On Mon, Jan 6, 2014 at 6:31 PM, Bruno Marchal <[email protected]> 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?
>
>
>
>
>
> 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
>
>
>
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> http://iridia.ulb.ac.be/~marchal/
>
>
>
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