Hi Brent,
On 09 Nov 2008, at 20:29, Brent Meeker wrote:
>
> Bruno Marchal wrote:
>>
>>
>> You don't get the point. Mechanism is incompatible with naturalism.
>> To
>> solve the mind body problem, keeping mechanism, the laws of physicist
>> have to be explained from computer science, even from the gap between
>> computer science and computer's computer science ...
>> Physics is the fixed point of universal machine self observation.
>
> That would be a very impressive result if you could prove it - and
> you could
> prove that there is no other empirically equivalent model.
I will try to explain, as simply as possible, that this has been
proved. Indeed by UDA[1...8].
> I've long been of
> the opinion that space and time are constructs. I also think the
> integers and
> arithmetic are constructs. But so far I understand your thesis to
> be that
> physics consists of certain relations among experiences regarded as
> mental
> events.
You can say so, although this is already a simplification. Useful to
give an idea to the layman, but also capable of making rise to non
genuine objection for the expert. I will not try to un-simplify your
point, if I can say, and I will interpret it favorably.
> This solves the mind-body problem by making the body a construct of
> the
> mind. So far, so good.
OK. OK. (well, to be sure, consciousness remains to be explained, but
consciousness will be explained by the gap between G and G*, but this
is locally out of the current topic).
> Further, you hold that these relations are Turing
> computable and so exist in Platonia as a subset of all arithmetic.
If by "these relations" you mean those related to my mind, then I am OK.
> I like this
> better than Tegmark's idea of our physics as a subset of all
> mathematics because
> your idea is more specific and leads to questions that may be
> answerable.
I don't think it is a question of "liking", but ... I share your liking.
Remember that I pretend that all what I say is a direct consequence of
the (digital) mechanist assumption. And then it is Church thesis which
makes such an approach so robust.
Nobody can know my opinion on the matter. (Except that once I said "I
don't know").
> But I
> still see some problems:
>
> First, it doesn't eliminate the possibility that some other subset
> of Platonia,
> e.g. geometry or topology, might also provide a representation of
> our physics.
> In fact, given that our knowledge of physics is imprecise, it seems
> likely that
> there are infinitely many subsets of Platonia that are models of our
> physics.
No. To predict first person experiences, we have to integrate (sum on,
taking into account of) ALL the representations occurring in the
universal deployment.
Ontologically, we have all computations. The UD generates, by
dovetailing all those computations. Your next state is determined by a
measure of uncertainty bearing on all computations going through your
present state.
What is obvious for the naturalist, i.e. the fact that your next state
is determined by your present state by a simple computational equation
(like SWE), is NOT obvious for the digital mechanist. There is already
a continuum of (infinite) computations---involving white rabbits,
white noise, and all computational and non computational beings---
going through your current state. If a physics emerges from that, it
is just an open problem if that physics is computational or not,
actually we just don't know yet if that physics even exists or not
(with comp). What we know, is that IF a physics emerges THEN it takes
into account, and sum up, infinities of computations.
This follows by taking steps 5, 6 and 7, and 8 (when not executing the
UD).
> Of course you can argue that even a non-computable model of physics
> may be
> approximated by a computable model to an adequate degree. But this
> just pushes
> the question off to what is "adequate" and it does not warrant
> rejecting
> materialism as explicated by Peter.
The "rejection of materialism" is really step 8 (the movie graph). It
explains why we don't have to run the UD, and why we can rely on the
"natural" UD determined by all true (and provable, here) sentence of
even just Robinson Arithmetic.
Your current state of mind, and indeed the state of mind of all
possible Loebian machines (far richer than Robinson Arithmetic) occurs
in all finite or enumerable approximations of any possible "model" of
physics rich enough to generate your states. But, mainly because you
cannot be aware of the delay done by the UD, you, from your first
person point of view, are living in the infinite union of all those
finite approximations. Again: there is no reason a priori why they
have to be computable (and giving the subdovetailing on the reals,
they have to posses uncomputable aspects when we look at ourself below
our level of substitution.
>
>
> Second, is the problem of finding the fixed point, or distinguishing
> the measure
> on all the Turing computations that picks out our physics. I
> understand you
> have some results, such as "no computation can know which
> computation it is",
> which are interesting, but do not pick out any particular physics.
All right. But I don't derive physics there. Physics is just shown to
be given by the science which pick your more probable "next first
person state" or OM, which exists in aleph_0 exemplars in the
Universal Deployment, and belongs to 2^aleph_0 histories. This is the
conclusion of UDA. We see here that comp predicts already something
"physical": the many worlds", or the many consistent histories.
Then to extract physics more precisely is very difficult, but that
should have been expected, giving the non constructive top-down
approach. We are just pushing the comp hyp to its ultimate consequences.
But then I recover a part of physics: the logic of the observable
propositions with probability/credibility one. For technical reason
they are modelized by the provability-and-consistency(-and-truth) of
the sigma_1 propositions. (four and fifth hypostases). And this gives
a quantum logic, and the shadow of measure on the computations as seen
by a universal machine embedded in the universal deployment. But this
is already AUDA. (arithmetical UDA).
> There's a
> general problem here in that the current best theories of physics
> are based on
> continuous variables.
This should be expected when we assume mechanism. Keep in mind the
step 7, physics should predict your next state of mind, and it depends
on 2^aleph_0 histories. If you look at yourself or at your
neighborhood close enough (below your substitution level) you can
expect to "see" the white rabbits somehow, you have to expect a
blurring of an infinity of computations, a bit like a cloud of
histories. The border of that cloud could be called the white rabbit
cloud: it is the extremely rare histories, like the border of an
electronic orbital describes very rare events (an electron far away
from the nucleus for example.
> Many physicists think that an ultimate theory would be
> discrete,
This is highly implausible, assuming comp. I know that if we want
quantize gravitation, then space and time should be quantized, but
then I hope other things will remain continuous, like the statistics
(hoping it is enough).
But for the reason above, the first persons cannot escape the
"feeling" or the "appearances" of continua (assuming mech.).
You really have to process carefully the step seven, and remember that
your first person point of view are determined by all the third person
describable computations going through your actual comp state (the
comp supervenience).
> but nobody knows how to make a discrete theory from which our
> continuous theories would emerge.
The comp hypothesis provides such a theory. Physics being a first
person (plural) construct, it has to rely on the infinite union of all
the finite piece of all computations accessing your state.
>
>
>> Let me know at which step (1?, ... 8?) you have a problem? The only
>> one not discussed thoroughly is the 8th one.
>>
>> To be sure, do you understand the nuance between the following
>> theses:
>>
>> WEAK AI: some machines can behave as if their were conscious (but
>> could as well be zombies)
>> STRONG AI: some machines can be conscious
>> COMP: I am a machine
>>
>> We have
>>
>> COMP => STRONG AI => WEAK AI
>>
>> WEAK does not imply STRONG AI which does not imply COMP. (it is not
>> because machine can be conscious that we are necessarily machine
>> ourself, of course with occam razor, STRONG AI go in the direction of
>> COMP).
>>
>> Does those nuances make sense? If not (1...8) does not, indeed, make
>> sense. You just don't believe in consciousness and/or person like in
>> the eliminative materialism of neuro-philosophers ( the Churchland,
>> amost Dennett in "consciousness explained").
>
> As my lawyer friend says, "I'm not in the belief business."
Scientists have beliefs.
Mystics have knowledge.
Beliefs are refutable and revisable. Science evolves and grow.
Knowledge is not refutable and not revisable, and, in its pure
platonic form, is invariant.
>
>
>>
>> Or you make us very special infinite analogical machines, but then
>> you
>> drop the digital mechanist thesis (even the naturalist one, which has
>> been shown inconsistent by 1...8.)
>
> I think it might be that the universe is not computable.
But, after step 1...8, what do you mean by universe?
If I am a (correct) machine, whatever supports me cannot be a machine.
Unless, to be complete, I am the entire universe. I say "yes" to the
doctor if the artificial brain simulates the entire cosmos and the
entire cosmological history. In that case there is only one universe,
only one "bruno marchal", and it can be a computational object
because, although the UD generates it an infinity of time, there are
no variations among the genuine computations. No white rabbits here.
But a big "others mind problem". I think I have to explain this to
Jason, so I will not insist here. I could also suggest to really
revised the seven and height steps, keeping cautiously in mind the
first and third person distinction.
> But I think it is very
> likely that one's consciousness is computable, at least for a finite
> time period.
That's the comp hyp. It entails my consciousness is "processed" in a
denumerable but infinite part of the deployment, and the measure is
determined by the continuum of computations which exists as domain of
comp indeterminacy. By step 5 (and 8) we are always under the fate of
that indeterminacy.
A set of computable things is not necessarily computable, and the comp
hyp makes the computability of the universe, or any big whole, very
implausible.
The mind body problem is that tricky!
If mind is computable, then the body is not.
If the body is computable, then the mind is not.
And if the body is computable, and if we still assume comp, then the
mind is computable (by comp) and the body is not, so we get that the
body is computable and the body is not computable. Contradiction.
Meaning, if comp is true, the body, or the universe is NOT computable.
The UD never generate a physical universe, it always generate set of
histories from inside which observers categorize into a universe, from
their points of view. The brain or more generally the lobian machine,
act as a filter or a selector of a reality from an uncomputable set of
computable histories.
I would be pleased if you could be kind enough to tell me if I have
been able to justify why the first person universe (be it physical or
mathematical, or whatever) cannot be computable.
Bruno Marchal
http://iridia.ulb.ac.be/~marchal/
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Received on Tue Nov 11 2008 - 10:45:36 PST