UDA exposed

From: Jacques Mallah <jackmallah.domain.name.hidden>
Date: Mon, 03 Sep 2001 20:28:04 -0400

>From: Marchal <marchal.domain.name.hidden>
>The full UDA appears at http://www.escribe.com/science/theory/m1726.html
>A better more recent version is in the conversation with Joel Dobrzelewski:
>see the main links at http://www.escribe.com/science/theory/m3044.html

    I will comment on the first version because it's the only mostly
complete one that's all in one place. If you have a better version, put it
all into one file if you want me to comment on it.
    The following is quoted from m1726:

> The Universal Dovetailer Argument. (UDA)
>UDA is a proof that: COMP entails REVERSAL physics/psychology.
>COMP is the hypothesis that there is a level such that I survive a digital
>functional substitution of my generalised body/brain (see above) made at
>that level, + Church Thesis (CT: digital = turing) + Arithmetical Platonism
>(AR: the belief that arithmetical propositions obeys classical logic, and
>this independently of my own cognitive ability).
>To sum up: COMP = \exists n SURV-SUBST(n) + CT + AR"

    Here we see the "COMP" with its survival talk. What it means is not
clear. "Me" is a matter of definition, and that has not been provided. But

>Note also that I'm assuming a minimal amount of folk psychology (FOLK)
without which such an enterprise would be meaningless. It is the
minimal amount of psychology to understand that you or someone else
could, in some situation, accept an artificial-digital brain graft,
and to understand the intuitive difference between first and third
person. (See below).

    Intuitive? I still have no clues about why you think "first person" and
"third person" are useful concepts. But lets go on ...

>(the modal 'chapter 5' of my thesis can be interpreted as an
attempt (at least) to eliminate FOLK by substituting it by the
godelian provability logics and its thaetetical variants).
But the real goal of the chapter 5 is to make the derivation of
physics real and concrete.

>Note also that it is the AR part of COMP which will makes COMP an
everything type of theory (explicitely so with the UD). This makes
'my' COMP assumption equivalent to Schmidhuber's one.

>To make the reasoning easy I introduce supplementary hypotheses.
I will eliminate these hypotheses in due course.

>a) NEURO: The neurophysiologist hypothesis. This is a supposition that the
>level of substitution is high, or that my generalised brain is my
>biological brain (the one in my skull) relevantly described at the
>molecular level (let us say).

    OK, I can't see a new problem with this one, although the old problem
that by "level of sub." I guess you would relate that back to the "would
survive" business which has not been defined, is a deeply hidden but
embedded problem here.

>b) CU: there is a Concrete Universe, whatever it is. This is need for the

    OK. Obviously you will get rid of this supplementary hypothesis at some
point, but for now I see no problem with it.

>c) CUD: there is a Concrete running of a UD in the concrete universe.

    This one is actually not obvious, since it requires a universe infinite
in both storage capacity and computing time. A closed universe (assuming no
omega point) wouldn't allow this, for example. An open universe might not
either for that matter. But for now I will accept this assumption. Clearly
though, UD's will be few and far between in any universe that looks like

>d) 3-locality: computations are locally implementable in the concrete
>universe. That is it is possible to separate two implementations of two
>computations in such a way that the result of one of these computations
>will not interfere with the result of the other one. Computations can be
>More generally the result of a computation is independant of any event
>occuring a long way (out of the light cone) from that computation.

    This seems fine.

>e) Conceptual OCCAM razor. I will not insist. That should be easy for
>many-worlder. The movie-graph argument in my thesis is really an
>elimination of occam razor. See also Maudlin's paper. We talk about that
>in the discussion list (key word: Maudlin, graph, movie, crackpot).

    You know I reject the "movie graph" argument, but Occam's razor is
certainly fine with me. Just use it correctly ...

>The proof. (in 15 steps).
>1) By COMP and NEURO you survive with an artificial digital (turing
>emulable, with TC) brain. OK? (CU is used implicitely).

    This is already not OK, since no meaning has been given to the term "you
survive". In particular, it could instead be that you die but some other
guy will live in that brain. That's perfectly compatible with
computationalism, if not with "COMP". It's really just a matter of
definition though. In any case, with a certain utility function you won't
care what definition is used, as long as someone will be in the artificial
brain. Let's see where this goes ...

>2) By COMP and NEURO you survive classical teleportation. This follows from
>1) where the building (reconstitution) of the brain is done a long way from
>the 'reading device' and the annihilation of the original body. (CU is used

    This one is equivalent to 1) I think, and suffers the same problem of

>3) By COMP and NEURO (and implicitely CU, I will not mention it again) you
>survive teleportation with a delay. After the annihilation, your body and
>brain description is keep intact during one year, and then you are

    This is the same issue again. So far at least, other than raising that
question of definition, there haven't been real problems with these
assumptions. Let's continue ...

>An important point is that you (from your first person point of view) will
>not see the difference with the simple teleportation case (case 2). But an
>exterior observator (third person) will see the difference. Indeed for him
>the delayed teleportation last one year.

    Here there is a new problem in that the term "1st person POV" appears.
To the extent that I can define such a view, it's basically what an
observer-moment experiences. Thus it can't extend across time, so there is
no meaning to it seeing teleportation. This problem may return, but again
it's basically a problem of definition so far.
    But caution is called for because the "first person" term is often used
synonymously with the FIN. Has the FIN already been assumed here?

>4) You are teleported from the center of the galaxy to its border. At the
>opposite border a star explodes. This changes nothing: you still survive.
>This follows easily from 3-locality.

    This one raises no new issues.

>5) You are teleported from the center of the galaxy to its border. At the
>opposite border you are reconstituted. (For exemple the scanned information
>has been send in opposite direction from the center of the galaxy, and
>reconstituting machines has been put on the edge of the galaxy). You still
>survive, by COMP and 3-locality.

    (I.e. you are copied twice, and one copy and the original are destroyed.
  Is the remaining copy the original "you"?)
    This one just begs the question of defining "your identity" once again,
though a bit more strongly and making it a little more obvious why the
question is important.

>6) You are duplicable. (Direct consequence of 5). More precisely:
You are 3-duplicable.

    I'm not sure what this one means, but I guess it means that if you are
copied, all copies are considered to be "you". That's one definition that
could be used, so I have no problem with that, although I probably wouldn't
use that defintion myself. The problem here is that it's by no means clear
that you realize it's just a matter of definition.

>And the first person doesn't *feel the split*

    This comment again raises the "1st person" definition problem.

>7) Although your surviving does not depend on the faraway events,
from the first person perspective the event "I survive at the
left edge (let us say) of the galaxy" could depend on the faraway
other reconstitution. The duplicability entails first person
indeterminisme, although everything is determinate for a third
person. (It is really the computationalist 3-determinateness
which entails the computationalist 1-indeterminateness).

    There is a huge problem with this one! I see no indeterminism entering
anywhere. If "you" is defined to include all copies, then by definition the
collective "you" see all copies' situations. If not, I can give no meaning
to #6.
    If I am copied, then with a reasonable utility function, I would care
about the fate of all copies regardless of whether they are defined to be
"me" or not. I will also note at this point that making copies is a process
that increases "my" (or "similar to me") measure, just as destroying copies
decreases it. That's not to be forgotten as measure will become important a
bit later.

>(exercise: show that the duplicability entails the unprovability
of COMP. Hint: consider teleportation without annihilation of the
original, with a delay, applied to a non-computationalist)

    I don't see what you're driving at here. In any case, both "COMP" and
computationalism itself are obviously not provable.

>8) You are 'read' and annihilated in Brussels and the information
is send to Washington and Moscow. You are reconstituted at Washington
and the information is keep intact at Moscow during one year. Then
you are reconstituted at Moscow. (Duplication with assymmetric
delay). The point is the following: whatever the way you choose for
quantifying the 1-indeterminisme in the symmetric duplication, you
must quantifify in the same manner the assymmetric duplication.
This follows from COMP and 3. The first person cannot be aware of
the delays.

    This one seems to raise no _new_ problems that I didn't mention already.

>9) There is also a form of 1-non-locality. Although your surviving
does not depend on faraway events, your expectation of personal
experience does depend on faraway events. Here also, it is the
strict 3-locality which entail the 1-non-locality.

    If you mean here the "indeterminism" I have already explained why that
is a problem. For practical purposes it may be convenient for me to reason
as though (for example) QM implies randomness in what I can expect, but this
is really not true.
    It's like, when I design a test to give to a class that I'm teaching, it
may be convenient for me to treat the student's knowledge as a random
variable, even if I know that some students know things that others don't.

>10) Here is an old argument you can find in all idealist school
of thought (Hindouist, Budhist, Platon, Descartes, Berkeley, etc.)
It is based on the notion of dream, but today it is more easy
(especially with COMP) to convey it with the notion of virtual reality. The
point is: For any neigborhood and any time interval, you can build a
computing machine simulating that "space-time" at such a level that a first
person will not be able to see any difference. (The computing machine
preserves the relevant counterfactuals). Roughly speaking a first person
cannot distinguish 'real neigborhood' with virtual (digitally simulated)
neighborhood (for all level 'below' its own substitution level).

    I think this one doesn't raise _new_ problems.

>11) To sum up: the way you quantify the indeterminisme is independent
of the time, the place and the nature (real/virtual) of the reconstitution.

    I see no _new_ problems with that statement.

>Note: the indeterminism is pure 1-indeterminism. Nevertheless, by
duplicating entire population, the indeterminism can be made
third person 'verifiable' inside each multiplied population. This
leads to what I call first person of the plural indeterminism.
(I would like to know a better english expression for that!).

    The note I guess refers to a situation like QM where the probabilistic
nature of it is (though false) known to the general population.

>12) A Universal Dovetailer exists. (Extraordinary consequence of
Church thesis and Arithmetical Realism). The UD simulates all
possible digital devices in a quasi-parallel manner).
>(Adding a line in the code of any UD, and you get a quasi-
computation of its Chaitin \Omega number).

    This 12) is just a statement of math, I take it. (As opposed to CUD
above.) Sure, some programs are UD's.

>13) So let us assume CU and CUD, that is let us assume explicitely
there is a concrete universe and a concrete running of a UD in it.
This need a sort of steady state universe or an infinitely expanding
universe to run the complete infinite UD.

    OK so far.

>Suppose you let a pen falls. You want predict what will happen.
Let us suppose your brain is in state S at the beginning of the
experiment. The concrete UD will go to that state infinitely often
and compute all sort of computational continuations. This is
equivalent to reconstitutions. It follows from 11 that your
expectation are undetermined, and the domain of the indeterminism
is given by the (infinite) set of reconstitutions. To predict,
with COMP, what will happen you must take into account all
possible histories going through the state S of your brain.
And here clearly the NEURO hypothesis is not used. Even if your
real brain state is the state of the actual concrete universe,
with COMP that state will be generated (infinitely often) by the
UD. Same reasoning if your brain state is the quantum state of
the universe, so the reasoning works even if the brain is a
non local quantum object (if that exists). So the physics is
determined by the collection of your computational continuations
relatively to your first person actual state.

    I take it that this is the crucial step, the real heart of the UDA. And
here the problem, perhaps related to the problems of defintion that I've
been pointing out, is that you ignore MEASURE.
    Sure, an infinite universe will contain some machines that simulate N
steps in a UDA. Consider an open universe like ours.
    But if the measure of such machines is m(N), then in a universe like
ours most likely m(N) will be proportional to V exp(-kN), where V is the
volume of space being considered (assume V is very large), and k is some
constant. Even worse, the UD itself will revisit any given computation more
and more slowly, so this decay of measure will have even worse effects on
the measure of each computation within the UD itself.
    It's also true that the measure of "normal" people (those implemented
outside UD's) will decay as V exp(- k' N), but surely the total measure of
"inside UD" will be negligable compared to "outside UD" people. (It's a lot
easier to built and maintain regular brains than to build and maintain a
    Now, even with the FIN that the "outsiders" would dominate would also be
true, so the UDA doesn't even hold up with the FIN.

>14) If 'that' physics is different from the traditional empirical physics,
>then you refute COMP. But with COMP you will not refute COMP, isn't it? So
>with COMP you will derive the laws of physics, i.e. invariant and
>similarities in the 'average' continuations of yourself (defining the
>measure on the computationnal continuations).

    This one would have been OK if 1)-13) had been well-defined and true, I
    But even then one must remember the assumptions such as CUD that might
be refuted by physics.

>15) Once you explain why arithmetical machines are statistically right
to believe in physical laws without any real universe, such a real
universe is redundant.

    That I agree with, and it's independent of the preceding stuff. That's
why I think "white rabbit" studies among the set of all possible
computations could be useful. But obviously, no one has come close to
showing that the typical experience would be statistically "right".

>By Arithmetical Realism and OCCAM razor, there is no need
to run the concrete UD, nor is there any need for a real concrete

    That would be true if "statistically right" had been shown. Even if
1-13) had been true, it would still leave the possibilty that CUD is false,
that CU is true, and that the statistics would not be right.

>(Or you can use the movie graph argument to show that a first
person is not able to distinguish real/virtual/and *Arithmetical*
nature of his own implementations, and this eliminates OCCAM.)

    I don't see why you'd bring in that. As you know, I reject the "movie
graph" argument, but I agree that mathematical implementations _might_ be
giving rise to consciousness.

    To sum up: the UDA contains four basic errors:
1. Key terms are not defined.
2. "Indeterminism" is assumed, but there is none.
3. The fact that the CUD's would have negligable measure is ignored. This
one invalidates the UDA even if FIN is assumed.
4. The fact that CU might be true but CUD false is mentioned, but then

                         - - - - - - -
               Jacques Mallah (jackmallah.domain.name.hidden)
         Physicist / Many Worlder / Devil's Advocate
"I know what no one else knows" - 'Runaway Train', Soul Asylum
         My URL: http://hammer.prohosting.com/~mathmind/

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Received on Mon Sep 03 2001 - 17:34:42 PDT

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