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.

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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? > > > > > > 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. 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