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 , i.e. F_777 = F_. It could be that
the computation (comp 777 i 24) and (comp 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 i
