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.
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 [email protected].
To post to this group, send email to [email protected].
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 [email protected].
To post to this group, send email to [email protected].
Visit this group at http://groups.google.com/group/everything-list.
For more options, visit https://groups.google.com/groups/opt_out.
