On 03 May 2009, at 09:00, Stathis Papaioannou wrote:
>
> 2009/5/3 Bruno Marchal <marchal.domain.name.hidden>:
>
>> I think that if you take a real forest with birds, here and there,
>> you
>> can interpret some behavior as NAND or NOR, but you will not succeed
>> ever in finding the computation of factorial(5).
>
> But you can interpret *any* behaviour as a NAND gate, in an ad hoc
> fashion. It doesn't even need to be consistent from moment. On a
> Tuesday 3 birds landing could stand for "1" while on a Wednesday 3
> birds landing could stand for "0", and on a Saturday it could stand
> for "1" again.
But this makes sense only relatively to a "stable universal" machine
in which you can encode what you are telling me.
> In this way you could take the physical activity
> carried out by a store-bought computer calculating factorial(5) and
> map it onto the forest with the birds.
All right, I see your point, you take any physical activity, and then
an ad hoc sequence of universal machine which interpret each piece of
birds behavior into a computation of fact(24). That sequence should be
capable to be infinite and the birds behavior have to resume more and
more complex problem dues to the adhocness of the representations.
The complexity of the sequence of universal machine will grow
exponentially. Hmm. perhaps. Again this will change nothing, After
all, the UD does generate *all* implementation of all computations
including your very complex (to encode) interpretation of rocks and
forest.
> Of course, this won't give you
> the answer to factorial(5) unless you already have the answer, but
> that just means that the computation is obscured,
It is obscured and blurred relatively to its most probable histories.
In normal physics (normal in the Gauss meaning) you cannot count on
those computations. It would be like saying you win the lottery given
that you have the right numbers, in disorder, but after all you can
read them in the right order, and someone in Platonia does read them
in that different order.
I could still disagree because, as you seem to accept, such "physical
implementation" can reduce to zero the needed amount of physical
activity, and an interpretation of your computation of the factorial
of 4, in the rock, will be made by an actual computation of 24 by a
"real universal machine" which does not need to be physical, in
platonia, and which has a lot of imagination in front of the rock. You
need something like this, for your argument to go through, but this
*is* mainly the comp supervenience. So what you show is that indeed,
we don't need, or cannot use in any genuine sense a primitive notion
of physical activity to build a notion of supervenience.
Yet I think that the notion of interpretation is more constrained that
just invoking some ad hoc sequence of platonist universal
interpreters. At some level, we must bet on "just one", if only to be
able to talk (even to talk to oneself).
> in the same way a
> message is obscured if encoded with a one-time pad that is
> subsequently destroyed and forgotten. In fact, even with the
> store-bought computer the computation is obscured if there are no
> intelligent beings around who can understand it.
Not at all. If the computer evaluate fact(4), even alone in a room,
the probability it gives 24 is one, in a verifiable way by a third
person. With or without physicalism we accept the idea that the
physical neighborhood is locally Turing universal, and does interpret
the computation of 4.
If I put a computer evaluating Stathis here and now, under your
substitution level, then, despite the computer being alone in the
room, the probability that you are where you feel you are (here and
now) or in that "room" is 1/2 (accepting the usual probability). Cf
step 5.
You will not say "yes doctor", but only if you take a permanent look
on my working artificial brain". The point of comp is that some
program can observe themselves (at some level). And this can be made
mathematically precise (by Kleene second recursion theorem).
Accpeting your "interpretation of the rock", The probability that you
are in the rocks, relatively to you here and now, is
0,00000000000000........1, given that you have to wait the UD
generates that immensely long sequences of more and more complex "ad
hoc" universal interpreters.
> So, if the
> computation supervenes on the activity of the store-bought computer
> without regard for whether any external observer is around to
> understand, then it also supervenes on the activity of the forest with
> the birds.
You illustrate well that the only question which makes sense is the
question of which most probable computation bears us, or which more
probable universal machine or number "executes" us. What you say is
that the UD will generate stupid program interpreting the empty input
like if it was a code for fact(4).
> Other possibilities are that the computation supervenes on
> physical activity only when an external observer understands it (which
> poses difficulties for a closed virtual reality with its own conscious
> observers),
And leads also to an infinite regression, unless you postulate an
absolute external witness with cognitive abilities based on ...
nothing (which makes not much sense).
> or that the computation does not supervene on physical
> activity at all.
It seems to me that we agree that physical supervenience leads to many
absurdities. Is your argument purely academical, or do you think it
can be used to prevent the conclusion that physics has to be explained
by the purely mathematical notion of "most probable computation as
seen from inside", among the 2^aleph_0 computations going through the
current states, in UD* or in arithmetic?
With you argument, the movie-graph is conscious. But is all
consciousness at once, not just the consciousness corresponding to the
filmed boolean graph. This not change the problem measure in any way.
It makes the primitive physicalness idea even more absurd.
It seems to me that your point just recall that in Platonia, there are
complex sequence of universal machine which can interpret any
computation, including the empty one, as being any other computations.
But this is akin to white rabbits (from the probability pov) and akin
to the fact that, with its terrible redundancy and "free
imagination", the UD generates also conspirator interpretations.
With just arithmetic, when we stop to postulate a primitive or
ontological material world, all primitive ad-hocness is removed, given
that the existing internal interpretations are all determined, with
their relative frequency, by addition and multiplication rules, and
physics will be defined by the (absolute) probability of relative
computations (here = probability of relative number theoretical
relations. "to be a finite piece of computation" is decidable even in
very tiny fragment of arithmetic, and this can be used to avoid any
starting ambiguity. This is made possible through Church thesis, and
it eventually forces us to realize that a rock is the result of an
infinity of computation, and the rock "we see" a crude local average,
but comp makes it possible that a rock implements all computations to,
but only by an explicit call to a sequence of universal machine in
Platonia. Meaning; there is no room for providing an explanative power
(both for mind and matter) to the notion of primitive substance and
primitive substancial incarnated laws. Due to the failure of logicism
we need numbers or combinators and primitive immaterial laws to agree
on, like addition and multiplication, or lambda abstraction and
application, etc. The measure does not depend on which first universal
system you choose, by non completely trivial application of computer
science. And to use a primitive quantum computer for a primitive
physics is treachery with respect to the comp mind body problem.
OK?
Bruno
http://iridia.ulb.ac.be/~marchal/
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Received on Sun May 03 2009 - 17:56:05 PDT