Jason + Stathis

From: Bruno Marchal <marchal.domain.name.hidden>
Date: Sun, 11 Feb 2007 11:48:44 +0100

Jason,

I am not against a wiki for the list, but I think it could lead to some
difficulties. I have already asked more than one time what are people's
main assumptions, without much success (only Hal Finney answered). For
my part I am just explaining results I got and published a long time
ago (and it is just a sort miracle which made me defends those result
as a thesis in France in 1998). I'm a bit annoyed for this sometimes.
Concerning the acronyms I am using (comp, UD, UDA, Movie-graph, AUDA G,
G*, ...) I refer to my papers available through my URL. I could make a
list if you want, but if you put them in a wiki, I will insist, for a
change, that correct references are joined.

My work has always consisted in two things:
1) an informal (but rigorous (rigor and formality have no
relationships)) argument showing that the computationalist hypothesis
in the cognitive science makes physics a branch of number
theory/computer science. See UDA in my papers or in the archive. I have
already explained this a couple of time. Physics appears to emerge from
a (n-person) computations statistic.
2) a "formalisation" of the argument (called AUDA (Arithmetical UDA) in
arithmetic. It adds nothing to the proof, except that it makes it
constructive and it shows a precise way how to extract physics from
comp, making comp Popper falsifiable. Here I don't succeed to explain
this to the list because it needs more involvement in mathematics.

Since my PhD, one open problem has been solved by Eric Vandenbussh
(hand manuscript, I will put it on my web page), and I have made two
extensions of my work.
a) a possible relation between the S4GRZ1, Z1* and X1* (modal logic of
the "material" hypostases) and a notion of arithmetical braiding (and
thus possibly quantum computing, cf Kauffman; see my url). I have
submit an abstract for a conference, but unfortunately I have
discovered since an error and I am stuck in the proof.
b) that the lobian interview (another name for AUDA) leads to a
thorough purely arithmetical interpretation of Plotinus' "theology". It
appears that "Plotinus' theology" can be seen as the best popular
version of the self-observing lobian machine discourse, including
physics (The "two Matters" of Enned 4 II. I have submit a paper
recently.

I am grateful for the kindness and patience of the people in this list.
There are not many person interested in such subject, which of course
is a difficult interdisciplinary subject, it helps me a lot. But to be
honest, the only notion I could (but not yet have) borrowed from the
list discussion is Bostrom Self-Sampling Assumption wording, and his
notion of Observer Moment. Indeed (n-person-points of view of the true
Sigma1 sentences can provide n-person points of view observer moment;
see below)
Schmidhuber left the list after denying any sense in the first and
third person notion (he is not open on the mind-body problem). I don't
remember Tegmark having participate in the list, except indirectly
through a post of James Higgo quoting a personal conversation where
Tegmark explains why he does not infer quantum immortality from quantum
suicide. Tegmark is a bit fuzzy on what is an observer.

Personally I believe that the mailing list would be formidably enhanced
if we could use a simple pen for simple drawing. Just a pen. I mostly
reason with simple images. And this is even more true about the quantum
topological target which can be seen as an intermediate step between
mind/matter and numbers.

Bruno

I will be busy newt week: here is an unfinished post I wrote. I send it
in case it helps a bit.


Le 03-fvr.-07, 10:05, Stathis Papaioannou a crit :

> Bruno Marchal writes:
>
> > What is correct, and has been singled out by Stathis, is that comp
> > eludes the "material implementation" problem, given that we take all
> > abstract possible relationship between those objects, and they are
> all
> > well defined as purely number theoretical relations. Note that this
> is
> > something I have tried to explain to Jacques Mallah sometimes ago,
> but
> > without much success. This does not make much sense in ASSA
> approaches,
> > but, like George Levy I think, I don't believe in absolute
> probability
> > of being me, or of living my current "observer moment". Such a
> > probability can be given the value one (said George) but it is close
> of
> > saying that the universe is here, which tells us nothing, really. It
> is
> > like answering "who are you?" by I am me".
>
> I'm satisfied with this summary. The physical implementation problem
> is not
> a problem when considering abstract machines.


So let us sum up (assuming comp once and for all at the start). (comp
= "Yes Doctor" + Church Thesis (Arithmetical realism as I use it is
implicit in Church thesis)

1) UDA+movie-graph entails that the physical science has to be a
sub-branch of computer-science/number theory.
    Specifically: physics = invariant for a notion of (1-person-plural)
self-observation. 1-person plural notions refer to multiplication of
couple or entangled computational histories.

OK?

2) This entails also that a self-observing universal machine, which
exists by Church Thesis, has to discover physics "in her head". This
provides a strategy: interview a "sufficiently platonist" universal
machine about herself.

3) This gives a sequence of theorems, actually: Godel, Lb, Solovay,
Boolos Goldlblatt, Visser ... (ref in my thesis). Such theorems (and
others) can be summarized by saying that the universal machines
discover what Plotinus discovered when looking inward, mainly all those
"person points of view" (hypostasis). Physics is arithmetic as seen
from one of those points of view; it is the one corresponding to a
first person plural indeterminacy.
This is made possible by the existence of the gap between truth and
provability.
The following, where p alone means "p (an arithmetical proposition like
1+1=2) is true": describes the definition of the main hypostases (Bp
means the the machine proves p, Dp abbreviates ~B~p, where "~" denotes
negation, and should be read "p is consistent for me" (or I cannot
prove ~p):

1) p (unameable, Plotinus' ONE)
2) Bp (G, G*) (nameable, Plotinus' Intellect)
3) Bp & p (S4Grz = S4Grz* (unameable, Plotinus All soul)

4) Bp & Dp (Z, Z*; nameable, Plotinus' intelligible matter)
5) Bp & Dp & p (X, X*; unameable, Plotinus' sensible matter)

Which makes a total of ... 8 hypostases! Why 8?
Because, not only the gap between truth and provability does entail,
from the machine point of view, the distinction between the logic
obeyed by the 5 hypostases, but it doubles each hypostasis, making thus
10 hypostases (the truth and the provable points of view about them).
But neither the ONE nor the Soul are duplicated by the G,
G*-distinction: thus 8 hypostases.


4) then add the arithmetical version of comp (actually something weaker
than comp): p -> Bp. Add it to G. The formula "p -> Bp" can be shown
to characterize the Sigma1 true sentences (= DU accessible states).
This changes all the hypostases. It is the acomp-hypostases (with acomp
the arithmetical translation of comp):

1) p (quasi nameable now (could be a problem), Plotinus'
ONE (in a more pythagorean version)
2) Bp (G1, G1*) (nameable, Plotinus' comp
Intellect)
3) Bp & p (S4Grz 1 = S4Grz1* (unameable, Plotinus comp All
soul)

4) Bp & Dp (Z1, Z1*; nameable, Plotinus' comp
intelligible matter)
5) Bp & Dp & p (X1, X1*; unameable, Plotinus' comp sensible matter)

My (modest) result: S4Grz1, Z1*, X1* gives rise to an arithmetical
quantization. The quantization of p is given by BDp (with B and D
interpreted in each of those three hypostases: it seems that the
arithmetical bottom is completely symmetrical.

5) Major defect considering the reasonable target: quantum mechanics,
or quantum computation (we have to find (by UDA) a reverse of Deutsch
justification of bits from qubits). No arithmetical tensor, no natural
coupling of true sigma_1 sentences, no braids (yet), nor Temperley Lieb
algebra. But I would propose to

I will send to the list some tutorial book references which can help. I
propose we work out better the "physical" target. I will send a post on
quantum computation, and on the Deutsch Friedman Kitaev thesis (the
corresponding "Church thesis" for quantum computation). Meanwhile I
would recommend the reading of Louis Kauffman's paper (ref in my URL)
on knots and quantum information. This is just a suggestion, but, it
could helps to explain or realise that the notion of computation and of
quantum computation are far richer than people usually think. Knots
provides combinatorial and discrete models of "physical universe" quite
interesting per se, also.

If all this is too technical, perhaps we could create a
"technical-everything-list" for those ready to do more math. This is a
suggestion, and it could provide a motivation for Jason's Wiki. I
don't want insist too much on technical issue if people are not
interested, and I remain interested in informal discussion. But, and
this is a proof we do have make progress, More and more often I feel
obliged to mention the technical AUDA to make clear informal talk.

Bruno


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

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Received on Sun Feb 11 2007 - 05:49:04 PST

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