Re: Does provability matter?

From: Marchal <>
Date: Fri Nov 16 06:32:41 2001

Quick, but not so quick, comment on Wei Dai, Juergen Schmidhuber
and Charles Goodwin. (I'm busy).
Apologises in advance for some length, though, I
guess you are busy too.
Apology also to those EverythingFOR-listers who get this
message twice. That's the effect of interference
of parallel lists, it doubles the intensity at some point :)

Wei Dai wrote (in the everything-list):

> On Wed, Oct 31, 2001 at 10:49:41AM +0100, Juergen Schmidhuber wrote:
> > Which are the logically possible universes? Tegmark mentioned a
> > somewhat
> > vaguely defined set of ``self-consistent mathematical structures,''
> > implying provability of some sort. The postings of Marchal also focus
> > on what's provable and what's not.
> Do you understand Marchal's postings? I really have trouble making sense
> of them. If you do, would you mind rephrasing his main ideas for me?

And Juergen Schmidhuber answered:

>No, unfortunately I do not understand him. But provability does seem
>important to him. Maybe someone else could post a brief and concise

What about telling me if it is the UDA or the Arithmetical UDA (AUDA) you
have problem with.

In case it is the UDA (that is the proof that comp entails a necessary
reversal between physics and machine/psychologycomputer-science/number
theory) it would be helpful if you tell me which step you don't understand
in the UDA in 11 steps.
(cf ). Frankly.

In case it is the AUDA, (the translation of UDA in arithmetic or in any
language of a sound UM) the difficulty of understanding is more normal,
because the AUDA needs some familiarity with Logic (Goedel Loeb ...).
The importance of provability comes from the fact that like Judson
Webb or John Myhill (ref in my thesis) I consider Godel's 2th theorem as
(the first) theorem in exact psychology, in particular machine
a consistent machine cannot prove its own consistency, or a machine
cannot prove she has (even just one) consistent extension(s).
Hume is right, and provable with comp, indeed.
Now the UDA proves that our "physics" is defined by a measure
on those consistent extensions. So the concept of consistency is very
important, and it is defined from the concept of provability: p is
consistent iff -p is not provable (-[]-p, = <>p).

Modal logic makes works on self-referential machine "easy", at least
with some familiarity in logic. Have you follow my "little course" to
George Levy on modal logic?

But in case you have not understand UDA, perhaps AUDA is premature, I
don't know, logicians understand more easily AUDA, at least formally.

I know a lot of people here developpe similar ideas. I bet a lot of
children, especially the dreamer one, brush against the idea.
And indeed many ScFi writers, like Daniel Galouye in SIMULACRON III, makes
quasi rigorously the point. Still I'm sorry/happy for what
is perhaps some advance from my part :-) I )-:
Simplifying a little bit I made
public the "UDA" including "amoeba-immortality" the ancestor
of "comp-immortality" in 1963. (ok I was young!). I was interested in
amoeba life-time. After that my brain became a battle field between
biology (which will give comp) and chemistry (making me doubt about
comp and becoming eventually the very shape of the comp-doubt).
James Watson says "cells obeys to the laws of chemistry".
To obvious to be true.

I got and proposed the idea of translating such UDA-like
question, in the Godel way, in arithmetic, in 1971, including the
that QM or chemistry should be justified in that way, and (admittedly a
subtil point) that chemistry was a product of the necessity of the
doubt about comp so that matter is defined by a measure on our
ignorance about our possible extensions.

That has given
a project of a thesis I made precise in 1976. The project (and other
projects more "serious" in pure math) have been
rejected, and things of life slowed me down a little bit, let us
say, untill I will publish, under the pression of sympathic belgium
logicians but also engineers, the whole thing in the Toulouse
(France) 1988 paper, and more concisely in 1991.

I will get the proof of LASE (Little Schroedinger Abstract
Equation) only in 1994. This is the first confirmation that not only
comp and its reversal are consistent, but that it is going in the
quantum/chemistry direction as I expected (it is empirically consistent).

You can see that, although I believe the empiry should be explain
by the logical and arithmetical, I really come from the empirical
science. My childhood was contemplation of amoeba, planaria, hydra,
all the animals, vegetals and minerals.

Until 1995 I was sure that someone would find a fatal error either
in UDA or in the arithmetical UDA. In the beginning nineties Brussels
University encourages me to make a Phd Thesis which (for administrative
reason!) I have been asked to propose first as project (again) in 1995.
The project-thesis has been judge non receivable without me being heard
even one second,
(again) pretexting the lack of enough original results (sic).
Although this made very bad publicity for both me and the work,
honest mathematicians and computer scientist in France verified it
thoroughly, so that
I did eventually defend the thesis in France in 1998.
I still have some strong support from paradoxal Brussel's university.
I dream some student in logic will progress in the math part of my work
even if that shows LASE being a mirage (which I doubt). According
to Albert Visser (great Deutsch logician) Russians should be able to
solve the simpler math problems. So it is not *so* easy.
Thanks to quantum computing a shy bridge begins to developpe between
physician and logicians.

Have you see the "mathematical" problems?
Sure, I must still publish an international paper, I am on it.
But still it would help me if you tell me what is that you
don't understand!
If someone found some fatal error please tell me, it is never
to late:)

The fact is that *I* don't understand how Juergen Schmidhuber
associates first person experiences and memories to single (third
person) computations. UDA shows at least that with comp we must take
that problem seriously, so that Schmidhuber proposal is at least
incomplete. Nor do Schmidhuber clearly states its ontology.

In some sense David Deutsch's FOR tackle both matter and mind
more rigorously, but, by still presupposing physicalness at the start
(which is apparent when he considers the Church-Turing "physical"
principle as an attempt to make Church-Turing "mathematical" thesis
more "precise") he fails to appreciate the possibility and still less
the necessity of the reversal, isn't it?

In fact I expect that the Church mathematical
thesis entails the negation of the physical Church principle.
comp entails the apparent universes cannot be entirely
computable (cf comp = I am a turing emulable, not: there is a
universe and it is turing emulable).

BTW I keep the logician expression Church Thesis, for what Deutsch
call "Church Turing thesis", and I am more and more willing
to call Deutsch's "Church Turing Principle" simply "Deutsch thesis".
This would help to prevent confusion between both.
So I conjecture: Church thesis entails the apparent (first person)
negation of Deutsch thesis.
Janusz Cyran send a question about the status of those theses, to the
FOR-list and nobody has answered tmk, but it's a key point we have to
address soon or later.

Charles Goodwin wrote (in the FOR list):

>If the multiverse is effectively a huge computation containing all
>possible information (which as some people have pointed out,
>effectively means that it contains NO information) then it can be regarded
>as simply an infinite array of numbers. The appearance of
>physical reality, time, consciousness etc emerge from the relations
>between these numbers.

If that is not a nice and short summary of my thesis! :-)
(No doubt it could and will summarize other thesis as well, and even
some very different one, I guess what is most original in my work is the
machine "psychological" apparent detour). The math of physical theories
bears also more and more similarities with pure number theory.

>Having re-read that I am starting to wonder what drugs quantum physicists
>are on. However that's the general idea, I believe...

If that were the result of drugs on quantum physicist, that would be
wonderful and I would encourage all physicist to take more drugs,
but I'm glad it is also the result of more prosaic simple working
logic :)

PS for those-FOR interested in QTI, it has been the subject of many
thread in the everything list. As I mention above QTI is most
probably a particular case of comp immortality. The exact form
of such "immortality" (including the range of possible backtracking
like in the post of Saibal Mitra) is obviously difficult to figure out.

The transporter with and/or without annihilation of the original,
with or without delay of reconstitution, play a most important
role in my work (it's the brick of the UDA). Thanks to Russell
and Brett for mentionning this. I hope I will find time to make
some precise comment on the very interesting transporter thread
in the FOR list but as a matter of fact Charles Goodwin gives
very comp-adequate answer so that at this stage I have no a lot
to add. The UDA can be considered as the transporter thought
experiment pushed at its ultimate limit (and the consequence
are that physico/psycho reversal).

About Tipler: its main error (I talk like Russell!) is that
(with comp) there is not one omega-point but a transfinite cloud
of them ... (Is that not also a consequence of reasonable
quantisation of gravitational space?).
Actually with comp you can only prove: that IF there is an omega
point, THEN there are a transfinity of omega point.

Still sorry for the personal remarks, but seing a little bit
where I am coming from (a self duplicating- amoeba fan) could help the
understanding. I will try to explain the precise relationship
 between "Godel" and self-replication on the
everything-list in the post "diagonalisation 2" asap.


Modal logic:
White Rabbit:
UD in lisp:
UDA step by step links:
Diagonalisation 1:
Diag 1 (answers)
Programs for G, G*, S4Grz, Z, Z*,...
Received on Fri Nov 16 2001 - 06:32:41 PST

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