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 ofreintroducing 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.`

I recall reading how much Einstein himself loved the idea and wasloath to give it up, thus motivating his quest for a classical grandunified 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 thesuccessor relation on the non negative integers. It is not aphysical time, as it is only the standard ordering of the naturalnumbers: 0, 1, 2, 3, etc.So, the 3p "outer structure" is very simple, conceptually, as it isgiven by the standard structure, known to be very complex,mathematically, of the additive/multiplicative (and hybrids ofcourse) structure of the numbers (or any object-of-talk of auniversal numbers).That is indeed a quite "static" structure (and usually we don'tattribute 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" fromeach 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 sciencecompletely take for granted that a computation is a process that canonly 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 tosuddenly start changing their positions and states due to outsideinteractions 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, thecooler 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 Neumanncomputation

von Neumann, Babbage, Turing, Church, Conway, Post, McCarthy, etc. OK.

is something that has to be separable and/or isolated to be able tobe 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 eachother and the One, such that we can coherently discuss them asactually being computations and not just "representations ofcomputations"?

`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

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