Re: A comment on Mauldin's paper “Computation and Consciousness”

[Rex Allen]

On Thu, Jan 27, 2011 at 7:58 PM, Brent Meeker  wrote:
> But if the
> emulation attempts to be local then it must include inherent randomness -
> which I think is not Turing computable.

The Turing machine could draw the required randomness from a tape of
random bits, couldn't it?

The question might then be asked:

"Where did the tape of random bits come from?"

To which I guess a response of sorts might be:

"Well, where did the Turing machine come from?  Probably from there."

If you can have unexplained order, then you can have unexplained
randomness, can't you?

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Re: A comment on Mauldin's paper “Computation and Consciousness”

[Rex Allen]

On Thu, Jan 27, 2011 at 4:12 PM, Brent Meeker  wrote:
>
> What does "locally" mean in this context?  I doubt that consciousness is
> strictly local in the physical sense; it requires and world to interact
> with.

I would have thought that dreams would be a pretty clear
counter-example to the claim that consciousness requires a world to
interact with...?


On Thu, Jan 27, 2011 at 7:58 PM, Brent Meeker  wrote:
> I think the whole world probably is Turing emulable, but then that does not
> get rid of materialism.  Material just becomes one of the things emulated
> along with consciousness.

But then the material world we observe doesn't cause our
consciousness.  Rather, the underlying emulation substrate (which we
have no access to) causes both the material world and consciousness.

For instance, it would not be the case that neurons cause
consciousness...neurons wouldn't be an extra layer that existed
between us and the emulation substrate.

What exists would be the emulation substrate, going about it's
business of existing.  As a (presumably) accidental side-effect of
that existence, there would be us with our experience of the world.

But, given the example of dreams - which aren't "of" anything external
to us (again, presumably) - why assume that there actually is a world
beyond our experience .

Perhaps the emulation substrate produces nothing but dreams?

Would there be any reason to predict that such an emulation substrate
would be governed by principles that we could comprehend?  How would
it be different from the Kantian noumenal realm?

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Re: A comment on Mauldin's paper “Computation and Consciousness”

[Brent Meeker]

On 1/27/2011 2:23 PM, Bruno Marchal wrote:


On 27 Jan 2011, at 22:12, Brent Meeker wrote:


On 1/27/2011 10:23 AM, Bruno Marchal wrote:


On 25 Jan 2011, at 15:47, Stephen Paul King wrote:




Mathematical structures do not “do” anything, they merely 
exist, if at all! We can use verbs to describe relations between 
nouns but that does not change the fact that nouns are nouns and 
not verbs. The movie graph is a neat trick in that is abstracts out 
the active process of organizing the information content of the 
individual frames and the order of their placement in the graph, 
but that some process had to be involved to perform the computation 
of the content and ordering cannot be removed, it is only pushed 
out of the field of view. This is why I argue that we cannot ignore 
the computational complexity problem that exist in any situation 
where we are considering a optimal configuration that is somehow 
selected from some set or ensemble.


I don't see how this would change anything in the argument, unless 
you presuppose consciousness is not locally Turing emulable, to 
start with.


What does "locally" mean in this context?  I doubt that consciousness 
is strictly local in the physical sense; it requires and world to 
interact with.


It means that, when saying yes to the doctor, you will not only 
survive, but you will feel the same physical laws.


Saying yes to the doctor who proposes to replace my brain with a digital 
computer still leaves my body and the rest of the world non-digital and 
non-local.


You will not change the relative measure on your computations. It 
might be necessary to duplicate a part of the environment, which, in 
that case has to be supposed to be Turing emulable in that same sense.


But this seems to me dubious.  All known theories of physics assume a 
continuum of space, time, and probability.  Many people think these may 
be approximations to a finer, discrete structure, but so far as I know 
there have not been any successful theories showing how these discrete 
structures could emulate the continuum.  You may object that the part of 
the environment needed in a simulation of my consciousness is quite 
small and so can easily be emulated by a discrete computation.  But that 
is only the case when my brain+other is treated as not entangled with 
the rest of the universe.  If this entanglement (including the whole 
universe) is emulated then as in Bohmian or Everett's quantum mechanics, 
the world is deterministic and at some level of precision Turing 
emulable.  But if the emulation attempts to be local then it must 
include inherent randomness - which I think is not Turing computable.  
So I think there is a tension here that is obfuscated by thinking of the 
doctor just replacing your brain or a part of your brain and helping 
yourself to the rest of the world.  Your brain is entangled with the 
rest of the world and either you need to leave the rest of the world in 
place so your Turing emulation can be entangled (non-local), or you need 
to emulate the whole world.


I think the whole world probably is Turing emulable, but then that does 
not get rid of materialism.  Material just becomes one of the things 
emulated along with consciousness.


Brent

That is why I mention the notion of generalized brain. If the 
environment is not Turing emulable, you have to use another theory of 
mind than the mechanist one.
Consciousness per se, and first person, and matter (first person 
plural) are not locally emulable. First person point of views are 
related with the infinite continuum of computations going through 
their states, and that is not algorithmic (assuming digital mechanism).


If my local body is a machine, my soul, I, is not a machine. I should say.

Bruno

http://iridia.ulb.ac.be/~marchal/ 



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Re: Observers and Church/Turing

[Stephen Paul King]

Hi Travis,

   I have really enjoyed the challenge of your paper. One difficulty that I 
have with it is that the "selection of a gauge" is a highly non-trivial 
problem (related to the fine tuning problem!) and thus needs a lot more 
attention. More comments soon.


Onward!

Stephen


-Original Message- 
From: Travis Garrett

Sent: Thursday, January 27, 2011 5:32 PM
To: Everything List
Subject: Re: Observers and Church/Turing

I am somewhat flabbergasted by Russell's response.  He says that he is
"completely unimpressed" - uh, ok, fine - but then he completely
ignores entire sections of the paper where I precisely address the
issues he raises.  Going back to the abstract I say:

"We then argue that the observers
collectively form the largest class of information
(where, in analogy with the Faddeev Popov procedure,
we only count over ``gauge invariant" forms of
information)."

The stipulation that one only counts over gauge-invariant (i.e.
nontrivial) information structures is absolutely critical!  This is a
well known idea in physics (which I am adapting to a new problem) but
it probably isn't well known in general.  One can see the core idea
embedded in the wikipedia article: 
http://en.wikipedia.org/wiki/Faddeev–Popov_ghost

- or in say "Quantum Field Theory in a Nutshell" by A. Zee, or
"Quantum Field Theory" by L. Ryder which is where I first learned
about it.  In general a number of very interesting ideas have been
developed in quantum field theory (also including regularization and
renormalization) to deal with thorny issues involving infinity, and I
think they can be adapted to other problems.  In short, all of the
uncountable number of uncomputable reals are just infinitely long
random sequences, and they are all eliminated (along with the
redundant descriptions) by the selection of some gauge.  Note also in
the abstract that I am equating the observers with the *nontrivial*
power set of the set of all information - which is absolutely distinct
from the standard power set!  I am only counting over nontrivial forms
of information - i.e. that which, say, you'd be interested in paying
for (at least in pre-internet days!).

I am also perfectly well aware that observers are more than just
passive information absorbers.  As I say in the paper:

"Observers are included among these complex structures,
and we will grant them the special name $y_j$
(although they are also
another variety of information structure $x_i$).
For instance a young child $y_{c1}$ may know about
$x_{3p}$ and $x_{gh}$:
$x_{3p}, x_{gh} \in y_{c1}$, while having not yet
learned about $x_{eul}$ or $x_{cm}$.
This is the key feature of the observers that we will utilize:
the $y_j$ are entities that can absorb various
$x_i$ from different regions of $\mathcal{U}$."

That is: "this is the key feature of the observers that we will
utilize"

And 4 paragraphs from the 3rd section:

" Consider then the proposed observer $y_{r1}$
(i.e. a direct element of $\mathcal{P}(\mathcal{U})$):
 $y_{r1} = \{ x_{tang}, x_3, x_{nept} \}$,
where $x_{tang}$ is a tangerine, $x_{3}$ is the
number 3, and $x_{nept}$ is the planet Neptune.
This random collection of various information structures
from $\mathcal{U}$ is clearly
not an observer, or any other from of nontrivial information:
$y_{r1}$ is redundant to its three elements, and would thus
be cut by the selection of a gauge.
This is the sense in which most of the direct elements of the
power set of $\mathcal{U}$ do not add any new real information.

snip 


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Re: A comment on Mauldin's paper “Computation and Consciousness”

[Stephen Paul King]

Hi Brent and Bruno,


From: Bruno Marchal 
Sent: Thursday, January 27, 2011 5:23 PM
To: everything-list@googlegroups.com 
Subject: Re: A comment on Mauldin's paper “Computation and Consciousness”

On 27 Jan 2011, at 22:12, Brent Meeker wrote:


  On 1/27/2011 10:23 AM, Bruno Marchal wrote: 


On 25 Jan 2011, at 15:47, Stephen Paul King wrote:





  Mathematical structures do not “do” anything, they merely exist, if 
at all! We can use verbs to describe relations between nouns but that does not 
change the fact that nouns are nouns and not verbs. The movie graph is a neat 
trick in that is abstracts out the active process of organizing the information 
content of the individual frames and the order of their placement in the graph, 
but that some process had to be involved to perform the computation of the 
content and ordering cannot be removed, it is only pushed out of the field of 
view. This is why I argue that we cannot ignore the computational complexity 
problem that exist in any situation where we are considering a optimal 
configuration that is somehow selected from some set or ensemble.

I don't see how this would change anything in the argument, unless you 
presuppose consciousness is not locally Turing emulable, to start with.

  What does "locally" mean in this context?  I doubt that consciousness is 
strictly local in the physical sense; it requires and world to interact with.


It means that, when saying yes to the doctor, you will not only survive, but 
you will feel the same physical laws. You will not change the relative measure 
on your computations. It might be necessary to duplicate a part of the 
environment, which, in that case has to be supposed to be Turing emulable in 
that same sense. That is why I mention the notion of generalized brain. If the 
environment is not Turing emulable, you have to use another theory of mind than 
the mechanist one.
Consciousness per se, and first person, and matter (first person plural) are 
not locally emulable. First person point of views are related with the infinite 
continuum of computations going through their states, and that is not 
algorithmic (assuming digital mechanism).

If my local body is a machine, my soul, I, is not a machine. I should say.

Bruno

http://iridia.ulb.ac.be/~marchal/


[SPK]

I agree with this but with the caveat that my previously posted definition 
was strictly physicalist. Bruno’s is the ideal mechanist version. I do not see 
these as mutually contradictory.

Onward!

Stephen

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Re: What is Locally mean?

[Stephen Paul King]

Hi Brent,

You ask the perfect question! By locally it is mean that all that can be 
defined and/or measured from a single frame of reference (as it is used in 
special relativity). This includes a notion of simultaneity that involves those 
aspects of the world that can be measured from that frame. For example, all of 
the content of experience that you have in any moment is locally attributable 
to your frame of reference in that moment. This idea is tricky because there 
are non-narratability issues that have to be managed if we extend the concept 
to talk about foliations of instances of frames. See: 
http://arxiv4.library.cornell.edu/abs/1002.1726v1 

Onward!

Stephen

From: Brent Meeker 
Sent: Thursday, January 27, 2011 4:12 PM
To: everything-list@googlegroups.com 
Subject: Re: A comment on Mauldin's paper “Computation and Consciousness”
On 1/27/2011 10:23 AM, Bruno Marchal wrote: 


  On 25 Jan 2011, at 15:47, Stephen Paul King wrote:


   snip



Mathematical structures do not “do” anything, they merely exist, if at 
all! We can use verbs to describe relations between nouns but that does not 
change the fact that nouns are nouns and not verbs. The movie graph is a neat 
trick in that is abstracts out the active process of organizing the information 
content of the individual frames and the order of their placement in the graph, 
but that some process had to be involved to perform the computation of the 
content and ordering cannot be removed, it is only pushed out of the field of 
view. This is why I argue that we cannot ignore the computational complexity 
problem that exist in any situation where we are considering a optimal 
configuration that is somehow selected from some set or ensemble.

  I don't see how this would change anything in the argument, unless you 
presuppose consciousness is not locally Turing emulable, to start with.

What does "locally" mean in this context?  I doubt that consciousness is 
strictly local in the physical sense; it requires and world to interact with.

Brent

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Re: JOINING: Travis Garrett

[Stephen Paul King]

Hi Travis,


Thank you for joining us. Please prepare to defend your paper. 

Onward!

Stephen

-Original Message- 
From: Travis Garrett 
Sent: Thursday, January 27, 2011 4:10 PM 
To: Everything List 
Subject: JOINING: Travis Garrett 

Hi everybody,

   My name is Travis - I'm currently working as a postdoc at the
Perimeter Institute.  I got an email from Richard Gordon and Evgenii
Rudnyi pointing out that my recent paper: http://arxiv.org/abs/1101.2198
is being discussed here, so yeah, I'm happy to join the conversation.
I'll respond to some specific points in the discussion thread, but
what the heck, I'll give an overview of my idea here...

  The idea flows from the assumption that one can do an arbitrarily
good simulation of arbitrarily large regions of the universe inside a
sufficiently powerful computer -- more formally I assume the physical
version of the Church Turing Thesis.  Everything that exists can then
be viewed as different types of information.  The Observer Class
Hypothesis then proposes that observers collectively form by far the
largest set of information, due to the combinatorics that arise from
absorbing information from many different sources (the observers
thereby roughly resemble the power set of the set of all
information).  One thus exists as an observer because it is by far the
most probable form of existence.

  A couple caveats are of crucial importance: when I say information,
I mean non-trivial, gauge-invariant, "real" information, i.e.
information that has a large amount of effective complexity (Gell-Mann
and Lloyd) or logical depth (Bennett).  I focus on "gauge-invariant"
because I can then borrow the Faddeev-Popov procedure from quantum
field theory: in essence, one does not count over redundant
descriptions.  I also borrow the idea of regularization from quantum
field theory: when considering systems where infinities occur, it can
be useful to introduce a finite cutoff, and then study the limiting
behavior as the cutoff goes to infinity.  For instance, regulating the
integers shows that the density of primes goes like 1/log(N) - without
the cutoff one can only say that there are a countable number of
primes and composites.  These ideas are well known in theoretical
physics, but perhaps not outside, and I am also using them in a new
setting...

  Let me give a simple example of the use of gauge invariance from the
paper - consider the mathematical factoid: {3 is a prime number}.
This can be re-expressed in an infinite number of different ways: {2+1
is a prime number}, {27^(1/3) is not composite}, etc, etc...  Thus, at
first it seems that just this simple factoid will be counted an
infinite number of times!  But no, follow Faddeev and Popov, and pick
one particular representation (it's fine to use, say, {27^(1/3) is not
composite}, but later we will want to use the most compact
representations when we regularize), and just count this small piece
of information once, which removes all of the redundant descriptions.
To reiterate, we only count over the gauge-invariant information.

  Consider a more complex example, say the Einstein equations: G_ab =
T_ab.  Like "3 is a prime number", they can be expressed in an
infinite number of different ways, but let's pick the most compact
binary representation x_EE (an undecidable problem in general, but say
we get lucky).  Say the most compact encoding takes one million bits.
Basic Kolmogorov complexity would then say that x_EE  contains the
same amount of information as a random sequence r_i one million bits
long - both are not compressible.  But x_EE contains a large amount of
nontrivial, gauge invariant information that would have to be
preserved in alternative representations, while the random sequence
has no internal patterns that must be preserved in different
representations: x_EE has a large amount of effective complexity, and
r_i has none.  Focusing on the gauge-invariant structures thus not
only removes the redundant descriptions, but also removes all of the
random noise, leaving only the "real" information behind.  For
instance, I posit that the uncomputable reals are nothing more than
infinitely long random sequences, which also get removed (along with
the finite random sequences) by the selection of a gauge.

In some computational representation, the real information structures
will thus form a sparse subset among all binary strings.  In the paper
I consider 3 cases - 1) there are a finite number of finitely complex
real information structures (which could be viewed as the null
assumption), 2) there are a infinite number of finitely complex
structures, and 3) there are irreducibly infinitely complex
information structures.  I focus on 1) and 2), with the assumption
that 3) isn't meaningful (i.e. that hypercomputers do not exist).
Even case 2) is extremely large, and it leads to the prediction of
universal observers: observers that continuously evolve in time, so
that they can eventually process arbitrarily comp

Re: A comment on Maudlin's paper “Computation and Consciousness”

[Stephen Paul King]

Dear Bruno,

Interleaving.

From: Bruno Marchal 
Sent: Thursday, January 27, 2011 1:23 PM
To: everything-list@googlegroups.com 
Subject: Re: A comment on Mauldin's paper “Computation and Consciousness”

On 25 Jan 2011, at 15:47, Stephen Paul King wrote:


  SPK: The supervenience thesis is separate from the Turing thesis and 
Mauldin does a good job in distinguishing them.
[BM]
Just to be clear, what Maudlin call "supervenience thesis" is what I called 
"physical supervenience thesis", to distinguish it from the computationalist 
supervenience thesis.
The computationalist supervenience thesis is basically what remains when we 
keep comp, and understand that the Phys. Sup. thesis has to go away in the comp 
frame.


[SPK] 
My claim is that we can push physical supervenience far into the background 
but in the cases where interaction between entities occurs it cannot be 
eliminated entirely. My proposal is that for interactions we must have both MEC 
and MAT, as MEC or MAT taken alone provide insufficient support for 
supervenience. This is what I see Maudlin’s argument proving.
***


  SPK: The problem that I see is in the properties of physicality that are 
assumed in Mauldin’s argument. It is one thing to not be dependent on what 
particular physical structure a computation can be run on (assuming a realistic 
supervenience), it is another thing entirely to say that a Turing machine can 
be “run” without the existence of any physical hardware at all.

[BM]
Well, in the branch ~MEC v ~MAT, Maudlin seems to prefer MAT, so he seems with 
you on this, I think.

[SPK] 
No, I am claiming that for interactions between entities (and the models 
thereof) we must have MEC and MAT. In situations, like in most of your theory, 
interactions are not a factor thus your thesis follows smoothly in that frame. 
This is why I constantly ding you for being solipsistic. I would hope that you 
would do the same for me if I where equivalently in error. One must be able to 
defend one’s beliefs. Judge and prepare to be judged.
***


  SPK: I am trying to make this distinction and trying to fix this problem that 
I found in the supervenience thesis within Mauldin’s argument. He does point 
out that there are contrafactuals that must have some physical instantiation. 
We see this on page 411 where he wrote:

  “The only physical requirement that a system must met in order to instantiate 
a certain machine table are that (1) there must be at least as many physically 
distinguishable states of the system as there are machine states in the table, 
(2) the system must be capable of reacting to and changing the state of the 
tape, and (3) there must be enough physical structure to support the 
subjunctive connections specified in the table.”

  It is in the subjunctive connections that we see the contrafactuals 
expressed. If one’s model of physical reality does not allow for the necessary 
subjunctive connections to be implemented then the supervenience thesis would 
fail independent of the Turing thesis. 
[BM]
OK.

[SPK] 
So if you agree with this then you must also agree that models that do not 
allow the necessary structure to support the subjunctive connections will fail 
to allow for consciousness to supervene. I am arguing that COMP +AR is 
insufficient for supervenience of consciousness other than in a 
crypto-solipsistic mode that is indistinguishable from a conscious state whose 
content has no information, i.e. is at best randomness. Such modes of 
consciousness would be of course included in the class of states of 
consciousness but we cannot identify our states of consciousness solely with 
them. Without the existence of multiple incarnations of mind to mutually 
restrain each other, the mind will have no means to limit what it is not and 
thus would be, by definition, at least insane. (This is one situation that 
results from Travis Garrett’s idea of Observers. I am still researching my 
comment on his paper http://arxiv.org/abs/1101.2198.) 
If there is no separable means to implement a mind, or at least the 
computable contents thereof, then there is no way to define a local converging 
measure of information. MAT gives us that means and thus I claim that some form 
of physical supervenience is necessary (but not sufficient). Hitoshi Kitada has 
written extensively of this possibility: http://www.kitada.com/
***



  SPK: My point is that we need to be careful about what exactly do we mean by 
“causally inactive piece of matter”. If there is material present within a 
physical system that does not affect the 3 requirements above then surely we 
can agree with Mauldin’s claim, but if there is a problem with the faithfulness 
of the model of what physicality involves, then this must be fixed if possible. 
This is why I say that there is a bit of a straw man in his argument. 

[BM]
Maudlin should have said: "causally inactive piece of matter *relevant* for the 
computation. This is what I did, an

Re: JOINING: Travis Garrett

[Travis Garrett]

Hi Russell,

   You'll see that I immediately followed my joining post with an ever-
so-slightly irate response to your comment ;-)  I need to go have
dinner with my family, so let me quickly say that taking existing as
an observer for granted is a very easy thing to do, but it well may
need an explanation :-)

   Sincerely,
  Travis

On Jan 27, 5:18 pm, Russell Standish  wrote:
> Hi Travis,
>
> Welcome to the list. Its great to see some new blood. I did get around
> to reading your paper a few days ago, and had a couple of comments
> which I posted.
>
> 1) Your usage of the term Physic Church-Turing Thesis. What I thought
> you were assuming seemed more accurately captured by Bruno's COMP
> assumption, or Tegmark's Mathematical Universe Hyporthesis. For
> instance, Wikipedia, following Piccinini states the PCTT as:
>
> "According to Physical CTT, all physically computable functions are
> Turing-computable".
>
> I guess one can argue about what precisely constitutes a physically
> computable function, but one implication of the PCTT would be that
> real random number generators are impossible, and that beta decay is
> not really random, but pseudo random. This is contradicted by COMP.
>
> But, this is only a debate about nomenclature, not about the worth of
> your paper.
>
> 2) There can only be a countable number of observers, but an
> uncountable number of bits of information, so I was suspicious of your
> Observer Class Hypothesis. However, it looks like I missed your use of
> the Faddeev-Popov procedure, which eliminates most of those uncountable
> bits of information, so the ball is definitely back in my court!
>
> BTW - I don't think the problem you are trying to solve with the OCH
> is a problem that needs solving - the reference class of Anthropic
> Reasoning must always be a subset of the set of observers (or observer
> moments depending on how strong your self-sampling assumption is).
>
> But it would nevertheless be intriguing if the OCH were true, and I
> could see it having other applications. Thanks for the notion.
>
> On Thu, Jan 27, 2011 at 01:10:50PM -0800, Travis Garrett wrote:
> > Hi everybody,
>
> >    My name is Travis - I'm currently working as a postdoc at the
> > Perimeter Institute.  I got an email from Richard Gordon and Evgenii
> > Rudnyi pointing out that my recent paper:http://arxiv.org/abs/1101.2198
> > is being discussed here, so yeah, I'm happy to join the conversation.
> > I'll respond to some specific points in the discussion thread, but
> > what the heck, I'll give an overview of my idea here...
>
> --
>
> --- -
> Prof Russell Standish                  Phone 0425 253119 (mobile)
> Mathematics                              
> UNSW SYDNEY 2052                         hpco...@hpcoders.com.au
> Australia                                http://www.hpcoders.com.au
> --- -

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Re: Observers and Church/Turing

[Travis Garrett]

I am somewhat flabbergasted by Russell's response.  He says that he is
"completely unimpressed" - uh, ok, fine - but then he completely
ignores entire sections of the paper where I precisely address the
issues he raises.  Going back to the abstract I say:

"We then argue that the observers
collectively form the largest class of information
(where, in analogy with the Faddeev Popov procedure,
we only count over ``gauge invariant" forms of
information)."

The stipulation that one only counts over gauge-invariant (i.e.
nontrivial) information structures is absolutely critical!  This is a
well known idea in physics (which I am adapting to a new problem) but
it probably isn't well known in general.  One can see the core idea
embedded in the wikipedia article: 
http://en.wikipedia.org/wiki/Faddeev–Popov_ghost
- or in say "Quantum Field Theory in a Nutshell" by A. Zee, or
"Quantum Field Theory" by L. Ryder which is where I first learned
about it.  In general a number of very interesting ideas have been
developed in quantum field theory (also including regularization and
renormalization) to deal with thorny issues involving infinity, and I
think they can be adapted to other problems.  In short, all of the
uncountable number of uncomputable reals are just infinitely long
random sequences, and they are all eliminated (along with the
redundant descriptions) by the selection of some gauge.  Note also in
the abstract that I am equating the observers with the *nontrivial*
power set of the set of all information - which is absolutely distinct
from the standard power set!  I am only counting over nontrivial forms
of information - i.e. that which, say, you'd be interested in paying
for (at least in pre-internet days!).

I am also perfectly well aware that observers are more than just
passive information absorbers.  As I say in the paper:

"Observers are included among these complex structures,
and we will grant them the special name $y_j$
(although they are also
another variety of information structure $x_i$).
For instance a young child $y_{c1}$ may know about
$x_{3p}$ and $x_{gh}$:
$x_{3p}, x_{gh} \in y_{c1}$, while having not yet
learned about $x_{eul}$ or $x_{cm}$.
This is the key feature of the observers that we will utilize:
the $y_j$ are entities that can absorb various
$x_i$ from different regions of $\mathcal{U}$."

That is: "this is the key feature of the observers that we will
utilize"

And 4 paragraphs from the 3rd section:

" Consider then the proposed observer $y_{r1}$
 (i.e. a direct element of $\mathcal{P}(\mathcal{U})$):
  $y_{r1} = \{ x_{tang}, x_3, x_{nept} \}$,
 where $x_{tang}$ is a tangerine, $x_{3}$ is the
 number 3, and $x_{nept}$ is the planet Neptune.
 This random collection of various information structures
 from $\mathcal{U}$ is clearly
 not an observer, or any other from of nontrivial information:
 $y_{r1}$ is redundant to its three elements, and would thus
 be cut by the selection of a gauge.
 This is the sense in which most of the direct elements of the
 power set of $\mathcal{U}$ do not add any new real information.

 However, one could have a real observer $y_{\alpha}$
 whose main interests happened to include types of fruit, the
integers, and
 the planets of the solar system and so forth.
 The 3 elements of $y_{r1}$ exist as a simple list,
 with no overarching structure actually uniting them.
 A physically realized computer, with some finite
 amount of memory and a capacity to receive
 input, resolves this by providing a
 unified architecture for the nontrivial
 embedding of various forms of information.
 A physical computer thus provides the glue to combine, say,
 $x_{tang}$, $x_{3}$, and $x_{nept}$ and
 form a new nontrivial structure in $\mathcal{U}$.

It is possible to also consider the existence
 of ``randomly organized computers"
 which indiscriminately embed arbitrary
 elements of $\mathcal{U}$ -- these
 too would conform to no real $x_i$.
 This leads to the specification of ``physically realized"
 computers, as the restrictions that
 arise from existing within a mathematical
 structure like $\Psi$ results in
 computers that process information in
 nontrivial ways.
 Furthermore, a structure like $\Psi$ allows for
 these physical computers to spontaneously
 arise as it evolves forward from an initial state of
 low entropy.
 Namely it is possible for replicating
 molecular structures to emerge, and
 Darwinian evolution can then drive to them
 to higher levels of complexity as they
 compete for limited resources.
 A fundamental type of evolutionary
 adaptation then becomes possible:
 the ability to extract pertinent information
 from one's environment so that it can
 be acted upon to one's advantage.
 The requirement that one extracts useful
 information
 is thus one of the key constraints that
 has guided the evolution of the
 sensory organs and nervous systems
 of the species in the animal kingdom.

 This evolutionary process has reached its current
 apogee with our species,
 as our b

Re: A comment on Mauldin's paper “Computation and Consciousness”

[Bruno Marchal]

On 27 Jan 2011, at 22:12, Brent Meeker wrote:


On 1/27/2011 10:23 AM, Bruno Marchal wrote:



On 25 Jan 2011, at 15:47, Stephen Paul King wrote:




Mathematical structures do not “do” anything, they merely  
exist, if at all! We can use verbs to describe relations between  
nouns but that does not change the fact that nouns are nouns and  
not verbs. The movie graph is a neat trick in that is abstracts  
out the active process of organizing the information content of  
the individual frames and the order of their placement in the  
graph, but that some process had to be involved to perform the  
computation of the content and ordering cannot be removed, it is  
only pushed out of the field of view. This is why I argue that we  
cannot ignore the computational complexity problem that exist in  
any situation where we are considering a optimal configuration  
that is somehow selected from some set or ensemble.


I don't see how this would change anything in the argument, unless  
you presuppose consciousness is not locally Turing emulable, to  
start with.


What does "locally" mean in this context?  I doubt that  
consciousness is strictly local in the physical sense; it requires  
and world to interact with.


It means that, when saying yes to the doctor, you will not only  
survive, but you will feel the same physical laws. You will not change  
the relative measure on your computations. It might be necessary to  
duplicate a part of the environment, which, in that case has to be  
supposed to be Turing emulable in that same sense. That is why I  
mention the notion of generalized brain. If the environment is not  
Turing emulable, you have to use another theory of mind than the  
mechanist one.
Consciousness per se, and first person, and matter (first person  
plural) are not locally emulable. First person point of views are  
related with the infinite continuum of computations going through  
their states, and that is not algorithmic (assuming digital mechanism).


If my local body is a machine, my soul, I, is not a machine. I should  
say.


Bruno

http://iridia.ulb.ac.be/~marchal/



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Re: JOINING: Travis Garrett

[Russell Standish]

Hi Travis,

Welcome to the list. Its great to see some new blood. I did get around
to reading your paper a few days ago, and had a couple of comments
which I posted.

1) Your usage of the term Physic Church-Turing Thesis. What I thought
you were assuming seemed more accurately captured by Bruno's COMP
assumption, or Tegmark's Mathematical Universe Hyporthesis. For
instance, Wikipedia, following Piccinini states the PCTT as:

"According to Physical CTT, all physically computable functions are
Turing-computable". 

I guess one can argue about what precisely constitutes a physically
computable function, but one implication of the PCTT would be that
real random number generators are impossible, and that beta decay is
not really random, but pseudo random. This is contradicted by COMP.

But, this is only a debate about nomenclature, not about the worth of
your paper.

2) There can only be a countable number of observers, but an
uncountable number of bits of information, so I was suspicious of your
Observer Class Hypothesis. However, it looks like I missed your use of
the Faddeev-Popov procedure, which eliminates most of those uncountable
bits of information, so the ball is definitely back in my court!

BTW - I don't think the problem you are trying to solve with the OCH
is a problem that needs solving - the reference class of Anthropic
Reasoning must always be a subset of the set of observers (or observer
moments depending on how strong your self-sampling assumption is).

But it would nevertheless be intriguing if the OCH were true, and I
could see it having other applications. Thanks for the notion.

On Thu, Jan 27, 2011 at 01:10:50PM -0800, Travis Garrett wrote:
> Hi everybody,
> 
>My name is Travis - I'm currently working as a postdoc at the
> Perimeter Institute.  I got an email from Richard Gordon and Evgenii
> Rudnyi pointing out that my recent paper: http://arxiv.org/abs/1101.2198
> is being discussed here, so yeah, I'm happy to join the conversation.
> I'll respond to some specific points in the discussion thread, but
> what the heck, I'll give an overview of my idea here...
> 

-- 


Prof Russell Standish  Phone 0425 253119 (mobile)
Mathematics  
UNSW SYDNEY 2052 hpco...@hpcoders.com.au
Australiahttp://www.hpcoders.com.au


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Re: A comment on Mauldin's paper “Computation and Consciousness”

[Brent Meeker]

On 1/27/2011 10:23 AM, Bruno Marchal wrote:


On 25 Jan 2011, at 15:47, Stephen Paul King wrote:


The supervenience thesis is separate from the Turing thesis and 
Mauldin does a good job in distinguishing them.


Just to be clear, what Maudlin call "supervenience thesis" is what I 
called "physical supervenience thesis", to distinguish it from the 
computationalist supervenience thesis.
The computationalist supervenience thesis is basically what remains 
when we keep comp, and understand that the Phys. Sup. thesis has to go 
away in the comp frame.




The problem that I see is in the properties of physicality that are 
assumed in Mauldin’s argument. It is one thing to not be dependent on 
what particular physical structure a computation can be run on 
(assuming a realistic supervenience), it is another thing entirely to 
say that a Turing machine can be “run” without the existence of any 
physical hardware at all.



Well, in the branch ~MEC v ~MAT, Maudlin seems to prefer MAT, so he 
seems with you on this, I think.




I am trying to make this distinction and trying to fix this problem 
that I found in the supervenience thesis within Mauldin’s argument. 
He does point out that there are contrafactuals that must have some 
physical instantiation. We see this on page 411 where he wrote:
“The only physical requirement that a system must met in order to 
instantiate a certain machine table are that (1) there must be at 
least as many physically distinguishable states of the system as 
there are machine states in the table, (2) the system must be capable 
of reacting to and changing the state of the tape, and (3) there must 
be enough physical structure to support the subjunctive connections 
specified in the table.”
It is in the subjunctive connections that we see the 
contrafactuals expressed. If one’s model of physical reality does not 
allow for the necessary subjunctive connections to be implemented 
then the supervenience thesis would fail independent of the Turing 
thesis.


OK.




My point is that we need to be careful about what exactly do we mean 
by “causally inactive piece of matter”. If there is material present 
within a physical system that does not affect the 3 requirements 
above then surely we can agree with Mauldin’s claim, but if there is 
a problem with the faithfulness of the model of what physicality 
involves, then this must be fixed if possible. This is why I say that 
there is a bit of a straw man in his argument.



Maudlin should have said: "causally inactive piece of matter 
*relevant* for the computation. This is what I did, and it makes the 
argument independent of the counterfactual re-instantiation. The 
movie-graph is simpler with that respect. But this can lead to some 
ambiguity too.




Mathematical structures do not “do” anything, they merely exist, 
if at all! We can use verbs to describe relations between nouns but 
that does not change the fact that nouns are nouns and not verbs. The 
movie graph is a neat trick in that is abstracts out the active 
process of organizing the information content of the individual 
frames and the order of their placement in the graph, but that some 
process had to be involved to perform the computation of the content 
and ordering cannot be removed, it is only pushed out of the field of 
view. This is why I argue that we cannot ignore the computational 
complexity problem that exist in any situation where we are 
considering a optimal configuration that is somehow selected from 
some set or ensemble.


I don't see how this would change anything in the argument, unless you 
presuppose consciousness is not locally Turing emulable, to start with.


What does "locally" mean in this context?  I doubt that consciousness is 
strictly local in the physical sense; it requires and world to interact 
with.


Brent

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JOINING: Travis Garrett

[Travis Garrett]

Hi everybody,

   My name is Travis - I'm currently working as a postdoc at the
Perimeter Institute.  I got an email from Richard Gordon and Evgenii
Rudnyi pointing out that my recent paper: http://arxiv.org/abs/1101.2198
is being discussed here, so yeah, I'm happy to join the conversation.
I'll respond to some specific points in the discussion thread, but
what the heck, I'll give an overview of my idea here...

  The idea flows from the assumption that one can do an arbitrarily
good simulation of arbitrarily large regions of the universe inside a
sufficiently powerful computer -- more formally I assume the physical
version of the Church Turing Thesis.  Everything that exists can then
be viewed as different types of information.  The Observer Class
Hypothesis then proposes that observers collectively form by far the
largest set of information, due to the combinatorics that arise from
absorbing information from many different sources (the observers
thereby roughly resemble the power set of the set of all
information).  One thus exists as an observer because it is by far the
most probable form of existence.

  A couple caveats are of crucial importance: when I say information,
I mean non-trivial, gauge-invariant, "real" information, i.e.
information that has a large amount of effective complexity (Gell-Mann
and Lloyd) or logical depth (Bennett).  I focus on "gauge-invariant"
because I can then borrow the Faddeev-Popov procedure from quantum
field theory: in essence, one does not count over redundant
descriptions.  I also borrow the idea of regularization from quantum
field theory: when considering systems where infinities occur, it can
be useful to introduce a finite cutoff, and then study the limiting
behavior as the cutoff goes to infinity.  For instance, regulating the
integers shows that the density of primes goes like 1/log(N) - without
the cutoff one can only say that there are a countable number of
primes and composites.  These ideas are well known in theoretical
physics, but perhaps not outside, and I am also using them in a new
setting...

  Let me give a simple example of the use of gauge invariance from the
paper - consider the mathematical factoid: {3 is a prime number}.
This can be re-expressed in an infinite number of different ways: {2+1
is a prime number}, {27^(1/3) is not composite}, etc, etc...  Thus, at
first it seems that just this simple factoid will be counted an
infinite number of times!  But no, follow Faddeev and Popov, and pick
one particular representation (it's fine to use, say, {27^(1/3) is not
composite}, but later we will want to use the most compact
representations when we regularize), and just count this small piece
of information once, which removes all of the redundant descriptions.
To reiterate, we only count over the gauge-invariant information.

  Consider a more complex example, say the Einstein equations: G_ab =
T_ab.  Like "3 is a prime number", they can be expressed in an
infinite number of different ways, but let's pick the most compact
binary representation x_EE (an undecidable problem in general, but say
we get lucky).  Say the most compact encoding takes one million bits.
Basic Kolmogorov complexity would then say that x_EE  contains the
same amount of information as a random sequence r_i one million bits
long - both are not compressible.  But x_EE contains a large amount of
nontrivial, gauge invariant information that would have to be
preserved in alternative representations, while the random sequence
has no internal patterns that must be preserved in different
representations: x_EE has a large amount of effective complexity, and
r_i has none.  Focusing on the gauge-invariant structures thus not
only removes the redundant descriptions, but also removes all of the
random noise, leaving only the "real" information behind.  For
instance, I posit that the uncomputable reals are nothing more than
infinitely long random sequences, which also get removed (along with
the finite random sequences) by the selection of a gauge.

In some computational representation, the real information structures
will thus form a sparse subset among all binary strings.  In the paper
I consider 3 cases - 1) there are a finite number of finitely complex
real information structures (which could be viewed as the null
assumption), 2) there are a infinite number of finitely complex
structures, and 3) there are irreducibly infinitely complex
information structures.  I focus on 1) and 2), with the assumption
that 3) isn't meaningful (i.e. that hypercomputers do not exist).
Even case 2) is extremely large, and it leads to the prediction of
universal observers: observers that continuously evolve in time, so
that they can eventually process arbitrarily complex forms of
information.  The striking fact that a technological singularity may
only be a few decades away lends support to this extravagant idea...

  Well anyways, that's probably enough for now.  I am interested in
seeing what people think of 

Re: A comment on Mauldin's paper “Computation and Consciousness”

[Bruno Marchal]

On 25 Jan 2011, at 15:47, Stephen Paul King wrote:


The supervenience thesis is separate from the Turing thesis and  
Mauldin does a good job in distinguishing them.


Just to be clear, what Maudlin call "supervenience thesis" is what I  
called "physical supervenience thesis", to distinguish it from the  
computationalist supervenience thesis.
The computationalist supervenience thesis is basically what remains  
when we keep comp, and understand that the Phys. Sup. thesis has to go  
away in the comp frame.




The problem that I see is in the properties of physicality that are  
assumed in Mauldin’s argument. It is one thing to not be dependent  
on what particular physical structure a computation can be run on  
(assuming a realistic supervenience), it is another thing entirely  
to say that a Turing machine can be “run” without the existence of  
any physical hardware at all.



Well, in the branch ~MEC v ~MAT, Maudlin seems to prefer MAT, so he  
seems with you on this, I think.




I am trying to make this distinction and trying to fix this problem  
that I found in the supervenience thesis within Mauldin’s argument.  
He does point out that there are contrafactuals that must have some  
physical instantiation. We see this on page 411 where he wrote:


“The only physical requirement that a system must met in order to  
instantiate a certain machine table are that (1) there must be at  
least as many physically distinguishable states of the system as  
there are machine states in the table, (2) the system must be  
capable of reacting to and changing the state of the tape, and (3)  
there must be enough physical structure to support the subjunctive  
connections specified in the table.”


It is in the subjunctive connections that we see the  
contrafactuals expressed. If one’s model of physical reality does  
not allow for the necessary subjunctive connections to be  
implemented then the supervenience thesis would fail independent of  
the Turing thesis.


OK.




My point is that we need to be careful about what exactly do we mean  
by “causally inactive piece of matter”. If there is material present  
within a physical system that does not affect the 3 requirements  
above then surely we can agree with Mauldin’s claim, but if there is  
a problem with the faithfulness of the model of what physicality  
involves, then this must be fixed if possible. This is why I say  
that there is a bit of a straw man in his argument.



Maudlin should have said: "causally inactive piece of matter  
*relevant* for the computation. This is what I did, and it makes the  
argument independent of the counterfactual re-instantiation. The movie- 
graph is simpler with that respect. But this can lead to some  
ambiguity too.




Mathematical structures do not “do” anything, they merely exist,  
if at all! We can use verbs to describe relations between nouns but  
that does not change the fact that nouns are nouns and not verbs.  
The movie graph is a neat trick in that is abstracts out the active  
process of organizing the information content of the individual  
frames and the order of their placement in the graph, but that some  
process had to be involved to perform the computation of the content  
and ordering cannot be removed, it is only pushed out of the field  
of view. This is why I argue that we cannot ignore the computational  
complexity problem that exist in any situation where we are  
considering a optimal configuration that is somehow selected from  
some set or ensemble.


I don't see how this would change anything in the argument, unless you  
presuppose consciousness is not locally Turing emulable, to start with.






Another question that I am asking is what relation does  
information have with matter. We had a paper that seems to propose  
that information is physical and then goes on to make some strange  
claims.


OK. And the problem with the word physical is that it means different  
things in different settings. The main confusion is between  
fundamentally physical, or material, with a conception of primary  
matter, or it means "related to this or that physical theory" based on  
abstract mathematical relations.





We also had a recent paper that discusses how “information is  
converted into free energy” by a Maxwell Demon-type feedback system.  
It seems to me that there is a lot of confusion about what  
relationship there is between information and matter, so my  
inquisitiveness could be seen as an attempt to make sense of this  
mess.


And the word "matter" is similarly ambiguous, and never defined,  
except by Aristotle which provides the "& Dp" idea, implicitly used by  
the Platonist Plotinus to define matter in the way used by the self- 
observing machine.
Matter is what is indeterminate, and oppose to intelligibility (Bp).  
It is of the type ~Bp, that is D#. This is coherent with the idea that  
a physics is, before all thing, a probability or plausibility  

Re: Observers and Church/Turing

[Bruno Marchal]

On 25 Jan 2011, at 18:24, Andrew Soltau wrote:


On 24/01/11 21:35, Bruno Marchal wrote:

Thanks for all this. I will do some reading and then go through the  
points again. And get back to you.


You are welcome. Ask any question.


Bruno



http://iridia.ulb.ac.be/~marchal/



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Re: Bruno-Colin-dicussion Jan-2011

[Bruno Marchal]

On 26 Jan 2011, at 11:31, Russell Standish wrote:


On Mon, Jan 24, 2011 at 09:31:23PM +0100, Bruno Marchal wrote:


My point is only that IF we accept digital mechanism THEN the
*appearance* of movement is an inside, first person, construction,
due to the gap between what a machine (number) can prove and what is
true.



It is interesting you say this. Is your reasoning for this that the  
logic of Bp

& p enables Kripke frames, which can be identified with the passage of
time?


The logic of Bp & p, that is S4Grz, and its computationalist variant,  
S4Grz1 (Bp & p + p -> Bp), enables Kripke frames, like most so called  
normal modal logic systems, which appears, in this S4 case,  to be a  
valuable temporal modal logic. In fact S4Grz is even more temporal, or  
"subjective-time temporal (cf Bergson's duration) because S4Grz = S4 +  
Grz, and Grz imposes antisymmetry for the relation of accessibility  
among worlds/states(*): times seems to fly irreversibly.


But S4Grz enables also intuitionistic logic, which is often related to  
a logic of evolving knowledge, and which made Brouwer linking  
consciousness and time.
Boolos and Goldblatt discovered independently the arithmetical self- 
referential S4Grz. Roughly speaking G proves Bp & p when S4Grz proves  
Bp.


What is remarkable is that S4Grz = S4Grz*. The G* (true) level does  
not add anything. This explains the confusion between truth and  
provability made by the pure (solipsistic) first person (the first  
person forgetting the existence of other persons).


Note that in the material hypostases, the one with "& Dt" (or "& Dp"),  
we lost the Kripke accessibility, and get topological neighborhoods  
instead, which is coherent with physicalness and the continuum of  
consistent computational continuation needed for the emergence of the  
physical laws.


Bruno

(*) Grz is  the rather awkward  B(B(p -> Bp) -> b) -> p, discovered  
earlier by Sobocynski. Grzegorczyk rediscovered it in the context of  
axiomatizing a modal form of propositional intuitionist logic.


http://iridia.ulb.ac.be/~marchal/



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