Wei Dai wrote:
>Marchal, I'm trying to understand your paper. I hope you can help by
>answering some questions.
I will try. Please tell me if I fail.
>1. Please define "computational extension". What is an extension? What is
>it an extension of? What does it mean for an extension to be consistent
>(consistent with what, in what way)?
>
>2. In your posts you often use the word "comp". What does it stand for,
>and can you please define it?
>
>3. In section 4, you use several results from what you call "the Godelian
>study of provability". What is this field formally known as? Is it
>metamathematics? Are there any good textbooks on this subject?
>
>> Moreover, if quantum mechanics is the correct description of reality, we
>> must derived it from computationalism.
>
>Why must we? I think it would be nice if we could, but we probably won't
>be able to. In order to do it we would need to show that quantum mechanics
>is the shortest algorithm for generating observers-moments. We may be able
>to obtain some evidence on this (for example by running simulations of
>alternative physical laws), but I don't think this is something you can
>derive by deduction or thought experiments.
I begin by question two. The word "comp" abbreviates "computationalism".
It means the conjonction of three hypothesis:
1) It exists a level of description of "myself" such that I remain
invariant through a functionnal substitution of part of "myself" by
digital devices, where the substitution is done at that level of course.
This hypothesis is a modern version of Descartes Mechanism. A short
way to enunciate it is "I am a machine", except that "myself" here is
anything which needs to be taken into account for my "surviving" through
the substitution. I don't pretend we know or we can know what is our
level of substitution. The thought experiment are more easy if we suppose
the level high, i.e. the level of brain neurons for exemple. At the end
of UDA I explain how to eliminate that "highness of level" supplementary
hypothesis. (UDA = Universal Dovetailer Argument).
A quasi operational view of that hypothesis is to say that a
computationalist practionner is someone saying "yes" to its brain
surgeon when he proposed an artificial digital brain (or body, universe,
etc.). Comp entails also the possible use of classical teletransporters.
I use here a minimum amount of "folk psychology" for the understanding
of "I remain invariant" or "I feel nothing". It is the same amount
which is need to understand that someone is anxious before going
to the hospital for an important operation. It is used in the UDA, but
"folk psychology" is replaced by the "provability logics" in the
Arithmetical translation of the UDA. What I call now AUDA to make
things more clear.
The two other hypotheses are needed only for making the reasoning
more precise:
2) Church Thesis: Anything computable is Turing computable. I give
the conceptual reason for this at
http://www.escribe.com/science/theory/m3344.html
I guess you know the empirical result: all attempts to define
the set of computable functions leads to the same set (from Babbage
to Deutsch!).
3) Arithmetical Realism: The truth of an arithmetical proposition
(like "24 is not a prime number" is independent of me, you, humanity,
etc.). In particular this entails that proposition like "the machine
with godel number n does not stop on the input 24" is absolutely
true or false. It means also that our background logic is classical.
It is my ontological commitment: numbers (at least) and their
definissable (in Fortran, or Turing ...) relations exists.
I use "comp" in the sense of 1)+2)+3). It is different from
Schmidhuber's comp where a universe is supposed to exist and to be
computable. I suppose only that "I" am computable whatever I
thing what "I" could be.
More on this in my first presentation of UDA in the list:
http://www.escribe.com/science/theory/m1726.html
(But the UDA is more simply done step by step at
http://www.escribe.com/science/theory/m3044.html).
I recall your question 1:
>1. Please define "computational extension". What is an extension? What is
>it an extension of? What does it mean for an extension to be consistent
>(consistent with what, in what way)?
I give you first exemples. The basic one is given by the WM
duplication thought experiment. In that experiment I am "cut" in
Brussels and pasted at both Washington and Moscow. The state of
my mind at Washington, with the belief "oh! it looks like Washington"
is a computational extension of my computational state in Brussels.
So, roughly speaking, computational extensions of my current
computational history are given by the accessible computational
states. (Extended with some "logical rules" so I can use local
reasoning by the computationalist practionners)
With comp, at Brussels I cannot prove that I will be at Washington
so it is possible that I will not be at Washington (here it means
I will be at Moscow). More generaly if I cannot prove p, it means
-p is consistent for me.
That is: if I cannot prove p, it means there is a consistent
extension of me such that p is true in that extension.
In such a talk I identify a "world" with some maximal extension.
In UDA you need only the simple definition: accessible computational
continuation.
>3. In section 4, you use several results from what you call "the Godelian
>study of provability". What is this field formally known as? Is it
>metamathematics? Are there any good textbooks on this subject?
It is metamathematics.
The best book is Boolos 1993 "The logic of provability" (ref in my
thesis, or look at "Boolos" in the archive).
A good intro is Boolos and Jeffrey.
A textbook is Smorynski "Self-reference and Modal logic".
A popular introduction is Smullyan's "Forever Undecided".
>> Moreover, if quantum mechanics is the correct description of reality, we
>> must derived it from computationalism.
>
>Why must we? I think it would be nice if we could, but we probably won't
>be able to. In order to do it we would need to show that quantum mechanics
>is the shortest algorithm for generating observers-moments. We may be able
>to obtain some evidence on this (for example by running simulations of
>alternative physical laws), but I don't think this is something you can
>derive by deduction or thought experiments.
I know. That is why I would appreciate people show me wrong, because
my point is a proof that IF comp is true THEN the physical laws are
derivable from the logic of provability (what I like to call Machine
Psychology). UDA is the proof.
Physics is given by some universal average on the machine consistent
extensions as viewed by themselve (cf the 1-person/3-person distinguo).
It is a (admittedly counter-intuitive) consequence of comp by the UDA.
The AUDA shows that the "probability 1" on those consistent extensions
(defined in the language of a sound universal machine) has some
quantum logic feature, which confirms comp (through UDA).
Also, when you say that QM should be the shortest algorithm, I am
afraid you share with Schmidhuber a proposition on the mind body
relationship which I show to be inconsistent with comp. You seem
to believe that the mind brain relation is one-one. That is why
I try to challenge you on this point. UDA is really a question. It
shows that although with comp we can associate a mind to a computing
machine, we cannot associate a computing machine to a mind but some
sort of infinity of them. Mind-body is one-many relation.
Hoping I'm not too quick or too long. Don't hesitate to ask me to
be more clear where you feel I am not. I never pretend my work
being simple. (My problem is that a lot of people find some
part difficult but it is rarely the same part).
Bruno
Received on Thu Nov 22 2001 - 09:27:53 PST