Re: on formally describable universes and measures

From: Marchal <>
Date: Thu Feb 8 07:40:15 2001

Hi Juergen,

You wrote:

>> Juergen wrote:
>> >Your vague answers to questions I did not ask keep evading the issue of
>> >continuum vs computability in the limit. I give up. JS
>> Let us try to be "very precise", then. I propose you the iterated
>> self-duplication experience.
>> Assuming computationalism, we survive. (I guess you agree).
>> Here is the question. Do you expect the (infinite) sequence in {W,M}*
>> appearing on your t-shirt to be
>> computable or uncomputable ?
>> In case you want to restrict to the finite sequences appearing at each
>> step,
>> I propose then we stop the experience after 1000 steps. In that experience
>> do you expect the sequence of W and M (lenght = 1000) to be
>> compressible or not compressible ?
>> Bruno

>Very precise? T-shirt? Never mind, I think I now completely understand
>your reasoning. Contradicting my announcement to give up I'll try once
>more to point out your unspoken assumptions and what is unsatisfactory
>about them.
>You expect finite future observation sequences to be incompressible,
>because most binary strings are incompressible.

I asked you a question. I didn't ask you to demolish a answer I have
not given !

>The unspoken assumption is a uniform distribution on equal-sized prefixes
>of possible futures.

I am afraid you anticipate to much. I agree that in the finite case
the uniform distribution is funny and almost inescapable. In particular
if we do the experience, my computationalist moral and my democratic
feelings entail that I will listen to each 'Schmidhubers' after 1000
And I will try to communicate with all of them, and feel more at ease with
the majority, who, as you agree below will answer "uncomputable".

But, actually, I do not pretend I am able to organize that democracy,
and that distribution. Through *all* my proof the distribution
remains unknown.

What I have done is terribly modest (even if it looks like a 180 degree
revolution). I (just) prove that IF there is a level such that I survive
a finite substitution) THEN the following are equivalent:

-solving the mind body problem,
-extracting the laws of physics from
-defining that distribution.

At least, that is what I do in the first part of my thesis. In the
second part I show how to isolate the distribution by the
interview of the UTM. But let us forget this second part for some

Note also:
1) with Everett: The iterated self-duplication experiment is not a
*thought* experiment, just look 1000 times a Schroedinger cat and
write M or W on your t-shirt according to the
death/alive state of the cat (of course each Schmidhuber will
be isolated, and can still *pretend* (without proof) to be a
'compressible' one).
2) with comp : it is not a thought experiment either, the UD
does slowly all the multiplications in the platonic realm.

(But I see in your second paper that you disagree with standart QM,
which does hold phenomenologically in Everett, though).

>When you say indeterminacy you just mean probability 2^-n for each prefix
>of size n. There is nothing "shocking" or "weird" about it (your words);
>you just assume one particular computable probability distribution on
>finite prefixes of futures.
>That's ok. Although it does represent a limitation, because there are many
>other computable probability distributions on possible universe histories,
>and theories of everything (TOEs) should take all of them into account.
>Then, however, you make a bold step and generalize from computable things
>to noncomputable things: you expect infinite future observation sequences
>to have no finite description, because most infinite binary strings do
>not have one.
>The unspoken assumption is a uniform distribution on all infinite strings.

I don't make that assumption. I aknowledge that sometimes I talk like
I am doing it, in general to simplify illustrations of some point. Sorry.

>The problem was pointed out repeatedly - one cannot generalize from
>finite prefixes to a continuum of infinite objects without leaving the
>realm of computation and dovetailers.

Here I disagree, but let's go on. (You are correct from the 3-person
point of view (3P-POV), but it is not necessarily correct from the

>Any dovetailer producing a growing
>binary tree can output only countably many nodes, never a continuum.

I agree here ! But I am not interest in the output of the UD. I even
considered the UD as a typically never stopping nor outputing program.
You misunderstand my use of the UD.

>The issue of 3rd person vs 1st person is irrelevant here.

No. It is *here* that the issue of 3rd person vs 1st person is quite
relevant. See below.

>So is the issue
>of enumerating the reals in a "list" - it is already enough to observe
>that in countable time you cannot produce uncountably many things, only
>their prefixes.

OK (but it will be no relevant)

>For a long time your claim that "there is no computable universe to which
>we belong" has not made any sense to me, but now I realize that what you
>really mean is just that if our universe is uniform randomly sampled from
>the interval of real numbers then with probability 1 it is not computable.
>This is an ancient result.

This is a progress in your understanding. And my point has
probably some relations with this ancien result, although I have not
prove that, still less use it in my thesis or paper.

>Your underlying assumption is the existence of a noncomputable selection
>process selecting one of uncountably many objects.

Not at all. The uncomputability comes frrom the fact that I don't
know in which computation I am.
I just do listen to Schmidhuber1 *and* Schmidhuber2 in the
(simple) duplication process, for exemple. In fact I don't believe
there is any selection process. I give a similar status to each
person (third person description) and I listen to the discourse of
each one (first person descriptionS).

"Taking the two" is really in the spirit of the *everything* list.
"listen to the discourse of each one" is exactly what Everett has
done, in .

> This has nothing to do
>with your computable 2^-n prefix probabilities above, or with computation
>in the limit, or with dovetailing, or with truly algorithmic TOEs. You
>have a NONalgorithmic approach here.

I have told you before that comp entails a necessarily NONalgorithmic
approach. If we are machine we cannot know which machine we are,
and we cannot know which computational pathS support us. We can
only make (hopefully correct) guesses. My realm is classical
arithmetical truth. That includes a lot of definite but uncomputable
truth. I can guess you will, like most people who eventually
understand my proof, reject COMP (the arithmetical platonist part).

But you should remember that the set of all total computable functions
has no total universal computable function. I should read more
carefully your second paper, but the great programmer in the first
paper create and execute programs which does not stop on some
input, and this in some unprovable ways.

>To summarize: There are many possible computable distributions on
>equal-sized prefixes of futures. You pick a uniform one, perhaps
>because unbiased coin tosses seem natural to you. But as soon as
>it comes to infinite objects the uniform distribution is LESS natural
>than many others, because infinite sequences of coin tosses do not yield
>describable results, and thus do not even exist from any descriptive point
>of view. You seem to think you can save the situation by "dovetailing"
>over ALL infinite sequences constituting a continuum. But the continuum
>is beyond dovetailing. This forces you to leave the countable and
>constructive realm and invoke your nonconstructive "arithmetic realism",
>whatever that may be. Your "proof" just restates that the reals are not
>countable, or that one cannot compute universes that are not computable
>in the limit. On the other hand you do assume the very existence of
>things noncomputable in the limit. This existence does not derive from
>your dovetailer argument, since the dovetailer always will stay in the
>computable realm. So you make a major assumption besides those rooted
>in computability theory.
>I guess Occam wouldn't like this additional noncomputability assumption,
>this assumption of the existence of nondescribable things, because it is
>unnecessary, given what we know. There are describable ways of assigning
>nonvanishing probabilities to certain infinite futures characterized by
>finite descriptions. Of course, the corresponding describable selection
>processes will never select any future that is not computable in the
>limit, but we can discard those anyway, because they don't even exist, in
>the sense that we cannot even describe them, not even through a dovetailer
>which at best can output finite representations of all futures computable
>in the limit, but never the full continuum!
>Such reasoning leads to algorithmic TOEs as opposed to nonalgorithmic
>approaches like yours (or Tegmark's, who does mention Kolmogorov
>complexity at some point but avoids details).

I am indeed closer to Tegmark. You takes too little. Tegmark
takes too much.

>As long as the distribution is approximable or computable
>in the limit, one can show that only histories with finite
>descriptions can have nonvanishing probability, and that only
>histories with short descriptions can have large probability:
>That's why flying rabbits etc. are unlikely.

To summarize: I don't make any assumtion on the distribution.
My result is a reduction of the mind-body problem to the
problem of the origin of the machine's belief in thelaws of physics,
itself reduced to the serach of that distribution.
Some aspect of your work woulod confirm my work, unfortunately
that will not happen if you don't take into account the
point of views of the machines embedded into the *grand*

Here you
demolish an answer I did not provide. You miss my point because
you still don't see the relevance of 1/3 person distinction.

I hope your are not really a constructivist because they don't
believe in neither the uncomputable nor in the third person.
They don't accept the arithmetical realism in my standart
(classical) view of comp. (They don't need to study my proof!).

I appreciate your work, but my proof shows it is just a beginning.
You can reject my "classical comp", as I should call it perhaps,
but then you will miss not only the solution of the mind-body
problem, but you will also miss the origin of the physical laws too.

At least you agree with something. In the experience of self
multiplication , there is an uncertainty, and so there is a
distribution of probability, belief, whatever ... I will call it
The Unknown Distribution TUD (not to confuse with the UD!).

Now let us go back to the relevance of 1/3 person distinction.
For reason of clarity, and because I'm not sure people will read
this post until here, I ask the next question in another
post. I let it in the same thread.
Well, I will post it tomorrow. (get late in my work ...).
It will be a little post with a "very precise" question.

Received on Thu Feb 08 2001 - 07:40:15 PST

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