Re: on formally describable universes and measures

From: Marchal <marchal.domain.name.hidden>
Date: Mon Feb 19 06:14:15 2001

Juergen Schmidhuber wrote:

>This time I'll annotate your entire message to demonstrate how many
>things I tend to find unclear in your texts.


Thank you. (Hereafter TE means "Thought Experiment")


>To derive consequences we need to know the assumptions. Of course, this
>holds for thought experiments as well. Without defining delays you cannot
>derive something from delays.


You have no problem (according to your post) with the TE where you
are annihilated in Brussels and reconstitute simultaneously at W
and at M. (TE1)

In the TE with delay, it is the same TE except that now you are
reconstitute in W, and only one year later (let us say) you are
reconstitute at M. (TE2)

It is a thought experiment. You must imagine I am really proposing you
that experiment, and I am using the expression "one year" in
the traditionnal english sense.

It is precise (although admittedly not formal) because with
comp I can in principle do the experience.

My question is "knowing that you are at Brussels before the
experience, are your expectation the same in TE1 and TE2?

I am using the word "delay" in the english traditional sense,
which is all what is need in the thought experiment.

Of course if you have still not understand more than 2/15
of the UDA TE, I can believe the rest of my work
*must* appear unclear.


>What is a "correct level of substitution"?

People of the list will be bored if I repeat this again.
I explain what is a correct level of substitution each time
I recall the definition of COMP.
(This prove BTW you don't have read neither ma thesis, nor
my paper CC&Q, nor the UDA posts.)


Those who knows can skip what follows. Of course some revisal can be
helpful.

Suppose that the neurophilosophers (like the Churchland,
Francis Crick, ...) are
correct. Then you can survive with an artificial brain which emulates
your neurons. In that case the "correct level of substitution" is
roughly speaking the level of neurons.
 
Suppose you "survive" only through a simulation of
the big bang at the level of the quantum superstring, membrane, etc.
then the "correct level of substitution" is the level of the quantum
superstring, membrane, etc.

Remember the definition of COMP, it says that *there exists* such a
level. It does not say that "this" or "that" *is* the correct level.
It is a sort of admission of ignorance. This ignorance is
fundamental. Indeed it has been shown (independently by a
lot of people---ref in my papers) that comp entails we cannot
know the correct levels.
We can bet on it, though, and we can make reasoning
relatively to correct bets.

Normally a constructive philosopher should abandon comp right here,
because it follows from that theorem that we cannot be machine in
any constructive sense.


>Where does the betting come in? On which alternatives can we bet?
>Which is the distribution on the alternatives?

The betting comes from the theorem mentionned just above.
(Although it follows partially from most of the UDA too).

In the W-M TE the alternatives are given by the reconstitutions.

With the assumption that we are living in something described by
schroedinger equation, the alternatives are given by some quantum rules.

The alternatives are unknown and part of the problem with
comp. It has been shown they are linked to the structure of UD*.
Defining the set of alternatives is part of our problem.

>What is the right level?

I don't know.
No machines will ever known "the" right level.


>Only the drunken Schmidhubers will say it is incomputable. Most will
>just say "the history so far is computable by a lengthy program".


You miss the point. Even the one who as PI on his T-shirt is
wrong if he believes PI helps him to predict the issue of the
next self-duplication.
Note that if the program remains as lenghty as the sequence, as it
happens for most Schmidhubers---in the iterated self-duplication,
these sequence are called uncomputable by Solovay, Chaitin, etc.


>> From the first person point of view the delay introduced by
>> the doctor
>> has not been and cannot been directly perceived.
>
>That seems obvious, but what exactly do you mean by "perceive,"


I am glad you see it is obvious, because it *was* my point.
What is your point asking
what I mean exactly by "perceive" at this stage. The goal
of the UDA TE is indeed to help people abandonning prejudice
about the easyness of the issue. To help them ro realise the
hardness of the mind/body problem with comp. (A lot of people
tend to belief that comp is the solution of the problem, I show
it helps on the road toward a formulation of the problem).

Try perhaps to read the
whole UDA for getting the general idea, first.


>> (that's why I insist sometimes that reconstition booth has no windows!).
>
>why sometimes, why sometimes not?

Are you just playing with me?
  
I use reconstitution booth without window to illustrate the fact
that no person can, from a first person point of view, guess if
he/she/it is the one reconstitute at W, or the one reconstitute at M,
with or without delay, by themselves (by introspection).

(It is the obvious fact you mentionned above indeed).

I use reconstitution booth with windows to illustrate that
a third person communicable observation (looking outside)
can provide the information.
Another obvious fact.

Most of the UDA steps are really obvious indees. Nevertheless, taken
together they entails the reversal.


>Maybe you are talking about a virtual reality that you
>can fully control?

No, no ... In the TE W/M with or without delay, I am just
considering our good old planet earth about 2000 after JC.
In the UDA at each step the decor changes a little bit.
At the end we meet the Great Bastard lazily dovetailing on
all computations. (And we don't need to control it either).

To be frank, I am less and less sure you are reading seriously
my posts.

> Then which is the precise set of virtual realities
>you are considering?

I am considering virtual realities much later in the argument.
Why are you making remarks which has indeed no relation at all
with the post ?


>Your point is the revival of an old science fiction theme.
>But as soon as you want to derive something you need to state formal
>assumptions, otherwise you'll end up with empty philosophic blabla.


You need only to make *precise* assumptions. You don't need
to make *formal* assumption. In most TE occuring in the
"philosophy of mind" (or cognitive science), but also in the
foundation of physics, you cannot be formal
without *first* choosing informal philosophical assumptions.


>Is there a probability distribution on this set
>(if not, you cannot predict anything)? Which one?


You talk really as if probability was the only manner you
know for quantifying uncertainty.


Beside probability there exist other ways to handle the
uncertain. The one I know
the best is Dempster-Shafer theory.
(I have work some years with expert in that field).

Glenn Shafer has written a
classical little treatise: "A mathematical theory of
evidence" 1976, Princeton University Press.

Some modal logic provides even quite different type of tools
for approaching uncertainty.
Some are genuinely useful when we handle uncertainty where the
domain of uncertainty itself is uncertain.
(the domain of uncertainty is not unrelated with the reference
class of Wei Dai's post).

But I told you: the whole UDA reasoning consists in showing that
the search of the way to quantify the computationalist uncertainty
is equivalent with comp to deriving the laws of physics from
the laws of machine's psychology.

Why Probability and not Dempster-Shafer credibility, should any
one (knowing Dempster-Shafer credibility or any other
way to handle uncertainty) asks.

Choosing probability at this stage is like giving an answer
before understanding the problem.

This is just a forbidden move after having accepted comp.
(you should
understand this clearly when you will proceed on the 15 point of
UDA).

Now, anticipating (the two part of my thesis) I admit I do
expect probabilities playing an important role and that is
why there are aspect of your work I appreciate.


>An essential issue is: are they all equally likely? Do you you assume
>a uniform distribution on the possible futures? Is that what you mean
>by indeterminacy? If so, why not simply call it a uniform distribution?
>
>Note there are many alternative distributions besides the uniform one,
>that is, there are many alternative TOEs. Different TOEs, different
>predictions. Why restrict yourself here to a uniform distribution?


I repeat. (I agree this is a subtil point: the way for handling
the unknown is itself unknown!).

Not only I do not restrict myself to the uniform distribution, but
I don't share your assumption that the only way for quantifying
uncertainty is probability. Why not Dempster-Shafer theory of evidence ?
or any other credibility theory you can find in the literature?

We just don't know how to quantify the Computationalist Uncertainty
(herafter QCU).

And we haven't clear a priori views even on the domain on which that
uncertainty bears.

One of the reason why it is difficult is that
with comp the uncertainty is *very* big, as Descartes saw (with
a weaker form of *mechanism*) : we could "dream".

The great programmer
like Descartes' Malin Genie, build conscientiously all dreams and other
fake realities.
But the real problem with comp is not really that we dont't know in which
computations "we are", the problem is that the first person (plural) are
spread onto rather complex structured set of computations, which put
enormous doubts on the very sensefulness of the idea that we belong
to a computation or that we belong to a universe.
 It is part of the problem to throw light on those complex structures.

When you will realise that all the UDA steps are obvious, you will
understand that even the word "universe" becomes quite vague, and
necessarily so.

But that huge ignorance does not prevent us *at all* to make precise
reasoning on the QCU, and to put it in relation whith known things.

In particular the thought-experiments with
comp are used to show that the QCU is invariant for a set of
transformations (describable in third person term) on UD*.
The thought experiment are all possible
*in principle* and are not vague at all. Some of which can even
be cheaply realised once we accept Everett formulation of QM.
(if only for the sake of the argument).


This makes possible going toward an equation in which the QCU itself
is the unknown.

And my main result is a reduction of the mind-body problem
to the problem of the origin of the laws of physics, itself
reduced to the search for that QCU.

In the first part of my thesis:
I am not pretending that I have solved the mind-body problem, nor
the problem of the origin of the physical laws, nor the QCU.
But I have rigorously proved that with comp these problems are
equivalent.


In the second part of my thesis I show with a little more than
comp (here I am vague, but look at the thesis) that the
certainty part of QCU obeys a "quantum logic" defined by
the aritmetical sentences of the form
BEW(p) & -BEW(-p) with p arithmetical sigma_1 formula.
(and BEW = Godel's Beweisbar's predicate).

Thanks to Solovay's theorem I provide theorem provers for these
logics. That is, in the second part, I propose a precise
100% mathematical road to the QCU.

A weakness is that I am lead toward hard mathematics.


>I accept all formal proofs derived from formal assumptions.


What does that means? I guess you mean a consistent set
of formal assumptions.
Assumption about what? And how will you link your assumptions
and your subject matter?
You speak here like a pregodelian formalist :-)

>Your point is the revival of an old science fiction theme.
>But as soon as you want to derive something you need to state formal
>assumptions, otherwise you'll end up with empty philosophic blabla.


You are confusing "rigor", precision, and formalisation,
again. You should perhaps read the nice little book by
James Brown "the laboratory of mind" which explain what
is a thought experiment. He shows that some informal but
precise TE can demolish philosophical prejudice. UDA is
of this type. (Brown J., Routledge, 1991).


>Which unique formalisation? Please write it down!
>How can you possibly isolate it by informal reasoning?

I was talking *there* about the modal logic G, G*,
S4Grz, Z1, Z1*, etc.
These formal logics are intensional (modal) variation of the
provability logics of the sound self-referentially correct
machine. I have provide semantics, and theorem provers.
See explanation and technical details in my thesis and in my
papers.

All formal systems are enfered by informal reasoning allied
with intuitive view of the subject matter.


>I found your CC&Q paper as vague as your other texts.


Obviously: you need a formal definition of delay in a thought
experiment where such a definition has no relevance at all.
So you are hardly willing to honestly *do* these thought experiment.
No doubt much of the paper and much of the posts should appear
 a little difficult.

You are also telling us that informal classical mathematics is vague
because they admit sets like the set of all functions from one
infinite set to another. I am not the one isolated here in making
sense of these sets. You cannot pretend I am the one
pretending 1+1=3! It is a dishonest rhetorical trick.

Those who have patiently follow the steps are in general quite
shocked by the conclusion (the reversal),
but then, at least, they act honestly: either searching or
hoping for a precise flaw, or just abandoning comp.

It looks like it does not occur to your mind that *perhaps*
I have a point and that you just don't have seen it yet.

Why not trying being a little more modest, mister "I-am-right".

Have you a prejudice against
the whole approach or what ?


>Without formal assumptions you have
>no theory of everything, no theory of something, no theory at all.

Without informal assumption you cannot use the theory in the
philosophy of mind and of matter aswell.
You persist confusing rigor and formalisation.
 

>> If I fall from a flying plane, being a realist (though not a
>> subtancialist) I believe I will fall somewhere, although I have
>> no means to describe or analyse where.
>
>This is again the issue of describability, given current knowledge, vs
>describability in principle. We are talking about the latter, of course.

"Of course" ? Certainly not in the TE. What are you saying?
Please read the archive, we have discussed this a lot
on this list (cf RSSA versus ASSA (relative self sampling assumption
versus absolute self sampling assumtion).

You always take the relation between observers and computations which
support them as granted. I don't. I cannot abstract any
question of prediction from the "current knowledge" at the moment of
the prediction.

There is no problem with having different opinion, but don't tell me
one is obviously wrong and one obviously correct.
This is again sort of rhetorical trick.


>> Are you among those who argues that talk on consciousness is a hoax ?

> Not necessarily.


:-))



>Algorithmic TOEs are about computable probability distributions on
>universe histories computable in the limit. Such histories subsume
>all computable evolutions of all computable observers, including the
>conscious ones, if there are any.


I am always afraid when I meet people who are doubting
the existence of people's consciousness.
My feeling is that you *do* think that consciousness is a hoax.
That was my impression, as I told you, after reading
your first paper. You just confirm that you don't
believe there is a mind/body problem. (Like so much "scientist" BTW).

Not a big problem, you can still understand the reversal
without studying the mind/body problem.


>No. There is no need for a definition of what it means to be conscious,
>or how to identify a conscious observer in his environment.


You ask me to give a formal definition of delay when I use it
in the every-day life folk sense, and you are willing to talk
on consciousness without clarification ????

We don't need a definition, that is true, but we need some
axiomatics.
That is we need to agree on some feature of consciousness, like
the fact that a conscious entity cannot prove (even informally, still
less formally) it is conscious to another conscious entity.
Here we must agree also on the difference betwen believing and
proving, etc. We can demolish prejudice about it through TE, and
we can make these distinction formaly precise through
formal modal logics. I propose both and explain the link.
 

>> >What exactly is this indeterminacy?
>
>Yes, what is it? Is it something different from an ordinary distribution?
>If so, what is it? If not, why don't you call it a distribution?


See above.


Bruno.

 

 
Received on Mon Feb 19 2001 - 06:14:15 PST