On 08 Dec 2010, at 22:15, Brent Meeker wrote:
On 12/8/2010 11:19 AM, Bruno Marchal wrote:
On 07 Dec 2010, at 22:40, Brent Meeker wrote:
My reservation about step 8 is that the activity, in order to be a
computation, must have an interpretation.
Hmm... This is already a bit ambiguous. Suppose some (real)
computer computes factorial(5). Some people could say that in order
to be a computation of factorial(5) we need a human interpreting
the physical process as a computation of factorial(5).
I would not. But I agree we need here some 'physical' interpreter
of the program.
Suppose someone dream that he computes fact(5). Here we can agree
that we need a physical interpreter interpreting or executing the
brain so as to compute the "dream of the computation of the
factorial by that person". But it is not the physical interpreter
which computes the factorial, it is the dreaming person. And the
person would be doing that computation even if nobody look at the
brain and interpret that brain as "dreaming that someone compute
factorial(5). OK?
Sure, the person is interpreting the meaning, but I would say he is
only doing so by reference to a world in which there are
quintuples. It is because he can wake up and hold up his hand say,
"I dreamed that this many fingers is prime."
All right. Of course, (but you know this), he is living in the
"standard model of arithmetic" where 5 is prime. Actually 5 is prime
in all the models of arithmetic: it is stable universal belief.
If the computation realizes "I'm thinking about the number 5."
then "the number 5" must mean something in this context.
It must mean something to the person thinking to the number 5. Not
to someone observing that person.
OK.
Otherwise the same strings of symbols might compute, "I'm thinking
of blxght." In order for "the number 5" to refer there must be a
context in which the number 5 exists in some sense. This is fine
for your theory and in fact that's how you ground it by noting
that we all agree on arithmetic and that there is a number 5 in
arithmetic. But then it seems the same applies to "I'm thinking
of a chair." In order for that to be a possible interpretation of
the strings there must be some referent for "chair". Of course
you can say the "chair" refers to some bundles of computations of
the UD that are related to "sitting" bundles, etc.
Hmm... the ambiguity is present throughout that reasoning. I think.
I will try to answer the next line:
But then you are just saving the theory by mapping the physical
world back into it.
Once we assume comp, and assuming that the 'generalized brain' is
the usual biological brain inside the skull (to make the pictures
more easy), all we need is a computation of the relevant states of
that brain.
But here is where I think you help yourself to too much. It is only
because the biological brain exists and evolved in a certain world
that it has "relevant states". We as outsiders cannot generally
observe what the brain is thinking about (it's as though it has
invented it's own simulation code for the world), but you help
yourself to the assumption that it is thinking about things - things
that you and I can communicate about, i.e. are in our common world.
But that point is valid both in the "real (putative) physical world"
and in a simulation of the "real physical world" occuring in UD* (the
entire execution of the UD).
So, this kind of argument will not work for distinguishing the two. In
both situations there is a referent relatively to the states of his
brain, even if immaterial in the second case (but he cannot know that
immateriality directly, or there is a magic, non Turing-emulable,
property of "real matter" playing a role in consciousness).
This create a human interpreter experience of "thinking" to the
chair. That computation might be a dream by someone who know well
about chair, and has seen many example of it in his memory-life.
Now the UD will "generate", in his special static way, infinitely
many computations going through those relevant states. They are all
described by sequence of phi_i^n (j), n = 0 to infinity, with the
different computations being distinguished by different i and j.
OK? "n" represents the computational steps of the computation of
phi_i(j), and the computation are really given by the arithmetical
(and computable, in the mathematical sense) relation linking (i,
j, n).
For example phi_587610093811908883744
(45456901000456338867611906369579006532113536953) could describe
the quantum state of a computer emulating that "human thinking of
the chair",
and many others with (actually) much bigger index i and data j.
(note that even with the same i and j there are infinitely many
computations, those being based on different universal interpreters.
But each universal interpreter provides a mapping from such numbers
to...what? another world, I think.
You can call that an "another world", but those type of worlds are not
distinguishable from just another universal computations.
A good thing, because in fine, if you ask to a physicist what is (the
scientific description of) a physical reality, he will just select one
universal computation. He will say something like DeWitt-Wheeler
equation + this or that initial condition, without reifying reality.
Only an anti-comp, or anti-marchal (I mean anti-UDA), philosopher will
insist on reifying matter. The trouble is that such a move makes
either my brain non Turing-emulable, or introduces a curious physical
supervenience thesis where either neurons have prescience, or where my
consciousness depends on future contingent events.
(below I will refer to ABOVE. It is here, I mean the paragraph just
above).
Some computation could emulate the quantum state evolution of the
super cluster of galaxies including the Milky way, and thus the sun
and earth and the guy thinking to that chair (and all his life with
all its chairs).
Now, UDA1-7 and the movie graph (UDA-8) shows that the guy, which
plays the role of the interpreter of its own brain state is unable
to distinguish any of those phi_i^n(j). Actually, it shows we
cannot distinguish a phi_i(j) computed by the real "galaxy" if that
exist, and the one emulated by the DU in arithmetic, emulating the
same galaxy (at a level relative to the relevant state of its brain
'course).
This is the tricky part. The same computation in the guy's brain
can be interpreted as an emulation of the milky way or as thinking
that five is prime. He provides the interpretation of the brain
state - in his world.
OK, except that "his world" is really "his most probable computational
history". Typically, like in QM-without-collapse, he "belongs" or is
"supported by" an infinity of computations "done" by the UD.
The physical activity are the one described by those many
computations, and this predicts that if the guy looks below its
substitution level, he should find the trace of the infinitely
computations going through those relevant states (by first person
indeterminacy).
Are you assuming that, at the substitution level, the interpretation
is unique - regardless of which world it is in?
That's the point. The interpretation is unique at the substitution
level. That is why I say yes to the doctor and have to pray he has
chosen the right substitution level. It is unique like the
interpretation that the heart is pumping the blood is unique once the
heart is substituted by a sufficiently genuine pump.
Suppose someone says that for consciousness to exists we need the
"real physical galaxy" (whatever that could mean). Then it means
that whatever computations going through its states, none are
enough for his consciousness to appear (he remains zombie).
Or that computations must be physically realized and that determines
where the consciousness appears.
See ABOVE.
But I'm not arguing that there must be a physical world (though
that would be one solution). I'm arguing that there has to be a
world that provides the interpretation of the numbers. I realize
that this world can consist of just some class of numbers, but
whatever it is, it seems to me it must be arbitrarily large and
arguments about brain states and substitution are fallacious because
they implicitly help themselves to the bigger world in order to
ground their interpretations.
Some reality has to provide the interpretation of the symbols, but
that is exactly what a model does in logic. To interpret 0, s, +, x,
we need a set (N) and the additive and multiplicative relations. That
is why comp (DM) needs some amount of arithmetical realism. We don't
need, and the argument shows we cannot need, to pick up any special
universal function at the bottom. So we can take arithmetic, or the
combinators, fortran, lisp, etc., and whatever is that choice, the
physics will be given by a "sum" on all computations going through my
actual finite computational state (which I hope my doctor has
correctly delineate).
But that means (assuming comp) that we have not choose the right
level of simulation, and this means that we have to go deeper in
the UD, using phi_i(j) with still bigger j and i. Or it means that
the real galaxy contains something which prevent any emulation of
it to appear in the UD, but that means that his generalized brain
(of the guy thinking to the chair) is not really emulable by any
computational process, and this means he should better say no to
the doctor.
So, depending of the substitution level, for emulating the right
amount of "activity" we have to map sufficiently deep digital
truncation of the 'physical world'. But that means that the real
physics, from the point of view of the guy who has his first person
(plural) reality) indeterminated on any of his relative
incarnations in the deployment of the UD, will be given by the sum
of all the truncated part of all the digital truncations of all the
multiverses/multidreams in the whole (sigma_1) arithmetic.
We will never been able to map the whole physics in one computation
of the UD, given that physics is a first person (plural) view
defined by all its digital incarnations in the UD, and that leads
to a sum on the entire work of the UD (this really comes from both
the invariance of the first person for the UD-delays, and step 8).
So you have to really address the step-8 point, to reject
immateriality, to link consciousness to something not Turing
emulable. But then I'm afraid you have to attribute a physical role
to object having no physical activity relevant to a computation
done in "real relative time". That seems to me to be an ad hoc move
close to non sense (assuming comp throughout). So consciousness is
not related to a physical active brain, but to the infinitely many
arithmetical relations relating those states.
It is not excluded that *some* universal number (a "physics") plays
special prominent role, but then, what the reasoning shows is that
the existence of such number(s) have to be derived from the
"arithmetical measure problem". The loss, is any simple basic
physics (but then try to predict an eclipse with Feynman integral
with all the decimal exacts). The gain, with the classical theory
of knowledge, is that we get both the quanta and the qualia (by the
G/G*, Z1/Z1*, etc. splittings).
But doesn't that splitting depend on interpreting relations between
computations as representing certain conscious thoughts? I don't
reject it on that account, since if it can be shown to predict
things that's as much as we ask of any theory. But it seems to me
that you have so far only an analogy between proof and belief.
At last. I was waiting that objection since more than 30 years!
That 'analogy' is NOT an analogy for the case of ideally correct
machine saying "yes" to their doctor. So all what is needed is that
your belief system to be close for the same logic as Peano Arithmetic
(or any Löbian theory) so that you can follow (if *you* want) the
doctor explanation when he talks about the third person description of
your brain. So you need only to agree that your beliefs result from
rules like "neuron 345 is connected to this and those neurons, and are
activated in such an such conditions, etc. + the belief that if you
belief A and A->B then you will belief B. This means that (B(a->b) &
Ba) -> Bb. etc. It makes you a mechanical extension of Peano
Arithmetic. Then, once you accept that there is finite digital
description of your instantaneous state, G/G* will apply on you, and
this at all level where you can describe yourself in a third person
way. It will not apply to your consciousness, which is not even
definable (it uses the Theaetetical Bp & p, which is not representable
in your brain-system). So G/G* applies to you ... as far as such
finite description exist, and as far as you (and your doctor) are
correct (which you cannot know, but still bet on) when working on your
brain.
Your everyday beliefs can be much less correct, making such a
mathematical notion of belief looking a bit analogical. But they have
to be correct when thinking about your brain, or more indirectly when
letting the doctor thinking about your brain, when you accept the
digital substitution, because if they are not, it means you will not
survive the substitution.
Such correctness is absolutely unprovable by you (nor by your doctor)
so that you have to be conscious that saying "yes" to the doctor
really ask for a leap of faith, making comp really like a religion,
which it is, given that it is a belief in a form of reincarnation.
And so, scientifically, comp protects, paradoxically, those who want
to say "no" to the doctor. The belief in non-comp is consistent with
comp, like the belief in the inconsistency of Peano Arithmetic is
consistent with Peano Arithmetic.
This makes comp a sort of absolute Gödelian sentence for all machine,
and this makes comp absolutely unbelievable (when true and it is still
'inductively inferable').
And that is why I never said that I belief in comp, because I know
since 30 years that such a belief would make me inconsistent.
And that is why I like to use the term "theology". Comp itself belongs
to G* minus G. It is a bit obvious because to say yes to the doctor is
like believing in a consistent extension of yourself, that is like to
belief in your own consistency, which you can't by Gödel second
incompleteness theorem.
Comp is a secret, (this is how I call the G* minus G proposition). It
is very near inconsistency. Nobody can even take it as an axiom: it is
a sort of meta-axiom, which we can bet on without ever being able to
prove it, even in a one line theory taking it as axiom.
Note that this is the case for any belief in any reality sufficiently
rich to encompass ourself. BDt -> Bf. (By Gödel Completeness Theorem,
Dt is equivalent with "there is a model (reality) of myself. To be
sure this is only provable for Löbian machines talking first order
language, and/or sufficiently effective higher order reasoners).
Bruno
http://iridia.ulb.ac.be/~marchal/
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