.com/group/everything-list. >> For more options, visit https://groups.google.com/groups/opt_out. > > > http://iridia.ulb.ac.be/~marchal/ > > > > -- > 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 http://groups.google.com/group/everything-list. > For more options, visit https://groups.google.com/groups/opt_out. -- You received this message because you are subscribed to the Google Groups "Everything List" group. 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