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-févr.-07, à 10:05, Stathis Papaioannou a écrit :

>  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, Löb, 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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