Re: on formally describable universes and measures

From: <juergen.domain.name.hidden>
Date: Fri, 16 Feb 2001 18:03:12 +0100

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

> From: Marchal <marchal.domain.name.hidden>
> Juergen wrote (among things):
>
> >But how to answer an ill-posed question? You promise that "time and
> >space will disappear at the end of the reasoning", but your question
> >is about delays, and how can we speak about delays without defining
> >time? Simulation time? Real time? Both? How? There is no way to continue
> >without formal framework.
>
> We were doing a thought experiment. I haven't say that the delays were
> virtual. This is done much later in the reasoning. Of course, as George
> Levy says the permutation real/virtual makes no changes in the first
> person point of view, and does not change the distribution either.

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.

> IF we accept COMP we survive with
> an artificial brain (Well: in case we were betting on a correct level
> of substitution).

What is a "correct level of substitution"?
Where does the betting come in? On which alternatives can we bet?
Which is the distribution on the alternatives?

> That means the doctor scan (at the right level) your brain, destroy

What is the right level?

> it, and then from the recollected information he builds a new one.
> The state of the artificial brain mirrors the state of your brain.
> You survive (with comp!).
>
> Now let us suppose the doctor keeps the information hidden in a drawer
> during one year.
> Real time delay, in the every day-type of life.
> After that delay he makes the "reconstitution".
> I am just saying that, with comp, from the point of view of the
> one who survive, that delay cannot be perceived. It has not influence
> the kept information of your brain.
> 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,"
as opposed to "directly perceive"? You open your eyes - things have
changed - another time, another place. Which are the limits of perception here?

> (that's why I insist sometimes that reconstition booth has no windows!).

why sometimes, why sometimes not? Anyway, in general things will
have changed - you may need some technical equipment to detect the
changes, still, in principle you could find out things are different,
at least in the real world. If you cannot, then why not - which are the
assumptions here? Maybe you are talking about a virtual reality that you
can fully control? Then which is the precise set of virtual realities
you are considering? Is there a probability distribution on this set
(if not, you cannot predict anything)? Which one?

> Are you seeing my point ? It does also not change first person perception
> in case of self-multiplication.

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.

> >There is no way to continue without formal framework.
>
> I isolate a unique formalisation by an informal reasoning.

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

> To formalise
> at this stage would automatically put the mind-body problem
> under the rug.

Didn't you just say there is a unique formalisation?
Why does formalisation suddenly "put the mind-body problem under the rug"?
What's the problem with the mind-body problem? Why is it incompatible
with formalisation?

> A TOE which doesn't address (at least) the mind-body
> problem is a TOS (a theory of *some* thing).

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

> But as I show below, those self-multiplication are easily
> formalised (at least the third person description of those experiment
> are easily formalised). You can easily write a program which multiplied
> yourself (still betting on a correct level of course) relatively to
> virtual environments.

Correct level? Betting? On what - which are the alternatives?
Which is the distribution on the alternatives?

The program that multiplies observers _seems_ to go into the direction
of a formal ansatz, although it remains vague. How does the program
identify an observer, or myself? It is much easier to write a program that
copies entire computable universes together with the embedded observers,
because such a simple program does not need to identify observers
and separate them from their environment. Please state precisely what
you really mean. Don't give another informal example, be precise.

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

Not necessarily.

> How do you manage consciousness in your TOE-approach?

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.

> How do you relate consciousness and computation.
> I'm afraid you are making "unspoken assumption" about the
> mind/body/computation relation all along your work.

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. We may
remain agnostic as to whether "consciousness" is a well-defined concept
at all. Just like we may remain agnostic as to whether "greenishness" is
a well-defined concept. If there are any conscious computable observers
then they will be computed as parts of certain computable universes.
If there are any greenish computable observers then they will be computed
as well.

> >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?

> Let us reiterate the self-duplications, applied on you, 16 times.
> I ask to all (2^16) Schmidhubers if they can predict the W,M
> sequences appearing on their T-shirt.
> Some, like WWMWWMWWWWMMMMMM will pretend that the sequence is
> computable: it is indeed the beginning of the binary
> developpement of PI. Most will accept it is just not computable.

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

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?

> To make things a little more formal, you can program that
> self-multiplication, including yourself as a subroutine, and
> making Washington and Moscow virtual.

As mentioned above the program P for self-multiplication within a given
universe is in principle much more challenging than program Q which
multiplies entire universe histories. Q does not care for any observers
it multiplies, while P somehow has to identify them and separate them
from their environment. It is far from clear what that might mean.

> In particular the UD does that. But I am still anticipating.

What is it you are anticipating?

> >Is the distribution computable?
> >How does the distribution depend on your delays and other computable (?)
> >things?
>
> The point is that the "credibility-distribution", whatever form
> it will take, cannot depend, with comp, on arbitrary delays for the
> reconstitutions. Nor can it depend on space, nor on any subtance ...

What is a "credibility-distribution"? Is it a probability distribution?
If so, why not call it a probability distribution? Define "credibility,"
define "arbitrary delays," define "reconstitutions," taking into account
the issue of separation of environment and reconstituted being, if that
is important to what you are doing.

> (I anticipate, but you can read my CC&Q paper, cf my URL below).

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

> In another post you say:
>
> >Yes. My point is: as long as we are not forced by evidence, why assume
> >the existence of something we cannot describe or analyze in principle?
>
> 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.

> Just to see how much constructive philosopher you are,
> if you have the time, tell me if you accept the
> following proof ? Perhaps you know it.

I accept all formal proofs derived from formal assumptions.

> So we know for sure that either (sqr(2)) ^ (sqr(2))
> or ((sqr(2)) ^ (sqr(2))) ^ (sqr(2)) provide the solution, although
> we don't know which one. Do you accept we have nevertheless
> prove that there exists couple of irrational numbers (x,y)
> such that x^y is rational ?
> (The problem with constructive philosophy is that there are
> quite a lot of them. I am trying to find which one).

If there is a formal system and a formal way of deriving theorems,
and one of the theorems is a symbol string such as:
exists(x, y): x^y=p/q and x,y in R and p,q in N,
then where should be the problem with this?

Since your example is about numbers computable in the limit, it is maybe
not quite as challenging as you wanted it to be. Let me try to give
another example that seems to pose a greater challenge to constructivists
as it seems to concern "uncountable" things: There is a formal system
producing theorems such as "exists(x): x=2^aleph_0".

No problem though. "exists(x): x=2^aleph_0" is just a finite bistring
derived from certain axioms that tell you how to manipulate finite symbol
sequences such as 2^aleph_0.

The interpretation of 2^aleph_0 is another issue. Some have a vague idea
of uncountably many things represented by the symbol string 2^aleph_0.
But that is indeed just a vague idea without formal justification.
Any first order theory with an uncountable model has a countable model
as well. There is no need to map the string 2^aleph_0 onto this vague,
undescribable concept of "cardinality of the continuum", whatever
that may be.
Received on Fri Feb 16 2001 - 09:32:00 PST