Le 01-févr.-07, à 18:46, Brent Meeker a écrit :
>
> Bruno Marchal wrote:
>>
>> Le 29-janv.-07, à 18:19, Brent Meeker a écrit :
>>
>>> Bruno Marchal wrote:
>>>> Le 28-janv.-07, à 20:21, Brent Meeker a écrit :
>>>>
>>>>
>>>>
>>>>> OK, but that means "observer moments" are not fundamental and the
>>>>> "illusion" of their continuity may be provided by the continuity of
>>>>> their underpinning. But I don't see how a strictly stepwise
>>>>> discrete
>>>>> process as contemplated in the UD can provide that continuity. It
>>>>> was
>>>>> my understanding that it assumed consciousness could be provided
>>>>> by a
>>>>> series of disjoint states.
>>>>
>>>>
>>>>
>>>> Yes. But a series of discrete states (or their godel number) has to
>>>> be
>>>> related by a computation for making sense.
>>>>
>>>> So it makes no sense to say that a sequence of number is a
>>>> computation.
>>>> You have to fix a "universal environment". Let us fix once and for
>>>> all
>>>> a godel numbering. Then it is only relative to some universal number
>>>> that a sequence of number can be counted as a computation.
>>> That sounds good - but I don't understand "universal environment" and
>>> "universal number". We adopt a goedel numbering of arithmetic
>>> expressions. Do we then represent the computation by a sequence of
>>> goedel numbers, each number corresponding to a mental state (assuming
>>> the computation is a simulation at a sufficient level to satisfy
>>> comp)? But what number is "universal"?
>>
>>
>> OK, remind me if I forget to comment this, but to explain what happens
>> here I do say a little more on the Fi and Wi. A universal number is
>> just the code of a universal machine or "interpreter" (in a nutshell).
>> I will come back on this.
>>
>>
>>
>>
>>
>>
>>>> Now, from a first person point of view, we don't know in which
>>>> computation we belong. So from a first person point of view, we have
>>>> to
>>>> take all equivalent computations (number sequence) relative to all
>>>> universal number.
>>>>
>>>> This is enough to explain why from first person points of view,
>>>> computations seem to require a continuum. In a sense we have to be
>>>> related to the continuum of computations going through our states
>>>> (it
>>>> includes the infinity of computations describing finer grained
>>>> histories with respect to our comp level of substitution.
>>> OK. So the order of computation provides the order of conscious
>>> states
>>> (which may really be very complex and include more than just atoms of
>>> experience); it is not inherent in the states. And this order is
>>> relative to different goedel numberings?
>>
>>
>> I am not sure to understand the relation of your quote of me and the
>> idea that the order of the computations provides the order of the
>> conscious state, unless you are refering to the logical order defined
>> by each computational state. If you run the UD, some "internal first
>> person future" could be implemented before some internal first person
>> past, buut this has nothing to do with the logical or arithmetical
>> order. OK?
>> I intend to explain a bit more through the use of the Fi and Wi, (=
>> the
>> partial recursive functions and their domain of definition), but it
>> would help me if you could explain what exactly (or more precisely)
>> you
>> mean by "order of computation". First person experiences have to be
>> related to infinities of computational histories, right?
>
> I'm not sure. I was considering two kinds of order of computation.
> One is the time order in the real world of processes in my brain or a
> computer simulating me.
Assuming some primitive existence of "real world" or "brain processes",
hypotheses whose coherence is put in doubt with the comp hypothesis.
> The other was the order of generation of "states" by the UD.
This is a bit ambiguous. The UD dovetails on all computations. Let us
write (comp i k j) for k-th step of computation i on input j.
One computation can then be identified (in a first approximation at
least) with a sequence like:
(comp 777 1 24) (comp 777 2 24) (comp 777 3 24) (comp 777 4 24) (comp
777 5 24) (comp 777 6 24) (comp 777 7 24) (comp 777 8 24) (comp 777 9
24) (comp 777 10 24) ....
This represents the computation of F_777(24), that is the 777th partial
recursive function on input 24.
Now we know that F_777(24) could be undefined, and that is why the UD
has to dovetetail. So the order of the "states" generated by the UD is
not, strictly speaking the order of states defining a computation.
Also, the UD is infinitely redundant: in particular the function F_777
has other code, for example 8888, i.e. F_777 = F_8888. It could be that
the computation (comp 777 i 24) and (comp 8888 i 24) are equivalent
(same algorithm) or completely different (different algorithm), but
actually it is not easy at all to define such equivalence relation
between computation an states.
I mean, even from a pure third person point of view, it is not obvious
to define computations and order on them.
Then, from a first person point of view, the difficulty is made bigger.
It could be, that although F_a and F_b computes different function (and
thus follows completely different algorithm), it could be that (comp a
234 24) and some sub-state of (comp b 34 1000), say, are equivalent
from a first person point of view, which needs to take into account all
the infinity of computations going through my "current state".
So I'm afraid that at some point we have to take a more abstract route
(like with the combinators, which better represent possible
computations, or like with the lobian interview).
What is correct, and has been singled out by Stathis, is that comp
eludes the "material implementation" problem, given that we take all
abstract possible relationship between those objects, and they are all
well defined as purely number theoretical relations. Note that this is
something I have tried to explain to Jacques Mallah sometimes ago, but
without much success. This does not make much sense in ASSA approaches,
but, like George Levy I think, I don't believe in absolute probability
of being me, or of living my current "observer moment". Such a
probability can be given the value one (said George) but it is close of
saying that the universe is here, which tells us nothing, really. It is
like answering "who are you?" by I am me".
> I understand from your answer above that the order of generation, in
> either case, is regarded as contingent and that 1st person experience
> is supposed to be ordered by inherent properties of the states.
From a first person point of view, if I am in state A, my next state
will be B in case most computation/histories going through A are led to
B in some direct way (with few intermediary states). But all states
have intermediary states, like all possible detour an electron can make
...
>
> If this is correct, it leads back to the question of how big is a
> "computational state".
I'm not sure. From the first person point of view, given that we have
to take into account all "histories"/3-computations, we have to
consider all possible "equivalent" computational state, and this means
the "bigness" you are alluding is not even bounded. You have to
consider the (non effective) infinity of states like: (comp 777 1 24)
(comp 8888 1 24) (comp 4560901 1 24) (comp 5676543091933 4 24) ... (an
infinity). And perhaps on different arguments too, ...
Now I have chose to interview the lobian machine, because I know that
it is very hard to just define a notion of computational equivalence.
> It seems that for the inherent order to be coded in the state, the
> state must be much bigger than what one is conscious of in an
> "observer moment".
This is too much ambiguous.
> It also implies, contra Stathis, that one cannot subdivide a conscious
> state very finely in time.
Eventually consciousness (or Plotinus' Universal Soul, or its
arithmetical interpretation) will be the responsible of time. From a
third person point of view, everything is discrete ... and atemporal.
Recall that UDA+MGA (Movie-Graph-Argument) makes it highly implausible
that consciousness supervene on a brain process. I know that is
counter-intuitive ...
> If you could then the finer you divided it, the less information it
> contained, then the more histories it would be consistent with.
This is correct, or at least makes sense. It is the main reason why
"first person amnesia" correspond to third person fusion of stories.
And if you forget all your beliefs, then your "theory" (or
belief-system) will be consistent with all histories. This is akin to
quantum erasure and the available technics for resuscitating
Schroedinger cat ( after they have been observed dead).
> So how do you decide how big a computational state is?
By the minimal number of bits to describe it perhaps. But I don't have
to measure that, given that for extracting physics from comp I have to
"integrate" on all computational stories. 'course, it is not easy.
> If you make it big enough it may pick out a unique history, or at
> least one that is unique over a significant time span (say many
> seconds)?
I don't think so. Incompleteness prevents such type of unicity. You can
add any effective infinity of axioms to a theory, it will keep an
infinity of non equivalent models/maximal consistent extension. And
this is worst with histories in place of models. Only by adding some
actual strong (non effective) axioms or bits, you can perhaps
singularize locally ("many seconds?") the history. This could lead to a
"Bohmian" many-world interpretation of arithmetic. I doubt this make
sense, but, strictly speaking, this cannot be entirely dismissed even
with comp (with, the, very low substitution level: comp remains true,
but false FAPP(*). The extremely weird behavior of prime numbers could
perhaps justifies such ONE-world-selction from comp as I said once.
Bruno
(*) For All Practical Purpose
http://iridia.ulb.ac.be/~marchal/
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Received on Fri Feb 02 2007 - 11:03:29 PST