On 29 Sep 2011, at 04:11, Pierz wrote:

Not at all. That would be a physicalist revisionist definition of
numbers. You need to "instantiate" 17, in some way, to talk about 17,
but 17 itself does not need instantiation. With or without any
physical universe, 17 remain a prime number.

With or without a mind too, I presume you believe. But this really is
a metaphysical assumption,

No, it is mathematical practice. When numbers are introduced in high school they are not defined by referring to mind or brain, which are more complex notion.


not something that is provable.

Axioms are never provable, except in redundant theories (for making them easier to use).



I would say
if you remove all minds, there is no 17, no primes, nothing, because
the numbers are lent existence by the mind and/or the physical
universe.

Mechanism makes mind definable from numbers, but nobody has succeeded in defining numbers from mind, without using numbers.



My preferred ontology is idealistic (in the philosophical
sense) rather than mathematical. I tend to believe consciousness is
prior. And you've agreed consciousness can't really be defined - and
therefore dealt with explicitly in your theory.

We cannot define consciousness, nor truth, etc. but we do have a good idea of what those things refer too.



I believe there is a
pure conscious state somewhere down there (in us) that comes before
everything else, before the structure which is required to give form
to mathematics. Buddhism, the void, all that.

We might be close, we can equivocate numbers and consciousness in different ways. Do you say "yes" to the doctor? (It looks like entheogen.com is out of line currently. Hope it will coma back!).



It seems to me I can
grant 17 is prime, without granting this instantiation of everything.

Well, that solves you of a very long and not so easy work.

Haha. Well, thank god we don't have to prove everything we believe -
unless, like you, we make a living out of it! Otherwise we'd have to
prove our own arses before we could shit. But OK, this is profound
stuff, so what "seems to me" may be way off, on deeper investigation.

Arithmetical truth is full of currently non human provable truth (unless we have actual infinite brains, which I doubt).



Now, an instanciation, or emulation, can be defined from the numbers
alone

I can believe that without the textbook. I'm just saying that the
instantiated emulation and the definition of the emulation aren't the
same.

You can define emulation in arithmetic, that is one thing. But you can prove that arithmetic is full of instantiated emulations. That is the thing explained in textbook I was referring too. If comp is true, you are conscious here and now, because an infinity of number relation emulate your computational histories.



But I do understand what you are arguing (I think). There's
nothing intrinsically illogical about granting numbers an existence
that is prior to the physical or the mental, but are you claiming it's
*provable*?

This is provable assuming you can survive with a material digital brain. That is comp, and comp is not provable.




Recently I have updated my spectrum of Löbian machine to the octopus,
and the jumping spider. I can argue that they have the cognitive
ability to get UDA.

I just find that quite funny. The socratic octopus. You can argue it
in theory, but it's kind of meaningless I think, since psychology
shows abstract reasoning is confined to humans above a certain age.

Conscious high level abstract reasoning is such confined, but all brain of all animals does "abstract reasoning" all the time. Seeing the difference between vertical and horizontal line require complex computations in the brain.



Still, I like the socratic octopus so much I'll believe you anyway.
I love the way the jumping spider literally falls off its perch when
there's no spider on the other side of the mirror. :)

Yes, that shows she makes inductive inference, which requires her to be Löbian. Insects seems unable to do this.



It is not a problem. It is an impossibility. You cannot prove that *I*
am conscious, can you?

No of course not, that's what I meant by a "problem". A very big one!

No, that is not a problem. Since Gödel we know that all machine are confronted with many unprovable truth.




Finally, as for obscurity, I rejected obscurity treated as a virtue,
not the necessary obscurity of certain difficult ideas - like QFT
mathematics. I suppose jumping spiders can do QFT equations too,
right?

They don't have a sufficiently big brain to handle the motivations for it. But they can in principle. A bit like a baby, except that a baby can develop better its brain than such little animals.

Bruno






On Sep 29, 2:07 am, Bruno Marchal <marc...@ulb.ac.be> wrote:
On 28 Sep 2011, at 05:44, Pierz wrote:

OK, well I think this and the other responses (notably Jason's) have
brought me a lot closer to grasping the essence of this argument. I
can see that the set of integers is also the set of all possible
information states, and that the difference between that and the UD is
the element of sequential computation. I can also see that my
objection to infinite computational resources and state memory comes
from the 1-p perspective. For me, in the "physical" universe, any
computation is restricted by the laws of matter and must be embedded
in that matter. Now one of the fascinating revelations of the
computational approach to physics is the fact that a quantity such as
position can only be defined to a certain level of precision by the
universe itself because the universe has finite informational
resources at its disposal. This was my objection to the UD. But I can
see that this restriction need not necessarily apply at the 'higher'
3-
p level of the UD's computations. What interests me is the question:
does UDA predict that the 1-p observer will see a universe with such
restrictions?

To be sure, this is an open problem.
To be sure, this is an open problem for physicists too.
Comp+"theatetus"  will be refuted if the comp-physics will be quasi
*contradicted* by some precise physical fact, not by any physical
theory (unless they predicts that precise physical fact).

If it explains why the 1-p observer seems to exist in a
world where there is only a finite number of bits available, despite
existing in a machine with an infinite level of bit resolution, then
that would be a most interesting result. Otherwise, it seems to me to remain a problem for the theory, or at least a question in need of an
answer, like dark matter in cosmology.

I am going to have to meditate further on arithmetical realism. I
don't believe in objective matter either (it seems refuted by Bell's
Theorem anyway), but a chasm seems to lie between the statement  "17
is prime" and "the UDA (Robinson arithmetic) executes all possible
programs".

Don't confuse the UD (Universal Dovetailer, a finite program) and UDA
(the UD Argument = the argument that, assuming digital mechanism,
physics is in principle a branch of number theory/computer science,
and in which the UD plays the role of the effective definable comp
ontological realm of *everything*).
Just a vocabulary remark, to avoid possible future confusion.

The problem is one of instantiation. I can conceive of a
universe - a singularity perhaps, with only one bit of information -
in which the statement "17 is prime" can never be made.

Don't confuse the sociological statement "some machine asserts "17 is
prime"", and the true fact that 17 is prime, which does not rely on
physical universes at all, a priori.

To formulate,
ie instantiate, 17, requires a certain amount of information.

In some physical theory, but this is not an assumption in the theory.
You cannot refute an argument by adding new assumptions.

To say
that a program executes, as opposed to saying it merely is implied by
a set of theoretical axioms, requires the instantiation of that
algorithm.

In Aristotelian metaphysics.
Also, even in platonia, a computation is described by a big number
(possibly infinite) of implications.

I suppose this is a restatement of the problem above.
Arithemetical realism then would be the postulate that everything
implied in arithmetic is actually instantiated.

Not at all. That would be a physicalist revisionist definition of
numbers. You need to "instantiate" 17, in some way, to talk about 17,
but 17 itself does not need instantiation. With or without any
physical universe, 17 remain a prime number.

Now, an instanciation, or emulation, can be defined from the numbers
alone. Some numbers are universal (a relative arithmetical property)
and we can say that a universal numbers instantiates 17 (say) if 17
appears in some of its purely arithmetical register.

To understand the detail of this, I can only refer you to some good
textbook in computer science. The main theorem for this is the proof
that all partial recursive functions can be represented in Robinson
arithmetic (Boolos and Jeffrey's book do this very well, Epstein and
carnielli also. ref in my theses).

It seems to me I can
grant 17 is prime, without granting this instantiation of everything.

Well, that solves you of a very long and not so easy work.



I'm also troubled by the statement that you have proved in the AUDA
that any Lobian machine can apprehend the UDA. Is not a three-year- old child and a cat a Lobian machine? Or indeed my senile father. How can
you assert they could comprehend such an abstraction? Either they
aren't Lobian machines, or there's hole in the proof somewhere,
surely!

Recently I have updated my spectrum of Löbian machine to the octopus,
and the jumping spider. I can argue that they have the cognitive
ability to get UDA. But they don't have a sufficiently big brain to
exploit this, and they don't have the motivation to use diaries and
books, and language to generate their infinite "turing tape memory"
like we do.
Symptoms of Löbianity are believe in repetition and notice them (like
believing in a notion of anniversary), or having empathy for an other
creature, etc. This needs some form of the induction axiom. Robinson
arithmetic (and Universal machines in general) are not Löbian. Peano
Arithmetic is Löbian (it is reallu just Robinson arithmetic + the
induction axiom for the first order describable formula).
But this is not important for the reasoning.



Jason mentions the anthropic principle (which of course I'm well
acquainted with) and the idea of the computations which contain
observers. I have read, without following, some of your propositions
involving the Beweisbar predicate and self-referential relations and
what have you. Is that the formalism that is supposed to define which
computations are conscious?

Not really. This is a subtle point. Notion like truth and
consciousness are not definable by any machine. But, like with God (or
Plotnus' one) we, the machines, can talk in indirect way, by taking
some precaution.

Is there a summary somewhere?

It is explained in the second part of the sane04 paper. AUDA is "the
interview of the Lôbian universal machine"

I am
wondering how consciousness can possibly be an attribute of some
computations and not others,

Let me be precise; consciousness is not an attribute of a computation,
but is an attribute of a person. Now a person can manifest itself
relatively to other person, once "enough" similar computations are
going through the states of the two person, in some sufficiently
cohesive way. The self-reference logics are used to single out the
conditions of cohesion (unlike in linear logic, or Girard geometry of
interaction, which extract such condition from symmetry intuition and
proof theory).

and why, if it's a matter of some certain
mathematical properties of the computations, we could not fairly
easily write a conscious algorithm?

It is easy. I tend to think, since recently, that all universal
algorithm are conscious. But their consciousness is disconnected, a
bit like if they were born ... in salvialand! And, yes, before doing
salvia I would have imposed Löbianity for consciousness, but I am much
less sure about that.
Now Löbianity is more than consciousness, it is self-consciousness.
Peano arithmetic is self-conscious, I think. That is why we can
discuss Plotinian theology with them, even without making their soul
falling on earth, that is without implementing them and sharing our
long story. Current computers have not yet long term memory, nor long
term goal. But I think that PA, the octopus, and the jumping spider
(but not worms, and most usual spider) are as conscious as you and me.

For the fun here is  video illustrating that a jumping spider can do
some inductive inference requiring some implicit beliefs in
arithmetical induction (look hw she reacts when she looks behind the
mirror).

http://www.youtube.com/watch?v=iND8ucDiDSQ

As opposed, here is a typical non Löbian behavior, or a non jumping
spider (yet jumping, note):

http://www.youtube.com/watch? v=lsqt2ywSqTQ&feature=channel_video_title

If not finding food on a top of a plant, she is programmed to jump
randomly on other plant, and, in case she get the ground, to climb on
a nearest plant. Here there is only a pen, perpendicularly installed
on a flat ground table.  She seems to repeat in cycle that behavior,
except for taking some rest.

But the bigger reason why I think jumping spiders are Löbian, is that
like cat and dog, they can bond with you, star at you, and perhaps
even recognize you. But this can be judged only by real interaction
with real spiders, not by looking at videoas, of course. Stiil, here
is a very cute one:

http://www.youtube.com/watch?v=MQBAIud6Twg&feature=related

Surely complexity can't be the
defining feature (at what arbitrary level of complexity does the light
come on?), so it should be a simple matter.

I agree. You don't need more than 10 lines instruction code for them,
well, in a high logical language like prolog, for example.

(Though the proof of
having created consciousness in the program would be a problem!)

It is not a problem. It is an impossibility. You cannot prove that *I*
am conscious, can you?

Don't
we have to define consciousness (not necessarily self-awareness, or
the awareness of being aware) as a property of numbers per se?

A quasi-definition is the ability by some universal numbers to
discover some non communicable truth by introspection. Consciousness
is not much more than the state of believing in ...

read more »

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