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.

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
>>>
>>>
>>>
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>>> http://iridia.ulb.ac.be/~marchal/
>>>
>>>
>>>
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> http://iridia.ulb.ac.be/~marchal/
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