>[Gilles:]
>...In all your thought experiment you seem to
>assume that it is possible to reproduce *exactly* the behaviour of a
>physical system (the brain) with some detailed computation.
[Bruno]
This is indeed my working hypothesis. To be precise I suppose there is a
level of description of myself such that I survive through a digital
substitution made at that level. I don't care if the level corresponds to
the quantum state of the entire cosmos or just the local concentration of
neurone's neurotransmettor ...
>I think it is
>impossible : the physical reality is not computable exactly, at least in
>our present knowledge...
I am not sure about that...
All solutions of Schroedinger equation are provably turing computable.
Classical mechanics (in all reasonnable representations) is turing
computable. deterministic chaos is turing computable...
Quantum computer are turing computable, even if that entails an
exponential slow down.
Actually it is rather hard to build a differential or fonctionnal
equation such that it admit non turing computable solution. It is even
not totaly unambiguous how to do that thanks to the different possible
choice of Real's representations. Pour-el and Richard did it, I mean they
build ad hoc differential equation and use an extension of turing
computability on the reals (which is not the one proposed by Turing)
which has non turing computable solutions. This has hardly convince
physicists of the existence of some non computable behaviour in nature.
This is so true that Penrose asks us a rather big leap of imagination to
get some uncomputable aspect in the universe.
I suspect you are using the computability notion in the sense of
"practically computable" function. I use it in the TURING sense ! It is
not a question of prediction, but just of emulation. You cannot predict
the weather for tomorow, but allowing arbitrary computationnal steps and
tapes, wheater is turing emulable. Remember that Schmidhuber's great
programmer is infinitely patient, which is enough for my purpose.
> A very profound reason for that is that we do not
>know how to describe it, independantly of the physical laws that govern it.
OK. That is why "operationnaly" computationnalism consist in a BET on a
substitution level.
But these remark are not relevant. I am not asking you if you belief in
comp, I am just asking you if you understand what I mean by comp, and to
accept it for the sake of the discussion.
>That's why you still have room to make any hypothesis on the nature of the
>reality! But that forbids to consider systems strictly "equivalent" to
>other ones. You can build machines that will "mimic" other machines up to
>some level and during some time, but their fate will necessarily diverge at
>some point.
Indeed, but this is true even for an appendicite operation.
I mean that, BY DEFINITION, if COMP is correct, and if the level of
substitution is correct then I will come back from the hospital with the
same feeling of someone coming back after a succesfull operation.
Of course it is an event in my life, and my life will diverge from the
possible life I would have had having not go to the hospital.
>I didn't find [PE-omega] in your thesis, may be because it is an
>English acronym for the experiment that you describe in French? I suppose
>you are speaking of the replacement of a brain by a digital one, with a
>possible infinite duplication of one person.
You can find the PE-omega experiment in the archive of this
discussion-list, for example in James Higgo's quotation, precisely at
http://www.escribe.com/science/theory/msg00473.html
In my thesis
http://iridia.ulb.ac.be/marchal it is the "argument du
deployuer universel".
>The problem that I see with this experiment is that it poses the problem of
>the definition of identity, which is a sand-heap like problem. It is not a
>*physical* problem but a *semantic* one. We, high mammifers that have had
> to
>struggle with the physical universe, have developed the notion of identity
>in a case where it was rather well defined, because there is no natural
>mechanism that duplicates large organisms. (however such a mechanism does
>exist for simple cells, as you remark yourselves at the beginning of your
>thesis). However, this notion, like all human notions, could become
>unappropriate in different conditions. If we were really able to
>"duplicate" the brain (which has to be proven),
That will never be proved (unless we are inconsistant). Actually it is
not difficult to proof that IF there is a level such that I survive the
substitution at that level, then I will never been able to prove that I
will survive the substitution at that level.
About "identity", it is not necessary to define it at the start of the
reasoning. Of course, the conclusion of the reasoning will shed some
light on new ways to understand the notion. At the first step an attempt
toward a "correct definition" is premature.
>...we should more carefully
>redefine this notion. We can argue that two realizations based on the same
>initial brain should be consider as the same entity, or the contrary. But
>again it is a semantic problem, and for me it cannot give you any clue on
>the nature of the world
I suspect this is because you are physicalist at the start. The question
"do I survive substitution ..." is not a semantical one. It is a natural
question anyone can ask his physician before any (serious) medical
operation. Only if you follow the reasonning (or if you find it by
yourself) will you see how comp provides precise and fundamental clues on
the nature of the world.
> (just like asking whether viruses are living
>organisms or not doesn't help to know their replication mechanism). Indeed
>in our real world, true twins are born from the same cell : in this case
>they *are* actually considered as different persons.
Sure !
>So I think that in the case where duplication would be possible, we would
>naturally modify our notion of identity. We may for example think us as an
>"array" I[1], I[2]...instead of a single person. The I[i] would share the
>same history at the beginning,,but differ after some time. All the
>questions and paradoxes related to the question "who is "I"?" would
>disappear simply because we would be led to adapt our notions to a new
>reality, and this question would loose any sense, because "I" would have
>lost its property of unicity.
I am not saying there is a paradox, we are just at a begining of a
reasoning
The important point is that each person remains a person from the first
person point of view. This is basic folk psychology without which term
like "consciousness", "survive", etc; has no meaning.
>(A comparable evolution has already been made
>in QM for example, where the question "where is the electron?" has lost its
>sense). That's why I call that a "semantic" problem, and not a physical
>one.
Indeed, but for those who think twice on Everett, we loose our identity a
long "time" ago. What is true for the electron is true for the physicist.
And this can be deduced from comp. QM is a rather unexpected confirmation
of comp.
> After this mental revolution , we would face the same problem of
>understanding the origin of thought!
>... but for this reason, and as a physicist, I wouldn't call it an
>"explanation" at all...
OK, But wait. I am not even searching such an explanation. I am just
proving that those who believes in comp MUST find such an explanation. I
also show in my work some necessary and important qualitative aspect such
an explanation must take (for exemple the many worlds phenomenology).
Note that, according to my proof, you are coherent. I am just showing the
incompatibility of comp and (even very weak form of) physicalism. If I am
correct, you are both physicalist and non-computationnalist. I tell you I
respect that position, and there is no reason my proof should change your
mind.
On the contrary, those who belief in comp AND in physicalism must either
change their mind, or tell me at which steps in PE-omega they find an
error.
If you are not willing to accept (at least momentarily) comp for the sake
of that proof, you will never see my point or find an error in it (My
point is that IF comp is correct THEN matter is a product of the mind,
and physics is ontologicaly reduced to psychology, where psychology is
defined by the discourses and silences of self-referentially correct
universal machines relatively to their most probable computationnal
histories.)
Comp is interesting because it gives astonishingly powerfull clues for
the logical and arithmetical origin of machine's belief in physical laws.
(The roots of the non-trivialness of these clues are linked to the
non-trivialness of Church classical thesis and subsequent incompleteness
phenomenon).
I strongly recommand Wheeler's paper "Laws without law" for a
pre-physical motivations for such an enterprise.
But of course, if you take the universe for granted, like most
physicalist, then "my proof" is just not relevant. Physics and the
Foundation of Physics are quite distinct matter.
So now, if you are still interested in the proof, keep in mind the
hypothetical nature of (turing) computationnalism.
Cheers, Bruno.
Received on Mon Mar 15 1999 - 02:35:22 PST