Dear Bruno,
Snipping a lot.
----- Original Message -----
From: "Bruno Marchal" <marchal.domain.name.hidden>
To: "Stephen Paul King" <stephenk1.domain.name.hidden>
Cc: <everything-list.domain.name.hidden>
Sent: Friday, January 31, 2003 6:44 AM
Subject: Re: "I" the mirror
> Hello Stephen,
>
>
> At 13:18 -0500 29/01/2003, Stephen Paul King wrote:
> >Could you translate these symbols into words so that I could better wrap
> >my mind around them and spin them around in my head?
>
>
> BM:
> Basically []p = provable p in such a precise way that
> 1) you can verify the proof in a finite number of mechanical steps
> 2) grosso modo p is made true in all recursively enumerable
> maximal extension of the machine/theory
> <>p is -[]-p you should read <>p by consistent p. That is the fact
> that -p is not probable, so that you get no contradiction by adding
> p as a new axiom to the theory or to the machine roots belief.
[SPK]
So <>p is "it is not provable that not p"? This is a double negative
implying that your logic follows the law of the excluded middle. That is ok,
but I was hoping that you would see that as being a logicwise subset of
Intuitionistic logic, ala Topos and Heyting Algebras...
snip
> SPK:
> > I take "consistent" means that given some
> >formal model, whose exact definition must be given somehow ...
>
> BM:
> Any machine or theory extending classical logic and capable of
> proving elementary arithmetical theorems.
[SPK]
Umm, what are the bounds of this "extension" of classical logic. Any
possibility of getting into contectual or modal aspects, such as []p iff
some x implies p, where x is some context that may vanish in some limit. An
example of this is found in solutions of the "grue" paradox.
snip
> SPK:
> > We may note that "machines" are usually defined by some set of
functions
> >N -> N, where N are the Natural numbers.
>
> BM: Read my to diagonalisation post for making this precise. I would say
that
> controlable machine, constructive reals, and total computable function
(where
> total means defined on all N, can be, in our context, identified. But
> such a set is not *recursively* (mechanically) enumerable!!!!
> All "my" enterprise, and actually Church thesis, are made consistent by
the
> fact that the set of total computable function is a necessarily fuzzy set
> include in the set of all computable functions.
[SPK]
You are avoiding my question! How is this "fuzzyness" defined? Is it
some analogy to the boundary of a recursively enumerable set or is it some
membership function that can range over [0,1] or some thing else?
> SPK:
> >I am very skeptical that this
> >(countable) set of numbers alone is sufficient in itself to cover the
range
> >of all possible systems in Nature (the Totality of possible existential
> >expressions, including all mathematics). Given this caveat, is this
within
> >your notion of a definition of these words?
>
> BM:
> Please read carefully the diagonalisation post. Church thesis is really
the
> "schroedinger equation" of comp. I mean a highly non trivial statement in
the
> fundamentals of mathematics. It is the roots of the incompleteness
phenomenon.
> Before Church thesis you could have believed that "to be a machine" is a
> simplifying assumption. After Church thesis we know that machines,
> and universal
> machines in particular" have unbounded complexity. Universal machines are
> mostly lucky unpredictable being.
[SPK]
What is the link to the diagonalization post? It is true that I have a
"problem" with the Church thesis, but it is that it seems to be myopic and
limited. I see no analogy between the Church thesis and SWE other than a
mapping function "->" such that Church thesis is about N -> N and SWE can be
considered to be about C -> C, but it is obvious that N \subset C and not
the otherway around.
snip
> >[SPK]
> >
> > What I am trying to argue is that we can not abondon eiter sup-phys
nor
> >comp except in the very very special case where the distinguishability
> >between the two vanishes, e.g. a neutal monism that obtains in the
infinite
> >limit of all possible existential (or ontological) expressions and,
> >additionally, we must not be so cavalier in our postulations.
> > As I have tried to argue before, the notion that the mind is UTM
> >emulable is not a proven fact and at this point should be considered to
be
> >merely a conjecture.
>
> BM:
> It cannot be taken as a conjecture. It is an hypothesis which has the
> curious feature that if you add it as an axioms it becomes false!
[SPK]
This is what bothers me about it, it is like the Createan what is honest
so long as he never speaks a word and yet you do not seem to allow for a
resolution of the Liar paradox other that demanding silence, ala Russell's
solution. I hope some day soon we can explore the notion of non well founded
sets that Peter Wegner proposed as a means to generalize the notion of
computation.
> (This is a known feature of modal logics or intensional mathematics).
> So "the notion that the mind is [consistently] UTM emulable" is not only
> not a proven fact, but it will never be a proven fact, even in the
> seemingly trivial sense as being provable in a theory which take it as
> axioms. I use modal logic because it is so easy to be wrong in intensional
> (modal) context.
[SPK]
I wish that you would be more specific on this "modal logic" other than
references to books that are impossible for me to buy. :-(
> SPK:
> >The thought experiement using classical cloning and or
> >teleporting of minds has several assumptions that are contrary to known
> >physical facts, such as the imposibility of simulataneously measuring the
> >position and momenta of all the required atoms of a brain such that a UTM
> >could be defined that would emulate its behaviour. This, in itself, leads
me
> >to reject the entire notion of "brain cloning" and any idea that depends
on
> >it as simple idealistic. It is as fantastic as a pink unicorn. I see not
way
> >in which the classical teleportation is possible in the "real world".
>
> BM:
> I use brain cloning (and the neuro hypothesis) to make my argument
> simpler. Then I explicitely eliminate that hypothesis.
> The elimination is based on the fact that the UD will generate all
> your digital quantum state.
[SPK]
How is it a "fact" that the UD will generate all "your digital quantum
state"? Since when is a quantum state reducible to a finite "digital"
sequence? Did you forget about Kochen-Specker already? You wrote that you
read the Calude, Svozil et al papers and yet do not seem to understand the
very simple notion that they prove: there does not exist a Binary or Boolean
valuation for a quamtum sustem whose Hilbert space is greater than 2
dimensional.
I could see that one could argue for finite approximations and propose
some kind of "superselection" rules that limit the linear superposition of
QM states but all of the models that I have seen that did this failed
miserably.
> You can postulate that you are not a quantum digital machine, for example
> that you are some analogical quantum machine capable
> of handling in finite time infinite precision. But in that case you are no
> more in the context of the comp hypothesis. I have no problem with that.
[SPK]
I am trying not to postulate anything, especially " analogical quantum
machine capable of handling in finite time infinite precision"! The closest
that I have read about are Malament-Hogarth Machines... It seems that you
misunderstand the notion of Qunatum computation in general ... :-(
snip
> >[SPK]
> >
> > Umm, this confuses me! How can we think of UD as "generating" all of
> >physicality via computational simulations but yet seems to require the
prior
> >existence of the reals (numbers), oracles, etc. This looks like a
"chicken
> >and the egg" problem!
>
> BM:
> You always seem to forget that I don't postulate any form of physicality.
> For me term like "matter" or "universe" are like the term "phlogistic" or
> "God". That is very, very, very, ..., very vague term which confuses us on
> fundamental questions. Those term have local use but we will not progress
> if we reify them and take their referent for granted. It would be like to
> finally criticize a molecular biologist because he has not yet explain the
> vital principle.
[SPK]
I agree, you do not postulate any for of "physicality", but that is not
the point that I am trying to make. Appeals to Platonia are just as "vague"
as "phlogistic" and thus I fail to understand your critisism. Notions such
as "position", "momentum", "spin", on the other hand, are not vague at all!
snip
> >[SPK]
> >
> > Again, you can not do this "postulating" and make ontological
claims.
> >This is not like Euclid's postulation of points! But furthermore, why do
you
> >not postulate more than just N-> N and arithmatic operations? It seems to
me
> >that Goedel's incompleteness theorems necessitate and infinite nesting of
> >metatheories to span the universe of mathematics such that a Totality of
the
> >"mathemacial universe" is not even enumerable!
>
> BM:
> You are right. But Godel's theorems are provable by the machines, and that
> is the reason why I don't need to postulate explicitily those tranfinite
> progressions. Numbers in numberland also dream about infinite nestings of
> metatheories. There is a sort of SKOLEM paradox here. I postulate just the
> meaningfulness of the standard model of "Peano Arithmetics" (let us say),
> and then I show that this countable model, seen from inside (1-view), is
> bigger than what any machines can ever imagine, and is highly structured
too.
> That 1-bigness will provide jobs for mathematical psychologists, for ...
ever.
[SPK]
Again, We are back to the question of "what is a machine"! Please
explain what a "machine" is! I am looking for a direct definition, not a
vague reference!
>
> SPK:
> > What is COMP other than N -> N functions? COuld you explain to us how
> >you can generate SWE using only N -> N functions, or, equivalently, how
to
> >embed complex valued functions in N?
>
>
> BM:
> Please, comp is PI (Personal Implication: you say "yes doctor" for his
> proposition of a artificial brain)
[SPK]
This is pure conjecture. Allow me to be agnostic on this. We need to get
a "machine" (whatever that is!) to pass the Turing test and then, maybe, I
will say "yes doctor"!
> TC (Church Thesis, see what I say above on it)
> RA (the believe that arithmetical truth is atemporal,
> aspatial, .... and that it does not depend on you,
me...)
>
[SPK]
I have no problem with the "truth" of mathematical objects being
atemporal, aspatial, etc. What I have a problem with is the idea that
mathematics is anything more than a "zero information set" unless there
exists, just as must ontologically and the "truthfullness", at least the
"posibility" of some form of "implementation" of each and every mathematical
function. Greg Egan has expressed this idea well in several of his
stories...
> Real numbers enters the show in two different ways: as constructive real,
> which can be identified with total computable function from N to N, and as
> being generated in the limit by the UD. This include the non
> constructive reals.
> Complex, quaternion, octonions, should be explained by Z1* (and *that* is
a
> conjecture!).
[SPK]
I would really like to better understand Z1and Z1*!!!
> SPK:
> >The manual containing an enumeration of all of the brain states of
> >Einstein is impossible by the Heisenberg Uncertainty principle.
>
> BM:
> Only if you postulate that einstein brain is an infinite *analogical*
> quantum computing machine.
[SPK]
Not at all. I am merely being consistent with the basic mathematics of
canonically conjugate operator spaces. YOu do not seem to understand this
basic aspect of the Heisenberg Uncertainty principle ...
SPK:
...
> >something amiss with the "Emperor's New Clothes" but not much. ;-) The
key
> >that strong AI and COMP believers in general seems to neglect the fine
point
> >that 1-person expereice is not 3-person observable.
>
> BM:
> But that was what I said in my last post to Colin Hales. Remember? I even
> have compared the first person to the vampire! It is the most striking
> feature of the first person: it is not a 3-machine!
[SPK]
I missed that post. Could you link it for us? And, what the heck is a
"3-machine"????
> SPK:
> >Just because for some
> >finite testing there could be no difference between a Machine's behavior
and
> >a "human" does NOT necessitate that they have equivalent 1-person
content.
>
> BM: Sure.
>
> SPK:
> > As a matter of fact, I have no way to prove that you are not a
machine
> >and you can not prove that this post is not just the output of a random
> >letter generator. All we have is likelyhoods and assumptions. ;-)
>
> BM:
> Sure.
[SPK]
Well, then how can you avoid my conclusion?! If I can prove nothing
except, maybe, "cognito ..." ...
> >SPK: I fail to see how notions such as "time", " casuality" and "1-person
/
> >3-person distinctions are shown to be necessary by your model. My point
is
> >that if our 1-person experience of a world is nothing more that a string
of
> >symbols existing a priori in Platonia,
>
> BM:
> But it is not! A first person is a person with her feelings, pains, hopes,
> joys, headache, and many personal memories. Nothing else. Certainly not
> a 3-string, not a 3-bunch of 3-particles, not a 3-machine, neither a
3-brain.
> The magic of comp, is that you can 3-study the 1-person discourse.
> The 1-person are much more than the arithmetical platonia, even if that
> much more is just platonia seen from inside.
[SPK]
This makes no sense to me, I am sorry. :-(
> SPK:
> >why do we have enless debates about
> >the notion of a "flow of consciousness"? It can not be "explained" away
as
> >just an illusion or "intensional stance". Immaterial strings might be
> >capable of encoding each other as subsets but unless we have some means
to
> >explain how Nature solves mathematical problems that are both intractible
by
> >finite TMs and require that we include the means of explaining concurrent
> >computations, e.g. we have to explain, at least, the appearence of
> >interactions between a plurality of systems not just a single
computational
> >system.
>
> BM: That's exactly what I begin to do in my thesis.
[SPK]
I look forward to reading more of it!
snip
> >SPK:
> > Let us continue our explorations of ideas and I hope to explain to
you
> >how I am neither a PHYSICAList nor a COMPutationalist. I have a thought
that
> >might show how there might be a flaw in your reasoning and it is that
just
> >because UTMs are independent of any particular physical implementation
does
> >not obtain that UTMs do not require, at least, some approximate
> >implementation in physicality. Numbers are meaningless if there does not
> >exist some 1-person notion of "numberness". Like the number three is a
> >meaningless symbol, at best, if there is not some set of objects that is
> >associable with "threeness". More on this in the next post. ;-)
>
> BM:
> I am not sure there is any problem between us. You don't like very much
> neither comp, nor what I derive from it. People who postulates comp and
> who does not like the consequence are more troubled, like most
> monist materialist.
> I have skip the "Finkelstein part of the post" because I prefer to reread
> him before). I am a little less finitist than Finkelstein, I think).
> Apology also for having (non purposefully) attribute some of my prose
> to you ;-).
snip
[SPK]
I think that Finkelstein is too finitistic, but that's ok. ;-)
Kindest regards,
Stephen
Received on Sun Feb 02 2003 - 00:16:40 PST
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