Russell Standish wrote:
> [...] Paraphrasing your thesis, COMP is the
>assertion that "you can survive the replacement of your brain by a
>digital machine" at some level of replacement. I am reasonably
>comfortable with what you mean by survive in this instance. I outlined
>a possible subsitution mechanism whereby the brain is replaced by
>analogue machines, which I don't doubt will allow survival. One can
>then replace these analogue devices by digital ones, simply by
>discretising the analogue quantities in a suitably fine way. Note,
>that there is still instrinsic randomness in the behaviour of the
>neurons, which can be discretised also with digital devices.
>
>I then asked you whether by digital device, you meant a "Universal
>Turing Machine". This is where I part company with you, as I suspect
>that (1-)randomness has something to do with free will.
In that case you abandon Church thesis. With Church thesis all
digital device are Turing emulable, and reciprocally.
I'm afraid I don't see how 1-randomness is related with free-will.
Suppose you are annihilated at some place and reconstituted in
three different cities: A B and C. You know that you are the
subject of that experience and you try to concentrate yourself,
'exercising your free-will' to be the one reconstituted in A.
I suppose that the right level of substitution has been choosed.
Then, although the one reconstituted in A will tell me: "you see
my free will has worked out", I, as a computationalist (here) will
say to the A-you: let us hear what the B-you and the C-you will
say. And of course they will at least appear to be less sure
they free-will has work.
Unless, like Niklas has suggested, the B-you and the C-you will
be so much disappointed that they will become zombie :-)
You are consistent because you are willing to accept zombie.
But that is a too big price for me.
>Therefore, I
>predict that Robot beings based on classical turing machines will
>never have free will (although how one can establish this from the
>outside via a Turing-like test I don't know).
OK, OK, same remark.
>However, if we relax the
>requirement that Robots be strict Turing machines, then I fully
>suspect a machine could be built that had free will, as I believe that
>human beings are no more than machines built from proteins.
Then you must explain me what is not turing-emulable in the proteins.
You are slipping dangerously into Penrose-like non computationalism
again here!
>Now, you are saying that the level of substitution implied in COMP is
>running the whole plenitude on a computer - Schmidhuber style. How
>does this relate to substitution of analogue brains by Turing machines
>within the individual observer world? It seems to me a case of chalk
>and cheese - two things that have nothing to do with each other.
This is really what the UDA explain. I remember that in one of the post
you were adressing to me, you ask me to explain the white rabbit
problem and it is fair enough because I have been rather short in
my explanation of it (cf PE-omega in the list).
See below. I prefer first to answer your last remark to prevent
a misunderstanding concerning the relation between Schmidhuber's work
and mine.
>It seems to me (although I haven't followed you argument to the nth
>degree), that you are claiming in your thesis that
>COMP=>Schmidhuber. That may be true, however, I would very much doubt
>that Schmidhuber=>COMP. You haven't advanced a poof of this.
I give you two proofs.
Remember that by COMP I mean there is a level of description of my
"generalized brain/body" such that I survive a digital substitution of my
"generalized brain" at that level.
Note that Digital = Turing machine, with Church thesis.
(To get the full power of Church thesis I accept also a minimal
amount of arithmetical or mathematical platonism).
By definition my "generalized brain" is the portion of the universe
(if that exists) which is necessary to emulate to make my
consciousness exists.
1) First Schmidhuber clearly believes in a stronger version of comp,
as he told us:
<<According to the computability-oriented view adopted in this
paper, life after death is a technological problem, not a religious
one. All that is necessary for some human's resurrection is to record
his defining parameters (such as brain connectivity and synapse
properties etc.), and then dump them into a large
computing device computing an appropriate virtual paradise.>>
This is at the end of his paper. He does not emphasize on it, but
clearly he believes in the existence of a level of substitution.
Of course I explain and insist that it is both a technological
problem and a religious one. Comp is not provable as self-duplication
experiments illustrates. It need some act of faith.
2) But even if you forget he is telling us that explicitely
you can derived it from the rest (non philosophical part) of
his paper. Indeed, suppose comp is wrong, then there is no level
of substitution such that I survive ..., then the universe or
multiverse cannot be computable or turing-emulable and the
'great programmer" will never generated it (because I belong to
it). Schmidhuber's approach would not even be a plausible
candidate for an everything theory at all in that case.
Note also that COMP => Schmidhuber is ambiguous, because
Schmidhuber postulates there is a (computable) universe.
I do not. (the existence of such a computable universe
follows from comp only in the case my "generalised brain" is the
"entire universe").
***
The Universal Dovetailer Argument. (UDA)
UDA is a proof that: COMP entails REVERSAL physics/psychology.
The reversal will be be epistemological: the branch "physics"
will be a branch of machine's psychology, and ontological: matter
will emerge from consciousness, in some sense, hopefully clearer
later.
Indeed such a reversal will change the meaning of term
like "psychology" and "physics" and the meaning is given ultimately
by the proof itself. By 'proof' here, I mean argument which either
should convince you, which means you are the only judge (no
authoritative argument) or you should find an error.
Of course if you belief that the REVERSAL
is an absurdity, you are free to interpret the proof as a
refutation of COMP (like Gilles Henri, BTW are you still here Gilles?).
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 (digital = turing) + Arithmetical
Platonism (= 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
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).
(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.
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).
b) CU: there is a Concrete Universe, whatever it is. This is need
for the decor.
c) CUD: there is a Concrete running of a UD in the concrete universe.
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 independent.
More generally the result of a computation is independant of
any event occuring a long way (out of the light cone) from that
computation.
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,
movie, crackpot).
The proof. (Apology for those who 'knows').
1) By COMP and NEURO you survive with an artificial digital (turing
emulable, with TC) brain. OK? (CU is used implicitely).
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 implicitely).
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 reconstituted. 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.
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.
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.
6) You are duplicable. (Direct consequence of 5).
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).
(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)
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.
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.
10) Here is an old argument you can find in all idealist school
of thought (Hindouist, Boudhist, 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).
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.
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!).
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).
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.
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.
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).
Exercice: why should we search a measure on the computational
continuations and not just the computational states? Hint: with
just the computational states only, COMP predicts white noise for
all experiences. (ok Chris ?). With the continuations, a priori
we must just hunt away the 'white rabbit' continuations.
You can also show that Schmidhuber's 'universal prior' solution
works only in the case the level of substitution
is so low that my generalised brain is the entire multiverse.
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.
By Arithmetical Realism and OCCAM razor, there is no need
to run the concrete UD, nor is there any need of a real concrete
Universe.
(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.
QED
16) Oh la la, I get tired. I'm sure I have forget things. I
would appreciate any comments, especially skeptical one.
The 'philosophical' proof really stop here. It is not a
derivation of physics from the psychology of machine, it is
a proof that physics MUST be derived from the psychology of
machine OR COMP IS FALSE.
Later I will show you how to eliminate the FOLK psychology
assumption, by substituting folk psychology by the
godelian provability logics and 'simulating' the first and
third person variants with the Thaetetical variations...
... and I will show how, by simulating the UD by the
Sigma_1 arithmetical sentences, the arithmetical version
of the present proof leads naturally toward an
arithmetical version of quantum logic (almost).
With an unexpected gift : a theorisation of the non
communicable part of the theory.
Explaining qualia as uncommunicable part of the observable.
This will also show that George Levy is valid in his recent
answer to James Higgo :-)
Am I dreaming ?
Have a nice weekend,
Bruno.
Received on Fri Jan 14 2000 - 10:54:01 PST