Dear Telmo
(I suppose a 'freer mind than several nat.-scientist listers) allow me some
musings (not that I want to hide them from the rest of the List).
Thinking of Bruno's *integer-restricted arithmetics* with addition and
subtraction only:
it is the* World Of ONE*, multiplied as much as you wish (two ways: + and
-). Numerals?
So we elevated to some understanding of the* "ONE"* (*unit?*) and our
uncontrollable mind made out of it the Entire World. Or we don't understand
even that 'one';
Bruno applied his extremely educated (and disciplined) mind to elevate this
'one' into sophisticated logical systems (what I never studied, sorry to
say).
There are also opinionated remarks about 'physical' (etc.?) *laws* with
fancy conclusions.
In my opinion a physical law is the summation of observations WITHIN limits
of our so far achieved knowledge and the 'majority' seems to be the "norm"
('law'). Then comes the condiment: lots of math and similar deductions and
voila: our conventional sciences.
Extend the limits (of our observations? or knowledge?) and the "laws"
change. That happened in our (cultural? human?) history continually. I do
not appreciate the level at which we are today: it will change as it
changed from the past.
Societal (communal?) 'law' is different: it is a compromise between
interests of diverse classes of members of a society including the
powerfuls' as giving the overtone.
Reality is beyond our (human) mental capabilities to detect, I humbly
disregard the "Slanted Realities" like mathematical, or religious, etc.
partial views. Same with truth.
I like to talk about my 'agnosticism' and *MY* beliefs based in it: the
'infinite copmp[lexity' beyond our (limited) model of knowables (because I
cannot comprehend "infinite" - or - "complexity" as a simple-minded human).
So after having passed an old fashioned rigorous Ph.D. at a 5century old
Universitas in chemistry, physics and math, published ~100 papers (both in
research and technical implementation of own results mostly in the
polymer-field) lectured on 3 continents and having gotten 38 patents to my
inventorship, I do not believe in 'atoms' (molecules?)
and consider the physical world a 'human' makeup for ever changing and
poorly understood phenomena as their synthesis into a 'scientifically
balanced' conventional view which, however, produced lots of (almost
perfect?) practical results into our lives.
Have a prosperous 2014 and then more to come
John Mikes D.Sc.
On Mon, Jan 6, 2014 at 2:05 PM, Telmo Menezes <[email protected]>wrote:
> 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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