Re: Turing vs math

From: Marchal <>
Date: Tue Nov 9 09:16:23 1999

Christopher Maloney wrote:

>I agree with Bruno in this thread, but I'm not sure I completely
>understand him, so I'm putting this out for comment.


>The question arises when we accept as a starting point what Bruno
>calls "comp", that the universe arises as a result of a computation.

Precisely I mean by comp that I can survive with a digital brain.
It means that I suppose it exists a level of description of
myself such that I survive a functional substitution done at that

I recall that the UD-argument (the PE-omega thought experiment) is
used to show, argue or even prove that with comp, physics is
ultimately a branch of the ``psychology of machines".
That ``psychology of machines" will itself appear as the study
of the stable discourses of self-referentialy correct machines.

For most steps of the UD argument, I am using also the hypothesis
that my brain is enclosed in my skull, and that my brain is a hot
machines (not a quantum brain). But in the last step, I eliminate
these supplementary hypothesis. It means that my reasoning does not
depend on the choice of the level.

Ultimately there is no more ``universe" or any physical *stuff*.
Physical laws and physical sensations should remain and be explained
from the ``psychology of machines".

>Then, we want to know, is it possible for the physical laws of space
>and time to be based on a continuum, or must everything be

Very fundamental questions. Even without deriving explicitely the
laws of physics from comp, the UD argument gives qualitative
information. In particular it shows that we are necessarily
facing continua and most plausibly some uncomputational beasts.

>Is the space we are embedded within really a fine grid,
>with each cell on the order of 10e-23 cm, or some such small number?

Difficult question. With comp we can expect that there are some
continuous observable spectrum, and I think position (unlike spin!)
could be a good canditate, but this is as yet not clear.

>Taking the question further, we can ask whether we should expect
>the probabilities of, say, a given observation to be a real number,
>or rational.

Comp implies that probabilities behave exactly like real numbers.

>If real, how is it possible that a TM can produce a
>real number (or an infinite number of real numbers, corresponding
>to the infinite number of observations)?

That is the point we are presently discussing in the thread.
A simple way to figure out how a TM can generates each real numbers
is by reiteration of the self-duplication experiment.
Let us say the machine duplicates itself in W and M.
Imagine we stop after 64 iterations. We got 2^64 machines.
Each machine makes a self-localisation experiment after each
duplication and write the result (W or M) in its diary.
>From the first person point of view most machines will rightly
consider their stories (obviously identifiable with the sequence of
W and M with a lenght equal to 64 written in their respective diary)
as random, even in Kolmogoroff-Chaitin sense.

>Then I agree with Bruno that due to computational indeterminacy, or
>what he calls the PE-omega (which name I hate, BTW, Bruno), that the
>answer is certainly yes, real numbers, ....

Yes. (BTW I hate "PE-omega" too. I use it because I once use it in
the list, and I thing it will not help to change names especially
for those like myself, and yourself if I remember correctly, who like to
trip in the archive). But ok. Enough is enough. From now one I will
use "UD argument" for the "PE-omega". UD = Universal Dovetailer.
"UD argument" is also the name of the argument in my thesis.

>.....continuous space and time.

I am not up to the point of being able to speak about space and time.
Still less about Lagrangian and Energy. Unfortunately.

>The point is that whenever we make measurements, we are in a
>1-perspective. I liked his description a few posts back of an oracle
>that we can ask for any digit of a real number. Whenever we ask for
>a digit, we get one, no matter how far down it is in significance.
>It doesn't matter that the UD will never produce _all_ the digits
>of any given real. It's enough that from a first person perspective,
>that any given digit will eventually be computed.

What happens is that the personal feeling of being oneself
reconstitute doesn't depend at all of the time the UD will
reconstitute your relevant (relative) computational state.
Whatever way you choose for putting a distribution of probability or
credibility on the set of reconstitutions, it will change nothing
if, in a third person description of the running of the UD, the time
between the reconstitutions is a googol^googol years. The first
person are not aware of such delays. That is why we must take into
account the infinite rather slow UD-generation of *each* real.

>As far as probabilities for observations, these don't have to
>actually be computed by the UTM at all.

... nor do we need an actual concrete stuffy universe in which
that UTM would be running.

>They are simply manifest
>to us, in our 1-perspective, because of the measure and because of
>computational indeterminism.

That follows from the UD argument + a conceptual use
of Occam's razor, like the one use by Everett.
We are using here also Church's thesis and a minimal amount of
arithmetical or computer-theoretical platonism, for sure.
(And with the movie-graph argument alias the crackpot proof we
can elimininate the use of Occam's razor. It's useful in case
you live in a country full of anti-occamists, but it is not
the case for this mailing list).

Note that in the UD argument I am also using a minimal amount of
folk-psychology for giving a meaning to the expression "survive".
This can also be eliminate, by using abstract definition of
knowledge, observation and belief. In that case we are lead to
the provability and modal logics. In that case an abstract form
of the UD leads naturally toward quantum logics.

Thanks for giving me the opportunity of summarizing myself.
I intend to put in my URL an english and detailed version of the
complete UD argument ... soon, hopefully for Christmas.

Received on Tue Nov 09 1999 - 09:16:23 PST

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