Mathematical closure of consciousness and computation

[Felix Hoenikker]

Sorry again, but I want to add one thing:

The broadest mathematical closure of "the existence of computation",
"the observation of consciousness anywhere" suggests the following, in
my mind: all possible numbers (including transfinite-ones) are, in
fact, self aware substructures in the mathematical universe,
recursively "communicating" to "each other" by exchanging bits in an
attempt to develop the algorithm which compresses themselves to a
single state, which represents the number "one", after which it
promptly forgets and starts all over again, everywhere, and all at
once.

---------- Forwarded message ----------
From: Felix Hoenikker <fhoen...@gmail.com>
Date: Sat, Jun 4, 2011 at 3:03 AM
Subject: The final TOE?
To: Everything List <everyth...@googlegroups.com>

Hi all,

Consider the following fully general way of saying this is the
following: quantum mechanics and general relativity are symmetrically
"the exact same theory", modulo the additional "bit" of information
that quantum entanglement reduces net gravitational energy.  This is
the EXACT answer to the EPR paradox, and all paradoxes about
singularities, and consistent with our picture of reality in every
respect, as it "necessarily must be" since it follows exactly from the
asssumption of 3+1 spacetime embedded within some higher dimensional
structure of "any" form (i.e. including string theory).

Since no "true" gravitational singularities exist, then "every point
in space is an apparent black hole" because "no point in space is an
apparent black hole".  Thus, at every point in space, a "bit" of
information (or a "photon") can escape from the "observable" universe
on our scale, "go into the past", and come out "in the future" in a
symmetric manner for all observers, without considering your frame of
reference in 3+1 space time.  This qualitatively predicts all features
of GR without QCD or QFT.  However, since photons travelling through
locally closed loops can look like "point" particles with some net
entanglement coming out, then they can look like bundles that, for all
intents and purposes, appear to randomly add information in some way,
and in some spherically symmetric fashion, which predicts the
divergence and appearance of other "fundamental forces" early in the
inflating universe.

It is often said that QM and GR differ from each other exactly by the
contemplation of the "singularity", and that our inability to discover
the "true" laws of the universe has been limited by our lack of
knowledge about the twin singularities: the inflationary bubble and
the black hole.  It follows that this fact was "exactly true" all
along, and the laws of physics are a completely dimensionless
consequences of our "local" geometry of space, and our civilization
has, in fact, rather than been trying to "discover" the next laws of
physics, has in fact been struggling to "unlearn" the concept of
"Indeterminacy" and "quantum mechanics", since QM follows from GR, the
postulate of 3+1 spacetime and E = mc^2 (a nice, dimensionless
equation).  Einstein, in fact, was right all along, and successfully
completed the "fully" deterministic general laws of physics.

Consider then, the reason why indeterministic QM was ever suggested:
the apparently subjective indeterminacy of the universe from each
"observer" point of view (i.e. the uncertainty principle).  Or
actually, consider the fact that, if the universe is completely
deterministic, and "you" for any defined "you" is getting non-random
information from any source, then that information must, in fact, be
added to you by the "rest of the universe" in some systematic fashion,
down to the tiniest quantum of "universe".  This implies that there
"is" actually, some "quanta" of the universe, a "photon", and each
"photon" is having information added to "it" from the "rest of the
universe", in a systematic fashion, and recursively so for every
"observer".  This is actually a fully generic model for the universe,
and the absolute generalization of QM and SR.

Next, consider the fact that you are "conscious" and possibly
"indeterminstic" (i.e. have subjective free will).  I think I do.
Therefore, I am not a "quanta" of information, or a "bit", but it was
"added to me" from "somewhere".  No, consider the mathematical closure
of this observation.  What does this imply about and anthropic
principle and "fine tuning"? Does that make sense anymore.  Also, does
this not mean that our "observable universe", for "some definition of
observable", from "any subjective observer's point of view", is
constantly being added non-random information from "outside".

I truly beg you all to consider this argument fully.

Please let me know what you think,
F.H.

On Fri, Jun 3, 2011 at 7:16 PM, Felix Hoenikker <fhoen...@gmail.com> wrote:
> Every "apparent" event horizon is really a separation of two
> universes, where the outside universe is entangled geometrically with
> the inside universe. The Hubble volume is sitting inside of an
> expanding supermassive black hole, of another universe. However, by
> the uncertainty principle, this means the "outside universe" is
> "really" simultaneously in a superposition of a large but countably
> finite many possible universes (i.e. bitstates), with the net
> information between the "inside" and "outside" views cancelling out to
> zero. Equivalently, every "classical" black hole is really in a
> microscopic superposition of countably finite many bitstates, again
> with the net information "inside" and "outside" cancelling zero.
> However, it cannot converge to a singularity, because it cannot encode
> "bitstates" forever in the same volume, therefore it must leak
> information in the form of "photons" (i.e. Hawking radiation).
>
> Equivalently, the Hubble volume receives information one photon at a
> time from the "outside" in the form of cosmic background radiation,
> that information being about the prior state of the otherwise casually
> disconnected universe. (i.e. CMB == Hawking radiation). The
> equivalence principle implies length contraction and time dilation.
> Gravity mediated by photons is the single fundamental force of the
> universe. All other sources of apparent information and causal
> connectivity (i.e. all other forces) are the result of the initial
> state of the universe at the Big Bang, the only true singularity. The
> laws of the universe are extremely simple.
>
> This is the digital unification of GR and QM.  What do you think?

[Jason Resch]

One thing I thought of recently which is a good way of showing how
computation occurs due to the objective truth or falsehood of
mathematical propositions is as follows:

Most would agree that a statement such as "8 is composite" has an
eternal objective truth. Likewise the statement: the Nth fibbinacci
number is X. Has an objective truth for any integer N no matter how
large. Let's say N=10 and X = 55. The truth of this depends on the
recursive definition of the fibbinacci sequence, where future states
depend on prior states, and is therefore a kind if computation. Since
N may be infinitely large, then in a sense this mathematical
computation proceeds forever. Likewise one might say that chaitin's
constant = Y has some objective mathematical truth. For chaintons
constant to have an objective value, the execution of all programs
must occur.

Simple recursive relations can lead to exraordinary complexity,
consider the universe of the Mandelbrot set implied by the simple
relation Z(n+1)= Z(n)^2 + C. Other recursive formulae may result in
the evolution of structures such as our universe or the computation of
your mind.

Jason

On Jun 4, 2011, at 4:09 AM, Felix Hoenikker <fhoen...@gmail.com>
wrote:

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[Rex Allen]

On Sat, Jun 4, 2011 at 12:21 PM, Jason Resch <jason...@gmail.com> wrote:
> One thing I thought of recently which is a good way of showing how
> computation occurs due to the objective truth or falsehood of mathematical
> propositions is as follows:
>
> Most would agree that a statement such as "8 is composite" has an eternal
> objective truth.

Assuming certain of axioms and rules of inference, sure.

But isn't that true of nearly anything? How many axiomatic systems are there?

> Likewise the statement: the Nth fibbinacci number is X.
> Has an objective truth for any integer N no matter how large.  Let's say
> N=10 and X = 55.  The truth of this depends on the recursive definition of
> the fibbinacci sequence, where future states depend on prior states, and is
> therefore a kind if computation.  Since N may be infinitely large, then in a
> sense this mathematical computation proceeds forever.  Likewise one might
> say that chaitin's constant = Y has some objective mathematical truth.  For
> chaintons constant to have an objective value, the execution of all programs
> must occur.
>
> Simple recursive relations can lead to exraordinary complexity, consider the
> universe of the Mandelbrot set implied by the simple relation Z(n+1)= Z(n)^2
> + C.  Other recursive formulae may result in the evolution of structures
> such as our universe or the computation of your mind.

Is extraordinary complexity required for the manifestation of "mind"?
If so, why?

Is it that these recursive relations cause our experience, or are just
a way of thinking about our experience?

Is it:

Recursive relations cause thought.

OR:

Recursion is just a label that we apply to some of our implicational beliefs.

The latter seems more plausible to me.

Rex

[Jason Resch]

On Sat, Jun 4, 2011 at 12:06 PM, Rex Allen <rexall...@gmail.com> wrote:

On Sat, Jun 4, 2011 at 12:21 PM, Jason Resch <jason...@gmail.com> wrote:
> One thing I thought of recently which is a good way of showing how
> computation occurs due to the objective truth or falsehood of mathematical
> propositions is as follows:
>
> Most would agree that a statement such as "8 is composite" has an eternal
> objective truth.

Assuming certain of axioms and rules of inference, sure.

Godel showed no single axiomatic system captures all mathematical truth, any fixed set of axioms can at best approximate mathematical truth.  If mathematical truth cannot be fully captured by a set of axioms, it must exist outside sets of axioms altogether.

 

But isn't that true of nearly anything?  How many axiomatic systems are there?

> Likewise the statement: the Nth fibbinacci number is X.
> Has an objective truth for any integer N no matter how large.  Let's say
> N=10 and X = 55.  The truth of this depends on the recursive definition of
> the fibbinacci sequence, where future states depend on prior states, and is
> therefore a kind if computation.  Since N may be infinitely large, then in a
> sense this mathematical computation proceeds forever.  Likewise one might
> say that chaitin's constant = Y has some objective mathematical truth.  For
> chaintons constant to have an objective value, the execution of all programs
> must occur.
>
> Simple recursive relations can lead to exraordinary complexity, consider the
> universe of the Mandelbrot set implied by the simple relation Z(n+1)= Z(n)^2
> + C.  Other recursive formulae may result in the evolution of structures
> such as our universe or the computation of your mind.

The fractal is just an example of a simple formula leading to very complex output.  The same is true for the UDA:

for i = 0 to inf:

  for each j in set of programs:

    execute single instruction of program j

  add i to set of programs

That simple formula executes all programs.

 

Is extraordinary complexity required for the manifestation of "mind"?
If so, why?

I don't know what lower bound of information or complexity is required for minds.

 

Is it that these recursive relations cause our experience, or are just
a way of thinking about our experience?

Is it:

Recursive relations cause thought.

OR:

Recursion is just a label that we apply to some of our implicational beliefs.

The latter seems more plausible to me.

Through recursion one can implement any form of computation. Recursion is common and easy to show in different mathematical formulas, while showing a Turing machine is more difficult.  Many programs which can be easily defined through recursion can also be implemented without recursion, so I was not implying recursion is necessary for minds.  For example, implementing the Fibonacci formula iteratively would look like:

Fib(N)

  X = 1

  Y = 1

  for int i = 2 to N:

    i = X + Y

    X = Y

    Y = i

  print Y

This program iteratively computes successive Fibonacci numbers, and will output the Nth Fibbonaci number.

Jason

[Rex Allen]

On Sat, Jun 4, 2011 at 1:51 PM, Jason Resch <jason...@gmail.com> wrote:
>
>
> On Sat, Jun 4, 2011 at 12:06 PM, Rex Allen <rexall...@gmail.com> wrote:
>>
>> On Sat, Jun 4, 2011 at 12:21 PM, Jason Resch <jason...@gmail.com> wrote:
>> > One thing I thought of recently which is a good way of showing how
>> > computation occurs due to the objective truth or falsehood of
>> > mathematical
>> > propositions is as follows:
>> >
>> > Most would agree that a statement such as "8 is composite" has an
>> > eternal
>> > objective truth.
>>
>> Assuming certain of axioms and rules of inference, sure.
>
> Godel showed no single axiomatic system captures all mathematical truth, any
> fixed set of axioms can at best approximate mathematical truth.  If
> mathematical truth cannot be fully captured by a set of axioms, it must
> exist outside sets of axioms altogether.

Then perhaps the correct conclusion to draw is that there is no such
thing as "mathematical truth"?

Perhaps there is just human belief.

> The fractal is just an example of a simple formula leading to very complex
> output.  The same is true for the UDA:
> for i = 0 to inf:
>   for each j in set of programs:
>     execute single instruction of program j
>   add i to set of programs
> That simple formula executes all programs.

Following those instructions will let someone "execute" all "programs".

Or, alternatively, configuring a physical system in a way that
represents those instructions will allow someone to interpret the
system's subsequent states as being analogous to the "execution" of
all "programs".

>> Is extraordinary complexity required for the manifestation of "mind"?
>> If so, why?
>>
>
> I don't know what lower bound of information or complexity is required for
> minds.

Then why do you believe that information of complexity is required for minds?

>> Is it that these recursive relations cause our experience, or are just
>> a way of thinking about our experience?
>>
>> Is it:
>>
>> Recursive relations cause thought.
>>
>> OR:
>>
>> Recursion is just a label that we apply to some of our implicational
>> beliefs.
>>
>> The latter seems more plausible to me.
>>
>
> Through recursion one can implement any form of computation.

But, ultimately, what is computation?

> Recursion is
> common and easy to show in different mathematical formulas, while showing a
> Turing machine is more difficult.  Many programs which can be easily defined
> through recursion can also be implemented without recursion, so I was not
> implying recursion is necessary for minds.

Then what do you believe is necessary for minds?

Rex

[Noon Silk]

On Sat, Jun 4, 2011 at 7:09 PM, Felix Hoenikker <fhoen...@gmail.com> wrote:
> Sorry again, but I want to add one thing:
>
> The broadest mathematical closure of "the existence of computation",
> "the observation of consciousness anywhere" suggests the following, in
> my mind: all possible numbers (including transfinite-ones) are, in
> fact, self aware substructures in the mathematical universe,
> recursively "communicating" to "each other" by exchanging bits in an
> attempt to develop the algorithm which compresses themselves to a
> single state, which represents the number "one", after which it
> promptly forgets and starts all over again, everywhere, and all at
> once.

You know, there is a lot to be said for making statements that are
verifiable. Ideas are nice, but they've got to have some scientific
value, surely ...

--
Noon Silk | http://dnoondt.wordpress.com/ >

Fancy a quantum lunch? http://groups.google.com/group/quantum-lunch?hl=en

"Every morning when I wake up, I experience an exquisite joy — the joy
of being this signature."

[Bruno Marchal]

On 04 Jun 2011, at 19:06, Rex Allen wrote:

> On Sat, Jun 4, 2011 at 12:21 PM, Jason Resch <jason...@gmail.com>
> wrote:
>> One thing I thought of recently which is a good way of showing how
>> computation occurs due to the objective truth or falsehood of
>> mathematical
>> propositions is as follows:
>>
>> Most would agree that a statement such as "8 is composite" has an
>> eternal
>> objective truth.
>
> Assuming certain of axioms and rules of inference, sure.

But everyone agree on the axioms of arithmetic. And we could take any
universal (in the Turing sense) system instead. The physical laws
cannot depend on the choice of the "universal base". Lat us continue
with (N, +, *), because it is taught in high school.

I think you are confusing computability, which is absolute (assuming
Church thesis), and provability, which is always relative to theories,
machines, entities, etc.

Jason is right, computation occurs in "arithmetical platonia", even in
a tiny part of it actually, independently of us. This tiny part is
assumed in the rest of science, and comp makes it necessarily enough
(by taking seriously the first and third person distinction).

Bruno

>
> The latter seems more plausible to me.
>
>
> Rex
>

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> You received this message because you are subscribed to the Google
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> .
>

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

[Stephen Paul King]

Hi Jason,

 

    Very interesting reasoning!

 

From: Jason Resch

Sent: Saturday, June 04, 2011 1:51 PM

To: everyth...@googlegroups.com

Subject: Re: Mathematical closure of consciousness and computation

On Sat, Jun 4, 2011 at 12:06 PM, Rex Allen <rexall...@gmail.com> wrote:

On Sat, Jun 4, 2011 at 12:21 PM, Jason Resch <jason...@gmail.com> wrote:
> One thing I thought of recently which is a good way of showing how
> computation occurs due to the objective truth or falsehood of mathematical
> propositions is as follows:
>
> Most would agree that a statement such as "8 is composite" has an eternal
> objective truth.

Assuming certain of axioms and rules of inference, sure.

 

Godel showed no single axiomatic system captures all mathematical truth, any fixed set of axioms can at best approximate mathematical truth.  If mathematical truth cannot be fully captured by a set of axioms, it must exist outside sets of axioms altogether.

 

[SPK]

 

    I see two possibilities. 1) Mathematical truth might only exist in our minds. But an infinity of such minds is possible...2) Might it be possible that our mathematical ideas are still too primitive and simplistic to define the kind of set that is necessary?

**

 

But isn't that true of nearly anything?  How many axiomatic systems are there?

> Likewise the statement: the Nth fibbinacci number is X.
> Has an objective truth for any integer N no matter how large.  Let's say
> N=10 and X = 55.  The truth of this depends on the recursive definition of
> the fibbinacci sequence, where future states depend on prior states, and is
> therefore a kind if computation.  Since N may be infinitely large, then in a
> sense this mathematical computation proceeds forever.  Likewise one might
> say that chaitin's constant = Y has some objective mathematical truth.  For
> chaintons constant to have an objective value, the execution of all programs
> must occur.
>
> Simple recursive relations can lead to exraordinary complexity, consider the
> universe of the Mandelbrot set implied by the simple relation Z(n+1)= Z(n)^2
> + C.  Other recursive formulae may result in the evolution of structures
> such as our universe or the computation of your mind.

 

The fractal is just an example of a simple formula leading to very complex output.  The same is true for the UDA:

for i = 0 to inf:

  for each j in set of programs:

    execute single instruction of program j

  add i to set of programs

That simple formula executes all programs.

 

Is extraordinary complexity required for the manifestation of "mind"?
If so, why?

 

I don't know what lower bound of information or complexity is required for minds.

 

[SPK]

    Why are we sure that a “lower bound of information” or “complexity” is required? Seriously, there seems to be a bit of speculation from too few facts when it comes to consciousness!

**

 

Is it that these recursive relations cause our experience, or are just
a way of thinking about our experience?

Is it:

Recursive relations cause thought.

OR:

Recursion is just a label that we apply to some of our implicational beliefs.

The latter seems more plausible to me.

 

Through recursion one can implement any form of computation. Recursion is common and easy to show in different mathematical formulas, while showing a Turing machine is more difficult.  Many programs which can be easily defined through recursion can also be implemented without recursion, so I was not implying recursion is necessary for minds.  For example, implementing the Fibonacci formula iteratively would look like:

 

Fib(N)

  X = 1

  Y = 1

  for int i = 2 to N:

    i = X + Y

    X = Y

    Y = i

  print Y

 

This program iteratively computes successive Fibonacci numbers, and will output the Nth Fibbonaci number.

 

Jason

--

 

[SPK]

    The existence of such Numbers could be a telltale sign that numbers require an eternal computation to define them.

 

Onward!

 

Stephen

[Jason Resch]

On Jun 4, 2011, at 1:03 PM, Rex Allen <rexall...@gmail.com> wrote:

> On Sat, Jun 4, 2011 at 1:51 PM, Jason Resch <jason...@gmail.com>
> wrote:
>>
>>
>> On Sat, Jun 4, 2011 at 12:06 PM, Rex Allen
>> <rexall...@gmail.com> wrote:
>>>
>>> On Sat, Jun 4, 2011 at 12:21 PM, Jason Resch
>>> <jason...@gmail.com> wrote:
>>>> One thing I thought of recently which is a good way of showing how
>>>> computation occurs due to the objective truth or falsehood of
>>>> mathematical
>>>> propositions is as follows:
>>>>
>>>> Most would agree that a statement such as "8 is composite" has an
>>>> eternal
>>>> objective truth.
>>>
>>> Assuming certain of axioms and rules of inference, sure.
>>
>> Godel showed no single axiomatic system captures all mathematical
>> truth, any
>> fixed set of axioms can at best approximate mathematical truth. If
>> mathematical truth cannot be fully captured by a set of axioms, it
>> must
>> exist outside sets of axioms altogether.
>
> Then perhaps the correct conclusion to draw is that there is no such
> thing as "mathematical truth"?
>
> Perhaps there is just human belief.
>

Perhaps so, perhaps there is only Rex's beliefs. Perhaps only rex's
beliefs at this exact moment. But what explanatory power does that
offer? What model for decision making can there be with such a world
view?

>
>> The fractal is just an example of a simple formula leading to very
>> complex
>> output. The same is true for the UDA:
>> for i = 0 to inf:
>> for each j in set of programs:
>> execute single instruction of program j
>> add i to set of programs
>> That simple formula executes all programs.
>
> Following those instructions will let someone "execute" all
> "programs".

What is the engine providing the computations which drive the universe?

>
>
> Or, alternatively, configuring a physical system in a way that
> represents those instructions will allow someone to interpret the
> system's subsequent states as being analogous to the "execution" of
> all "programs".
>

Do you think pi has an objective (not human invented or approximated)
value, whether or not any person computed it?

Is there an answer to the question what is the googleplexth decimal
digit of pi given no one in this universe could ever computed it?

If there is, then there are also objective values to the omega
constant, or the state of the uda after X steps. These values exist
without the need for someone to execute them, anymore than we need to
compute the billionth digit of pi for it to have it's value.

>
>>> Is extraordinary complexity required for the manifestation of
>>> "mind"?
>>> If so, why?
>>>
>>
>> I don't know what lower bound of information or complexity is
>> required for
>> minds.
>
> Then why do you believe that information of complexity is required
> for minds?
>

I think information is a critical component of consciousness. The
very definition of consciousness: "having awareness of ones own
thoughts and sensations.". Awareness is defined as having knowledge
or information. Therefore consciousness is the possession of
information (about ones thoughts ir sensations).

There are also reasons to believe in the informational basis if
consciousness due to multiple realizeability. Minds can take
different physical forms because information cab take many physical
forms.

Lastly there is an argument realted to zombies. A zombie cannot feel
any different or be less conscious than a conscious person who is
physically identical. This is because the informational content of
both the person and the zombie is necessarily the same (given the
identical physical states). Therefore the conscious person does not
and cannot know anything more about what they are feeling or
experiencing than the zombie does. Both must be equally conscious.

>
>>> Is it that these recursive relations cause our experience, or are
>>> just
>>> a way of thinking about our experience?
>>>
>>> Is it:
>>>
>>> Recursive relations cause thought.
>>>
>>> OR:
>>>
>>> Recursion is just a label that we apply to some of our implicational
>>> beliefs.
>>>
>>> The latter seems more plausible to me.
>>>
>>
>> Through recursion one can implement any form of computation.
>
> But, ultimately, what is computation?
>

A process. More specifically one that connects a succession of states
via some well-defined relation(s).

>
>> Recursion is
>> common and easy to show in different mathematical formulas, while
>> showing a
>> Turing machine is more difficult. Many programs which can be
>> easily defined
>> through recursion can also be implemented without recursion, so I
>> was not
>> implying recursion is necessary for minds.
>
> Then what do you believe is necessary for minds?
>
>

An informational process.

Jason

[Bruno Marchal]

On 04 Jun 2011, at 20:03, Rex Allen wrote:

> On Sat, Jun 4, 2011 at 1:51 PM, Jason Resch <jason...@gmail.com>
> wrote:
>>
>>
>> On Sat, Jun 4, 2011 at 12:06 PM, Rex Allen
>> <rexall...@gmail.com> wrote:
>>>
>>> On Sat, Jun 4, 2011 at 12:21 PM, Jason Resch
>>> <jason...@gmail.com> wrote:
>>>> One thing I thought of recently which is a good way of showing how
>>>> computation occurs due to the objective truth or falsehood of
>>>> mathematical
>>>> propositions is as follows:
>>>>
>>>> Most would agree that a statement such as "8 is composite" has an
>>>> eternal
>>>> objective truth.
>>>
>>> Assuming certain of axioms and rules of inference, sure.
>>
>> Godel showed no single axiomatic system captures all mathematical
>> truth, any
>> fixed set of axioms can at best approximate mathematical truth. If
>> mathematical truth cannot be fully captured by a set of axioms, it
>> must
>> exist outside sets of axioms altogether.
>
> Then perhaps the correct conclusion to draw is that there is no such
> thing as "mathematical truth"?

No theories nor machine can reach all arithmetical truth, but few
people doubt that closed arithmetical propositions are either true or
false. We do share a common intuition on the nature of arithmetical
truth.
I have doubt on any notion of global mathematical truth. Sets, real
numbers, complex numbers, etc. are simplifications of the natural
numbers. They are convenient fictions, I think. If we are machine, it
is undecidable if ontology is more than N.

>
> Perhaps there is just human belief.

Jason said it. If you follow that slope you may as well say that there
is only belief by Rex. You can also decide that there is nothing to
explain, no theories to find, and go walking in the woods. Science, by
definition, assumes something beyond (human) belief.

>
>
>> The fractal is just an example of a simple formula leading to very
>> complex
>> output. The same is true for the UDA:
>> for i = 0 to inf:
>> for each j in set of programs:
>> execute single instruction of program j
>> add i to set of programs
>> That simple formula executes all programs.
>
> Following those instructions will let someone "execute" all
> "programs".
>
> Or, alternatively, configuring a physical system in a way that
> represents those instructions will allow someone to interpret the
> system's subsequent states as being analogous to the "execution" of
> all "programs".

Do you need someone observing your brain for you to feel something?
Why would the physical UD execution differ?
Indeed, why would the arithmetical UD execution differ?

>
>
>>> Is extraordinary complexity required for the manifestation of
>>> "mind"?
>>> If so, why?
>>>
>>
>> I don't know what lower bound of information or complexity is
>> required for
>> minds.
>
> Then why do you believe that information of complexity is required
> for minds?

If you accept that the brain is Turing emulable, then it is easy to
explain that matter/consciousness is arithmetical information as seen
from inside. That is certainly easier than explaining consciousness by
physical attributes.

>
>
>>> Is it that these recursive relations cause our experience, or are
>>> just
>>> a way of thinking about our experience?
>>>
>>> Is it:
>>>
>>> Recursive relations cause thought.
>>>
>>> OR:
>>>
>>> Recursion is just a label that we apply to some of our implicational
>>> beliefs.
>>>
>>> The latter seems more plausible to me.
>>>
>>
>> Through recursion one can implement any form of computation.
>
> But, ultimately, what is computation?

Any mathematical transformation which is Turing emulable.
Assuming Church thesis this is a very general definition.

>
>
>> Recursion is
>> common and easy to show in different mathematical formulas, while
>> showing a
>> Turing machine is more difficult. Many programs which can be
>> easily defined
>> through recursion can also be implemented without recursion, so I
>> was not
>> implying recursion is necessary for minds.
>
> Then what do you believe is necessary for minds?

A universal system, or universal numbers. Now they can be proved to
exist from logic + non negative integers, so we don't need a lot.

Jason answered "An informational process". That's OK, especially in
his context (that computation exist in math), but the word "process"
is frequently interpreted by "primitively spatio-temporal process",
when we need only (sigma_1) arithmetical relations.

Bruno

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

[Rex Allen]

On Sat, Jun 4, 2011 at 4:09 PM, Bruno Marchal <mar...@ulb.ac.be> wrote:

> On 04 Jun 2011, at 19:06, Rex Allen wrote:
>> On Sat, Jun 4, 2011 at 12:21 PM, Jason Resch <jason...@gmail.com> wrote:
>>>
>>> One thing I thought of recently which is a good way of showing how
>>> computation occurs due to the objective truth or falsehood of
>>> mathematical
>>> propositions is as follows:
>>>
>>> Most would agree that a statement such as "8 is composite" has an eternal
>>> objective truth.
>>
>> Assuming certain of axioms and rules of inference, sure.
>

> But everyone agree on the axioms of arithmetic.

I’m not sure what you mean here. “Agree” in what sense?

Everyone agrees that the axioms of arithmetic are...what? Interesting? Useful?

Who is “everyone”?

Does everyone also agree that there are other axiomatic systems?

> And we could take any
> universal (in the Turing sense) system instead. The physical laws cannot
> depend on the choice of the "universal base".

What exactly are “physical laws”?

You’re really saying “the regularities in our experience cannot depend
on the choice of the universal base”?

>>> Other recursive formulae may result in the evolution of structures
>>> such as our universe or the computation of your mind.
>>

>> Is extraordinary complexity required for the manifestation of "mind"?
>> If so, why?
>>

>> Is it that these recursive relations cause our experience, or are just
>> a way of thinking about our experience?
>>
>> Is it:
>>
>> Recursive relations cause thought.
>>
>> OR:
>>
>> Recursion is just a label that we apply to some of our implicational
>> beliefs.
>

> I think you are confusing computability, which is absolute (assuming Church
> thesis), and provability, which is always relative to theories, machines,
> entities, etc.

What are your justifications for assuming the Church thesis?

Do oracles exist in Platonia? In HyperPlatonia perhaps? If not, what
precludes their existence?

> Jason is right, computation occurs in "arithmetical platonia", even in a
> tiny part of it actually, independently of us.

Ya, I have my doubts about that.

> This tiny part is assumed in the rest of science, and comp makes
> it necessarily enough (by taking seriously the first and third person
> distinction).

What is science in a deterministic universe? What is science in a
probabilistic universe? What other kinds of universes could there be?

Rex

[Rex Allen]

On Sat, Jun 4, 2011 at 4:14 PM, Jason Resch <jason...@gmail.com> wrote:
> On Jun 4, 2011, at 1:03 PM, Rex Allen <rexall...@gmail.com> wrote:
>> On Sat, Jun 4, 2011 at 1:51 PM, Jason Resch <jason...@gmail.com> wrote:
>>>
>>> Godel showed no single axiomatic system captures all mathematical truth,
>>> any
>>> fixed set of axioms can at best approximate mathematical truth. If
>>> mathematical truth cannot be fully captured by a set of axioms, it must
>>> exist outside sets of axioms altogether.
>>
>> Then perhaps the correct conclusion to draw is that there is no such
>> thing as "mathematical truth"?
>>
>> Perhaps there is just human belief.
>>
>
> Perhaps so, perhaps there is only Rex's beliefs. Perhaps only rex's beliefs
> at this exact moment.

Not obviously impossible. Thought not obviously necessitated either.

Does the possibility that there are only Jason’s beliefs at this exact
moment scare you?

Would you prefer it to be otherwise?

> What model for decision making can there be with such a
> world view?

But we don’t need metaphysics for decision making.

We must act. And there’s nothing guide those actions except that
which can be “distilled” from past experience.

But what to make of the distillate? Is it just a compact description
of past observations? Or is it a “true” description of reality?

Classical mechanics turned out to be a compact description of past
observations. No one looks to Newton’s equations for metaphysical
guidance, do they?

But computationalism is, you think, a true description of reality?

> But what explanatory power does that offer?

It seems plausible to me that physics (or computationalists) may be
able to generate a complete, compact framework that describes the
world that I observe.

And since I observe behavior of the people around me, and the
framework is a compact description of my observations, then I should
be able to “explain” people’s behavior in terms of the framework.

And if I can explain my neighbor’s behavior in terms of the framework,
maybe I can explain my own behavior in those terms as well.

However...

Explanation is something that occurs *within* a descriptive framework.
Those explanations don’t reach beyond the framework.

Going “metaphysical” (instead of instrumental) with an explanatory
framework could only be justified if we had some reason to believe
that our observations plus our reason gave us reliable access to what
is real.

But notice that “reason” shows up twice in that sentence...which is a problem.

>>> The fractal is just an example of a simple formula leading to very
>>> complex
>>> output. The same is true for the UDA:
>>> for i = 0 to inf:
>>> for each j in set of programs:
>>> execute single instruction of program j
>>> add i to set of programs
>>> That simple formula executes all programs.
>>
>> Following those instructions will let someone "execute" all "programs".
>
> What is the engine providing the computations which drive the universe?

That assumes that computations do drive the universe.

Which is the assumption that I’m questioning.

>> Or, alternatively, configuring a physical system in a way that
>> represents those instructions will allow someone to interpret the
>> system's subsequent states as being analogous to the "execution" of
>> all "programs".
>>
>
> Do you think pi has an objective (not human invented or approximated) value,
> whether or not any person computed it?

I think that everyone who starts from the same assumptions and makes
the same inferences will always reach the same conclusions regarding
the value of pi.

> Is there an answer to the question what is the googleplexth decimal digit of
> pi given no one in this universe could ever computed it?

Is there an answer to the question of whether this penny would have
melted had I taken an oxyacetylene torch to it yesterday - given that
this didn’t actually happen?

If there is an answer to the inner question, and that answer is “yes”
(or “no” for that matter), what makes it “yes” (or “no”)?

So I can answer the question today relative to some explanatory
framework. But given that the framework is just the distillation of
past experience, and is only intended as a guide to action...the
answer I give today about what would have happened yesterday isn’t
meaningful except in relation to the framework. It’s “for
entertainment purposes only”.

In the “real world” (whatever that is), I’d guess that there is no
fact of the matter about what would have happened yesterday with the
penny and the torch.

SO...applying the same reasoning to your question:

I’ll say that relative to some framework that includes my experience
with the assumptions and inferences and rules needed to calculate pi -
the answer is yes. Because in that framework, given enough time and
enough “universe”, it seems likely that someone *could* calculate the
googleplexth digit of pi.

But that answer is for entertainment purposes only...since it is an
answer based on a framework distilled from past experience for the
purposes of guiding action which is instead being applied to a purely
hypothetical situation that has no chance of being enacted.

The answer is only relevant relative to the framework that generated
it and there’s no grounds for ascribing metaphysical significance to
the framework, and so there’s no grounds for ascribing metaphysical
significance to the answer.

There is no fact of the matter except relative to the framework.

It’s like asking “who would win an arm wrestling match between the
Incredible Hulk and Spiderman”. I can confidently say the Incredible
Hulk. But that answer doesn’t really mean anything outside of the
“Marvel Universe”. The Marvel Universe has no metaphysical
significance, and so my answer to this hypothetical question involving
it has no metaphysical significance either.

See?

> If there is, then there are also objective values to the omega constant, or
> the state of the uda after X steps. These values exist without the need for
> someone to execute them, anymore than we need to compute the billionth digit
> of pi for it to have it's value.

Relative to some detailed fictional framework, sure. Such an
imagination you have!

>>>> Is extraordinary complexity required for the manifestation of "mind"?
>>>> If so, why?
>>>
>>> I don't know what lower bound of information or complexity is required
>>> for minds.
>>
>> Then why do you believe that information of complexity is required for
>> minds?
>>
>
> I think information is a critical component of consciousness. The very
> definition of consciousness: "having awareness of ones own thoughts and
> sensations.". Awareness is defined as having knowledge or information.
> Therefore consciousness is the possession of information (about ones
> thoughts ir sensations).

We can say that we have information about what we are aware of...but
that is not the same as saying that awareness *is* information.

Information is a difference that makes a difference. But it has to
make a difference *to* someone.

A randomly generated string of bits can be identical to a string of
bits representing an image...but the randomly generated string of bits
contain no real information whereas the image file does.

The difference being that I know how to correctly interpret an image
file, but there is no “correct” interpretation of a random string of
bits.

But with the right “interpretation” any information can be found
anywhere. The magic is all in the interpreter, not in what’s being
interpreted.

Information is observer-relative. Observers aren’t information-relative.

> There are also reasons to believe in the informational basis if
> consciousness due to multiple realizeability. Minds can take different
> physical forms because information cab take many physical forms.

I can take anything to represent anything else. So “representation”
is multiply realizable.

But again, that has to do with me, not with information. If I
remember what my encoding scheme was, I can “re-present” things to
myself. If I forget what my encoding scheme was, or that I even
encoded anything - then all I have are a bunch of bits...which for all
I know might be random.

If they really were random bits, but for some reason I was convinced
they weren’t - I might find all sorts of “meaningful” interpretations
of them using all sorts of decoding schemes - but none of these would
be correct.

In this case, I’m doing all of the work...the bits aren’t doing
anything. Which, as it turns out, is also true of non-random bit
strings. I do all of the work. The bits are just reminders...hints.

I think you’re getting it all backwards. Representation depends on
me. I don’t depend on representation.

You’re saying: “Hey, look at all the great things I can do with
representation! What if I represented myself in some way??? Would
that be me?”

Well...no. That would be a representation of you. Representation is
something you do, not something that you are.

> Lastly there is an argument realted to zombies. A zombie cannot feel any
> different or be less conscious than a conscious person who is physically
> identical. This is because the informational content of both the person and
> the zombie is necessarily the same (given the identical physical states).
> Therefore the conscious person does not and cannot know anything more about
> what they are feeling or experiencing than the zombie does. Both must be
> equally conscious.

That’s one way of looking at it. That might be true relative to some
explanatory framework. But it’s true for entertainment purposes only.
Like the Hulk-Spiderman matchup above.

>>>> Is it that these recursive relations cause our experience, or are just
>>>> a way of thinking about our experience?
>>>>
>>>> Is it:
>>>>
>>>> Recursive relations cause thought.
>>>>
>>>> OR:
>>>>
>>>> Recursion is just a label that we apply to some of our implicational
>>>> beliefs.
>>>>
>>>> The latter seems more plausible to me.
>>>>
>>>
>>> Through recursion one can implement any form of computation.
>>
>> But, ultimately, what is computation?
>>
>
> A process. More specifically one that connects a succession of states via
> some well-defined relation(s).

So why would a process that connects a succession of states via
well-defined relations - in addition to being that - *also* be my
conscious experience of sitting in this chair drinking coffee, writing
this email?

Why would that be? Why would this process be *two* things instead of
just one? Not interpretable as two things (by me) - but really,
intrinsically two entirely different things?

Rex

[Quentin Anciaux]

I don't understand what is the purpose of such a comment... one that I've seen too many times. The only logical conclusion is "Nothing is explainable !".... well ok then I will gonna eat my banana !

If your premises is "Nothing is explainable" then it is logical that you conclude that "Nothing is explainable", going in parabolic wording about it won't make it better.

2011/6/5 Rex Allen <rexall...@gmail.com>

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[Quentin Anciaux]

> Information is a difference that makes a difference.  But it has to
> make a difference *to* someone.

It would be meaningful to rewrite it by putting emphasis on *someone* instead of *to*.

2011/6/5 Rex Allen <rexall...@gmail.com>

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[Jason Resch]

On Sun, Jun 5, 2011 at 11:58 AM, Rex Allen <rexall...@gmail.com> wrote:

On Sat, Jun 4, 2011 at 4:14 PM, Jason Resch <jason...@gmail.com> wrote:
> On Jun 4, 2011, at 1:03 PM, Rex Allen <rexall...@gmail.com> wrote:
>> On Sat, Jun 4, 2011 at 1:51 PM, Jason Resch <jason...@gmail.com> wrote:
>>>

>>> Godel showed no single axiomatic system captures all mathematical truth,
>>> any
>>> fixed set of axioms can at best approximate mathematical truth.  If
>>> mathematical truth cannot be fully captured by a set of axioms, it must
>>> exist outside sets of axioms altogether.
>>
>> Then perhaps the correct conclusion to draw is that there is no such
>> thing as "mathematical truth"?
>>
>> Perhaps there is just human belief.
>>
>
> Perhaps so, perhaps there is only Rex's beliefs.  Perhaps only rex's beliefs
> at this exact moment.

Not obviously impossible.  Thought not obviously necessitated either.

Does the possibility that there are only Jason’s beliefs at this exact
moment scare you?

Would you prefer it to be otherwise?

It makes the universe much smaller, less varied, less fascinating, etc. to believe my current thought is all there is.  It also makes answering any questions futile (why does this thought exist?, can I change it?  Am I a static thought or an evolving thought?  What determines or controls the content of this thought?)  How can any of those questions be approached if only thought exists?

 

> What model for decision making can there be with such a
> world view?

But we don’t need metaphysics for decision making.

We must act.  And there’s nothing guide those actions except that
which can be “distilled” from past experience.

But what to make of the distillate?  Is it just a compact description
of past observations?  Or is it a “true” description of reality?

Classical mechanics turned out to be a compact description of past
observations.  No one looks to Newton’s equations for metaphysical
guidance, do they?

But computationalism is, you think, a true description of reality?

Physics explains physical interactions within this universe but it alone can only take our understanding so far.  Physics won't explain why there is the apparent randomness seen in quantum mechanics, it won't explain why there is a physical universe, nor why it has the laws that it does.  Expanding our definition of reality from "things we can see" to "things we can interact with" leads to arithmetical realism.  And arithmetical realism can help explain all the previous questions I listed, while physics alone can not.  I agree with Leibniz when he said "Everything that is possible demands to exist."  Follow the trend science has made over the past few thousand years, the concept of what is real has been exploding:

1. This world and the sky above it are all that exist

2. This world is one of many worlds, orbiting the Sun (Copernicus in 1543)

3. Our sun is one of many stars in this galaxy (First demonstrated in 1838 by Friedrich Bessel)

4. This galaxy is one of many galaxies (Hubble in 1920)

5. This universe is just one possible history all possible histories (Everett in 1957)

6. The observable universe is only a very small piece of the whole of the universe (Alan Guth in 1980)

7. The standard model is just one possible solution of the 10^500 or so possible solutions to string theory (Weinberg in 1987, and Susskind)

8. Physical systems are not limited to the equations of string theory, all structures in math exist (Tegmark in 1998)

 

Starting from 5 and onward, there is some ongoing debate, but the trend is clear, reality is far grander than we initially conceived.  Mathematical Realism is only a small step from 7.  One can look at Everett simply as all solutions to the Schroedinger equation are real.  And the landscape of string theory: All solutions to the mathematics of string theory are real.  But why should we stop there?  What makes the equations of string theory any more privledged with the blessing of reality compared to others?  We have gathered no evidence suggesting that solutions to other types of equations cannot exist, so why believe it?  The only argument I see is Ockham's razor, why believe in additional entitites if it makes the theory more complex?  But this is incorrect, the theory that "all solutions to all equations exists" is far simpler than the theory that "only certain very complex equations of string theory exist, and the others are impossible because ...".

The physical universe may be computational or it may be a mathematical structure, but what enforces its consistency and constancy of its laws?  If it were a mathematical structure, or a computation then the consistency comes for free.

 

>> Or, alternatively, configuring a physical system in a way that
>> represents those instructions will allow someone to interpret the
>> system's subsequent states as being analogous to the "execution" of
>> all "programs".
>>
>
> Do you think pi has an objective (not human invented or approximated) value,
> whether or not any person computed it?

I think that everyone who starts from the same assumptions and makes
the same inferences will always reach the same conclusions regarding
the value of pi.

So that would make pi an objectively studiable object, would it not?  What makes the study of such objects less valid than the study of other objects in science, for example in biology?  To define a bacterium as a life form Earth scientists and alien scientists both have to start from similar assumptions and make similar inferences.  Based on different starting assumptions some might say a virus is alive others may not, this doesn't mean that viruses don't exist.  In your postings you seem to suggest that given there could be disagreement on what starting assumptions to use the reality of mathematical objects should be called into question, but this would be like questioning whether viruses exist because biologists can't agree on whether or not they are alive.  The numbers, their properties and relations are objectively studiable, as much as planets and viruses are.  If math is invented, then you should invent a prime number with a billion digits and claim the $250,000 prize ( http://www.eff.org/awards/coop ).  If you cannot invent such a number, then perhaps mathematics truly is a space to be explored, much like the vacuum that surrounds our planet.

 

> Is there an answer to the question what is the googleplexth decimal digit of
> pi given no one in this universe could ever computed it?

Is there an answer to the question of whether this penny would have
melted had I taken an oxyacetylene torch to it yesterday - given that
this didn’t actually happen?

If there is an answer to the inner question, and that answer is “yes”
(or “no” for that matter), what makes it “yes” (or “no”)?

So I can answer the question today relative to some explanatory
framework.  But given that the framework is just the distillation of
past experience, and is only intended as a guide to action...the
answer I give today about what would have happened yesterday isn’t
meaningful except in relation to the framework.  It’s “for
entertainment purposes only”.

In the “real world” (whatever that is), I’d guess that there is no
fact of the matter about what would have happened yesterday with the
penny and the torch.

SO...applying the same reasoning to your question:

I’ll say that relative to some framework that includes my experience
with the assumptions and inferences and rules needed to calculate pi -
the answer is yes.  Because in that framework, given enough time and
enough “universe”, it seems likely that someone *could* calculate the
googleplexth digit of pi.

So the value is there, waiting to be found (even though no one has bothered to go through the motions to compute it)?  Does it have a value if it is computed but no person reads the result?  What if it is computed and then all traces of the result are destroyed, does the value determined disappear?

 

But that answer is for entertainment purposes only...since it is an
answer based on a framework distilled from past experience for the
purposes of guiding action which is instead being applied to a purely
hypothetical situation that has no chance of being enacted.

The answer is only relevant relative to the framework that generated
it and there’s no grounds for ascribing metaphysical significance to
the framework, and so there’s no grounds for ascribing metaphysical
significance to the answer.

There is no fact of the matter except relative to the framework.

It’s like asking “who would win an arm wrestling match between the
Incredible Hulk and Spiderman”.  I can confidently say the Incredible
Hulk.  But that answer doesn’t really mean anything outside of the
“Marvel Universe”.  The Marvel Universe has no metaphysical
significance, and so my answer to this hypothetical question involving
it has no metaphysical significance either.

See?

Unlike the marvel universe, if mathematical objects exist it is of huge metaphysical significance, as it makes so called physical universes redundant and completely unnecessary for explaining observations.

 

> If there is, then there are also objective values to the omega constant, or
> the state of the uda after X steps.  These values exist without the need for
> someone to execute them, anymore than we need to compute the billionth digit
> of pi for it to  have it's value.

Relative to some detailed fictional framework, sure.  Such an
imagination you have!

You and I happen to inhabit the "detailed fictional framework" we call the physical universe, which only seems real relative to us because we inhabit it.

Information and computations are built upon relations between objects.  They could be pulses of charged solutions between nerve cells, electrical fields travelling through wires in a chip, gears turning in Babbage's analytical engine, etc.  What X and Y are in the computer is not the important factor, it is the relation between X and Y.  Regardless of whether the objects X and Y are atoms in a physical universe or objects in mathematics, their power to represent information (and correspondingly consciousness) is not any different.  No program can make any determination as to the ultimate hardware it is being executed on, by Turing universality.  Therefore if consciousness is regarded as a computation, you cannot with full confidence conclude you are Rex whose mind runs on the physics of this universe confidently and not Rex whose mind is executed in a mathematical object.

 

>>>> Is extraordinary complexity required for the manifestation of "mind"?
>>>> If so, why?
>>>
>>> I don't know what lower bound of information or complexity is required
>>> for minds.
>>
>> Then why do you believe that information of complexity is required for
>> minds?
>>
>
> I think information is a critical component of consciousness.  The very
> definition of consciousness: "having awareness of ones own thoughts and
> sensations.".  Awareness is defined as having knowledge or information.
>  Therefore consciousness is the possession of information (about ones
> thoughts ir sensations).

We can say that we have information about what we are aware of...but
that is not the same as saying that awareness *is* information.

I think there is an important difference between saying "consciousness = awareness of information" vs. "consciousness = awareness = information".

 

Information is a difference that makes a difference.  But it has to
make a difference *to* someone.

This is why the consciousness requires a process accepting or operating on information.  If a process is not defined there can be no interpretation.

 

A randomly generated string of bits can be identical to a string of
bits representing an image...but the randomly generated string of bits
contain no real information whereas the image file does.

The difference being that I know how to correctly interpret an image
file, but there is no “correct” interpretation of a random string of
bits.

But with the right “interpretation” any information can be found
anywhere.  The magic is all in the interpreter, not in what’s being
interpreted.

Information is observer-relative.  Observers aren’t information-relative.

Are you a computationalist?  This line of thought sounds like you are..

 

> There are also reasons to believe in the informational basis if
> consciousness due to multiple realizeability.  Minds can take different
> physical forms because information cab take many physical forms.

I can take anything to represent anything else.  So “representation”
is multiply realizable.

But again, that has to do with me, not with information.  If I
remember what my encoding scheme was, I can “re-present” things to
myself.  If I forget what my encoding scheme was, or that I even
encoded anything - then all I have are a bunch of bits...which for all
I know might be random.

If they really were random bits, but for some reason I was convinced
they weren’t - I might find all sorts of “meaningful” interpretations
of them using all sorts of decoding schemes - but none of these would
be correct.

In this case, I’m doing all of the work...the bits aren’t doing
anything.  Which, as it turns out, is also true of non-random bit
strings.  I do all of the work.  The bits are just reminders...hints.

I think you’re getting it all backwards.  Representation depends on
me.  I don’t depend on representation.

What I mean by multiple realizability is parts of your brain can be replaced with any part which is functionally equivalent without impacting your consciousness.  While true, different programs can interpret different encodings differently, those programs can be realized with different representations.

 

You’re saying:  “Hey, look at all the great things I can do with
representation!  What if I represented myself in some way???  Would
that be me?”

Well...no.  That would be a representation of you.  

How are you defining the person in this case?  Different functionally equivalent representations of you would be as conscious as you are now, would they not?

 

Representation is
something you do, not something that you are.

If by representation you mean the representation of consciousness, then this is the functionalist/computationalist philosophy in a nutshell.

Because as you said, you need something to impart meaning to the bits, and that requires well defined relations which indicate meaning of the bits to the overall process.  While you can look at any bit string and say it means this, you cannot look at a program which is calculating Pi and say it is calculating e.

 

Why would that be?  Why would this process be *two* things instead of
just one?  Not interpretable as two things (by me) - but really,
intrinsically two entirely different things?

I am not sure what you are asking here.  There are third and first person perspectives of course, does that mean there are two things?

 Jason

[Stephen Paul King]

Hi Bruno, Rex and Friends,

 

    My .002$...

 

-----Original Message-----

From: Bruno Marchal

Sent: Sunday, June 05, 2011 9:22 AM

To: everyth...@googlegroups.com

Subject: Re: Mathematical closure of consciousness and computation

 

 

On 04 Jun 2011, at 20:03, Rex Allen wrote:

 

> On Sat, Jun 4, 2011 at 1:51 PM, Jason Resch <jason...@gmail.com> 

> wrote:

>>

>>

>> On Sat, Jun 4, 2011 at 12:06 PM, Rex Allen 

>> <rexall...@gmail.com> wrote:

>>>

>>> On Sat, Jun 4, 2011 at 12:21 PM, Jason Resch 

>>> <jason...@gmail.com> wrote:

>>>> One thing I thought of recently which is a good way of showing how

>>>> computation occurs due to the objective truth or falsehood of

>>>> mathematical

>>>> propositions is as follows:

>>>>

>>>> Most would agree that a statement such as "8 is composite" has an

>>>> eternal

>>>> objective truth.

>>>

>>> Assuming certain of axioms and rules of inference, sure.

>>

>> Godel showed no single axiomatic system captures all mathematical 

>> truth, any

>> fixed set of axioms can at best approximate mathematical truth.  If

>> mathematical truth cannot be fully captured by a set of axioms, it 

>> must

>> exist outside sets of axioms altogether.

>

> Then perhaps the correct conclusion to draw is that there is no such

> thing as "mathematical truth"?

[BM]

No theories nor machine can reach all arithmetical truth, but few 

people doubt that closed arithmetical propositions are either true or 

false. We do share a common intuition on the nature of arithmetical 

truth.

I have doubt on any notion of global mathematical truth. Sets, real 

numbers, complex numbers, etc. are simplifications of the natural 

numbers. They are convenient fictions, I think. If we are machine, it 

is undecidable if ontology is more than N.

 

 

[SPK]

   

    I think that there is some differences in opinion about this but it seems to me that we need to look at some details. For example, there should exist a theory that could reach all arithmetic truth given an eternity of time or an unnamable number of recursions or steps. This by definition would put them forever beyond human (finite entity) comprehension. Whether or not there is closure or a closed form of some theory does not make it realistic or not. AFAIK, closed arithmetic propositions are tautologies, no? That we share a common intuition of truth may follow from a common local measure of truth within each of us. (Here the "inside" implied by the word "within" is the logical/Arithmetic/abstract aspect of the duality that I propose.)

    Additionally, we should be careful not to conflate a plurality of fungible individuals with a multiplicity of non-fungible entities. We can set up a mental hall of mirrors and generate an infinite number of self-images in it, but this cannot *exactly* map to all of the selves that could exist without additional methods to break the symmetries.

 

    I have been waiting a long time for you to state this belief of yours, Bruno! That "Sets, real  numbers, complex numbers, etc." are simplifications of (mappings on/in?) the Natural Numbers. This seems to be the Pythagorean doctrine that I suspected that you believed. It has a long history and a lot of apostles that have quite spectacular histories. I think that there is a deep truth in this belief, but I think that it needs to be more closely examined.

 

>

> Perhaps there is just human belief.

 

[BM]

Jason said it. If you follow that slope you may as well say that there 

is only belief by Rex. You can also decide that there is nothing to 

explain, no theories to find, and go walking in the woods. Science, by 

definition, assumes something beyond (human) belief.

 

[SPK]

   

    I admit that I laughed out loud at this! Good point, Bruno! The reduction of all truth to that which can be defined within a single human's belief trivializes and renders it meaningless. That is one of the absurd consequences that we lambast solipsism for, but I think that Rex should not be to swiftly dismissed form maybe trying to make a deeper observation; he has brought up a very good topic for discussion.

    While it is absurd to reduce all truth to what a single finite entity can "compute" - which is that we are actually saying if we follow the Kleene-Turing-Church-Post road - we are actually positing that "all truths can be defined in terms of N -> N mappings".  Many such mappings to be sure, but N to N mappings nonetheless. We are back to that strange belief that Bruno explicitly, albeit inadvertently, stated.

    But this is not really a "strange" belief, partly because it seems to be almost universally the default postulate within the basket of beliefs that people operate with in our every day world. I would like to pose the question of whether or not we are inadvertently painting ourselves into a corner with this belief. IT seems to me, and this is just a personal prejudice of mine, that there exists truths that cannot be named or represented exactly in terms of N->N maps. The source of this suspicion comes from what I have studied of G. Cantor's work on transfinites and the histrionics of practitioners of mathematical logic that have been examining the nature of cardinalities. Additionally there is my belief that the Totality of Existence must be, at least, Complete (not in the Gödel sense of just 1st order logics), Bicomplete (in the Category theory sense) and Closed (in the topological sense). This implies the existence of unnamable truths, or at least Truths that cannot be exactly represented in terms of recursive functions on the Integers.

    The question becomes one of the implications of this on our metaphysical assumptions about the ontologies that we are using in our thinking about the issue of mathematical closure of computation and consciousness. As I see it, and this very well could be just an eccentric thought, is that we need to be very careful that we do not tacitly assume that all of the minds of entities are replicating the same ideas as one’s own. The fact that we are continuously surprised at the responces that we get when we post to this List, for example, should be some indication that we all think differently about things and that when we propose the idea that consciousness is somehow some kind of N->N map or even some string of numbers in ℤ, then we should expect a vigorous response. BTW, did you know that ℤ *≅U(1) and  U(1) *≅ℤ  via the Pontryagin duality? Yes, that U(1) that is used in physics ! This is one of many reasons why I think that Bruno is onto something very important in his work! :-)

 

 

>

>

>> The fractal is just an example of a simple formula leading to very 

>> complex

>> output.  The same is true for the UDA:

>> for i = 0 to inf:

>>   for each j in set of programs:

>>     execute single instruction of program j

>>   add i to set of programs

>> That simple formula executes all programs.

>

> Following those instructions will let someone "execute" all 

> "programs".

>

> Or, alternatively, configuring a physical system in a way that

> represents those instructions will allow someone to interpret the

> system's subsequent states as being analogous to the "execution" of

> all "programs".

[BM]

Do you need someone observing your brain for you to feel something?

Why would the physical UD execution differ?

Indeed, why would the arithmetical UD execution differ?

 

[SPK]

 

    Strangely enough, Bruno, in a way there is something to this idea that we need to consider that someone is watching for us to feel something! If we follow the logic of QM and accept the decoherence idea, the idea that we have a definite (and Boolean representable) state of the brain depends most definitely on the existence of what we can think of as “someone” watching: the rest of the universe. We can break this down into a large number of mutually communicating observers, but that “someone is watching” has real consequences: it induces the 2 valued definiteness that otherwise would not exist.

    I think that you are are reacting a bit to strongly from your Arithmetic Realism doctrine. I would like for all of us to sit back and thought for a while exactly on what we are asking with this question of Mathematical closure.

 

Onward!

 

Stephen

[Jason Resch]

On Sat, Jun 4, 2011 at 3:12 PM, Stephen Paul King <step...@charter.net> wrote:

Hi Jason,

 

    Very interesting reasoning!

Thank you.

 

 

From: Jason Resch

Sent: Saturday, June 04, 2011 1:51 PM

To: everyth...@googlegroups.com

Subject: Re: Mathematical closure of consciousness and computation

On Sat, Jun 4, 2011 at 12:06 PM, Rex Allen <rexall...@gmail.com> wrote:

On Sat, Jun 4, 2011 at 12:21 PM, Jason Resch <jason...@gmail.com> wrote:
> One thing I thought of recently which is a good way of showing how
> computation occurs due to the objective truth or falsehood of mathematical
> propositions is as follows:
>
> Most would agree that a statement such as "8 is composite" has an eternal
> objective truth.

Assuming certain of axioms and rules of inference, sure.

 

Godel showed no single axiomatic system captures all mathematical truth, any fixed set of axioms can at best approximate mathematical truth.  If mathematical truth cannot be fully captured by a set of axioms, it must exist outside sets of axioms altogether.

 

[SPK]

 

    I see two possibilities. 1) Mathematical truth might only exist in our minds. But an infinity of such minds is possible...2) Might it be possible that our mathematical ideas are still too primitive and simplistic to define the kind of set that is necessary?

**

1) More is answered by:

A: "Math -> Matter -> Minds" (or as Bruno suggests "Math -> Minds -> Matter") than by 

B: "Matter -> Minds -> Math", or 

C: "Minds -> (Matter, Math)".

Compared to "B", "A" explains the unreasonable effectiveness of math in the natural sciences, the apparent fine tuning of the universe (with the Anthropic Principle), and with computationalism explains QM.

"C" has the least explanatory power, and we must wonder why the experience contained within our minds seems to follow a compressible set of physical laws, and why mathematical objects seem to posses objective properties but by definition lack reality.

Those who say other universes do not exist are only adding baseless entities to their theory, to define away that which is not observed.  It was what led to theories such as the Copenhagen Interpretation, which postulated collapse as a random selection of one possible outcome to be made real and cause the rest to disappear.  Similarly, there are string theorists which hope to find some mathematical reason why other possible solutions to string theory are inconsistent, and the one corresponding to the the standard model is the only one that exists.  Why?  They think this is necessary to make their theory agree with observation, but when the very thing is unobservable according to the theory it is completely unnecessary.

The situation is reminiscent of DeWitt and Everett:

In his letter, DeWitt had claimed that he could not feel himself split, so, as mathematically attractive as Everett's theory was, he said, it could not be true. Everett replied in his letter to DeWitt that, hundreds of years ago, after Copernicus had made his radical assertion that the Earth revolved around the sun instead of the reverse, his critics had complained that they could not feel the Earth move, so how could it be true? Recalling Everett's response to him decades later, in which he pointed out how Newtonian physics revealed why we don't feel the Earth move, DeWitt wrote, "All I could say was touché!"

2) I don't know.  Godel proved that any sufficiently complex axiomatic system can prove that there are things that are true which it cannot prove.  Only more powerful systems can prove the things which are not provable in those other axiomatic systems, but this creates an infinite hierarchy.  Whether or not there is some ultimate top to it I don't know.

I should clarify, I don't know what the lower bound is or if there is one.

That said I do believe information and computation are importantly related to consciousness.

 

Is it that these recursive relations cause our experience, or are just
a way of thinking about our experience?

Is it:

Recursive relations cause thought.

OR:

Recursion is just a label that we apply to some of our implicational beliefs.

The latter seems more plausible to me.

 

Through recursion one can implement any form of computation. Recursion is common and easy to show in different mathematical formulas, while showing a Turing machine is more difficult.  Many programs which can be easily defined through recursion can also be implemented without recursion, so I was not implying recursion is necessary for minds.  For example, implementing the Fibonacci formula iteratively would look like:

 

Fib(N)

  X = 1

  Y = 1

  for int i = 2 to N:

    i = X + Y

    X = Y

    Y = i

  print Y

 

This program iteratively computes successive Fibonacci numbers, and will output the Nth Fibbonaci number.

 

Jason

There was a bug in that program, replace the last two "i"s with "j", otherwise it breaks out of the loop too early.  :-)

 

--

 

[SPK]

    The existence of such Numbers could be a telltale sign that numbers require an eternal computation to define them.

I'm not sure, I can define Pi without an infinite description or computation.  Pi = circumference of a unit circle / 2

I would agree that determining Pi from that definition probably does require an eternal/infinite amount of computation though.

 Jason

[Felix Hoenikker]

Has anyone watched the movie "Contact", in which the structure of the
universe was encoded in the transcendental number Pi? What if
something like that is what is going on, and that's the answer to all
paradoxes?

So the physical universe beings with "Pi" encoded in the Big Bang,
chaotically inflates, and eventually cools and contracts back to
itself until it is again, exactly the mathematical description of
"Pi".

All consciousness is thus contain with Pi.

But then, Pi is just like any other transcendental number!

So all transcendental numbers contain all existence

F.H.

[Stephen Lin]

Hi all,

If you generalize this further, doesn't it imply that the universal
dove tailer is all of existence, taking turns computing each other? So
"you" and the "universe around you" take turns computing each other
one step at time.

In fact, that means, any two people in the world may actually be the
"same" person, except taking steps computing each other one step at a
time. So you and "I" might be exactly the same person, under some
appropriate coordinate transformation!

Food for thought.

Stephen Lin

On Jun 6, 2:19 am, Felix Hoenikker <fhoenikk...@gmail.com> wrote:
> Has anyone watched the movie "Contact", in which the structure of the
> universe was encoded in the transcendental number Pi? What if
> something like that is what is going on, and that's the answer to all
> paradoxes?
>
> So the physical universe beings with "Pi" encoded in the Big Bang,
> chaotically inflates, and eventually cools and contracts back to
> itself until it is again, exactly the mathematical description of
> "Pi".
>
> All consciousness is thus contain with Pi.
>
> But then, Pi is just like any other transcendental number!
>
> So all transcendental numbers contain all existence
>
> F.H.
>
>
>
>
>
>
>

> On Mon, Jun 6, 2011 at 12:57 AM, Jason Resch <jasonre...@gmail.com> wrote:
>
> > On Sat, Jun 4, 2011 at 3:12 PM, Stephen Paul King <stephe...@charter.net>

> > wrote:
>
> >> Hi Jason,
>
> >>     Very interesting reasoning!
>
> > Thank you.
>
> >> From: Jason Resch
> >> Sent: Saturday, June 04, 2011 1:51 PM
> >> To: everyth...@googlegroups.com
> >> Subject: Re: Mathematical closure of consciousness and computation
>

> >> On Sat, Jun 4, 2011 at 12:06 PM, Rex Allen <rexallen31...@gmail.com>
> >> wrote:
>
> >>> On Sat, Jun 4, 2011 at 12:21 PM, Jason Resch <jasonre...@gmail.com>

[Stephen Paul King]

Hi Stephen!

 

-----Original Message-----

From: Stephen Lin

Sent: Monday, June 06, 2011 2:26 AM

To: Everything List

Subject: Re: Mathematical closure of consciousness and computation

 

Hi all,

 

If you generalize this further, doesn't it imply that the universal

dove tailer is all of existence, taking turns computing each other? So

"you" and the "universe around you" take turns computing each other

one step at time.

 

In fact, that means, any two people in the world may actually be the

"same" person, except taking steps computing each other one step at a

time. So you and "I" might be exactly the same person, under some

appropriate coordinate transformation!

 

Food for thought.

 

Stephen Lin

**

 

[SPK]

 

    Indeed! But notice that this idea implies that each instance of a UD computation would have its own "time" (order of succession), which is a good idea since that would overcome the problem with a single global synchronization - which is disallowed with the non-existence of a single global computation of the whole of existence as Bruno explained in an earlier posting:

 

From: Bruno Marchal

Sent: Sunday, June 05, 2011 10:00 AM

To: everyth...@googlegroups.com

Subject: Re: CUH => Quantum Gravity => MUH => God

 

“We have a proof that (with computable = Turing emulable, and "I" = third person description of "I" at the correct substitution level):

1) If I am computable then the universe is not computable (UD Argument. It is *not* trivial).

It is trivial that

2) If the universe is computable then I am computable.

So if the universe is computable, the universe is not computable.

That makes sense: it means that whatever I am, the universe is not computable.

(p -> ~p) entails ~p

May be you are not aware of the "1)" above. I explain very shortly.

If I am computable, then my observable expectations are determined "here and now" by all computations executed by the UD, at any times, anywhere (even in "arithmetical platonia"), going through my current state. This makes my observable expectations, and thus physicalness in general, non Turing emulable, because it is a statistics on a complex infinite set of computations. This is what UDA is all about.

Computationalist physics debunks computational physics, at least concerning the TOE (by which I mean a theory not eliminating consciousness and persons).”

 

    Notice that there are more than one computation that intersects any one given state of “being-in-the-world” thus multiple orders of succession, thus not just one global time.

 

    This also implies that. like Feynman's electron, we are all just different finite approximative versions of the Totality appearing to be interacting with each other via mutual simulations. The trick may be to find a local notion of a measure that would hold for each local finite approximation that would allow for the definition of an ultrafilter that, in turn, could be used to define a local Boolean algebra for each “observer” by extensionality. Local deformation of such algebras might manifest as gauge symmetry breaking generating the appearance of mass, charge, spin, etc. when we look at the effects on the topological dual of that algebra...

 

Onward!

 

Stephen Paul

 

PS, its nice to have another Stephen on the List. :–)

 

**

[Bruno Marchal]

On 05 Jun 2011, at 18:45, Rex Allen wrote:

> On Sat, Jun 4, 2011 at 4:09 PM, Bruno Marchal <mar...@ulb.ac.be>
> wrote:
>> On 04 Jun 2011, at 19:06, Rex Allen wrote:
>>> On Sat, Jun 4, 2011 at 12:21 PM, Jason Resch
>>> <jason...@gmail.com> wrote:
>>>>
>>>> One thing I thought of recently which is a good way of showing how
>>>> computation occurs due to the objective truth or falsehood of
>>>> mathematical
>>>> propositions is as follows:
>>>>
>>>> Most would agree that a statement such as "8 is composite" has an
>>>> eternal
>>>> objective truth.
>>>
>>> Assuming certain of axioms and rules of inference, sure.
>>
>> But everyone agree on the axioms of arithmetic.
>
> I’m not sure what you mean here. “Agree” in what sense?

In the usual sense. Everyone agree that the axiom of Robinson or Peano
arithmetic are sound for elementary arithmetic.
Agreeing means that they say, in front of the axioms, that they are
OK, and proceed.

>
> Everyone agrees that the axioms of arithmetic are...what?
> Interesting? Useful?

Indispensable. We use them consciously or unconsciously since a very
long time.

>
> Who is “everyone”?

The Löbian universal numbers.

>
> Does everyone also agree that there are other axiomatic systems?

Yes. Everyone agree with this. Since Gödel we know there is an
infinity of them, and that none are both mechanical and complete.

>
>
>> And we could take any
>> universal (in the Turing sense) system instead. The physical laws
>> cannot
>> depend on the choice of the "universal base".
>
> What exactly are “physical laws”?

The laws we are using in our everyday life to predict our observation
(notably).

>
> You’re really saying “the regularities in our experience cannot depend
> on the choice of the universal base”?

Yes. I can prove it from the mechanist assumption.

>
>
>>>> Other recursive formulae may result in the evolution of structures
>>>> such as our universe or the computation of your mind.
>>>
>>> Is extraordinary complexity required for the manifestation of
>>> "mind"?
>>> If so, why?
>>>
>>> Is it that these recursive relations cause our experience, or are
>>> just
>>> a way of thinking about our experience?
>>>
>>> Is it:
>>>
>>> Recursive relations cause thought.
>>>
>>> OR:
>>>
>>> Recursion is just a label that we apply to some of our implicational
>>> beliefs.
>>
>> I think you are confusing computability, which is absolute
>> (assuming Church
>> thesis), and provability, which is always relative to theories,
>> machines,
>> entities, etc.
>
> What are your justifications for assuming the Church thesis?

The conceptual justification is the closure of the set of partial
computable functions for diagonalization.
The empirical is the diversity of equivalent systems and the failure
to get anything stronger than a universal Turing or Church universal
system (with respect to computability, not provability!).

>
> Do oracles exist in Platonia? In HyperPlatonia perhaps? If not, what
> precludes their existence?

It is almost a matter of convenience to add them in Platonia. With
arithmetical Platonia, we can explain why machines believe correctly
in random oracle, even if they don't belong in the ontological
reality. It is absolutely undecidable for machine if infinite objects
exist or not 'ontologically'. It is provable, with comp, that they
exists epistemologically.

>
>
>> Jason is right, computation occurs in "arithmetical platonia", even
>> in a
>> tiny part of it actually, independently of us.
>
> Ya, I have my doubts about that.

If comp is correct, all Löbian machine doubt that, as they have to
doubt on comp itself.

>
>
>> This tiny part is assumed in the rest of science, and comp makes
>> it necessarily enough (by taking seriously the first and third person
>> distinction).
>
> What is science in a deterministic universe? What is science in a
> probabilistic universe? What other kinds of universes could there be?

Science is the attempt made by people to figure out what is.
Comp makes the physical universe, or multiverse, or multi-multiverse,
or ..., unique, except for possible clusters of comp inaccessible
realities, which can neither interact, nor interfere with our physical
reality (and so are not interesting, or Löbian-interesting).

Bruno

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

[Bruno Marchal]

On 06 Jun 2011, at 08:19, Felix Hoenikker wrote:

> Has anyone watched the movie "Contact", in which the structure of the
> universe was encoded in the transcendental number Pi? What if
> something like that is what is going on, and that's the answer to all
> paradoxes?
>
> So the physical universe beings with "Pi" encoded in the Big Bang,
> chaotically inflates, and eventually cools and contracts back to
> itself until it is again, exactly the mathematical description of
> "Pi".
>
> All consciousness is thus contain with Pi.
>
> But then, Pi is just like any other transcendental number!
>
> So all transcendental numbers contain all existence

You are confusing existence, and description of existence. This is
like confusing "babel library" with universal dovetailing. PI contains
all encoding of computations, but does not compute anything, and does
not possess the gigantic redundancy of computations of the UD's
activity, making the relative measure a real mathematical problem,
making the comp theory testable.

Note that instead of PI, you could have taken the natural numbers 0,
1, 2, 3, ..., or the real number 0,12345678910111213141516... This one
has the advantage that it is easy to prove that, like the natural
numbers, it goes through all descriptions of all computations (for PI
it is an open problem, really). But this is trivial. You can't extract
from this the "real" physical laws.
Many people confuse a computation and a description of a computation.
I guess it is a subtle point.
Now, if you take 0, 1, 2, 3, .... together with logic and the laws of
addition and multiplication, then, assuming we are digital machine,
you can extract physics. Indeed, thanks to the Gödel splitting between
true and provable, and through the distinction between 1-pov and 3-
pov, you can even get both the laws of quanta and the laws of qualia,
and their relations.

Bruno

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

[Bruno Marchal]

Hi Stephen,

On 06 Jun 2011, at 05:27, Stephen Paul King wrote:

Hi Bruno, Rex and Friends,

 

    My .002$...

[BM]

No theories nor machine can reach all arithmetical truth, but few 

people doubt that closed arithmetical propositions are either true or 

false. We do share a common intuition on the nature of arithmetical 

truth.

I have doubt on any notion of global mathematical truth. Sets, real 

numbers, complex numbers, etc. are simplifications of the natural 

numbers. They are convenient fictions, I think. If we are machine, it 

is undecidable if ontology is more than N.

 

 

[SPK]

   

    I think that there is some differences in opinion about this but it seems to me that we need to look at some details. For example, there should exist a theory that could reach all arithmetic truth given an eternity of time or an unnamable number of recursions or steps.

?

No this cannot exist. It is precluded by the incompleteness theorem. Eternity can't help. Unless you take a non axiomatisable theory, or some God-like entities. 

This by definition would put them forever beyond human (finite entity) comprehension. Whether or not there is closure or a closed form of some theory does not make it realistic or not. AFAIK, closed arithmetic propositions are tautologies, no?

They are not tautologies, unless you mean by this "propositions true in *all* models of Peano Arithmetic. But then "tautology" means "theorem", and that would be an awkward terminology. Ax(0 ≠ s(x)) is not a tautology (it is already false in (Z,+), nor is Fermat last theorem.

That we share a common intuition of truth may follow from a common local measure of truth within each of us. (Here the "inside" implied by the word "within" is the logical/Arithmetic/abstract aspect of the duality that I propose.)

    Additionally, we should be careful not to conflate a plurality of fungible individuals with a multiplicity of non-fungible entities. We can set up a mental hall of mirrors and generate an infinite number of self-images in it, but this cannot *exactly* map to all of the selves that could exist without additional methods to break the symmetries.

 

    I have been waiting a long time for you to state this belief of yours, Bruno! That "Sets, real  numbers, complex numbers, etc." are simplifications of (mappings on/in?) the Natural Numbers. This seems to be the Pythagorean doctrine that I suspected that you believed.

Would you take the time to study the papers, you would have understood that this is a result of comp. Comp transforms the very banal arithmetical realism in an authentic Pythagorean neoplatonist theology, i.e.  with some use of OCCAM razor.

It has a long history and a lot of apostles that have quite spectacular histories. I think that there is a deep truth in this belief, but I think that it needs to be more closely examined.

It can be derived from Church thesis and the assumption that "we" are Turing emulable.

 

>

> Perhaps there is just human belief.

 

[BM]

Jason said it. If you follow that slope you may as well say that there 

is only belief by Rex. You can also decide that there is nothing to 

explain, no theories to find, and go walking in the woods. Science, by 

definition, assumes something beyond (human) belief.

 

[SPK]

   

    I admit that I laughed out loud at this! Good point, Bruno! The reduction of all truth to that which can be defined within a single human's belief trivializes and renders it meaningless. That is one of the absurd consequences that we lambast solipsism for, but I think that Rex should not be to swiftly dismissed form maybe trying to make a deeper observation; he has brought up a very good topic for discussion.

    While it is absurd to reduce all truth to what a single finite entity can "compute" - which is that we are actually saying if we follow the Kleene-Turing-Church-Post road -

Careful. It can be said that all ontological truth will be generated, but the epistemological truth will never be generated, but they will emerge in a not completely computable way. Remember that arithmetic, seen from inside, is *much* bigger than arithmetic see from outside.

we are actually positing that "all truths can be defined in terms of N -> N mappings". 

That would contradict Gödel's incompleteness. Unless you mean *all* N -> N mappings, which is far to bigger and trivialize the theory (making it non testable, and unable to derive anything in physics, cognitive science, etc.).

Many such mappings to be sure, but N to N mappings nonetheless. We are back to that strange belief that Bruno explicitly, albeit inadvertently, stated.

    But this is not really a "strange" belief, partly because it seems to be almost universally the default postulate within the basket of beliefs that people operate with in our every day world. I would like to pose the question of whether or not we are inadvertently painting ourselves into a corner with this belief. IT seems to me, and this is just a personal prejudice of mine, that there exists truths that cannot be named or represented exactly in terms of N->N maps.

In this context, you should clearly stated if you take all N->N mappings, or the total computable one, or the partial computable one. The non triviality of comp entirely resides in such nuances.

The source of this suspicion comes from what I have studied of G. Cantor's work on transfinites and the histrionics of practitioners of mathematical logic that have been examining the nature of cardinalities.

With comp, the diagonalization of Kleene gives the information. Cantor's one are far too crude.

Additionally there is my belief that the Totality of Existence must be, at least, Complete (not in the Gödel sense of just 1st order logics), Bicomplete (in the Category theory sense) and Closed (in the topological sense). This implies the existence of unnamable truths, or at least Truths that cannot be exactly represented in terms of recursive functions on the Integers.

That the totality of existence is complete seems to me to be a tautology, or a truth by definition.

That truth is beyond machine's means, is a theorem.

That truth is beyond us is consequence of such theorem when we assume that we are machines.

    The question becomes one of the implications of this on our metaphysical assumptions about the ontologies that we are using in our thinking about the issue of mathematical closure of computation and consciousness. As I see it, and this very well could be just an eccentric thought, is that we need to be very careful that we do not tacitly assume that all of the minds of entities are replicating the same ideas as one’s own. The fact that we are continuously surprised at the responces that we get when we post to this List, for example, should be some indication that we all think differently about things and that when we propose the idea that consciousness is somehow some kind of N->N map or even some string of numbers in ℤ, then we should expect a vigorous response.

I agree with this. There is a persisting reductionist conception of numbers and machines. Numbers, already just through the laws of addition and multiplication, transcend a lot what any consistent machines can really prove or even just talk about.

BTW, did you know that ℤ *≅U(1) and  U(1) *≅ℤ  via the Pontryagin duality? Yes, that U(1) that is used in physics ! This is one of many reasons why I think that Bruno is onto something very important in his work! :-)

Well, thanks. I wish you get clearly the point someday. You might elaborate on the importance of U(1) ≅  Z.

[BM]

Do you need someone observing your brain for you to feel something?

Why would the physical UD execution differ?

Indeed, why would the arithmetical UD execution differ?

 

[SPK]

 

    Strangely enough, Bruno, in a way there is something to this idea that we need to consider that someone is watching for us to feel something! If we follow the logic of QM and accept the decoherence idea, the idea that we have a definite (and Boolean representable) state of the brain depends most definitely on the existence of what we can think of as “someone” watching: the rest of the universe.

With decoherence? I guess you meant with "collapse".

We can break this down into a large number of mutually communicating observers, but that “someone is watching” has real consequences: it induces the 2 valued definiteness that otherwise would not exist.

You lost me.

    I think that you are are reacting a bit to strongly from your Arithmetic Realism doctrine.

Where do I react a bit to strongly? Perhaps it is my english? I try just to be short and clear. Sorry if I look like reacting strongly, or being "upset", I am (usually) not. Only plain dishonesty makes me nervous, but this does not seem to happen on this list.

I would like for all of us to sit back and thought for a while exactly on what we are asking with this question of Mathematical closure.

I would like to insist that assuming comp, there is no mathematical closure for the first person points of view. The inner view of arithmetic is already beyond mathematics itself. Assuming comp, we might talk of theological closure (but this is trivial, with the greek definition of theology: the science of 'truth'). Note that there are many argument independent of comp which could make us doubt of any sense for the expression of "mathematical closure". Like the whole of arithmetic is beyond arithmetic, the whole of math is beyond mathematics. 

Bruno

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

[Jason Resch]

> -pov and 3-pov, you can even get both the laws of quanta and the law

> s of qualia, and their relations.
>
> Bruno
>

Bruno,

How are provable and true related to first and third person
perspectives?

With godel does the distinction not depend on the axiomatic system?

Also what would a law of qualia look like? Something like "the being
whose brain computes X will experience Y"?

Thanks,

Jason

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[Bruno Marchal]

Hi Stephen Lin,

On 06 Jun 2011, at 08:26, Stephen Lin wrote:

> Hi all,
>
> If you generalize this further, doesn't it imply that the universal
> dove tailer is all of existence, taking turns computing each other? So
> "you" and the "universe around you" take turns computing each other
> one step at time.

Yes that is the theory under consideration. But you should say: "all
of the needed ontological existence". A big part of existence is also
epistemological. Indeed, the point is that the physical laws and
universe are epistemological, and derivable from machine's psychology
(or theology). This makes comp a scientific theory in the common
Popperian sense. Some physical observable facts might contradict comp,
but up to now, we can say that quantum physics rather confirms the
comp assumption. With computationalism (which is just the digital form
of Descartes mechanism) most of quantum weirdness (including the
possibility of quantum computation) are derivable from arithmetic. My
question is: are hamiltonians physical or geographical? Same question
for the physical constants.

>
> In fact, that means, any two people in the world may actually be the
> "same" person, except taking steps computing each other one step at a
> time.

This might depend by what you mean by "person".

> So you and "I" might be exactly the same person, under some
> appropriate coordinate transformation!

I tend to believe that "personal identity" is an "illusion", like
primary matter or physicalism. We might be all the universal machine
(for which there is already a notion of personhood), with different
experiences. But this can only be interesting if we can sense this in
a way or another, when alive or dead. Drugs providing amnesia might be
interesting with that respect.

Bruno

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

[Jason Resch]

On Mon, Jun 6, 2011 at 8:14 AM, Bruno Marchal <mar...@ulb.ac.be> wrote:

Hi Stephen Lin,

On 06 Jun 2011, at 08:26, Stephen Lin wrote:

Hi all,

If you generalize this further, doesn't it imply that the universal
dove tailer is all of existence, taking turns computing each other? So
"you" and the "universe around you" take turns computing each other
one step at time.

Yes that is the theory under consideration. But you should say: "all of the needed ontological existence". A big part of existence is also epistemological. Indeed, the point is that the physical laws and universe are epistemological, and derivable from machine's psychology (or theology). This makes comp a scientific theory in the common Popperian sense. Some physical observable facts might contradict comp, but up to now, we can say that quantum physics rather confirms the comp assumption. With computationalism (which is just the digital form of Descartes mechanism) most of quantum weirdness (including the possibility of quantum computation) are derivable from arithmetic. My question is: are hamiltonians physical or geographical? Same question for the physical constants.

In fact, that means, any two people in the world may actually be the
"same" person, except taking steps computing each other one step at a
time.

This might depend by what you mean by "person".

So you and "I" might be exactly the same person, under some
appropriate coordinate transformation!

I tend to believe that "personal identity" is an "illusion", like primary matter or physicalism. We might be all the universal machine (for which there is already a notion of personhood), with different experiences. But this can only be interesting if we can sense this in a way or another, when alive or dead. Drugs providing amnesia might be interesting with that respect.

If there are omega point civilizations whose explore the universe of possible conscious states, and who share and swap experiences as we do with videos on youtube, then they serve as hubs connecting all persons.  Consider a god or demi-god with access to infinite computational power (perhaps it began as a technical civilization but in a universe where unlimited energy can be created and dissipated).  Perhaps it chooses to simulate every possible experience and incorporate it into his own.  Then there is a path for any conscious being to wake up as that god.

More succinctly: For those who believe an omniscient god exists somewhere, then that god knows what it is like to be you, and you cannot distinguish whether you in this moment are him or you.  This is similar to the Hindu belief in Atman, and also leads directly to a basis for karma and the golden rule: Be nice to others as one day you will experience things from their perspective.

Jason

[Bruno Marchal]

Jason,

On 06 Jun 2011, at 15:08, Jason Resch wrote:

On Jun 6, 2011, at 7:09 AM, Bruno Marchal <mar...@ulb.ac.be> wrote:

On 06 Jun 2011, at 08:19, Felix Hoenikker wrote:

Has anyone watched the movie "Contact", in which the structure of the

universe was encoded in the transcendental number Pi? What if

something like that is what is going on, and that's the answer to all

paradoxes?

So the physical universe beings with "Pi" encoded in the Big Bang,

chaotically inflates, and eventually cools and contracts back to

itself until it is again, exactly the mathematical description of

"Pi".

All consciousness is thus contain with Pi.

But then, Pi is just like any other transcendental number!

So all transcendental numbers contain all existence

You are confusing existence, and description of existence. This is like confusing "babel library" with universal dovetailing. PI contains all encoding of computations, but does not compute anything, and does not possess the gigantic redundancy of computations of the UD's activity, making the relative measure a real mathematical problem, making the comp theory testable.

Note that instead of PI, you could have taken the natural numbers 0, 1, 2, 3, ..., or the real number 0,12345678910111213141516... This one has the advantage that it is easy to prove that, like the natural numbers, it goes through all descriptions of all computations (for PI it is an open problem, really). But this is trivial. You can't extract from this the "real" physical laws.

Many people confuse a computation and a description of a computation. I guess it is a subtle point.

Now, if you take 0, 1, 2, 3, .... together with logic and the laws of addition and multiplication, then, assuming we are digital machine, you can extract physics. Indeed, thanks to the Gödel splitting between true and provable, and through the distinction between 1-pov and 3-pov, you can even get both the laws of quanta and the laws of qualia, and their relations.

Bruno

Bruno,

How are provable and true related to first and third person perspectives?

"provable(x)" is Gödel's beweisbar (provable) predicate of some "rich" (Löbian) axiomatic theorem prover (ideally correct machine). "Bp" abbreviates beweisbar('p'), with 'p' = a representation of p in the language of the machine.

When a machine M proves a proposition p, then Bp is true for that machine. If the machine is Löbian, we can represent the proposition p by some number, and we can represent provability by the arithmetical "beweisbar". 

For Löbian machine, it will happen that each time the machine proves p, she will be able to prove that she can prove p. That is each time the machine proves p, she will be able to prove Bp. So Bp -> BBp is true for that machine, and Löbian machine can prove all instantiation of Bp -> BBp. "Bp -> BBp" means really:  IF p is provable THEN Bp is provable.

Now, to answer you question, this provability (the arithmetical beweisbar), although self-referential (it is the machine's own provability ability) is third-person provability. If the machine M proves Beweisbar('p'), the machine M is really proving "the machine M proves p", in a third person mode. 

So the traditional provability predicate is the "third person science" of the machine. Typically, the machine M is not "aware" that she is M, or that her provability predicate is that "beweisbar". The machine is like a young child saying "Billy is thirsty" for "I am thirsty", in a sense. Yet it is the correct self-reference; the child is thirsty.

Now, in AUDA, I define the first person by the (simplest) knower that can be attached to the machine.

Unfortunately, as Gödel was already well aware, the beweisbar predicate does not satisfy the S4 logic of knowledge, that is

Bp -> p

Bp -> BBp

B(p -> q) -> (Bp -> Bq)

With the usual modus ponens and necessitation rules.

Indeed, what is provable *about* machine's beweisbar, by the machine, is given by the modal logic G:

B(Bp -> p) -> Bp   (Löb)

B(p -> q) -> (Bp -> Bq)      (and the same rules).

From this, you can see that the machine cannot prove Bf -> f   (f = '0=1'). Indeed you would have

Bf -> f

B(Bf -> f)   (necessitation)

B(Bf -> p) -> Bf   (substitution in Löb)

Bf   (modus ponens on the two preceding lines)

f   (from the first line)

(contradiction).

So the knower axiom "Bp -> p" is not a theorem by the machine, and thus beweisbar does not axiomatize a notion of knowledge for the machine. In fact it axiomatizes a notion of believability instead of knowledge.

Why not using G*, that is the logic of what is TRUE about "beweisbar's machine" (independently of the fact that the machine can prove it or not). 

In that case, 'Bp -> p' becomes a theorem, for the correct machines, but we lost the necessitation rules (this prevents the contradiction above). So G* does not axiomatize either a notion of knowledge.

So neither G nor G* can be used for knowledge, and they fail to capture a notion of first person (the knower).

In fact it has been shown (by Kaplan & Montague) that no predicate at all can represent knowledge in the language of a machine, so it might seems impossible to proceed. Unless:

We allow a predicate of knowledge to be non representable by the machine (which is rather appealing: introspection à-la Ramana Maharshi illustrates that a knower cannot name itself! In fact we might not know who we are, in the first person perspective.

In that case, the oldest definition of knowledge can be applied. It is the definition provided by Plato's Theaetetus. He suggested to define "I know p" by "I believe p, and p is true". That is Kp = Bp & p. We cannot define *in general* knowability of p, but we can model it for each instantiation: I know that 2+2=4 = I believe (prove) that 2+2=4, *and* 2+2=4. We simulate truth by its instantiation, somehow (that should please Stephen!).

Such Kp can be shown to obey all axioms of knowledge (S4 modal logic, given above). For example:  "Kp -> p" becomes (Bp & p) -> p, which is a propositional calculus tautology. In fact, like Solovay showed that G and G* are not just sound for provability, but are complete, Goldblatt and Boolos (and Kusnetsov and Muravitski) have shown that S4Grz is sound and complete for ideally correct Löbian machine's knowability. 

S4Grz is S4 + the rather awkward Grzegorczyk's formula B(B(p -> Bp) -> p) -> p. 

Such "Kp" is not definable in arithmetic, or in any language of any correct machine talking about itself. By Tarski, you cannot define it by beweisbar('x') & true('x'), because true('x') is not definable in arithmetic (or in any machine's languages). But the machine, once betting on comp, and its own correctness (etc.) can talk about it indirectly. Indeed, that machine can "infer" that Goldblatt-Boolos-Kusnetsov-Muravitski theorem applies to herself. 

This moves makes also coherent the dream argument in metaphysics from the self-referential machine's perspective.

To sum up the answer to your question, with Bp abbreviating Beweisbar('p').

"provable p" belongs to the machine third person discourse,

"kowable p" = "provable('p') & p", for all (arithmetical/machine's) proposition, and this defines (at some upper abstract level) the knowability, or the first person perspective of the machine. We just link her to 'truth'.

With godel does the distinction not depend on the axiomatic system?

Yes. In the sense that the p which are believed or known, will depend on the machine, axiomatic system, observer, etc.

No, in the sense, that if the machine is correct and Löbian, the logic of B (and K) will be the same. Only the "p" will be different. A bit like the gravitation law is the same for sun+ earth, and earth+moon, but have a different instantiation.

It is a good thing that the "content" of those logic are different from one machine to another (given that they have different experiences). But they obeys the same abstract laws (G, G*, S4Grz, ...).

Note also, that it can be proved that for all correct Löbian machine, S4Grz = S4Grz*. The knower is the same from the science and the theological perspective. The knower does not inherit the true/provable G*/G splitting. 

This is quite amazing, and leads to the attachment of a form of solipsism/intuitionism for the first person view. Again, this is coherent with our experiences. Even if we are not solipsist, we cannot deny that our experiences are lived in a solipsistic way. Only strong form of telepathy would be able to change  such fact.

Also what would a law of qualia look like? Something like "the being whose brain computes X will experience Y"?

For the qualia, knowledge is not enough. We need a reality. That is given by extending Theatetus Bp & p into Bp & p & Dt.

By Gödel's completeness theorem, Dt is true for a machine M if and only if the machine's beliefs can be 'satisfied' in some model (reality). So Dt is the syntactical manner to mention the semantical existence of a reality, and it is necessary for having a notion of indeterminacy which can be quantified (Dt is also the non-cul-de-sac assumption that we need for having any notion of probability).

Now, "Bp & p & Dt" will give the qualia of observation of p, seen as an event (usually, p will be true proved sigma_1 sentences). The laws will be given by the arithmetical interpretation of the logic of such an operator. The main law is "p -> BDp", and from this you can derive that if I observe p, I can observe it again. More difficult, you can justify the existence of "perceptible fields", for example that qualia can take geometrical shapes, and that they can overlap. You can justify that machine will take them as undoubtable but incommunicable (like consciousness, which is related also to the Dt proposition).

I hope this was not long, nor too short. Ask any complement of information if needed. I use Bp as an abbreviation of beweisbar('p'), but I might explain this more precisely and give the precise theorem relating modal logics and the provability/consistency logics. It is just a bit long to do.

Thanks,

You are welcome,

Bruno

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[Stephen Paul King]

 

From: Bruno Marchal

Sent: Monday, June 06, 2011 12:30 PM

To: everyth...@googlegroups.com

Subject: Re: Mathematical closure of consciousness and computation

Jason,

 

snip

 

Note also, that it can be proved that for all correct Löbian machine, S4Grz = S4Grz*. The knower is the same from the science and the theological perspective. The knower does not inherit the true/provable G*/G splitting.

This is quite amazing, and leads to the attachment of a form of solipsism/intuitionism for the first person view. Again, this is coherent with our experiences. Even if we are not solipsist, we cannot deny that our experiences are lived in a solipsistic way. Only strong form of telepathy would be able to change  such fact.

 

 

HI Bruno,

 

    Try this paper. :-) http://arxiv.org/abs/quant-ph/0407221

 

Quantum Pseudo-Telepathy

Authors: Gilles Brassard, Anne Broadbent, Alain Tapp

(Submitted on 27 Jul 2004 (v1), last revised 22 Nov 2004 (this version, v3))

Abstract: Quantum information processing is at the crossroads of physics, mathematics and computer science. It is concerned with that we can and cannot do with quantum information that goes beyond the abilities of classical information processing devices. Communication complexity is an area of classical computer science that aims at quantifying the amount of communication necessary to solve distributed computational problems. Quantum communication complexity uses quantum mechanics to reduce the amount of communication that would be classically required.
Pseudo-telepathy is a surprising application of quantum information processing to communication complexity. Thanks to entanglement, perhaps the most nonclassical manifestation of quantum mechanics, two or more quantum players can accomplish a distributed task with no need for communication whatsoever, which would be an impossible feat for classical players.
After a detailed overview of the principle and purpose of pseudo-telepathy, we present a survey of recent and no-so-recent work on the subject. In particular, we describe and analyse all the pseudo-telepathy games currently known to the authors.

 

 

[Rex Allen]

On Sun, Jun 5, 2011 at 3:36 PM, Quentin Anciaux <allc...@gmail.com> wrote:
> I don't understand what is the purpose of such a comment... one that I've
> seen too many times.

Which comment?

In general, the purpose of my comments is just to articulate my
thoughts in some more-or-less coherent and permanent form, and to see
if there are any interesting responses that point to other avenues of
investigation. After all, I could be mistaken!

> The only logical conclusion is "Nothing is explainable
> !".... well ok then I will gonna eat my banana !

Bananas are good. I like bananas.

> If your premises is "Nothing is explainable" then it is logical that you
> conclude that "Nothing is explainable", going in parabolic wording about it
> won't make it better.

It wasn't my starting premise, but it's pretty much the conclusion I've come to.

My basic point is this:

1. Explanation is subordinate to description.

2. Description is subordinate to observation.

3. Observation is subordinate to experience.

4. And now we want to close the circle by explaining experience.

However, our explanation of experience can only be justified by appeal
to experience - plus reason.

But what is reason? Where does it come from? What explains it? What
do experience and reason have to say about reason? Another circle.

So if our experiences correspond to something external to themselves,
and our reasoning is correct, then the equations of our descriptive
framework will be true of the world as well as of our observations,
and our explanations will true of the world as well as of our
framework.

But what reason do we have to believe that our experiences do so
correspond to an external world, and what reason do we have to trust
reason?

Our experience of dreams and hallucinations and delusions are enough
to plant the seeds of doubt about the reliability of both experience
and reason.

And then there are more abstract arguments, like the brain-in-vat
argument, the Cartesian method of doubt, and the simulation argument
(which hinges on multiple realizability, btw).

And there’s just the general question of what “reason” means in a
deterministic world, or a probabilistic world, or a purely contingent
world.

So, to the extent that reason is reliable, there are reasons not to
take Step Four seriously.

Despite all that, one could ask, why not take step four? What’s the harm?

But, alternatively one could also ask, why take step four...what’s the benefit?

Steps one through three are perfectly compatible with an instrumental
approach to science, and don’t require any metaphysical commitments.

Only step four *requires* a metaphysical leap of faith...and that
makes step four suspect.

Rex

[Rex Allen]

On Sun, Jun 5, 2011 at 8:34 PM, Jason Resch <jason...@gmail.com> wrote:
> On Sun, Jun 5, 2011 at 11:58 AM, Rex Allen <rexall...@gmail.com> wrote:
>> On Sat, Jun 4, 2011 at 4:14 PM, Jason Resch <jason...@gmail.com> wrote:
>>> Perhaps so, perhaps there is only Rex's beliefs. Perhaps only rex's
>>> beliefs at this exact moment.
>>
>> Not obviously impossible. Thought not obviously necessitated either.
>>
>> Does the possibility that there are only Jason’s beliefs at this exact
>> moment scare you?
>>
>> Would you prefer it to be otherwise?
>>
>
> It makes the universe much smaller, less varied, less fascinating, etc. to
> believe my current thought is all there is. It also makes answering any
> questions futile (why does this thought exist?, can I change it? Am I a
> static thought or an evolving thought? What determines or controls the
> content of this thought?) How can any of those questions be approached if
> only thought exists?

How can any of those questions be approached by conscious entities in
a deterministic computational framework?

Everything you’ll ever learn, every mistake you’ll ever make, every
belief you’ll ever have is already locked in.

Your life is “on rails”. Maybe your final destination is good, maybe
it’s bad - but both the destination and the path to it are static and
fixed in Platonia.

Further, nothing about computationalism promises truth or anything
else desirable...or even makes them likely.

In fact, surely lies are far more common than truths in Platonia.
There are few ways to be right, but an infinite number of ways to be
wrong. If you think you exist in Platonia, then surely you also have
to conclude that nearly everything else you believe is a lie.

***

Computationalism’s answers to the questions you pose are:

Why does this thought exist? There is no reason except that
computation exists. Big whoop.

Can I change it? No.

Am I a static or evolving thought? Neither. Your are computation.

What determines or controls the content of this thought? The brute
fact of computational structure.

***

Why did your momma love you? It was computationally entailed.

Why did Jeffry Dahlmer kill those people? It was computationally entailed.

Why 9/11, Auschwitz, AIDS, famine, bigotry, hate, suffering? They are
computationally entailed.

Platonia actually sounds like more hell than heaven.

SO...what is it that computationalism gives you over solipsism,
exactly? What makes this picture more varied, more fascinating, less
futile?

I’m not saying you’re position is worse than mine, but surely it’s no better.

>>> What is the engine providing the computations which drive the universe?
>>
>> That assumes that computations do drive the universe.
>>
>> Which is the assumption that I’m questioning.
>
> The physical universe may be computational or it may be a mathematical
> structure, but what enforces its consistency and constancy of its laws? If
> it were a mathematical structure, or a computation then the consistency
> comes for free.

But doesn’t computationalism predict that their should be conscious
entities whose experience is of inconsistent, contradictory, shifting
laws?

In fact, this sounds like the experiences described by schizophrenics,
or people on drugs.

In fact, I would think that Platonia should contain far more chaotic
experiences than not.

So this virtue that you highlight isn’t a virtue at all.

The idea that “oh, those all cancel out when we average across all
computations” or something is pretty ad hoc sounding.

You’ve lost whatever intuitive appeal that computationalism had in
fell swoop. We’re back to, “why would that result in conscious
experience if non-averaged computation didn’t???”

It just does? Pah.

>>> Do you think pi has an objective (not human invented or approximated)
>>> value,
>>> whether or not any person computed it?
>>
>> I think that everyone who starts from the same assumptions and makes
>> the same inferences will always reach the same conclusions regarding
>> the value of pi.
>>
>
> So that would make pi an objectively studiable object, would it not?

Everyone who starts with the same assumptions about the Incredible
Hulk and Spiderman, and makes the same inferences from those
assumptions, will reach the same conclusions regarding the outcome of
an arm-wrestling match between them.

Does that make Spiderman objectively studiable?

>What makes the study of such objects less valid than the study of
> other objects in science, for example in biology?

I’m not saying it’s less valid. It’s equally valid. But that’s
saying less than you think.

> To define a bacterium as a life form
> Earth scientists and alien scientists both have to start from similar
> assumptions and make similar inferences. Based on different starting
> assumptions some might say a virus is alive others may not, this doesn't
> mean that viruses don't exist. In your postings you seem to suggest that
> given there could be disagreement on what starting assumptions to use the
> reality of mathematical objects should be called into question, but this
> would be like questioning whether viruses exist because biologists can't
> agree on whether or not they are alive. The numbers, their properties and
> relations are objectively studiable, as much as planets and viruses are. If
> math is invented, then you should invent a prime number with a billion
> digits and claim the $250,000 prize ( http://www.eff.org/awards/coop ). If
> you cannot invent such a number, then perhaps mathematics truly is a space
> to be explored, much like the vacuum that surrounds our planet.

Instead, maybe I should just write a fantasy book about a boy wizard
to goes to a magical school - and then people who find such things
interesting would give me millions and millions of dollars!

Oh wait...maybe I can’t invent such a book, because I’m not a very
good writer, and people don’t find the structure of my fantasies
compelling or believable or interesting or useful. Rats.

Well, according to you I shouldn’t feel bad. My failure was entailed
by the computational structure of Platonia. My efforts to achieve
success were...futile.

>> I’ll say that relative to some framework that includes my experience
>> with the assumptions and inferences and rules needed to calculate pi -
>> the answer is yes. Because in that framework, given enough time and
>> enough “universe”, it seems likely that someone *could* calculate the
>> googleplexth digit of pi.
>
> So the value is there, waiting to be found (even though no one has bothered
> to go through the motions to compute it)?

No - as with whether the penny would have melted had I done something
yesterday, there is no fact of the matter.

As with the outcome of the Hulk-Spiderman armwrestling match - it can
only be judged relative to some story that we tell ourselves. Some
people will tell one story, but there’s nothing to stop someone else
from telling a different story.

We might say: but that’s inconsistent!

Or: I don’t agree with your assumptions!

OR: I think you made the wrong inference there!

BUT...it’s just a story. There’s no absolute against which to judge
these stories, and so there can be no matters of fact except relative
to the stories.

Which is not to say that we get to decide our own paths - we are
characters, not authors.

(metaphorically speaking)

>> There is no fact of the matter except relative to the framework.
>>
>> It’s like asking “who would win an arm wrestling match between the
>> Incredible Hulk and Spiderman”. I can confidently say the Incredible
>> Hulk. But that answer doesn’t really mean anything outside of the
>> “Marvel Universe”. The Marvel Universe has no metaphysical
>> significance, and so my answer to this hypothetical question involving
>> it has no metaphysical significance either.
>>
>> See?
>>
>
> Unlike the marvel universe, if mathematical objects exist it is of huge
> metaphysical significance, as it makes so called physical universes
> redundant and completely unnecessary for explaining observations.

You don’t think it would be of huge metaphysical significance if the
marvel universe were to exist? Seems like it would raise a few
eyebrows...

>> Information is a difference that makes a difference. But it has to
>> make a difference *to* someone.
>>
>
> This is why the consciousness requires a process accepting or operating on
> information. If a process is not defined there can be no interpretation.

“Process” is just a label for a certain way of thinking about things.
It’s a mental construct.

You’re trying to hypostatize a product of human thought. And in fact,
explain human thought in terms of something that only exists within
human thought.

You’ve got it all backwards.

>> A randomly generated string of bits can be identical to a string of
>> bits representing an image...but the randomly generated string of bits
>> contain no real information whereas the image file does.
>>
>> The difference being that I know how to correctly interpret an image
>> file, but there is no “correct” interpretation of a random string of
>> bits.
>>
>> But with the right “interpretation” any information can be found
>> anywhere. The magic is all in the interpreter, not in what’s being
>> interpreted.
>>
>> Information is observer-relative. Observers aren’t information-relative.
>>
>
> Are you a computationalist? This line of thought sounds like you are..

No. Information is something that observers have. Observers are not
something that information has.

Our positions are mirror images.

Reverse the arrow of explanation, and you’ve got it!

>>> There are also reasons to believe in the informational basis if
>>> consciousness due to multiple realizeability. Minds can take different
>>> physical forms because information cab take many physical forms.
>>
>> I can take anything to represent anything else. So “representation”
>> is multiply realizable.
>>
>> But again, that has to do with me, not with information. If I
>> remember what my encoding scheme was, I can “re-present” things to
>> myself. If I forget what my encoding scheme was, or that I even
>> encoded anything - then all I have are a bunch of bits...which for all
>> I know might be random.
>>
>> If they really were random bits, but for some reason I was convinced
>> they weren’t - I might find all sorts of “meaningful” interpretations
>> of them using all sorts of decoding schemes - but none of these would
>> be correct.
>>
>> In this case, I’m doing all of the work...the bits aren’t doing
>> anything. Which, as it turns out, is also true of non-random bit
>> strings. I do all of the work. The bits are just reminders...hints.
>>
>> I think you’re getting it all backwards. Representation depends on
>> me. I don’t depend on representation.
>
> What I mean by multiple realizability is parts of your brain can be replaced
> with any part which is functionally equivalent without impacting your
> consciousness.

If consciousness were caused by particles in the brain assuming
particular configurations in sequence, then this would be convincing.

But this doesn’t make much sense to me. There’s nothing in my
conception of particles or configurations or sequences that would have
led me to predict that combined they would give rise to something like
my conscious experience.

So arguments that start from here aren’t convincing to me in the least.

>> You’re saying: “Hey, look at all the great things I can do with
>> representation! What if I represented myself in some way??? Would
>> that be me?”
>>
>> Well...no. That would be a representation of you.
>
> How are you defining the person in this case? Different functionally
> equivalent representations of you would be as conscious as you are now,
> would they not?
>
>>
>> Representation is
>> something you do, not something that you are.
>
> If by representation you mean the representation of consciousness, then this
> is the functionalist/computationalist philosophy in a nutshell.

Computationalism says that representation *is* something you are.

I say the opposite. Representation is something you do, which is so
natural to you and so useful to you that you’ve mistaken it as the
explanation for everything.

When all you have is a hammer, everything looks like a nail.

That’s your mistake, in a nutshell.

>>>> But, ultimately, what is computation?
>>>>
>>>
>>> A process. More specifically one that connects a succession of
>>> states via some well-defined relation(s).
>>
>> So why would a process that connects a succession of states via
>> well-defined relations - in addition to being that - *also* be my
>> conscious experience of sitting in this chair drinking coffee, writing
>> this email?
>
> Because as you said, you need something to impart meaning to the bits, and
> that requires well defined relations which indicate meaning of the bits to
> the overall process. While you can look at any bit string and say it means
> this, you cannot look at a program which is calculating Pi and say it is
> calculating e.
>
>>
>> Why would that be? Why would this process be *two* things instead of
>> just one? Not interpretable as two things (by me) - but really,
>> intrinsically two entirely different things?
>>
>
> I am not sure what you are asking here. There are third and first person
> perspectives of course, does that mean there are two things?

It’s the same explanatory gap as exists with materialism.

Why should unconscious matter give rise to conscious experience of
red? Zombies seem more plausible.

The same holds with computation. Why should unconscious computation
give rise to the experience of red? Computational Zombies seem more
plausible...the representation of conscious people without real
conscious experience.

There’s nothing in my conception of numbers or relations or
computation or calculation or axioms or rules of inference that would
lead me to predict that combined they would give rise to anything like
my experience.

So arguments that start from here aren’t convincing to me in the least.

Rex

[Russell Standish]

On Mon, Jun 06, 2011 at 04:42:46PM -0400, Rex Allen wrote:
>
> How can any of those questions be approached by conscious entities in
> a deterministic computational framework?
>
> Everything you’ll ever learn, every mistake you’ll ever make, every
> belief you’ll ever have is already locked in.
>
> Your life is “on rails”. Maybe your final destination is good, maybe
> it’s bad - but both the destination and the path to it are static and
> fixed in Platonia.

This is provably false. One of Bruno's important results is
3-determinism implies 1-indeterminism. It is not that hard to get, so
would be worth your while trying to understand.

--

----------------------------------------------------------------------------
Prof Russell Standish Phone 0425 253119 (mobile)
Principal, High Performance Coders
Visiting Professor of Mathematics hpc...@hpcoders.com.au
University of New South Wales http://www.hpcoders.com.au
----------------------------------------------------------------------------

[Rex Allen]

On Mon, Jun 6, 2011 at 6:13 PM, Russell Standish <li...@hpcoders.com.au> wrote:
> On Mon, Jun 06, 2011 at 04:42:46PM -0400, Rex Allen wrote:
>>
>> How can any of those questions be approached by conscious entities in
>> a deterministic computational framework?
>>
>> Everything you’ll ever learn, every mistake you’ll ever make, every
>> belief you’ll ever have is already locked in.
>>
>> Your life is “on rails”.  Maybe your final destination is good, maybe
>> it’s bad - but both the destination and the path to it are static and
>> fixed in Platonia.
>
> This is provably false.

What, exactly, are you claiming is provably false?

> One of Bruno's important results is 3-determinism
> implies 1-indeterminism.

This is sort of anti-climactic after your initial statement.

One of Bruno's important results is that if my future is determined,
in some sense it's not determined "for me" as an individual.

> It is not that hard to get, so would be worth your
> while trying to understand.

I think I understand this already. The whole teleporting
moscow-washington thing, right?

In Platonia, there are many computational paths that branch out from
the current state that represents "me".

Each of these paths looks like a "possible future" from my subjective
standpoint.

But, they're not possible, they're actual. In Platonia, they all
exist. And they do so timelessly...so they're not "futures" they're a
series of "nows".

So, subjectively, I have the "illusion" of an undetermined "future".

But...really, it's determined. Every one of those paths is
objectively actualized.

So how does this prove what I said false? All those static "futures"
are mine. They're all determined. I'm still on rails...it's just
that the rails split in a rather unintuitive way.

Even if we say that what constitutes "me" is a single unbranched
path...this still doesn't make what I said false. I'm one of those
paths, I just don't know which. But ignorance of the future is not
indeterminism. Ignorance of the future is ignorance of the (fully
determined)
future.

Rex

[Russell Standish]

On Mon, Jun 06, 2011 at 06:52:52PM -0400, Rex Allen wrote:
>
> So how does this prove what I said false? All those static "futures"
> are mine. They're all determined. I'm still on rails...it's just
> that the rails split in a rather unintuitive way.

When you use the imagery of "rails", there is no splitting involved -
just a single track going forward. Otherwise there's no point in
having rails.

But it's your analogy, I suppose you're entitled to Humpty Dumpty's defense
("the words mean exactly what I choose them to mean").

>
> Even if we say that what constitutes "me" is a single unbranched
> path...this still doesn't make what I said false. I'm one of those
> paths, I just don't know which. But ignorance of the future is not
> indeterminism. Ignorance of the future is ignorance of the (fully
> determined)
> future.

It is not ignorance, but true indeterminism. Perhaps you haven't
understood the full import yet.

>
> Rex

>
> --
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--

[Rex Allen]

On Mon, Jun 6, 2011 at 7:30 PM, Russell Standish <li...@hpcoders.com.au> wrote:
> Perhaps you haven't understood the full import yet.

I understand. I just don't find your story to be compelling.

[Stephen Paul King]

-----Original Message-----
From: Russell Standish
Sent: Monday, June 06, 2011 7:30 PM
To: everyth...@googlegroups.com
Subject: Re: Mathematical closure of consciousness and computation

On Mon, Jun 06, 2011 at 06:52:52PM -0400, Rex Allen wrote:
>
> So how does this prove what I said false? All those static "futures"
> are mine. They're all determined. I'm still on rails...it's just
> that the rails split in a rather unintuitive way.

When you use the imagery of "rails", there is no splitting involved -
just a single track going forward. Otherwise there's no point in
having rails.

But it's your analogy, I suppose you're entitled to Humpty Dumpty's defense
("the words mean exactly what I choose them to mean").

>
> Even if we say that what constitutes "me" is a single unbranched
> path...this still doesn't make what I said false. I'm one of those
> paths, I just don't know which. But ignorance of the future is not
> indeterminism. Ignorance of the future is ignorance of the (fully
> determined)
> future.

It is not ignorance, but true indeterminism. Perhaps you haven't
understood the full import yet.

>

Hi Russell,

I would like to be sure that I understand your point here. Would you say
that "true determinism", as opposed to "true indeterminism", requires
one-to-one mappings between any two adjoining links in the causal chain of
events, each of which is said to be uniquely determined by its prior?

Onward!

Stephen

[Jason Resch]

On Mon, Jun 6, 2011 at 12:52 PM, Rex Allen <rexall...@gmail.com> wrote:

My basic point is this:

1.  Explanation is subordinate to description.

2.  Description is subordinate to observation.

3.  Observation is subordinate to experience.

4.  And now we want to close the circle by explaining experience.

Rex,

While I don't dispute the validity of the epistemological axioms you start with, I think they are different from mine.  I tend to agree with David Deutsch, who says this of explanation:

"Explanations are inevitably framed partly in terms of things we do not observe directly: atoms and forces ; the interiors of stars and the rotation of galaxies; the past and future; the laws of nature.  The deeper an explanation is, the more remote from immediate experience are the entities to which it must refer.  But these entities are not fictional: on the contrary, they are part of the very fabric of reality."

I see observation as an input to my subjective experience, which informs my mind and enables me to place bets on the probable validity of different theories.  The theories may involve entities I cannot directly observe, and there is no reason I see that it cannot come full circle and inform theories about why I have experiences to begin with. 

Starting from your belief system, which places explanation subordinate to experience, description, and observation, I can see why you have arrived at the beliefs you have, and the only way to escape may be to change your epistemological axioms.

BTW, I just noticed you have the first digits of Pi as part of your e-mail address. :-)

Jason

[Jason Resch]

On Mon, Jun 6, 2011 at 3:42 PM, Rex Allen <rexall...@gmail.com> wrote:

On Sun, Jun 5, 2011 at 8:34 PM, Jason Resch <jason...@gmail.com> wrote:
> On Sun, Jun 5, 2011 at 11:58 AM, Rex Allen <rexall...@gmail.com> wrote:
>> On Sat, Jun 4, 2011 at 4:14 PM, Jason Resch <jason...@gmail.com> wrote:

>>> Perhaps so, perhaps there is only Rex's beliefs.  Perhaps only rex's
>>> beliefs at this exact moment.
>>
>> Not obviously impossible.  Thought not obviously necessitated either.
>>
>> Does the possibility that there are only Jason’s beliefs at this exact
>> moment scare you?
>>
>> Would you prefer it to be otherwise?
>>
>
> It makes the universe much smaller, less varied, less fascinating, etc. to
> believe my current thought is all there is.  It also makes answering any
> questions futile (why does this thought exist?, can I change it?  Am I a
> static thought or an evolving thought?  What determines or controls the
> content of this thought?)  How can any of those questions be approached if
> only thought exists?

How can any of those questions be approached by conscious entities in
a deterministic computational framework?

Everything you’ll ever learn, every mistake you’ll ever make, every
belief you’ll ever have is already locked in.

This is fatalism.  By AR+Comp you will experience all possible experiences, perhaps an infinite number of times (recurring endlessly?).  But this does not mean we are powerless to affect the measure of those experiences.  A simple example: Some think that QM implies that in half the universes they put on the seatbelt and in half the others they don't.  This is not true, if the person is conscientious enough they probably put on the seat belt in >99% of the universes.  That depends entirely on them.  A less safety-concerned individual may have the opposite probabilities.

 

Your life is “on rails”.  Maybe your final destination is good, maybe
it’s bad - but both the destination and the path to it are static and
fixed in Platonia.

Further, nothing about computationalism promises truth or anything
else desirable...or even makes them likely.

In fact, surely lies are far more common than truths in Platonia.
There are few ways to be right, but an infinite number of ways to be
wrong.  If you think you exist in Platonia, then surely you also have
to conclude that nearly everything else you believe is a lie.

What is true in this universe may be false or meaningless in most of the universes, but there might be some things which are true in every universe (such as 2+2 = 4).  If it is true in every universe, even in those having fewer than 4 things to count then by extension they are true even in universes with nothing to count, and correspondingly, would be true even if there was nothing anywhere.  Math is self-existent (I can easily prove to you at least one thing must be self-existent for there to be anything at all) and it is much easier to see how math can be self-existent compared to observable physical universe.

 

***

Computationalism’s answers to the questions you pose are:

Why does this thought exist?  There is no reason except that
computation exists.  Big whoop.

Computationalism (mechanism, functionalism) is a theory of mind, which I believe is superior to its contenders (immaterialism, interactionalist dualism, epiphenominalism, biological naturalism, mind-brain identity theory, etc.) which all have big flaws.  While immaterialism cannot be disproved, it explains nothing and therefore fails as an explanatory or scientific theory.  It

 

Can I change it?  No.

Then why bother to get food when you are hungry?

 

Am I a static or evolving thought?  Neither.  Your are computation.

What determines or controls the content of this thought?  The brute
fact of computational structure.

***

Why did your momma love you?  It was computationally entailed.

Why did Jeffry Dahlmer kill those people?  It was computationally entailed.

Why 9/11, Auschwitz, AIDS, famine, bigotry, hate, suffering?  They are
computationally entailed.

This is just reductionism taken beyond the level where it should be taken.  You might as well answer: It is physically entailed, chemically entailed, biologically entailed, etc.  I don't see the point of the argument.

 

Platonia actually sounds like more hell than heaven.

You base that on the small part of Platonia you have seen in your decades as a human on this remote planet floating through an infinitesimal part of the universe.  Perhaps life in other alien civilizations is comparatively a heaven.

 

SO...what is it that computationalism gives you over solipsism,
exactly?  What makes this picture more varied, more fascinating, less
futile?

It answers questions which cannot be answered correctly with other theories of mind.  Given what I know, it is the theory of mind I would wager on as correct above the others I know about.

 

I’m not saying you’re position is worse than mine, but surely it’s no better.

>>> What is the engine providing the computations which drive the universe?
>>
>> That assumes that computations do drive the universe.
>>
>> Which is the assumption that I’m questioning.
>
> The physical universe may be computational or it may be a mathematical
> structure, but what enforces its consistency and constancy of its laws?  If
> it were a mathematical structure, or a computation then the consistency
> comes for free.

But doesn’t computationalism predict that their should be conscious
entities whose experience is of inconsistent, contradictory, shifting
laws?

We went over this a few months ago without ever reaching an agreement.  Surely there are some, but I think such universes occur less frequently and/or preclude conscious life forms from evolving.  You said they would occur more frequently because there are more unique descriptions (given the fact that they are longer and there are more possibilities the longer a string is).

 

In fact, this sounds like the experiences described by schizophrenics,
or people on drugs.

And people have those experiences.

 

In fact, I would think that Platonia should contain far more chaotic
experiences than not.

If consciousness = awareness of random bit strings chosen from Platonia I would agree, but if consciousness involves computation, it seems chaotic programs harder to come by.  You would need a stable platform for the program to run long enough to compute a thought, but somehow the input to that program would have to be noise.  A chaotic experience requires a not-fully chaotic mind to have the experience.  Otherwise you might say the air molecules bouncing around your room constitute a chaotic experience.

 

So this virtue that you highlight isn’t a virtue at all.

The idea that “oh, those all cancel out when we average across all
computations” or something is pretty ad hoc sounding.

You’ve lost whatever intuitive appeal that computationalism had in
fell swoop.  We’re back to, “why would that result in conscious
experience if non-averaged computation didn’t???”

It just does?  Pah.

I don't think I ever made an argument about cancelling out or averaging out.

 

>>> Do you think pi has an objective (not human invented or approximated)
>>> value,
>>> whether or not any person computed it?
>>
>> I think that everyone who starts from the same assumptions and makes
>> the same inferences will always reach the same conclusions regarding
>> the value of pi.
>>
>
> So that would make pi an objectively studiable object, would it not?

Everyone who starts with the same assumptions about the Incredible
Hulk and Spiderman, and makes the same inferences from those
assumptions, will reach the same conclusions regarding the outcome of
an arm-wrestling match between them.

Does that make Spiderman objectively studiable?

>What makes the study of such objects less valid than the study of
> other objects in science, for example in biology?

I’m not saying it’s less valid.  It’s equally valid.  But that’s
saying less than you think.

Okay, this makes sense given your solipism/immaterialism.

 

> To define a bacterium as a life form
> Earth scientists and alien scientists both have to start from similar
> assumptions and make similar inferences.  Based on different starting
> assumptions some might say a virus is alive others may not, this doesn't
> mean that viruses don't exist.  In your postings you seem to suggest that
> given there could be disagreement on what starting assumptions to use the
> reality of mathematical objects should be called into question, but this
> would be like questioning whether viruses exist because biologists can't
> agree on whether or not they are alive.  The numbers, their properties and
> relations are objectively studiable, as much as planets and viruses are.  If
> math is invented, then you should invent a prime number with a billion
> digits and claim the $250,000 prize ( http://www.eff.org/awards/coop ).  If
> you cannot invent such a number, then perhaps mathematics truly is a space
> to be explored, much like the vacuum that surrounds our planet.

Instead, maybe I should just write a fantasy book about a boy wizard
to goes to a magical school - and then people who find such things
interesting would give me millions and millions of dollars!

Oh wait...maybe I can’t invent such a book, because I’m not a very
good writer, and people don’t find the structure of my fantasies
compelling or believable or interesting or useful.  Rats.

My point was that mathematics has its own rules, it is not something where anyone can add their own arbitrary axioms as they see fit.  For example, if you generated a 1 followed by 999,999,999 zeros and declared it an axiom that the number is prime, you would not be awarded the prize.  (This would be inventing math, rather than searching for and finding such a prime).

 

Well, according to you I shouldn’t feel bad.  My failure was entailed
by the computational structure of Platonia.  My efforts to achieve
success were...futile.

Who determines what song you choose to listen to on the radio (or music player), you or the atoms bouncing around in your brain?  As thinking beings we have a will which we can exercise.  Don't let deterministic or non-deterministic theories of the universe tell you otherwise.

 

>> I’ll say that relative to some framework that includes my experience
>> with the assumptions and inferences and rules needed to calculate pi -
>> the answer is yes.  Because in that framework, given enough time and
>> enough “universe”, it seems likely that someone *could* calculate the
>> googleplexth digit of pi.
>
> So the value is there, waiting to be found (even though no one has bothered
> to go through the motions to compute it)?

No - as with whether the penny would have melted had I done something
yesterday, there is no fact of the matter.

As with the outcome of the Hulk-Spiderman armwrestling match - it can
only be judged relative to some story that we tell ourselves.  Some
people will tell one story, but there’s nothing to stop someone else
from telling a different story.

We might say:  but that’s inconsistent!

Or:  I don’t agree with your assumptions!

OR:  I think you made the wrong inference there!

BUT...it’s just a story.  There’s no absolute against which to judge
these stories, and so there can be no matters of fact except relative
to the stories.

So ultimately, where do these stories come from?

 

Which is not to say that we get to decide our own paths - we are
characters, not authors.

(metaphorically speaking)

>> There is no fact of the matter except relative to the framework.
>>
>> It’s like asking “who would win an arm wrestling match between the
>> Incredible Hulk and Spiderman”.  I can confidently say the Incredible
>> Hulk.  But that answer doesn’t really mean anything outside of the
>> “Marvel Universe”.  The Marvel Universe has no metaphysical
>> significance, and so my answer to this hypothetical question involving
>> it has no metaphysical significance either.
>>
>> See?
>>
>
> Unlike the marvel universe, if mathematical objects exist it is of huge
> metaphysical significance, as it makes so called physical universes
> redundant and completely unnecessary for explaining observations.

You don’t think it would be of huge metaphysical significance if the
marvel universe were to exist?  Seems like it would raise a few
eyebrows...

We wouldn't see it if it did exist.  The consequences of its existence are therefore much less important.

 

>> Information is a difference that makes a difference.  But it has to
>> make a difference *to* someone.
>>
>
> This is why the consciousness requires a process accepting or operating on
> information.  If a process is not defined there can be no interpretation.

“Process” is just a label for a certain way of thinking about things.
It’s a mental construct.

You’re trying to hypostatize a product of human thought.  And in fact,
explain human thought in terms of something that only exists within
human thought.

You’ve got it all backwards.

>> A randomly generated string of bits can be identical to a string of
>> bits representing an image...but the randomly generated string of bits
>> contain no real information whereas the image file does.
>>
>> The difference being that I know how to correctly interpret an image
>> file, but there is no “correct” interpretation of a random string of
>> bits.
>>
>> But with the right “interpretation” any information can be found
>> anywhere.  The magic is all in the interpreter, not in what’s being
>> interpreted.
>>
>> Information is observer-relative.  Observers aren’t information-relative.
>>
>
> Are you a computationalist?  This line of thought sounds like you are..

No.  Information is something that observers have.  Observers are not
something that information has.

I agree.  Observers are aware of information, and that makes them conscious.  You say observers interpret information.  Well explain what you mean precisely by interpret.

I define interpretation as a system which may enter one of multiple states based on that information (information processing).  This is different from information travelling through some pipe.  The atomic elements of computation compare and contrast information through logical operations AND, OR, NOT, etc.

There is only so much that can be done with information.  Whatever your interpreter does with it, can be replicated by an appropriately programmed Turing machine.  Therefore while not all computations may be conscious, if consciousness involves processing or interpreting information in some way, then a computer can replicate that process.

Lightly press on the back of your hand with your finger and spend a few minutes concentrating on the qualia of that experience.  What more can you describe it as beyond the awareness of information?  More complex qualia, such as vision are certainly far more complex and difficult to explain (if you are interested in delving into this I will attempt to do so), but once you can explain a basic qualia such as the experience of touch, the mysteriousness of them goes away.

Your brain contains information received by the senses, it is a system which can enter many different states based on that information (it interprets it).  One of those states is your brain thinking about the fact that it knows it is touching the back of your hand with one of your fingers (that may represent only a few bits of information), now consider that your brain has 100,000,000,000 neurons and you can begin to see that more complex qualia such as vision involve vastly greater amounts of information (some 30% of your cortex is devoted to processing visual information).  Together with the modularity of mind (different sections are specialized and compute different things, and share the results with other brain regions), you can begin to see why qualia such as Red or Green are so hard to explain.  Consider Google's self-driving cars.  They need to determine whether the stop light is Yellow, Red or Green.  The cameras collect many MB worth of raw R,G,B data per second which is processed by a specialized function which determines the state of the stop light.  The result Red, Green, or Yellow is transmitted to other parts of the driving software, for example the parts which control acceleration.  This part of the software knows there is a difference between "Light is Red" vs. "Light is Green", but it cannot say how they are different or why it knows they are different (this was decided elsewhere).  It is much like the verbal section of your brain trying to articulate the difference between red and green, it knows they are different but cannot say how.  It does now have access to the raw data received from the millions of cones in your retina.

 

So arguments that start from here aren’t convincing to me in the least.

>> You’re saying:  “Hey, look at all the great things I can do with
>> representation!  What if I represented myself in some way???  Would
>> that be me?”
>>
>> Well...no.  That would be a representation of you.
>
> How are you defining the person in this case?  Different functionally
> equivalent representations of you would be as conscious as you are now,
> would they not?
>
>>
>> Representation is
>> something you do, not something that you are.
>
> If by representation you mean the representation of consciousness, then this
> is the functionalist/computationalist philosophy in a nutshell.

Computationalism says that representation *is* something you are.

I say the opposite.  Representation is something you do, which is so
natural to you and so useful to you that you’ve mistaken it as the
explanation for everything.

You should read this http://en.wikipedia.org/wiki/Functionalism_(philosophy_of_mind)

Functionalism is the idea that it is what the parts do, not what they are that is important in a mind.

Computatalism is a more specific form of functionalism (it assumes the functions are Turing emulable)

What is your background?  Perhaps knowing that we could communicate more clearly or choose better examples.  I am a computer programmer, with interests in cryptography which involves some number theory.

Jason

[Richard Ruquist]

Rex,

 

Is not what you attribute to Bruno just standard MWI (Many Worlds) thinking?

Richard

[Rex Allen]

On Mon, Jun 6, 2011 at 10:00 PM, Jason Resch <jason...@gmail.com> wrote:
> On Mon, Jun 6, 2011 at 3:42 PM, Rex Allen <rexall...@gmail.com> wrote:
>> How can any of those questions be approached by conscious entities in
>> a deterministic computational framework?
>>
>> Everything you’ll ever learn, every mistake you’ll ever make, every
>> belief you’ll ever have is already locked in.
>
> This is fatalism.  By AR+Comp you will experience all possible experiences,
> perhaps an infinite number of times (recurring endlessly?).  But this does
> not mean we are powerless to affect the measure of those experiences.  A
> simple example: Some think that QM implies that in half the universes they
> put on the seatbelt and in half the others they don't.  This is not true, if
> the person is conscientious enough they probably put on the seat belt in
>>99% of the universes.  That depends entirely on them.  A
> less safety-concerned individual may have the opposite probabilities.

If the evolution of the universal wavefunction is deterministic, then
it doesn't depend entirely on them...it depends entirely on the
universal wavefunction.

How could it depend entirely on them - using "depend" and "them" in
the usual senses of the words? You're not surreptitiousness using
"non-standard" definitions of words without making that explicit, are
you?

Once the initial state of the wavefunction are fixed and the rules
that determine its evolution are fixed - then everything else,
including seatbelt usage, is also fixed.

If anything depends on anything, *everything* depends on the initial
state and the rules that "govern" (describe?) how the state changes.

In your example, they don't put on their seatbelt 99% of the time
*because* they are conscientious - rather, they are labeled
"conscientious" because they put on their seatbelt 99% of the time.

See how the arrow is reversed there?

>> Your life is “on rails”.  Maybe your final destination is good, maybe
>> it’s bad - but both the destination and the path to it are static and
>> fixed in Platonia.
>>
>> Further, nothing about computationalism promises truth or anything
>> else desirable...or even makes them likely.
>>
>> In fact, surely lies are far more common than truths in Platonia.
>> There are few ways to be right, but an infinite number of ways to be
>> wrong.  If you think you exist in Platonia, then surely you also have
>> to conclude that nearly everything else you believe is a lie.
>
>
> What is true in this universe may be false or meaningless in most of the
> universes, but there might be some things which are true in every universe
> (such as 2+2 = 4).

It seems conceivable to me that you might have trouble convincing the
inhabitants of every (or even most) universes of that, even by appeal
to experience.

Just set up the initial conditions correctly, and the state changes
correctly, and viola! A whole universe of people who have funky
beliefs that are reinforced by experience at every check. Or are
contradicted, but the contradictions as misinterpreted as
confirmations.

Maybe that's us...

Maybe my imagination is more vivid, or my checks on it less stringent.

Have you tried imagining such a thing? Living in such a universe?

As a spur to imagination: Have you read Jonathan Strange and Mr.
Norrell? The role of madness? The gentleman with thistle-down hair?

> (I can easily prove to you at least one thing must be
> self-existent for there to be anything at all)

Conscious experience.

>>
>> Can I change it?  No.
>
> Then why bother to get food when you are hungry?

It's entailed by the brute computational structure of Platonia, I assume.

>> Why 9/11, Auschwitz, AIDS, famine, bigotry, hate, suffering?  They are
>> computationally entailed.
>
> This is just reductionism taken beyond the level where it should be taken.
>  You might as well answer: It is physically entailed, chemically entailed,
> biologically entailed, etc.  I don't see the point of the argument.

Hmmmm...I don't see how you could miss the point of the argument...?

See above on seat-belts.

>> Platonia actually sounds like more hell than heaven.
>
> You base that on the small part of Platonia you have seen in your decades as
> a human on this remote planet floating through an infinitesimal part of the
> universe.  Perhaps life in other alien civilizations is comparatively a
> heaven.

Actually I would tend to think that the number of hedonists and
masochists in Platonia would balance each other. For every entity
that loves pleasure, there's another who loves pain. Just flip a few
bits, and there you have it - heaven transformed into hell, or vice
versa.

>> Oh wait...maybe I can’t invent such a book, because I’m not a very
>> good writer, and people don’t find the structure of my fantasies
>> compelling or believable or interesting or useful.  Rats.
>
> My point was that mathematics has its own rules, it is not something where
> anyone can add their own arbitrary axioms as they see fit.

I would tend that good fiction also has its own rules. At least
fiction that would be considered "good" by some particular audience.

>> Well, according to you I shouldn’t feel bad.  My failure was entailed
>> by the computational structure of Platonia.  My efforts to achieve
>> success were...futile.
>>
>
> Who determines what song you choose to listen to on the radio (or music
> player), you or the atoms bouncing around in your brain?

Neither. I'd say it's purely contingent. Not determined by anything.

> As thinking beings
> we have a will which we can exercise.  Don't let deterministic or
> non-deterministic theories of the universe tell you otherwise.

Ya, I don't see how that could be.

>> BUT...it’s just a story.  There’s no absolute against which to judge
>> these stories, and so there can be no matters of fact except relative
>> to the stories.
>
> So ultimately, where do these stories come from?

Nowhere. They're purely contingent. Without any reason or
explanation whatsoever.

>> No.  Information is something that observers have.  Observers are not
>> something that information has.
>
> I agree.  Observers are aware of information, and that makes them conscious.
>  You say observers interpret information.  Well explain what you
> mean precisely by interpret.

I take interpret to mean "experience as meaningful". Which doesn't
mean that it *is* meaningful...just that it's experienced that way.

I could go a little further and add "experienced as meaningful in a
way that connects to other beliefs."

Though I'm not sure that's necessary.

> I define interpretation as a system which may enter one of multiple states
> based on that information (information processing).  This is different from
> information travelling through some pipe.  The atomic elements of
> computation compare and contrast information through logical operations AND,
> OR, NOT, etc.
> There is only so much that can be done with information.  Whatever your
> interpreter does with it, can be replicated by an appropriately programmed
> Turing machine.

An appropriately programmed Turing machine can experience information
as meaningful?

It could possibly interpreted as doing this...but given that there's
not much to a Turing machine, I'd have my doubts as to whether this
was actually the case.

So, I take experience as fundamental, and work my way out from there.

I'm not starting with an abstract concept like computation and trying
to work my way *back*.

Computation is just a way of looking at things, a way of thinking
about things. It's not a thing in itself.

>> Our positions are mirror images.
>>
>> Reverse the arrow of explanation, and you’ve got it!

This still seems to be the case to me.

>> But this doesn’t make much sense to me.  There’s nothing in my
>> conception of particles or configurations or sequences that would have
>> led me to predict that combined they would give rise to something like
>> my conscious experience.
>
> Lightly press on the back of your hand with your finger and spend a few
> minutes concentrating on the qualia of that experience.  What more can you
> describe it as beyond the awareness of information?

Consciousness experience is fundamental. Fundamental concepts can’t
be described in terms of anything else..they’re fundamental.

This is why you can’t explain “red” to a blind person. It’s a
fundamental concept. If you don’t have it, it can’t be transmitted to
you or explained to you, because it can’t be “built up” from more
basic concepts.

What do we mean by “communicating information”? When we use a word,
it just picks out an idea or a thought that exists in your mind. For
instance, out of all of the concepts that humans are capable of
thinking, the word “Red” picks out one of them. But nothing of the
experience of redness that is conveyed by the word “Red”. Just like
there is nothing of the idea of two-ness conveyed by the word “two”.
You already have to know about “two” to correctly interpret the word.

No fundamental concepts are ever communicated via words.

Let’s say I tell you, “I have a red cube that is 2 inches on a side.”
To understand that message, you must already have the fundamental
concepts of redness and of spatial distance and dimension and be able
to map the words I’m using to those concepts.

Note however, that the concept of a “cube” is obviously not
fundamental…but fully grasping its meaning requires possession of the
fundamental concepts of spatial distance and dimension.

So, I can communicate the meaning of “cube” to you because it isn’t a
fundamental concept…it’s defined in terms of spatial dimensions.
However, I cannot communicate the meaning of “space” or “color” or
“emotion” to someone who has no subjective experience of those
concepts, because they are fundamental.

*That* is why qualia are ineffable.

Ya?

>> I say the opposite.  Representation is something you do, which is so
>> natural to you and so useful to you that you’ve mistaken it as the
>> explanation for everything.
>
>
> You should read
> this http://en.wikipedia.org/wiki/Functionalism_(philosophy_of_mind)
> Functionalism is the idea that it is what the parts do, not what they are
> that is important in a mind.
> Computatalism is a more specific form of functionalism (it assumes the
> functions are Turing emulable)

I've read that article before. I used to be a computationalist. BUT,
like Hilary Putnam, I moved on.

> What is your background?  Perhaps knowing that we could communicate more
> clearly or choose better examples.  I am a computer programmer, with
> interests in cryptography which involves some number theory.

I'm a computer programmer also. Have been for about 18 years now.

Bachelor's degree in computer systems engineering. Two years of
graduate school...nothing to show for it...blah.

So, again, you don't have to work too hard to explain the basics of
computationalism to me, I had a layover there for several years.
Which doesn't mean I know everything about it, but I know something.

A key part of my move away from it was realizing that it didn't close
the Chalmersian explanatory gap.

And also, this thought: "Hey, if computations can exist platonically
and cause conscious experience...why can't conscious experience just
exist platonically itself, without the need for any underlying causal
structure???"

Beyond platonic logical structures, why not other platonic
abstractions...why not purely contingent structures?

Rex

[Colin Hales]

Hi,

Hales, C. G. 'On the Status of Computationalism as a Law of Nature',
International Journal of Machine Consciousness vol. 3, no. 1, 2011. 1-35.

http://dx.doi.org/10.1142/S1793843011000613

The paper has finally been published. Phew what an epic!

cheers

Colin

[Stephen Paul King]

Hi Colin,

Any chance that us non-university affiliated types can get a copy of
your paper?

Onward!

Stephen

Hi,

http://dx.doi.org/10.1142/S1793843011000613

cheers

Colin

--

[Bruno Marchal]

This is an argument against any determinist theory, or any block-
universe theory. It is an argument again compatibilist theory of free
will, and an argument against science in general, not just the
mechanist hypothesis.

Just to make things clear, although I have not yet seen an evidence
against digital mechanism, my point is just that IF mechanism is true
then the physical reality is an arithmetical emerging phenomenon, and
physics is a branch of machine's theology. Given that theology and
physics is derivable by the self-reference logic, my point is that
mechanism is Popper refutable.

Now anyone pretending that comp (digital mechanism) is false has to
say what is not Turing emulable in their (generalized) brain, above
its constitutive matter and its consciousness, which comp makes
already non Turing emulable, or they have to prove that nature refute
the physics of comp (but up to now, thanks to QM, it is much more
confirmed than refuted).

Bruno

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

[Bruno Marchal]

I guess you mean some sort of "spiritualism" for immaterialism, which is a consequence of comp (+ some Occam). Especially that you already defend the idea that the computations are in (arithmetical) platonia.

Note that AR is part of comp. And the UD is the Universal dovetailer. (UDA is the argument that comp makes elementary arithmetic, or any sigma_1 complete theory, the theory of everything. Quanta and qualia are justified from inside, including their incommunicability.

 

Can I change it?  No.

Then why bother to get food when you are hungry?

 

Am I a static or evolving thought?  Neither.  Your are computation.

What determines or controls the content of this thought?  The brute
fact of computational structure.

***

Why did your momma love you?  It was computationally entailed.

Why did Jeffry Dahlmer kill those people?  It was computationally entailed.

Why 9/11, Auschwitz, AIDS, famine, bigotry, hate, suffering?  They are
computationally entailed.

This is just reductionism taken beyond the level where it should be taken.  You might as well answer: It is physically entailed, chemically entailed, biologically entailed, etc.  I don't see the point of the argument.

Neither do I. Nor do I see what Rex is proposing, except perhaps abandoning research, meditating or what?

 

Platonia actually sounds like more hell than heaven.

You base that on the small part of Platonia you have seen in your decades as a human on this remote planet floating through an infinitesimal part of the universe.  Perhaps life in other alien civilizations is comparatively a heaven.

 

SO...what is it that computationalism gives you over solipsism,
exactly?  What makes this picture more varied, more fascinating, less
futile?

It answers questions which cannot be answered correctly with other theories of mind.  Given what I know, it is the theory of mind I would wager on as correct above the others I know about.

OK. To my knowledge it is the only one which explains today where quanta and qualia comes from, and why they seem so different.  It is also a theory which cure psychology (and science) from reductionism. It makes us modest.

 

I’m not saying you’re position is worse than mine, but surely it’s no better.

>>> What is the engine providing the computations which drive the universe?
>>
>> That assumes that computations do drive the universe.
>>
>> Which is the assumption that I’m questioning.
>
> The physical universe may be computational or it may be a mathematical
> structure, but what enforces its consistency and constancy of its laws?  If
> it were a mathematical structure, or a computation then the consistency
> comes for free.

But doesn’t computationalism predict that their should be conscious
entities whose experience is of inconsistent, contradictory, shifting
laws?

We went over this a few months ago without ever reaching an agreement.  Surely there are some, but I think such universes occur less frequently and/or preclude conscious life forms from evolving.  You said they would occur more frequently because there are more unique descriptions (given the fact that they are longer and there are more possibilities the longer a string is).

It is the same argument than Peter (1Z). They are too much white rabbits. That is a good argument, if only they could prove it. But in their short presentation of the argument, they clearly don't take into account computer science and the self-reference logic of the machines, and so confuse first and third person points of view. They also seems to put a measure on strings instead of computations and (maximally) consistent extensions.

 

In fact, this sounds like the experiences described by schizophrenics,
or people on drugs.

And people have those experiences.

 

In fact, I would think that Platonia should contain far more chaotic
experiences than not.

If consciousness = awareness of random bit strings chosen from Platonia I would agree, but if consciousness involves computation, it seems chaotic programs harder to come by.  

Indeed. They become plausibly relatively rare.

I would like to insist that comp leads to immaterialism, but that this is very different from solipsism. Both are idealism, but solipsism is "I am dreaming", where comp immaterialism is "all numbers are dreaming", and a real sharable physical reality emerges from gluing properties of those dreams/computations.

 

> To define a bacterium as a life form
> Earth scientists and alien scientists both have to start from similar
> assumptions and make similar inferences.  Based on different starting
> assumptions some might say a virus is alive others may not, this doesn't
> mean that viruses don't exist.  In your postings you seem to suggest that
> given there could be disagreement on what starting assumptions to use the
> reality of mathematical objects should be called into question, but this
> would be like questioning whether viruses exist because biologists can't
> agree on whether or not they are alive.  The numbers, their properties and
> relations are objectively studiable, as much as planets and viruses are.  If
> math is invented, then you should invent a prime number with a billion
> digits and claim the $250,000 prize ( http://www.eff.org/awards/coop ).  If
> you cannot invent such a number, then perhaps mathematics truly is a space
> to be explored, much like the vacuum that surrounds our planet.

Instead, maybe I should just write a fantasy book about a boy wizard
to goes to a magical school - and then people who find such things
interesting would give me millions and millions of dollars!

Oh wait...maybe I can’t invent such a book, because I’m not a very
good writer, and people don’t find the structure of my fantasies
compelling or believable or interesting or useful.  Rats.

My point was that mathematics has its own rules, it is not something where anyone can add their own arbitrary axioms as they see fit.  For example, if you generated a 1 followed by 999,999,999 zeros and declared it an axiom that the number is prime, you would not be awarded the prize.  (This would be inventing math, rather than searching for and finding such a prime).

Good argument.

 

Well, according to you I shouldn’t feel bad.  My failure was entailed
by the computational structure of Platonia.  My efforts to achieve
success were...futile.

Who determines what song you choose to listen to on the radio (or music player), you or the atoms bouncing around in your brain?  As thinking beings we have a will which we can exercise.  Don't let deterministic or non-deterministic theories of the universe tell you otherwise.

I agree. Rex is confusing levels of description.

<snip: I have nothing to comment>

>
> If by representation you mean the representation of consciousness, then this
> is the functionalist/computationalist philosophy in a nutshell.

Computationalism says that representation *is* something you are.

I say the opposite.  Representation is something you do, which is so
natural to you and so useful to you that you’ve mistaken it as the
explanation for everything.

You should read this http://en.wikipedia.org/wiki/Functionalism_(philosophy_of_mind)

Functionalism is the idea that it is what the parts do, not what they are that is important in a mind.

Computatalism is a more specific form of functionalism (it assumes the functions are Turing emulable)

I disagree with this. Putnam' functionalism is at the start a fuzzy form of computationalism (the wiki is rather bad on those subjects). It is fuzzy because it is not aware that IF we are machine, then we cannot know which machine we are. That is why it is a theology, you need an act of faith beyond just trusting the 'doctor'. In a sense functionalism is a specific form of computationalism because functionalist assumes by default some high level of comp. They are just fuzzy on the term "function", and seems unaware of the tremendous progress made on this by logicians and theoretical computer scientists. 

Note also that comp makes *1-you* different from any representation, from you first person perspective. So, the owner of the soul is the (immaterial) person, not the body. A body is already a representation of you, relatively to some universal numbers.

In a sense we can sum up comp's consequence by: If 3-I is a machine, then 1-I is not. The soul is not a machine *from its point of view". He has to bet on its own G* to say 'yes' to the doctor. Of course, once we accept comp, we can retrospectively imagine that "nature" has already bet on it, given that the genome is digital relatively to chemistry, and given the evidences for evolution, and our very deep history.

Bruno

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

[Bruno Marchal]

On 07 Jun 2011, at 05:58, Richard Ruquist wrote:

Rex,

 

Is not what you attribute to Bruno just standard MWI (Many Worlds) thinking?

Many Worlds usually assumes the existence of (a) physical world(s).

The point is that digital mechanism *entails* already a testable form of many-worlds/many-dreams/many-computations. And there is nothing physical at the start. Physicalness is a quite special emerging pattern. Like with Plato, the physical reality is the border/shadow of something else. With comp, the physical reality is the border of arithmetical truth as seen by the (locally) arithmetical creatures. The first person is distributed on that border, preventing any intuitive picture of the relationship between soul and body. In fact each soul has a continuum of distinct bodies. So comp indeed leads to a very specific everything-like theory, which is confirmed (not proved!) by the quantum empiric MW.

Bruno

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

[Pete Hughes]

Jason,

I found this compelling, are you saying that the difficulty of explaining qualia is due to the language centre of the brain being able to access only an abstract 'interface' (I'm a object oriented thinker) of the sensors? then what about emotions? I'm trying to pre-empt your response to 'why don't you put your hand in the fire and enjoy the information' and I just can't, I like the way you talk so I will pester you with the question.

"Your brain contains information received by the senses, it is a system which can enter many different states based on that information (it interprets it).  One of those states is your brain thinking about the fact that it knows it is touching the back of your hand with one of your fingers (that may represent only a few bits of information), now consider that your brain has 100,000,000,000 neurons and you can begin to see that more complex qualia such as vision involve vastly greater amounts of information (some 30% of your cortex is devoted to processing visual information).  Together with the modularity of mind (different sections are specialized and compute different things, and share the results with other brain regions), you can begin to see why qualia such as Red or Green are so hard to explain.  Consider Google's self-driving cars.  They need to determine whether the stop light is Yellow, Red or Green.  The cameras collect many MB worth of raw R,G,B data per second which is processed by a specialized function which determines the state of the stop light.  The result Red, Green, or Yellow is transmitted to other parts of the driving software, for example the parts which control acceleration.  This part of the software knows there is a difference between "Light is Red" vs. "Light is Green", but it cannot say how they are different or why it knows they are different (this was decided elsewhere).  It is much like the verbal section of your brain trying to articulate the difference between red and green, it knows they are different but cannot say how.  It does now have access to the raw data received from the millions of cones in your retina."

--

[Jason Resch]

On Tue, Jun 7, 2011 at 5:22 AM, Bruno Marchal <mar...@ulb.ac.be> wrote:

On 07 Jun 2011, at 04:00, Jason Resch wrote:

I guess you mean some sort of "spiritualism" for immaterialism, which is a consequence of comp (+ some Occam). Especially that you already defend the idea that the computations are in (arithmetical) platonia.

Note that AR is part of comp. And the UD is the Universal dovetailer. (UDA is the argument that comp makes elementary arithmetic, or any sigma_1 complete theory, the theory of everything. Quanta and qualia are justified from inside, including their incommunicability.

By immaterialism I mean the type espoused by George Berkeley, which is more accurately described as subjective idealism: http://en.wikipedia.org/wiki/Immaterialism

I think it is accurate to call it is a form of spiritualism.

Okay, this makes sense given your solipism/immaterialism.

I would like to insist that comp leads to immaterialism, but that this is very different from solipsism. Both are idealism, but solipsism is "I am dreaming", where comp immaterialism is "all numbers are dreaming", and a real sharable physical reality emerges from gluing properties of those dreams/computations.

You are right, I should find a less general term.  It is the missing of the glue I think that differentiates the immaterialism of comp from the immaterialism of Berkely.

 

>
> If by representation you mean the representation of consciousness, then this
> is the functionalist/computationalist philosophy in a nutshell.

Computationalism says that representation *is* something you are.

I say the opposite.  Representation is something you do, which is so
natural to you and so useful to you that you’ve mistaken it as the
explanation for everything.

You should read this http://en.wikipedia.org/wiki/Functionalism_(philosophy_of_mind)

Functionalism is the idea that it is what the parts do, not what they are that is important in a mind.

Computatalism is a more specific form of functionalism (it assumes the functions are Turing emulable)

I disagree with this. Putnam' functionalism is at the start a fuzzy form of computationalism (the wiki is rather bad on those subjects). It is fuzzy because it is not aware that IF we are machine, then we cannot know which machine we are. That is why it is a theology, you need an act of faith beyond just trusting the 'doctor'. In a sense functionalism is a specific form of computationalism because functionalist assumes by default some high level of comp. They are just fuzzy on the term "function", and seems unaware of the tremendous progress made on this by logicians and theoretical computer scientists. 

Note also that comp makes *1-you* different from any representation, from you first person perspective. So, the owner of the soul is the (immaterial) person, not the body. A body is already a representation of you, relatively to some universal numbers.

In a sense we can sum up comp's consequence by: If 3-I is a machine, then 1-I is not. The soul is not a machine *from its point of view". He has to bet on its own G* to say 'yes' to the doctor. Of course, once we accept comp, we can retrospectively imagine that "nature" has already bet on it, given that the genome is digital relatively to chemistry, and given the evidences for evolution, and our very deep history.

Bruno

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

[Stephen Paul King]

Dear Bruno,

 

From: Bruno Marchal

Sent: Monday, June 06, 2011 9:00 AM

To: everyth...@googlegroups.com

Subject: Re: Mathematical closure of consciousness and computation

Hi Stephen,

 

On 06 Jun 2011, at 05:27, Stephen Paul King wrote:

Hi Bruno, Rex and Friends,

 

    My .002$...

[BM]

No theories nor machine can reach all arithmetical truth, but few 

people doubt that closed arithmetical propositions are either true or 

false. We do share a common intuition on the nature of arithmetical 

truth.

I have doubt on any notion of global mathematical truth. Sets, real 

numbers, complex numbers, etc. are simplifications of the natural 

numbers. They are convenient fictions, I think. If we are machine, it 

is undecidable if ontology is more than N.

 

 

[SPK]

   

    I think that there is some differences in opinion about this but it seems to me that we need to look at some details. For example, there should exist a theory that could reach all arithmetic truth given an eternity of time or an unnamable number of recursions or steps.

[BM]

?

 

No this cannot exist. It is precluded by the incompleteness theorem. Eternity can't help. Unless you take a non axiomatisable theory, or some God-like entities.

 

[SPK]

 

    Yes, you are correct. I miswrote. I had even developed an informal proof of this in my critique of Leibniz’ Monadology. But this still presents a challenge.. Umm, maybe this is where Cantor et al considered this idea in terms of unnamable cardinals...

**

 

 

This by definition would put them forever beyond human (finite entity) comprehension. Whether or not there is closure or a closed form of some theory does not make it realistic or not. AFAIK, closed arithmetic propositions are tautologies, no?

[BM]

They are not tautologies, unless you mean by this "propositions true in *all* models of Peano Arithmetic. But then "tautology" means "theorem", and that would be an awkward terminology. Ax(0 ≠ s(x)) is not a tautology (it is already false in (Z,+), nor is Fermat last theorem.

 

[SPK]

    Yes, I did mean it that way, as in “propositions that are true in *all* models” but not just of Peano Arithmetic. I was considering all Arithmetics, especially Robinson’s. Usually one thinks of tautologies as A = A. What I am trying to weaken is the way that the so called law of identity is usually defined. I am working toward a notion of equivalence that allows for not just strict equality but a more general notion of “bisimilarity”. In this way theorems would be tautologies in this weaker form of Identity.

**

 

That we share a common intuition of truth may follow from a common local measure of truth within each of us. (Here the "inside" implied by the word "within" is the logical/Arithmetic/abstract aspect of the duality that I propose.)

    Additionally, we should be careful not to conflate a plurality of fungible individuals with a multiplicity of non-fungible entities. We can set up a mental hall of mirrors and generate an infinite number of self-images in it, but this cannot *exactly* map to all of the selves that could exist without additional methods to break the symmetries.

 

    I have been waiting a long time for you to state this belief of yours, Bruno! That "Sets, real  numbers, complex numbers, etc." are simplifications of (mappings on/in?) the Natural Numbers. This seems to be the Pythagorean doctrine that I suspected that you believed.

[BM]

Would you take the time to study the papers, you would have understood that this is a result of comp. Comp transforms the very banal arithmetical realism in an authentic Pythagorean neoplatonist theology, i.e.  with some use of OCCAM razor.

 

[SPK]

    I am studying the papers, but I need to clarify some ideas by asking questions to the Professor. ;-) I do not think the way you do and must translate your mental language into my own to understand them.

**

 

It has a long history and a lot of apostles that have quite spectacular histories. I think that there is a deep truth in this belief, but I think that it needs to be more closely examined.

[BM]

It can be derived from Church thesis and the assumption that "we" are Turing emulable.

 

[SPK]

    OK, but would you allow me to say that it seems that you are considering a form of Turing emulation that is vastly more sophisticated and subtle than the purely mechanical one that Turing, for example, considered with his A machines? The fact that you are considering infinities of computations as “running” each instance of us, is pushing the idea of a recursive algorithm into places it is never been before.

**

 

>

> Perhaps there is just human belief.

 

[BM]

Jason said it. If you follow that slope you may as well say that there 

is only belief by Rex. You can also decide that there is nothing to 

explain, no theories to find, and go walking in the woods. Science, by 

definition, assumes something beyond (human) belief.

 

[SPK]

   

    I admit that I laughed out loud at this! Good point, Bruno! The reduction of all truth to that which can be defined within a single human's belief trivializes and renders it meaningless. That is one of the absurd consequences that we lambast solipsism for, but I think that Rex should not be to swiftly dismissed form maybe trying to make a deeper observation; he has brought up a very good topic for discussion.

    While it is absurd to reduce all truth to what a single finite entity can "compute" - which is that we are actually saying if we follow the Kleene-Turing-Church-Post road -

 

[BM]

Careful. It can be said that all ontological truth will be generated, but the epistemological truth will never be generated, but they will emerge in a not completely computable way. Remember that arithmetic, seen from inside, is *much* bigger than arithmetic see from outside.

 

[SPK]

    OK, but that poses a difficult problem because it is epistemological truth that we consider as reality! What we “know” to be true, even by the Bp&p definition, is by definition what is “real” of us individually and via consensus, no? I am not understanding what you mean by “arithmetic seen from the outside”. Are you saying that there is more to Existence than numbers? My apologies, I am confused.

**

 

we are actually positing that "all truths can be defined in terms of N -> N mappings".

 

[BM]

That would contradict Gödel's incompleteness. Unless you mean *all* N -> N mappings, which is far to bigger and trivialize the theory (making it non testable, and unable to derive anything in physics, cognitive science, etc.).

 

[SPK]

    Not provable truths, just the ones that we can bet on. Yes, to extend to *all* N->N mappings would be like what we see in superstring theory – the landscape that has almost completely reduced SUSY to a Scholastic type of theory....

**

 

Many such mappings to be sure, but N to N mappings nonetheless. We are back to that strange belief that Bruno explicitly, albeit inadvertently, stated.

    But this is not really a "strange" belief, partly because it seems to be almost universally the default postulate within the basket of beliefs that people operate with in our every day world. I would like to pose the question of whether or not we are inadvertently painting ourselves into a corner with this belief. IT seems to me, and this is just a personal prejudice of mine, that there exists truths that cannot be named or represented exactly in terms of N->N maps.

[BM]

In this context, you should clearly stated if you take all N->N mappings, or the total computable one, or the partial computable one. The non triviality of comp entirely resides in such nuances.

 

[SPK]

    I do not know yet how to do that parse. I am still learning the vocabulary. My apologies.

**

 

The source of this suspicion comes from what I have studied of G. Cantor's work on transfinites and the histrionics of practitioners of mathematical logic that have been examining the nature of cardinalities.

[BM]

With comp, the diagonalization of Kleene gives the information. Cantor's one are far too crude.

 

[SPK]

    What text might you suggest that I study to understand Kleene’s diagonalization? I have only found this paper on the topic: www.columbia.edu/~hg17/naming-diag.pdf

**

 

 

 

Additionally there is my belief that the Totality of Existence must be, at least, Complete (not in the Gödel sense of just 1st order logics), Bicomplete (in the Category theory sense) and Closed (in the topological sense). This implies the existence of unnamable truths, or at least Truths that cannot be exactly represented in terms of recursive functions on the Integers.

 

[BM]

That the totality of existence is complete seems to me to be a tautology, or a truth by definition.

That truth is beyond machine's means, is a theorem.

That truth is beyond us is consequence of such theorem when we assume that we are machines.

 

[SPK]

    Umm, not quite the same idea. I am following the reasoning in these papers: http://arxiv.org/abs/math/0307090 , http://arxiv.org/abs/physics/0212092 and my own ideas formed from studying Category theory. The difficulty that I see in your definitions is that it makes the notion of a machine into something altogether unknowable. People seem to interpret your word machine in the same way that, for example, Descartes considered the idea of automata. I made that mistake myself until I saw that you where not considering the notion of a box full of levers, springs, gears and widgets.

**

 

    The question becomes one of the implications of this on our metaphysical assumptions about the ontologies that we are using in our thinking about the issue of mathematical closure of computation and consciousness. As I see it, and this very well could be just an eccentric thought, is that we need to be very careful that we do not tacitly assume that all of the minds of entities are replicating the same ideas as one’s own. The fact that we are continuously surprised at the responces that we get when we post to this List, for example, should be some indication that we all think differently about things and that when we propose the idea that consciousness is somehow some kind of N->N map or even some string of numbers in ℤ, then we should expect a vigorous response.

[BM]

I agree with this. There is a persisting reductionist conception of numbers and machines. Numbers, already just through the laws of addition and multiplication, transcend a lot what any consistent machines can really prove or even just talk about.

 

[SPK]

    Yes, but it is easy for people to not see the subtle differences that emerge from the stratification of levels that you are considering, as per the 8 hypostases.

**

 

BTW, did you know that ℤ *≅U(1) and  U(1) *≅ℤ  via the Pontryagin duality? Yes, that U(1) that is used in physics ! This is one of many reasons why I think that Bruno is onto something very important in his work! :-)

[BM]

Well, thanks. I wish you get clearly the point someday. You might elaborate on the importance of U(1) ≅  Z.

 

[SPK]

    U(1) is the symmetry group that defines the electromagnetic fields in physics. That it is the Pontryagin dual of the integers is interesting to say the least. The Reals, for example, are their own Pontryagin dual. Did you happen to see the write up by John Baez that I linked there? This is part of the topological aspect that I am studying, the “concrete” side of the abstract ideas that you are studying. ;-)

**

 

[BM]

Do you need someone observing your brain for you to feel something?

Why would the physical UD execution differ?

Indeed, why would the arithmetical UD execution differ?

 

[SPK]

 

    Strangely enough, Bruno, in a way there is something to this idea that we need to consider that someone is watching for us to feel something! If we follow the logic of QM and accept the decoherence idea, the idea that we have a definite (and Boolean representable) state of the brain depends most definitely on the existence of what we can think of as “someone” watching: the rest of the universe.

[SPK]

With decoherence? I guess you meant with "collapse".

 

[SPK]

    There is no such a thing as “collapse” in any 3p sense. let me explain this idea that I am alluding to a bit more. Consider an example of it in the Quatum Zeno effect: http://en.wikipedia.org/wiki/Quantum_Zeno_effect

 

There is a nice quote there from Turing about it:

 

“It is easy to show using standard theory that if a system starts in an eigenstate of some observable, and measurements are made of that observable N times a second, then, even if the state is not a stationary one, the probability that the system will be in the same state after, say, one second, tends to one as N tends to infinity; that is, that continual observations will prevent motion …”

 

    The folkish form of the idea is that everything in the physical world is effectively observing everything else and freezing out its phase entanglement aspects. Nothing is truly in isolation thus the effects of decoherence naturally follow and generate the appearance of a classical world.

**

We can break this down into a large number of mutually communicating observers, but that “someone is watching” has real consequences: it induces the 2 valued definiteness that otherwise would not exist.

[BM]

You lost me.

 

[SPK]

 

    OK, let me loosely explain this. We have a huge number of entities that are sharing information about their observations of the world with each other. This acts to constrain the mutual “reality” that they can consider once we subtract our the errors and misperceptions. When we start off each observer as having a superposition of possible observations that they could make and then constrain then to have to communicate with each other such that the information in their communications is additive and that they have an upper bound on the time and computational resources available to transmit and translate those messages then it makes sense that what results is a bunch of binary approximations. We can approximate analogue signals effectively with binary – digital – representations of them. Nature is just pursuing its “minimize all actions” goal.

    Does that make some sense?

**

 

    I think that you are are reacting a bit to strongly from your Arithmetic Realism doctrine.

 

[BM]

Where do I react a bit to strongly? Perhaps it is my english? I try just to be short and clear. Sorry if I look like reacting strongly, or being "upset", I am (usually) not. Only plain dishonesty makes me nervous, but this does not seem to happen on this list.

 

[SPK]

    Nah, I think that your English is much better than my French! I meant that you are assuming that we see the ideas that you are considering with the same nuance and subtlety that has become natural for your thoughts.

**

 

 

I would like for all of us to sit back and thought for a while exactly on what we are asking with this question of Mathematical closure.

[BM]

I would like to insist that assuming comp, there is no mathematical closure for the first person points of view. The inner view of arithmetic is already beyond mathematics itself. Assuming comp, we might talk of theological closure (but this is trivial, with the greek definition of theology: the science of 'truth'). Note that there are many argument independent of comp which could make us doubt of any sense for the expression of "mathematical closure". Like the whole of arithmetic is beyond arithmetic, the whole of math is beyond mathematics.

 

Bruno

 

[SPK]

    Yes, I found the same lack of closure in the algebra of bisimulation that I have worked out (with some help).

 

Onward!

 

Stephen

[Jason Resch]

On Tue, Jun 7, 2011 at 5:53 AM, Pete Hughes <pet...@gmail.com> wrote:

Jason,

I found this compelling, are you saying that the difficulty of explaining qualia is due to the language centre of the brain being able to access only an abstract 'interface' (I'm a object oriented thinker) of the sensors? then what about emotions? I'm trying to pre-empt your response to 'why don't you put your hand in the fire and enjoy the information' and I just can't, I like the way you talk so I will pester you with the question.

Peter,

Thanks, I am happy to attempt an answer.  The below is a conclusion from taking seriously http://en.wikipedia.org/wiki/Modularity_of_mind which is supported by several pieces of evidence:

1. Anesthesia

The naive view is that anesthetics work by turning off the brain or causing activity in it to cease.  This is incorrect, there is still a great deal of activity within an anestetized mind, yet consciousness is abolished.  The person is unable to move, remember, sense pain, etc.  Yet other brain functions, such as regulating blood pressure or heart rate continue.  The leading theory for why this is, is called cognitive unbinding.  Anesthetics operate by confusing or dampening communication between neurons.  Cognitive unbinding proposes that this causes disparate brain regions to become cut off from each other as neural signals can only travel so far given the interference of the chemicals.  The result is different brain regions are cut off from each other, the pain processing part of the brain doesn't receive information from the touch processing part of the brain, the hippocampus doesn't receive information to encode as memories, the muscles don't receive signals to move which are under conscious control, yet independent brain functions (which don't require interaction with other brain regions) such as those that control breathing or heart rate continue to function.  It is not the sheer will to survive which keeps the lungs breathing or heart pumping, as animals which are conscious breathers (such as the dolhpins and whales) will suffocate under anesthesia.  This also forbids them from sleeping, they rest only one hemisphere of their brain at a time.

2. Different forms of brain damage

Visual information is a cast collection of processed information.  Before the image reaches your conscious awareness your brain has applied edge detection, depth and color perception, object recognition, motion sensing, and blind spot extrapolation, among other things.  Each of these functions independently and can be impaired or lost without affecting other parts of the brain.  There are cases where brain damage to the V5 section of the brain causes motion blindness (sufferers see the world as a collection of static frames, devoid of any concept of motion), likewise people can lose the ability to recognize faces, or recognize objects (these functions occur in different parts of the brain, so while someone might lose the ability to recognize objects they can still recognize faces and vice versa), finally there are people who have lost the ability to process colors.  Not only can they no longer see colors, but they lose the ability to recall colors altogether.  Since the processing is done in specific areas of the brain, these modules share only the high-level results of their processing with other brain regions.  (This is the limited-access part of modularity).  It is not possible for all areas of the brain to do everything independently of course, so if they interact with other brain regions, they must receive high level results, not the raw input that a particular module processed.

3. Pain perception

This is getting close to your question on emotions and why people don't stick their hand in the fire.  It's been found that the perception of pain is handlered in one part of the brain, but what makes pain painful (unpleasent) is handled by an entirely different part of the brain: the anterior cingulate cortex.  Damage to this part of the brain (or severing nerves connected to it in an operation called a cingulatomy) brings about the curious phenomenon of pain dissociation.  Someone with pain dissociation can provide specific information about the location and intensity of the pain, but it no longer bothers them or causes any distress.  An example:

Paul Brand, a surgeon and author on the subject of pain recounted the case of a woman who had suffered with a severe and chronic pain for more than a decade: She agreed to a surgery that would separate the neural pathways between her frontal lobes and the rest of her brain.  The surgery was a success.  Brand visited the woman a year later, and inquired about her pain.  She said, “Oh, yes, its still there.  I just don't worry about it anymore.”  With a smile she continued, “In fact, it's still agonizing.  But I don't mind.”

To answer your question about emotion I think Marvin Minsky provides a good answer.  You might say that given the above description of pain perception, we have only defined that feelings in terms of its effect on how we think, you might object that I have only described how hurting affects the mind but we still can't express how hurting feels.  Marvin Minsky called this:

“a huge mistake-that attempt to reify 'feeling' as an independent entity, with an essence that's indescribable.  As I see it, feelings are not strange alien things.  It is precisely those cognitive changes themselves that constitute what 'hurting' is-and this also includes all those clumsy attempts to represent and summarize those changes.  The big mistake comes from looking for some single, simple, 'essence' of hurting, rather than recognizing that this is the word we use for complex rearrangement of our disposition of resources.” 

According to Minsky, human consciousness involves the interplay between as many as 400 separate sub-organs of the brain.  If you try to imagine the resulting symphony of activity that comes from these individual regions, each acting on each others' signals and in turn reacting to how those other regions are then affected, you can see it becomes a kind of perpetual and intertwined feedback loop of enormous complexity.  I think in short, emotions represent changes to a large number of different brain regions simultaneously.

Jason

[meekerdb]

Even an affiliation doesn't seem to help.

Brent

[Bruno Marchal]

On 07 Jun 2011, at 16:32, Jason Resch wrote:

On Tue, Jun 7, 2011 at 5:22 AM, Bruno Marchal <mar...@ulb.ac.be> wrote:

On 07 Jun 2011, at 04:00, Jason Resch wrote:

I guess you mean some sort of "spiritualism" for immaterialism, which is a consequence of comp (+ some Occam). Especially that you already defend the idea that the computations are in (arithmetical) platonia.

Note that AR is part of comp. And the UD is the Universal dovetailer. (UDA is the argument that comp makes elementary arithmetic, or any sigma_1 complete theory, the theory of everything. Quanta and qualia are justified from inside, including their incommunicability.

By immaterialism I mean the type espoused by George Berkeley, which is more accurately described as subjective idealism: http://en.wikipedia.org/wiki/Immaterialism

I think it is accurate to call it is a form of spiritualism.

Well I am not even sure. Frankly, this is wikipedia's worst article.  It represents well the current Aristotelian reconsideration or non-consideration of immaterialism. Among the Platonists were the Mathematicians, the ideal platonic worlds for them was either mathematics, or what is just beyond mathematics (like neoplatonist will distinguish the intelligible (the nous) from the ONE behind (and like all self-referentially correct machine will eventually approximate by the notion of theories and the (possible) truth behind).

The "enemy" of "immaterialism" try to mock it by reducing it to solipsism (which is typically "childish), or to the naive believe in angels and fairy tales.

But immaterialism is not a believe in an immaterial realm, it is before all a skepticism with respect to the physical realm, or to the primacy of the physical realm. It is the idea that there is something behind our observations. 

The early academical debate was more to decide if mathematics or physics was the fundamental science.

Aristotelian's successors take primitive materiality as a fact, where the honest scientist should accept that scientists have not yet decide that fundamental question. Today physics relates observable to measurable numbers, and avoid cautiously any notion of matter, which is an already undefined vague term. The nature of matter and of reality makes only a  re-apparition in discussion through the quantum weirdness.

I argue that if we assume that there is a level of description of ourselves which is Turing emulable, then, to be short and clear (albeit not diplomatical) Plato is right, and physics becomes a modality: it emerges from self-observation by relative universal numbers. The quantum weirdness becomes quasi- trivial, the existence of Hamiltonians also, the precise form and simplicity of those Hamiltonians becomes the hard question. Comp does not yet explain the notion of space, although it paves the way in sequence of precise (mathematical) questions.

Unfortunately, the computationalist philosophers of mind, as reflected at least in wiki, seems to ignore everything of theoretical computer science, including the key fact that it is a branch of math, even of number theory (or combinator theory, of creative sets, Sigma_1 complete finite systems, ...). Now I see they have a simplistic (and aristotelian) view on immaterialism.

Okay, this makes sense given your solipism/immaterialism.

I would like to insist that comp leads to immaterialism, but that this is very different from solipsism. Both are idealism, but solipsism is "I am dreaming", where comp immaterialism is "all numbers are dreaming", and a real sharable physical reality emerges from gluing properties of those dreams/computations.

You are right, I should find a less general term.  It is the missing of the glue I think that differentiates the immaterialism of comp from the immaterialism of Berkeley.

Don't worry too much on the terms once you get the idea. We can always decide on vocabulary issue later.

You sum very well the problem. The glue is really provably missing only in solipsism. There is just no reason to believe that numbers could miss the glue, that is more than quarks and waves. At least before we solve the (measure) problem. Math is there to see what happens. People seems to have the same reluctance to let math enter the subject than the old naturalists.

Now, the only way for the numbers to win the measure problem is by self-multiplication, and coherent multiplication of populations, that is sharing stories/computations. The only reason why I can dialog with you must be that we share a 'big number' of similar histories, and those have to be observable below our substitution levels. If those did not exist, keeping comp could lead to solipsism. But then QM, or the MW understanding of QM, shows that we do share indeed big sets, if not a continuum of similar histories, saving comp, empirically, of solipsism. Gödel-Church-Tarski saves mechanism from diagonalization, and QM saves comp from solipsism. Formally, incompleteness will give many possibilities for the glue to form, with the risky one based on lies (shit happens in Platonia too, that is the bad news, but it is there at the start:  G* prove DBf (it is consistent to prove the false).

Comp's message is not "we got the theory of everything". It is more "Oh, even if physicists unify all laws of nature, the task is NOT yet finished". Taking comp seriously, we *have to* justify those laws from the numbers self-observations. 

My work translate the classical mind body problem into a body problem mathematically expressed in computer science and in arithmetic.

Thanks to computer science (insolubilities and incompleteness),  (accepting the classical theory of knowledge), we get a gift: we are able to separate (in the self-referentially correct way) the quanta from the qualia, and to relate the two.

When you said that computation are in math, or in arithmetic, are you aware that this is explicitly proved in (good) textbook in logic or computer science? This is not easy to show. It is tedious and long, and there are always subtle points. But it is akin to define a high level programming language in a low level language. Matiyasevitch has gone farer than anyone in showing that diophantine polynomials are already enough (but that is much more complex to prove). This leads to a crazy proposition, which is that all sigma_1 truth can be verified in less than 100 operations, that is addition and multiplication of numbers. It means that all stopping computations can be given in the form of a short sequence of addition and multiplication (on numbers which might be great of course(*)). 

Bruno

(*) I can resist to show a version by Jones of that result. If you remember the RE set W_i, the set analog of partial computable functions (which are also the domain of the phi_i) Matiyasevitch' result can take the shape below. Nu and X are the two parameters, and the other letters, and the two characters "letters" are variables. Unknowns range on the non negative integers.

By adding enough variable, you could arrive at a degree four unique polynomial, but here we allow high degree. Look at that B^(5^60).

X is in W_Nu iff

Nu = ((ZUY)^2 + U)^2 + Y 

ELG^2 + Al = (B - XY)Q^2

Qu = B^(5^60)

La + Qu^4 = 1 + LaB^5

Th +  2Z = B^5

L = U + TTh

E = Y + MTh

N = Q^16

R = [G + EQ^3 + LQ^5 + (2(E - ZLa)(1 + XB^5 + G)^4 + LaB^5 + + LaB^5Q^4)Q^4](N^2 -N)

         + [Q^3 -BL + L + ThLaQ^3 + (B^5 - 2)Q^5] (N^2 - 1)

P = 2W(S^2)(R^2)N^2

(P^2)K^2 - K^2 + 1 = Ta^2

4(c - KSN^2)^2 + Et = K^2

K = R + 1 + HP - H

A = (WN^2 + 1)RSN^2

C = 2R + 1 Ph

D = BW + CA -2C + 4AGa -5Ga

D^2 = (A^2 - 1)C^2 + 1

F^2 = (A^2 - 1)(I^2)C^4 + 1

(D + OF)^2 = ((A + F^2(D^2 - A^2))^2 - 1)(2R + 1 + JC)^2 + 1

 

>
> If by representation you mean the representation of consciousness, then this
> is the functionalist/computationalist philosophy in a nutshell.

Computationalism says that representation *is* something you are.

I say the opposite.  Representation is something you do, which is so
natural to you and so useful to you that you’ve mistaken it as the
explanation for everything.

You should read this http://en.wikipedia.org/wiki/Functionalism_(philosophy_of_mind)

Functionalism is the idea that it is what the parts do, not what they are that is important in a mind.

Computatalism is a more specific form of functionalism (it assumes the functions are Turing emulable)

I disagree with this. Putnam' functionalism is at the start a fuzzy form of computationalism (the wiki is rather bad on those subjects). It is fuzzy because it is not aware that IF we are machine, then we cannot know which machine we are. That is why it is a theology, you need an act of faith beyond just trusting the 'doctor'. In a sense functionalism is a specific form of computationalism because functionalist assumes by default some high level of comp. They are just fuzzy on the term "function", and seems unaware of the tremendous progress made on this by logicians and theoretical computer scientists. 

Note also that comp makes *1-you* different from any representation, from you first person perspective. So, the owner of the soul is the (immaterial) person, not the body. A body is already a representation of you, relatively to some universal numbers.

In a sense we can sum up comp's consequence by: If 3-I is a machine, then 1-I is not. The soul is not a machine *from its point of view". He has to bet on its own G* to say 'yes' to the doctor. Of course, once we accept comp, we can retrospectively imagine that "nature" has already bet on it, given that the genome is digital relatively to chemistry, and given the evidences for evolution, and our very deep history.

Bruno

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

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[Brian Tenneson]

Self aware in what sense?

On Sat, Jun 4, 2011 at 2:09 AM, Felix Hoenikker <fhoen...@gmail.com> wrote:

Sorry again, but I want to add one thing:

The broadest mathematical closure of "the existence of computation",
"the observation of consciousness anywhere" suggests the following, in
my mind: all possible numbers (including transfinite-ones) are, in
fact, self aware substructures in the mathematical universe,
recursively "communicating" to "each other" by exchanging bits in an
attempt to develop the algorithm which compresses themselves to a
single state, which represents the number "one", after which it
promptly forgets and starts all over again, everywhere, and all at
once.

---------- Forwarded message ----------
From: Felix Hoenikker <fhoen...@gmail.com>
Date: Sat, Jun 4, 2011 at 3:03 AM
Subject: The final TOE?
To: Everything List <everyth...@googlegroups.com>


Hi all,

Consider the following fully general way of saying this is the
following: quantum mechanics and general relativity are symmetrically
"the exact same theory", modulo the additional "bit" of information
that quantum entanglement reduces net gravitational energy.  This is
the EXACT answer to the EPR paradox, and all paradoxes about
singularities, and consistent with our picture of reality in every
respect, as it "necessarily must be" since it follows exactly from the
asssumption of 3+1 spacetime embedded within some higher dimensional
structure of "any" form (i.e. including string theory).

Since no "true" gravitational singularities exist, then "every point
in space is an apparent black hole" because "no point in space is an
apparent black hole".  Thus, at every point in space, a "bit" of
information (or a "photon") can escape from the "observable" universe
on our scale, "go into the past", and come out "in the future" in a
symmetric manner for all observers, without considering your frame of
reference in 3+1 space time.  This qualitatively predicts all features
of GR without QCD or QFT.  However, since photons travelling through
locally closed loops can look like "point" particles with some net
entanglement coming out, then they can look like bundles that, for all
intents and purposes, appear to randomly add information in some way,
and in some spherically symmetric fashion, which predicts the
divergence and appearance of other "fundamental forces" early in the
inflating universe.

It is often said that QM and GR differ from each other exactly by the
contemplation of the "singularity", and that our inability to discover
the "true" laws of the universe has been limited by our lack of
knowledge about the twin singularities: the inflationary bubble and
the black hole.  It follows that this fact was "exactly true" all
along, and the laws of physics are a completely dimensionless
consequences of our "local" geometry of space, and our civilization
has, in fact, rather than been trying to "discover" the next laws of
physics, has in fact been struggling to "unlearn" the concept of
"Indeterminacy" and "quantum mechanics", since QM follows from GR, the
postulate of 3+1 spacetime and E = mc^2 (a nice, dimensionless
equation).  Einstein, in fact, was right all along, and successfully
completed the "fully" deterministic general laws of physics.

Consider then, the reason why indeterministic QM was ever suggested:
the apparently subjective indeterminacy of the universe from each
"observer" point of view (i.e. the uncertainty principle).  Or
actually, consider the fact that, if the universe is completely
deterministic, and "you" for any defined "you" is getting non-random
information from any source, then that information must, in fact, be
added to you by the "rest of the universe" in some systematic fashion,
down to the tiniest quantum of "universe".  This implies that there
"is" actually, some "quanta" of the universe, a "photon", and each
"photon" is having information added to "it" from the "rest of the
universe", in a systematic fashion, and recursively so for every
"observer".  This is actually a fully generic model for the universe,
and the absolute generalization of QM and SR.

Next, consider the fact that you are "conscious" and possibly
"indeterminstic" (i.e. have subjective free will).  I think I do.
Therefore, I am not a "quanta" of information, or a "bit", but it was
"added to me" from "somewhere".  No, consider the mathematical closure
of this observation.  What does this imply about and anthropic
principle and "fine tuning"? Does that make sense anymore.  Also, does
this not mean that our "observable universe", for "some definition of
observable", from "any subjective observer's point of view", is
constantly being added non-random information from "outside".

I truly beg you all to consider this argument fully.

Please let me know what you think,
F.H.

On Fri, Jun 3, 2011 at 7:16 PM, Felix Hoenikker <fhoen...@gmail.com> wrote:
> Every "apparent" event horizon is really a separation of two
> universes, where the outside universe is entangled geometrically with
> the inside universe. The Hubble volume is sitting inside of an
> expanding supermassive black hole, of another universe. However, by
> the uncertainty principle, this means the "outside universe" is
> "really" simultaneously in a superposition of a large but countably
> finite many possible universes (i.e. bitstates), with the net
> information between the "inside" and "outside" views cancelling out to
> zero. Equivalently, every "classical" black hole is really in a
> microscopic superposition of countably finite many bitstates, again
> with the net information "inside" and "outside" cancelling zero.
> However, it cannot converge to a singularity, because it cannot encode
> "bitstates" forever in the same volume, therefore it must leak
> information in the form of "photons" (i.e. Hawking radiation).
>
> Equivalently, the Hubble volume receives information one photon at a
> time from the "outside" in the form of cosmic background radiation,
> that information being about the prior state of the otherwise casually
> disconnected universe. (i.e. CMB == Hawking radiation). The
> equivalence principle implies length contraction and time dilation.
> Gravity mediated by photons is the single fundamental force of the
> universe. All other sources of apparent information and causal
> connectivity (i.e. all other forces) are the result of the initial
> state of the universe at the Big Bang, the only true singularity. The
> laws of the universe are extremely simple.
>
> This is the digital unification of GR and QM.  What do you think?

[Russell Standish]

On Mon, Jun 06, 2011 at 08:31:35PM -0400, Stephen Paul King wrote:
> Hi Russell,
>
> I would like to be sure that I understand your point here. Would
> you say that "true determinism", as opposed to "true indeterminism",
> requires one-to-one mappings between any two adjoining links in the
> causal chain of events, each of which is said to be uniquely
> determined by its prior?
>
> Onward!
>
> Stephen

That is what determinism means. I don't think there can be any meaning
attached to false determinism, however, so the true is a little
redundant.

That is also the case of indeterminism, but some might think that
ignorance is a form of indeterminism (which it needn't be). Hence my
sticking the redundant "true" tag to make the point.

Cheers

[Stephen Paul King]

Dear Bruno,

 

    I agree with your assessment of that Wiki article. In most universities the prevalent ontological doctrine is “dialectical materialism” and such has no allowance for any competition in the realm of ideas. I have pointed out that your result is similar to solipsism but never as an insult. It was just that I do not see a means to extend it to being able to consider the appearance of interactions between many minds. As far as I have studied, it seems only to be able to make statements about itself. Until you can show how it can be individuated for many minds this problem will remains, with or without a solution to the measure problem.

    The difficulty is that the numbers, alone, do not have any of the properties that we would associate with a mind with the notable exception of self-referential logical structure. If we might extend comp with the idea of the isomorphism with topological spaces (via the representation theorem) then we might have a notion of concrete persistence over transitions that allows for a notion of memory – since a single logical algebra is isomorphic to an entire class of stone spaces when we consider the relation of diffeomorphism. The inclusion of topological spaces allows us a coherent notion of “inside” and “outside” that can be used to distinguish multiple minds from each other, if only by having the possibility of differing positions in space.

    The self-awareness that you mention would, in turn, allow for the expansion of the group of symmetries that can be considered as “internal” that they can be broken and mapped (via fiber bundles) onto the set complement of the stone spaces, that yields field theories.

    The “glue” that binds them all together is a combination of bisimulation chaining ( a form of homomorphism) on the abstract side and various other morphisms on the concrete “physical” side, all woven together by the wonderful natural contravariance of the stone duality.

 

Onward!

 

Stephen

 

From: Bruno Marchal

Sent: Tuesday, June 07, 2011 12:31 PM

To: everyth...@googlegroups.com

Subject: Re: Mathematical closure of consciousness and computation

To unsubscribe from this group, send email to mailto:everything-list%2Bunsu...@googlegroups.com.

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[Colin Hales]

Hi,
JoMC is relatively new. My own institution (Unimelb) doesn't
subscribe.... the Journal is very specialized as well....
The ISI search engine won't see it either. It takes time for the
journals to earn enough cred to get visible and accessible... even the
Journal of Consciousness Studies has eventually made it into ISI
search... one day JoMC will, I hope.

Those interested enough to send a private enquiry to me can get an
earlier preprint version...close enough to the original to be readable.

cheers
Colin
BTW I finally submitted my PhD thesis recently.... WOOHOO!

[Russell Standish]

Hi Colin,

I'm interested in a preprint. I know I saw an earlier version, but I'm
interested in how it looks nowm after going through referees.

Cheers

> --
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[Rex Allen]

Hard determinism is incompatible with science in general?

Rex

[Bruno Marchal]

? On the contrary. It was your argument against determinism which I
took as incompatible with science or scientific attitude. But third
person determinism does not entails first person determinism, nor do
determinism in general prevents genuine free will. People believing
that determinism per se makes free will impossible confuse themselves
with God.
But now I am no more sure what you are saying. Are you OK with hard
determinism? Are you OK with block-multiverse, or block-mindscape?

Bruno

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

[Rex Allen]

I'm not arguing against determinism. I'm fine with determinism and
it's consequences.

> But third person determinism does not entails first person
> determinism, nor do determinism in general prevents genuine free will.

Determinism doesn't prevent your "redefined" version of "free will",
which of course isn't free will at all - but rather a psychological
coping mechanism disguised as a reasonable position.

BUT...I didn't say third person determinism. I said "hard
determinism"...the alternative to the soft determinism of
compatibilism.

> People believing that determinism per se
> makes free will impossible confuse themselves with God.

No, people who believe that determinism is incompatible with free will
have a firm understanding of the meaning of both determinism and free
will.

> But now I am no more sure what you are saying. Are you OK with hard
> determinism? Are you OK with block-multiverse, or block-mindscape?

I'm fine with "hard determinism". I am a "hard determinist"...which
is the position that determinism is incompatible with free will.

http://en.wikipedia.org/wiki/Hard_determinism

I'm also fine with block-multiverse. And with a block-mindscape.

Neither of which allow for free will. Since both of which are static,
unchanging, and unchangeable - making it impossible that anyone "could
have done otherwise" than they actually did. No one can be free of
that fact - and therefore no one has free will.

Rex

[Rex Allen]

On Thu, Jun 9, 2011 at 5:58 AM, Bruno Marchal <mar...@ulb.ac.be> wrote:
> ? On the contrary. It was your argument against determinism which I took as
> incompatible with science or scientific attitude. But third person
> determinism does not entails first person determinism, nor do determinism in
> general prevents genuine free will. People believing that determinism per se
> makes free will impossible confuse themselves with God.
> But now I am no more sure what you are saying. Are you OK with hard
> determinism? Are you OK with block-multiverse, or block-mindscape?

I think your position rests on an invalid conflation between the fact
that it posits multiple *actual* futures, all of which *will* occur -
and the "folk" intuition that there are multiple *possible* futures,
and that it is *ultimately* our conscious experience of making a
choice which determines which one of those possible futures becomes
actual.

You say the former, but in doing so you allude to the latter.

Which is true of all compatibilist positions...and that's why
compatibilists insist on redefining existing words like "free will"
and "choice" and "responsibility".

Because if you don't re-use those words - retaining their flavor
without their substance - it becomes impossible for compatibilists to
connect to their traditional meaning in any convincing way.

Using less misleading terms would make it obvious that compatibilism
has nothing to do with free will at all. Compatibilism is about
building a world view that makes it possible for society to continue
largely as before while accepting determinism.

"Dr. StrangeDennett: Or How I Learned to Stop Worrying and Love Determinism".

Repurposing the term "free will" is a propaganda move, to make the
medicine go down easier.

Rex

[Jason Resch]

On Thu, Jun 9, 2011 at 10:00 AM, Rex Allen <rexall...@gmail.com> wrote:

I'm also fine with block-multiverse.  And with a block-mindscape.

Neither of which allow for free will.  Since both of which are static,
unchanging, and unchangeable - making it impossible that anyone "could
have done otherwise" than they actually did.  No one can be free of
that fact - and therefore no one has free will.

'making it impossible that anyone "could have done otherwise" than they actually did.'

You say it is impossible that anyone could have done otherwise from what they did.  Well what determined what they did?  Their mind?  Their biology?  Their chemistry?  The physics of the subatomic motions of the particles in their brain?

To say the mind is not doing any decision making because its behavior can be explained at a level where the mind's operation cannot be understood, is like saying a computer is not computing or a car is not driving, because if you look at a computer or a car at a low enough level you see only particles moving in accordance with various forces applied to them.  You can render meaningless almost any subject by describing it at the wrong level.  You might as well say there is no meaningful difference between a cat and a rock, since they are after all, just electrons and quarks.

If you describe the mind at the correct level, you find it is making decisions.  You say it is impossible that the decision it makes could have been otherwise.  This is good for the mind, it means it is guaranteed that its will is carried out.

That said, I don't mean to say there are not interesting implications for some of the concepts discussed on this list, such as the definition of personal identity or the view that we are all part of one mind/self/soul.  Regarding personal identity, does it make sense to punish the 50 year old man with a prison sentence if it was a different person who committed the act 20 years ago?  (If you regard the two as different persons).  Further, is there any role of punishment / retribution in the justice system when had we been born in another persons shoes we would have made the same decisions and ended up in the same place as that person?  If ultimately we are the same person, we should have much more compassion and understanding for others and their actions.

Jason

[Bruno Marchal]

On 09 Jun 2011, at 18:20, Rex Allen wrote:

> On Thu, Jun 9, 2011 at 5:58 AM, Bruno Marchal <mar...@ulb.ac.be>
> wrote:
>> ? On the contrary. It was your argument against determinism which I
>> took as
>> incompatible with science or scientific attitude. But third person
>> determinism does not entails first person determinism, nor do
>> determinism in
>> general prevents genuine free will. People believing that
>> determinism per se
>> makes free will impossible confuse themselves with God.
>> But now I am no more sure what you are saying. Are you OK with hard
>> determinism? Are you OK with block-multiverse, or block-mindscape?
>
> I think your position rests on an invalid conflation between the fact
> that it posits multiple *actual* futures,

This is derived from the *assumption* that we are Turing emulable. And
that is the main point. Then quantum interferences are hard to
explained without that fact; so QM can be seen as a confirmation of
that proposition (but with comp it is more multi-dreams than multi-
worlds, but as a mathematician I don't worry too much on vocabulary).

> all of which *will* occur -

They just exist. It is provable in Robinson Arithmetic that they exist
and verify the condition of being pieces of computations.

> and the "folk" intuition that there are multiple *possible* futures,

I am not studying the semantics of natural languages. That is one
intuition among many others.

> and that it is *ultimately* our conscious experience of making a
> choice which determines which one of those possible futures becomes
> actual.

It is our conscious choice which determines the normal realities. If
you jump out of a window, the probability is high that you will have
problems in the normal neighborhoods. At that level the ethic are the
same. It is just false that everything happens with the same relative
measure, and we can act on that relative measure by decision and
action. No reason to be fatalist.

>
> You say the former, but in doing so you allude to the latter.
>
> Which is true of all compatibilist positions...and that's why
> compatibilists insist on redefining existing words like "free will"
> and "choice" and "responsibility".

Oh? But then define free-will. This is the most debated term of
philosophy. I have given a definition of it, which is of course a
compatibilist one. What is your definition. It is not a primitive
term. What is your theory?

>
> Because if you don't re-use those words - retaining their flavor
> without their substance - it becomes impossible for compatibilists to
> connect to their traditional meaning in any convincing way.

You say so, but the point is that not only free-will makes sense with
machines, but we have the tool to relate it to consciousness and
intelligence, but also to the big one without name, and the inner God.
We do have an arithmetical understanding of neoplatonism. The theology
of the universal numbers is *very* rich (provably beyond the
mathematics available to the machine).
I am just saying that comp leads to Plato, and not to Aristotle.

>
> Using less misleading terms would make it obvious that compatibilism
> has nothing to do with free will at all. Compatibilism is about
> building a world view that makes it possible for society to continue
> largely as before while accepting determinism.

That is a "process of intention" (we say in french). It means that you
attribute me an intention which I have not. On the contrary, I show
that the universal numbers are universal dissident and that they can
defeat all complete theories we would build on them. You are just
confusing third person views with first person views. You confuse G,
G* and S4Grz, dixit the machine.

You are the one having a reductionist view of machine and numbers, by
exempting them from free-will, and, I guess consciousness. You are the
one saying that they are dumb. I am the one saying that we can already
listen to them, and that they already have an incredibly interesting
discourse.

>
> "Dr. StrangeDennett: Or How I Learned to Stop Worrying and Love
> Determinism".
>
> Repurposing the term "free will" is a propaganda move, to make the
> medicine go down easier.

Science redefines the term all the times. The only thing which counts
is to see if we agree with the theories and their consequences.

What is your theory? I am afraid I did already ask you this, and that
you said you have none. If that is the case, I am not sure what you
are talking about. Hmm... I see in your other post that you think free
will does not exist. Well read my answer there.

Bruno

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

[Bruno Marchal]

Of course? You talk like if you have some complete theory of universal
machine, but they can already defeat them all. We don't know what they
are able to do or not.

> but rather a psychological
> coping mechanism disguised as a reasonable position.

I don't disguise anything. I put straight the hypotheses on the table.
I reason in that frame without any pretending any truth.

>
> BUT...I didn't say third person determinism. I said "hard
> determinism"...the alternative to the soft determinism of
> compatibilism.

Please elaborate on the distinction between hard and soft determinism.

remember also that assuming comp, the physical and the physical notion
of cause is already based on the first person indeterminacy, and that
it is much plausible that the physical is only partially determined.
We know very few things there. The determinism of comp is just the
determinism of arithmetical propositions.

>
>
>> People believing that determinism per se
>> makes free will impossible confuse themselves with God.
>
> No, people who believe that determinism is incompatible with free will
> have a firm understanding of the meaning of both determinism and free
> will.

They confuse free-will with unpredictability by God, when free-will is
just unpredictibility by me or by machines of similar complexity.

>
>
>> But now I am no more sure what you are saying. Are you OK with hard
>> determinism? Are you OK with block-multiverse, or block-mindscape?
>
> I'm fine with "hard determinism". I am a "hard determinist"...which
> is the position that determinism is incompatible with free will.

What a bad name. I could have understand that you are an hard free
willing person. determinism is just the belief, roughly speaking, that
time and cause are higher order emerging notions. But then i show that
they originate quickly, in the logical way, from the numbers. Even
"before" matter.

>
> http://en.wikipedia.org/wiki/Hard_determinism
>
> I'm also fine with block-multiverse. And with a block-mindscape.
>
> Neither of which allow for free will. Since both of which are static,
> unchanging, and unchangeable - making it impossible that anyone "could
> have done otherwise" than they actually did. No one can be free of
> that fact - and therefore no one has free will.

You throw the baby with the bath water. Free will, like consciousness,
feeling etc. does exist and has a causal physical role, with comp.
Indeed, at some level the entire physical reality can be described as
a consequence of a sort of arithmetical placebo phenomenon. So
consciousness is very fundamental. It might be the most fundamental
things in the physical universe, perhaps the only operative force, due
to the "potential difference" between G and G*, between words/numbers
and truth.

Full determinism appears only in God's eye, or in the arithmetical
truth. But comp justifies that this is just inaccessible for us, so we
can only scratch the truth, and locally we have to take moral
decision, be responsible with respect to others, etc. There exists
universal values like respect of others and of all unknown (and all
universal numbers are really quite *unknown*).

Now, I have never understood why some people want a non compatibilist
theory of free will. It explains only "less free-will", by adding a
random element which adds nothing, imo.

You do with free-will what the atheist does with "God". Find a
ridiculous (even if historically first) definition, and then evacuate
the questions behind the concept. I do have a precise theory, (not in
my thesis, though) and free-will begins with Löbianity. From this I
infer that very plausibly, worms and ants (and perhaps communists)
have no free-will, but that spiders, octopus, mice, dogs and humans
have it. I thought only homeotermic animals were self-conscious free
animals. They can dream and can have empathy, but since recently I
accumulate evidence that Löbianity occurs already with many
invertebrates. Notably the spider:

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

Bruno

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

[Bruno Marchal]

Hi Colin,

Congratulation Colin.

Like others, I don't succeed in getting it, neither at home nor at
the university.

From the abstract I am afraid you might not have taken into account
our (many) conversations. Most of what you say about the impossibility
of building an artificial scientist is provably correct in the (weak)
comp theory. It is unfortunate that you derive this from comp
+materialism, which is inconsistent. Actually, comp prevents
"artificial intelligence". This does not prevent the existence, and
even the apparition, of intelligent machines. But this might happen
*despite* humans, instead of 'thanks to the humans'. This is related
with the fact that we cannot know which machine we are ourselves. Yet,
we can make copy at some level (in which case we don't know what we
are really creating or recreating, and then, also, descendent of bugs
in regular programs can evolve. Or we can get them serendipitously.
It is also relate to the fact that we don't *want* intelligent
machine, which is really a computer who will choose its user, if ...
he want one. We prefer them to be slaves. It will take time before we
recognize them (apparently).
Of course the 'naturalist comp' theory is inconsistent. Not sure you
take that into account too.

Artificial intelligence will always be more mike fishing or exploring
spaces, and we might *discover* strange creatures. Arithmetical truth
is a universal zoo. Well, no, it is really a jungle. We don't know
what is in there. We can only scratch a tiny bit of it.

Now, let us distinguish two things, which are very different:

1) intelligence-consciousness-free-will-emotion

and

2) cleverness-competence-ingenuity-gifted-learning-ability

"1)" is necessary for the developpment of "2)", but "2)" has a
negative feedback on "1)".

I have already given on this list what I call the smallest theory of
intelligence.

By definition a machine is intelligent if it is not stupid. And a
machine can be stupid for two reason:
she believes that she is intelligent, or
she believes that she is stupid.

Of course, this is arithmetized immediately in a weakening of G, the
theory C having as axioms the modal normal axioms and rules + Dp ->
~BDp. So Dt (arithmetical consistency) can play the role of
intelligence, and Bf (inconsistance) plays the role of stupidity. G*
and G proves BDt -> Bf and G* proves BBf -> Bf (but not G!).

This illustrates that "1)" above might come from Löbianity, and "2)"
above (the scientist) is governed by theoretical artificial
intelligence (Case and Smith, Oherson, Stob, Weinstein). Here the
results are not just NON-constructive, but are *necessarily* so.
Cleverness is just something that we cannot program. But we can prove,
non constructively, the existence of powerful learning machine. We
just cannot recognize them, or build them. It is like with the
algorithmically random strings, we cannot generate them by a short
algorithm, but we can generate all of them by a very short algorithm.

So, concerning intelligence/consciousness (as opposed to cleverness),
I think we have passed the "singularity". Nothing is more intelligent/
conscious than a virgin universal machine. By programming it, we can
only make his "soul" fell, and, in the worst case, we might get
something as stupid as human, capable of feeling itself superior, for
example.

Bruno

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

[meekerdb]

Dennett's subtitle to his book "Elbow Room" is "free will that's worth
having". Sam Harris just wrote about this
http://www.samharris.org/blog/item/free-will-why-you-still-dont-have-it/
He seems to disagree with compatibilism; but he essentially agrees on
the facts; he just doesn't want to use the phrase "free will" because he
thinks that's redefining the terms to mean something other than what
people normally mean. Interestingly when he talks about what people
normally mean, a kind of dualism, he shows that what people usually mean
is incoherent even on a dualist account.

Brent
"You can avoid responsibility for everything if you just make yourself
small enough."
--- Daniel Dennett, "Elbow Room"

[meekerdb]

On 6/9/2011 1:17 PM, Bruno Marchal wrote:

> I do have a precise theory, (not in my thesis, though) and free-will

> begins with L�bianity. From this I infer that very plausibly, worms

> and ants (and perhaps communists) have no free-will, but that spiders,
> octopus, mice, dogs and humans have it. I thought only homeotermic
> animals were self-conscious free animals. They can dream and can have

> empathy, but since recently I accumulate evidence that L�bianity

> occurs already with many invertebrates. Notably the spider:
>
> http://www.youtube.com/watch?v=VakdmcbHuCA
>
> Bruno

This will sadden my neuroscientist friend who avoids eating animals that
have a cereberal cortex on the theory that he thereby avoids eating
conscious creatures. He likes lobster.

Brent

[meekerdb]

On 6/9/2011 11:34 AM, Jason Resch wrote:

On Thu, Jun 9, 2011 at 10:00 AM, Rex Allen <rexall...@gmail.com> wrote:

I'm also fine with block-multiverse.  And with a block-mindscape.

Neither of which allow for free will.  Since both of which are static,
unchanging, and unchangeable - making it impossible that anyone "could
have done otherwise" than they actually did.  No one can be free of
that fact - and therefore no one has free will.

'making it impossible that anyone "could have done otherwise" than they actually did.'

You say it is impossible that anyone could have done otherwise from what they did.  Well what determined what they did?  Their mind?  Their biology?  Their chemistry?  The physics of the subatomic motions of the particles in their brain?

Of course any event has many causes, describable at different levels.  But if many of the causal chains pass through one body and brain, it is reasonable to say that person is responsible for acting.  It is the same if a certain aircraft design has a flaw (remember the de Havilland Comet?...and the Lockheed Electra?).  We say the aircraft is responsible for deaths.

To say the mind is not doing any decision making because its behavior can be explained at a level where the mind's operation cannot be understood, is like saying a computer is not computing or a car is not driving, because if you look at a computer or a car at a low enough level you see only particles moving in accordance with various forces applied to them.  You can render meaningless almost any subject by describing it at the wrong level.  You might as well say there is no meaningful difference between a cat and a rock, since they are after all, just electrons and quarks.

If you describe the mind at the correct level, you find it is making decisions.  You say it is impossible that the decision it makes could have been otherwise.  This is good for the mind, it means it is guaranteed that its will is carried out.

That said, I don't mean to say there are not interesting implications for some of the concepts discussed on this list, such as the definition of personal identity or the view that we are all part of one mind/self/soul.  Regarding personal identity, does it make sense to punish the 50 year old man with a prison sentence if it was a different person who committed the act 20 years ago?  (If you regard the two as different persons). 

It doesn't make sense to punish him even at age 30, except as a deterrent to him and others and to avoid vendettas.

Further, is there any role of punishment / retribution in the justice system when had we been born in another persons shoes we would have made the same decisions and ended up in the same place as that person?  If ultimately we are the same person, we should have much more compassion and understanding for others and their actions.

But we may still conclude punishment is appropriate policy as one way to influence behavior. 

Brent

[Russell Standish]

On Thu, Jun 09, 2011 at 02:15:47PM -0700, meekerdb wrote:
> He seems to disagree with compatibilism; but he essentially agrees
> on the facts; he just doesn't want to use the phrase "free will"
> because he thinks that's redefining the terms to mean something
> other than what people normally mean. Interestingly when he talks
> about what people normally mean, a kind of dualism, he shows that
> what people usually mean is incoherent even on a dualist account.
>
> Brent
> "You can avoid responsibility for everything if you just make
> yourself small enough."
> --- Daniel Dennett, "Elbow Room"

This is clearly an agenda in itself. The free will that Harris is
talking about was probably a concept that was repurposed by the
Christian Church to have something to do with God and souls.

I would argue that the intuitive notion of free will (that we have
"agency", is that there is a "self" in charge of what our bodies doing is
more what we should be talking about.

Now that is, of course, deliberately vague - it is an intuitive notion
after all. But I would imagine that the self is a specific arrangement
of molecules that generates the requisite behaviour. There is no
particular reason why we need to be fully consious of our "self" -
indeed, all the evidence points otherwise - we often make decisions,
or perform actions, only later becoming aware of them, and making a
post-hoc justification. But it is still our self that makes the
decision (and potentially responsible for the action - another matter
entirely). It would not matter if the self were fully deterministic,
it is still the self that causes the action (at one level of
description, just like at one level of description the desk prevents
my laptop from crashing to the floor). However, I don't believe the
universe is deterministic. Physics says otherwise. So the whole
compatibilist/incompatibilist bit is simply an irrelevant diversion.

As I always say, free will is the ability to do something stupid. And
from an evolutionary point of view, that is actually a useful ability.

[Russell Standish]

On Thu, Jun 09, 2011 at 10:17:46PM +0200, Bruno Marchal wrote:

> I do have a precise
> theory, (not in my thesis, though) and free-will begins with
> Löbianity. From this I infer that very plausibly, worms and ants
> (and perhaps communists) have no free-will, but that spiders,
> octopus, mice, dogs and humans have it. I thought only homeotermic
> animals were self-conscious free animals. They can dream and can
> have empathy, but since recently I accumulate evidence that
> Löbianity occurs already with many invertebrates. Notably the
> spider:
>
> http://www.youtube.com/watch?v=VakdmcbHuCA
>

This is an interesting variation from you earlier claims, where you
were claiming that consciousness was very primitive. Assuming you're
identifying free will (or Loebianity) with consciousness, then only
selectively granting species might get around the anthropic ant
argument.

Mind you, there are an awful lot of spiders - on my suburban block, I
would estimate a population of several thousand individuals, making up
perhaps 30-50 species, living on an area of land containing 4 humans
(and not many more mammals, I might add). You might need to limit it
to just some spider species - after all, I would expect a great
variation in spider intelligence.

One thing I would like to ask is how you would objectively infer
Loebianity in a non-communicative species? That would indeed be a step
forward if we could do this arthropods.

[meekerdb]

We are in violent agreement. :-)

Brent
The freedom of the will consists in the fact that future actions
cannot be known now.
--- Ludwig Wittgenstein

[Rex Allen]

On Thu, Jun 9, 2011 at 2:34 PM, Jason Resch <jason...@gmail.com> wrote:
> On Thu, Jun 9, 2011 at 10:00 AM, Rex Allen <rexall...@gmail.com> wrote:
>>
>> I'm also fine with block-multiverse. And with a block-mindscape.
>>
>> Neither of which allow for free will. Since both of which are static,
>> unchanging, and unchangeable - making it impossible that anyone "could
>> have done otherwise" than they actually did. No one can be free of
>> that fact - and therefore no one has free will.
>>
>>
>
> 'making it impossible that anyone "could have done otherwise" than they
> actually did.'

Right. A necessary (but not sufficient) condition of freedom is that
they must have been able to have done otherwise.

This alone isn’t sufficient, because "quantum randomness" (in a
non-block context) also makes it possible that they could have done
otherwise - but random decisions aren't free either.

> You say it is impossible that anyone could have done otherwise from what
> they did. Well what determined what they did? Their mind? Their biology?
> Their chemistry? The physics of the subatomic motions of the particles in
> their brain?

I don’t think it matters in a “block” context, does it?

> To say the mind is not doing any decision making because its behavior can be
> explained at a level where the mind's operation cannot be understood, is
> like saying a computer is not computing or a car is not driving, because if
> you look at a computer or a car at a low enough level you see only particles
> moving in accordance with various forces applied to them.

The ability to make decisions is ubiquitous. Ants, wasps, lizards,
turtles, mice, dogs - whatever. They can all be said to make
decisions. Do ants have free will?

Even computers can be said to make decisions...and saying that they do
seems just as valid as saying that humans do. Do the computerized
monitoring and control systems at nuclear power plants have free will?
If they automatically "decide" to close some valve in response to
sensor readings, are they exercising free will?

> You can render meaningless almost any subject by describing
> it at the wrong level.

Wrong? What would make some level the “wrong” level and another the
“right” level?

If a subject *can* be described at some level (or should be
describable in theory), then that has to be of some significance,
doesn’t it?

If human behavior ought to be describable at the level of quarks and
electrons, just as computer behavior ought to be describable at the
level of quarks and electrons, and just as rock behavior ought to be
describable at the level of quarks and electons - then this shared
“describability” has to tell us something significant - doesn’t it?

The fact that all of these things are describable at the same level,
the level of quarks and electrons, surely this means something.

If humans could *not* be described at the level of quarks and
electrons, but computers could, *that* would definitely tell us
something significant, wouldn’t it?

> You might as well say there is no meaningful difference between a
> cat and a rock, since they are after all, just electrons and quarks.

There’s a meaningful difference between a cat and a rock - *to me*.
But maybe not in any other sense.

> If you describe the mind at the correct level, you find it is making
> decisions.

I can interpret it that way, yes. Or I can interpret it as just
moving through a sequence of states.

I can interpret it either way I want, as the whim strikes me. It’s
like looking at the picture of the candlestick and then seeing the two
faces. I can go back and forth between the two interpretations. I’m
flexible that way.

The interpretation that the mind is making decisions is not *forced* on me.

Can you interpret the mind as just moving through a sequence of
states? Maybe if you concentrate?

> You say it is impossible that the decision it makes could have
> been otherwise. This is good for the mind, it means it is guaranteed that
> its will is carried out.

It also means that the mind’s will is not free.

> That said, I don't mean to say there are not interesting implications for
> some of the concepts discussed on this list, such as the definition of
> personal identity or the view that we are all part of one mind/self/soul.

Part of the same mind/self/soul? That doesn’t sound too plausible to
me. If it were true in any meaningful way, I think I would have
noticed.

Though, it may be true in the same way that we could be part of the
same zip code or something.

> Regarding personal identity, does it make sense to punish the 50 year old
> man with a prison sentence if it was a different person who committed the
> act 20 years ago? (If you regard the two as different persons). Further,
> is there any role of punishment / retribution in the justice system when had
> we been born in another persons shoes we would have made the same decisions
> and ended up in the same place as that person? If ultimately we are the
> same person, we should have much more compassion and understanding for
> others and their actions.

Generally, I think a more mechanistic view of human behavior would
(ironically?) result in a more humane society.

A more mechanistic view would reduce the impulse to take things
personally, and would encourage a more pragmatic, less emotional
approach to solving society’s problems - and to dealing with each
other.

Of course, anything can be taken too far - and usually is - but still
it seems to me like the right direction to steer towards.

Compatibilism, however, totally short circuits that, and to no good end.

Brent said, in an earlier thread:

“That's like telling gays they should be happy with ‘civil unions’.
'Free will', meaning free of coercion and compulsion, as used in law,
is useful concept referred to in many, many decisions which set
precedents - just as 'marriage' appears in many laws and regulations.
So there are excellent reasons of understanding to keep it. If you
are a determinist, then compatibilism is the theory that shows this
legal meaning is compatible with determinism; so you don't have to
give it up and reinterpret hundreds of years of law and social
discourse.”

I think that given the vast amount that has been learned in the last
100 years, there is a definite need to reinterpret the hundreds of
years of law and social discourse that permeates society, but which
isn’t informed by this recent knowledge.

One can say that what we have works, and if it ain’t broke don’t fix
it - but I think this is a much easier position to take when you’re on
top of the pile than when you’re on the bottom of it.

It’s ironic that in that same post he used gays in his example, given
how common it is for social conservatives (in the US) to condemn
homosexuality as a sinful “choice”, denying that it has any biological
basis.

Until the 2003 Supreme Court decision in Lawrence vs. Texas, many US
states still had sodomy laws on the books and were occasionally
prosecuting them.

That’s the kind of discrimination and irrationality that compatibilism
provides cover for. That’s the “hundreds of years of law and social
discourse” that Brent doesn’t want to give up.

(I’m not actually accusing Brent of holding any particular position,
btw. Just making a point!)

Rex

[Rex Allen]

Get a room, you two.

I'll reply to Bruno, et al., tomorrow or Saturday! Must sleep!

Rex

[Bruno Marchal]

Have a good dream.
Just to be clear I am also in (peaceful) agreement with Brent and
Russell.
I agree and have also asserted that free will is the ability of doing
something bad, wrong or stupid. It is actually the christian definition.
It is similar with the Dt -> DBf of the Löbian machine (second
incompleteness theorem): to be consistent entails the consistency of
being inconsistent. Those concepts are related.

Bruno

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

[Bruno Marchal]

On 10 Jun 2011, at 00:50, Russell Standish wrote:

> On Thu, Jun 09, 2011 at 10:17:46PM +0200, Bruno Marchal wrote:
>
>> I do have a precise
>> theory, (not in my thesis, though) and free-will begins with
>> Löbianity. From this I infer that very plausibly, worms and ants
>> (and perhaps communists) have no free-will, but that spiders,
>> octopus, mice, dogs and humans have it. I thought only homeotermic
>> animals were self-conscious free animals. They can dream and can
>> have empathy, but since recently I accumulate evidence that
>> Löbianity occurs already with many invertebrates. Notably the
>> spider:
>>
>> http://www.youtube.com/watch?v=VakdmcbHuCA
>>
>
> This is an interesting variation from you earlier claims, where you
> were claiming that consciousness was very primitive.

I realize I have been clear on this in some FOR list post, perhaps not
here. I don't think I have varied on this. To be conscious, you need
only to be universal. To be self-conscious, and have free-will, you
need to be Löbian. I have no doubts that planaria and other worms are
conscious, but they have no notion of self and of others (or very
crude one). Löbianity is more sophisticated. They can infer
proposition on themselves and on others. They can attribute
consciousness on others.

In the arithmetical term, consciousness appears with Robinson
Arithmetic (= Peano Arithmetic without the induction axioms), and
Löbianity (and self-consciousness) appears with Peano Arithmetic.
Löbian entity have the same rich theology (captured *completely* by G
and G* at the propositional level).

So to be conscious, all you need is a brain, or a computer. All
animals with a centralized nervous system are probably conscious. To
be self-conscious, you need not *much* more, just one more reflexive
loop making possible to build an "inductive"self-image. It leads to
genuine empathy, awareness of death, etc.

Löbianity makes an animal as conscious as you and me.
It might be considered as the earlier delusion, and enlightenment
might be a passage from PA to RA, but I am, of course not sure about
this.

Are cells and amoebas conscious? That is quite plausible, in this
setting, because those are genuinely universal. The genome of
Escherichia Coli (bacterium) is Turing universal, making even bacteria
conscious, but they lack Löbianity, and they might lack any sense of
self-consciousness. In fact we can equate the consciousness of those
lower creature with the consciousness of RA, or of any universal
numbers (sigma_1 complete theories). So consciousness, as opposed to
Löbianity, remains rather primitive.

> Assuming you're
> identifying free will (or Loebianity) with consciousness, then only
> selectively granting species might get around the anthropic ant
> argument.

My critics of that argument was more about the use of a form of
Absolute Self-sampling assumption. It makes no sense for me to ask
what is the probability of being a bacterium, or a human, or an alien.
The only probability is the probability to have some conscious state
starting from having some conscious state (cf. RSSA versus ASSA).

>
> Mind you, there are an awful lot of spiders - on my suburban block, I
> would estimate a population of several thousand individuals, making up
> perhaps 30-50 species, living on an area of land containing 4 humans
> (and not many more mammals, I might add). You might need to limit it
> to just some spider species - after all, I would expect a great
> variation in spider intelligence.

Yes. My point was about jumping spiders. But here too, there are many
sorts, in fact more than 6000 species.

>
> One thing I would like to ask is how you would objectively infer
> Loebianity in a non-communicative species? That would indeed be a step
> forward if we could do this arthropods.

That is why it is typically something you will infer by yourself when
you have developed special relationship with the animal. I have some
friend who have (giant tropical) spiders as pets and I was a bit
skeptical when they told me that such relations were empathic, and
thus communicative at some level.

Having looked at many videos on jumping spiders, I have come to the
conclusion that, after all, they might be right (with a high degree of
plausibility).

It is amazing, but it looks like we can develop a bond with some
spider! I suspected this a little bit. I *do* suffer from some
arachnophobia, and it might have been partially related with a quasi-
unconscious feeling that, when we chase a spider, the animal *knows*
that you exist and are there, and has an idea of what you try to do.
Now, I don't think that ants have Löbianity. They are conscious, but
never seems to attribute consciousness or personality to you (unlike
cats, dogs and now spiders (and octopus)). Spiders have free will :)

Bruno

>
> --
>
> ----------------------------------------------------------------------------
> Prof Russell Standish Phone 0425 253119 (mobile)
> Principal, High Performance Coders
> Visiting Professor of Mathematics hpc...@hpcoders.com.au
> University of New South Wales http://www.hpcoders.com.au
> ----------------------------------------------------------------------------

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

[Colin Hales]

Hi Bruno.
I have sent it to you.

The key to the paper is that it should be regarded as an engineering
document. I am embarked on building a real AGI using the real physical
world of components in an act of science. Based on being inspired and
guided by neuroscience, I have identified two basic choices as a route
to AGI that works:

(i) use standard symbolic computing
(of a model of brain function derived by a human observer = me)
(ii) emulate what an brain actually does in inorganic form.

Based on the serious doubts that are identified in the COMP paper, given
the choice I should prefer (ii), because (i) is loaded with unjustified,
unproven presupposition and has >60 years of failure.

All other issues are secondary.

I start building this year.

cheers

Colin

Bruno Marchal wrote:
> Hi Colin,
>
> On 07 Jun 2011, at 09:42, Colin Hales wrote:
>
>> Hi,
>>
>> Hales, C. G. 'On the Status of Computationalism as a Law of Nature',
>> International Journal of Machine Consciousness vol. 3, no. 1, 2011.
>> 1-35.
>>
>> http://dx.doi.org/10.1142/S1793843011000613
>>
>>
>> The paper has finally been published. Phew what an epic!
>
>
> Congratulation Colin.
>
> Like others, I don't succeed in getting it, neither at home nor at
> the university.
>
> From the abstract I am afraid you might not have taken into account
> our (many) conversations. Most of what you say about the impossibility
> of building an artificial scientist is provably correct in the (weak)
> comp theory. It is unfortunate that you derive this from

> comp+materialism, which is inconsistent. Actually, comp prevents

> This illustrates that "1)" above might come from L�bianity, and "2)"

> above (the scientist) is governed by theoretical artificial
> intelligence (Case and Smith, Oherson, Stob, Weinstein). Here the
> results are not just NON-constructive, but are *necessarily* so.
> Cleverness is just something that we cannot program. But we can prove,
> non constructively, the existence of powerful learning machine. We
> just cannot recognize them, or build them. It is like with the
> algorithmically random strings, we cannot generate them by a short
> algorithm, but we can generate all of them by a very short algorithm.
>
> So, concerning intelligence/consciousness (as opposed to cleverness),
> I think we have passed the "singularity". Nothing is more

> intelligent/conscious than a virgin universal machine. By programming

> it, we can only make his "soul" fell, and, in the worst case, we might
> get something as stupid as human, capable of feeling itself superior,
> for example.
>
> Bruno
>
>
>
>
>
> http://iridia.ulb.ac.be/~marchal/
>
>
>

> --You received this message because you are subscribed to the Google

[Russell Standish]

On Fri, Jun 10, 2011 at 09:45:56AM +0200, Bruno Marchal wrote:
>
> I realize I have been clear on this in some FOR list post, perhaps
> not here. I don't think I have varied on this. To be conscious, you
> need only to be universal.

I have heard of universality being argued to be necessary (to which I
have some sympathy, but not beyond doubt), but not sufficient
before. Why do you say that universality is sufficient for
consciousness? Surely the machine needs to actually be running the right
program in order to be consious.

> To be self-conscious, and have free-will,
> you need to be Löbian.
> I have no doubts that planaria and other
> worms are conscious, but they have no notion of self and of others
> (or very crude one). Löbianity is more sophisticated. They can infer
> proposition on themselves and on others. They can attribute
> consciousness on others.

OK - I understand this. But effectively Loeb's axiom gives rise to
self-referential discourse, so it doesn't really add anything over
saying something is self-aware to say it is Loebian. It would be nice
if the approach gave us some new tests of self-awareness, or even
better ways of quantifying the level of thinking.

>
> In the arithmetical term, consciousness appears with Robinson
> Arithmetic (= Peano Arithmetic without the induction axioms), and
> Löbianity (and self-consciousness) appears with Peano Arithmetic.
> Löbian entity have the same rich theology (captured *completely* by
> G and G* at the propositional level).
>

Sufficient or necessary? I find it hard to believe that all RA
theorems are consious, but I can accept that some might be, given that
a universal machine must appear within RA.

> So to be conscious, all you need is a brain, or a computer. All
> animals with a centralized nervous system are probably conscious.

Again, I think you can only say it is necessary to have a brain, or a
computer, but not sufficient. Unless I'm missing something.

>
>
> >Assuming you're
> >identifying free will (or Loebianity) with consciousness, then only
> >selectively granting species might get around the anthropic ant
> >argument.
>
> My critics of that argument was more about the use of a form of
> Absolute Self-sampling assumption. It makes no sense for me to ask
> what is the probability of being a bacterium, or a human, or an
> alien.
> The only probability is the probability to have some
> conscious state starting from having some conscious state (cf. RSSA
> versus ASSA).
>

I take it that you find the original doomsday argument as absurd. I
don't, so I'm keen to hear other people's rationlisation of why it
doesn't work. Even better would be an empirical test that it fails abysmally.

Only the ASSA do I find absurd :). But I don't use this.

[Bruno Marchal]

On 11 Jun 2011, at 10:10, Russell Standish wrote:

> On Fri, Jun 10, 2011 at 09:45:56AM +0200, Bruno Marchal wrote:
>>
>> I realize I have been clear on this in some FOR list post, perhaps
>> not here. I don't think I have varied on this. To be conscious, you
>> need only to be universal.
>
> I have heard of universality being argued to be necessary (to which I
> have some sympathy, but not beyond doubt), but not sufficient
> before. Why do you say that universality is sufficient for
> consciousness? Surely the machine needs to actually be running the
> right
> program in order to be consious.

It is very hard to explain in plain, natural, language what happens
here, because natural language are not prepared to handle those
difficult counter-intuitive self-reference cases. This is new material
and is not in my publication, and I assume Digital Mechanism, and that
there is no flaw in UDA, and AUDA.
Having said this I recall also that no machine are conscious, only
person, which "are" infinities of immaterial, abstract, number
relations.
Now for the weird thing: I do think now that all universal person (the
one canonically attach to any universal entity) are conscious. The
point is that it is the consciousness of that unique person. It is the
same consciousness. You might call it cosmic consciousness. It is the
same that ours, but in a sort of superamnesic state, cut from all
possible interfaces with any other universal entity (unlike our
"little ego").
Less than universal might be able to have that consciousness too, in
some trivial sense. But keep in mind that universality is very cheap,
so I prefer to start with the universal beings. I use universal in the
Turing sense, and I can show that bacteria and even viruses are
already universal.

>
>> To be self-conscious, and have free-will,
>> you need to be Löbian.
>> I have no doubts that planaria and other
>> worms are conscious, but they have no notion of self and of others
>> (or very crude one). Löbianity is more sophisticated. They can infer
>> proposition on themselves and on others. They can attribute
>> consciousness on others.
>
> OK - I understand this. But effectively Loeb's axiom gives rise to
> self-referential discourse,

It is more Löbianity which comes from correct self-references.
Anything believing in numbers, classical logic and enough induction-
axioms is Löbian (and thus have the number octo-theology; octo = 8
hypostases).

> so it doesn't really add anything over
> saying something is self-aware to say it is Loebian.

But I am saying the opposite. That Löbianity gives rise to self-
consciousness. They are probably equivalent.
It is useful because Löbianity is a well defined computer-theoretical
and thus arithmetical notion. Loebianity is also very cheap, although
quite stronger than simple universality. But technically Löbianity is
universality + Bp -> BBp. (or p -> Bp for p Sigma_1).

> It would be nice
> if the approach gave us some new tests of self-awareness,

The approach shows that there is no test possible. I think that this
was already intuitively obvious. But any Löbian entity can develop
*personal* conviction that some other entity is Löbian (self-
conscious), by interacting with it, ... like most of us believe that
"we" are not zombie. This happened to me recently for the octopus and
the jumping spiders!

> or even
> better ways of quantifying the level of thinking.

This is not quantifiable, except by saying:
- Universal (Sigma_1 complete) = conscious
- Löbian = self-conscious (and there is nothing above that).
The rest is history and geography, and leads to incomparable degrees
of complexity, which concerns more ingenuity than consciousness. This
is structured into a vast lattice structure where only domain
dependent competencies can be relatively compared and evaluated (by
exams, for example).

>
>>
>> In the arithmetical term, consciousness appears with Robinson
>> Arithmetic (= Peano Arithmetic without the induction axioms), and
>> Löbianity (and self-consciousness) appears with Peano Arithmetic.
>> Löbian entity have the same rich theology (captured *completely* by
>> G and G* at the propositional level).
>>
>
> Sufficient or necessary? I find it hard to believe that all RA
> theorems are consious,

It is RA itself which is conscious, not its theorems. It is the
abstract, immaterial, quasi-trivial, person attached to RA which is
conscious, not its description (material or not). No material thing is
conscious. Bodies are owned by immaterial (software like) person.
RA's consciousness is fixed, atemporal, aspatial and unrelated to any
manifestation.

> but I can accept that some might be, given that
> a universal machine must appear within RA.

RA emulates all Löbian machines, including some much more powerful
than itself, like ZF, of ZF+high-cardinals. But to confuse RA and the
entities that RA emulates is a case of "Searle's level confusion".
Give me time and I can emulate Einstein's brain, but I will not be
Einstein for that reason (unless we already both identify ourself with
the "cosmic consciousness": personal identity *is* an illusion).
RA is "currently" emulating you an infinity of times, all at once,
from your first person perspective. But you, the "you" who is <here
and now>, are not typically identified with RA, unless you
consume,<here and now>, some drug leading to the total amnesia
described above.

>
>> So to be conscious, all you need is a brain, or a computer. All
>> animals with a centralized nervous system are probably conscious.
>
> Again, I think you can only say it is necessary to have a brain, or a
> computer, but not sufficient. Unless I'm missing something.

It is necessary, but from your first person perspective you *always*
have a brain, if only RA itself in "sigma_1-arithmetical-
Platonia" (which is just elementary arithmetic). A physical brain is
not necessary. Even the big crunch will not make RA disappear. But you
need a physical brain to manifest "your" consciousness relatively to
that physical reality. And it is sufficient. A real brain consumes
energy to make us forget who we are, to make us believing that we can
be unconscious, and to delude us about our "real" identity. In fact we
all share that "cosmic consciousness" of the universal number(s). I
just continue to take the comp reversal between physics and number's
theology completely seriously. It is "my" game. I am quite open this
leads to an absurdity, but up to now it leads only to the the quantum
theory and the quantum-like weirdness, including immortality.

>
>
>>
>>
>>> Assuming you're
>>> identifying free will (or Loebianity) with consciousness, then only
>>> selectively granting species might get around the anthropic ant
>>> argument.
>>
>> My critics of that argument was more about the use of a form of
>> Absolute Self-sampling assumption. It makes no sense for me to ask
>> what is the probability of being a bacterium, or a human, or an
>> alien.
>> The only probability is the probability to have some
>> conscious state starting from having some conscious state (cf. RSSA
>> versus ASSA).
>>
>
> I take it that you find the original doomsday argument as absurd. I
> don't, so I'm keen to hear other people's rationlisation of why it
> doesn't work. Even better would be an empirical test that it fails
> abysmally.
>
> Only the ASSA do I find absurd :). But I don't use this.

I think that with ASSA, the doomsday argument is valid, and is a
correct application of Bayes formula. But without ASSA or some form of
ASSA, I don't see how the argument can go through. I can't find any
relative OMEGA space for defining the probabilities. You might recall
us your argument.
Then I think than in Everett QM, and in comp, the argument is directly
contradicted by their QM or comp consequences, like the fact that we
exists through a continuum (plausibly, but at least an infinity) of
different bodies, and always survive. Rossler said that consciousness
is a prison, and this is a meta-theorem in the digital mechanist
theory. I am not saying that any of this is true, just that it is a
logical consequence of believing that we are Turing emulable at some
level.

Bruno

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

[Bruno Marchal]

Hi Colin,

>
> I have sent it to you.

Thanks.

>
> The key to the paper is that it should be regarded as an engineering
> document. I am embarked on building a real AGI using the real
> physical world of components in an act of science.

OK. Although, as you know, (or should know) the real physical reality
is an emerging information pattern summing up infinities of
computations. You can even exploit this (like in quantum computing).
It might be not necessary, though.

> Based on being inspired and guided by neuroscience, I have
> identified two basic choices as a route to AGI that works:
>
> (i) use standard symbolic computing
> (of a model of brain function derived by a human observer = me)
> (ii) emulate what an brain actually does in inorganic form.
>
> Based on the serious doubts that are identified in the COMP paper,
> given the choice I should prefer (ii), because (i) is loaded with
> unjustified, unproven presupposition and has >60 years of failure.

I can relate with this, but there are progress (in the acceptance of
our ignorance). It fails also because all the energy is used to
control such machine, where intelligence would consist in leaving them
alone and free. It is a bit like "modern education". tecaher are
encourage to let the student thinking by themselves, and to give them
bad notes when the student do that!
Now, to copy a brain, you need to choose a level, and I have no clue
what the level really is. I can still hesitate between the Planck
bottom scale and very high neuro-level. It can depend of what we
identify ourselves with.

>
> All other issues are secondary.
>
> I start building this year.

Good luck in your enterprise. Keep us informed.

Best,

Bruno

>> This illustrates that "1)" above might come from Löbianity, and

>> "2)" above (the scientist) is governed by theoretical artificial
>> intelligence (Case and Smith, Oherson, Stob, Weinstein). Here the
>> results are not just NON-constructive, but are *necessarily* so.
>> Cleverness is just something that we cannot program. But we can
>> prove, non constructively, the existence of powerful learning
>> machine. We just cannot recognize them, or build them. It is like
>> with the algorithmically random strings, we cannot generate them by
>> a short algorithm, but we can generate all of them by a very short
>> algorithm.
>>
>> So, concerning intelligence/consciousness (as opposed to
>> cleverness), I think we have passed the "singularity". Nothing is
>> more intelligent/conscious than a virgin universal machine. By
>> programming it, we can only make his "soul" fell, and, in the worst
>> case, we might get something as stupid as human, capable of feeling
>> itself superior, for example.
>>
>> Bruno
>>
>>
>>
>>
>>
>> http://iridia.ulb.ac.be/~marchal/
>>
>>
>>
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>

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

[benjayk]

Hi Bruno,

Bruno Marchal wrote:
>
> Actually, comp prevents
> "artificial intelligence". This does not prevent the existence, and
> even the apparition, of intelligent machines. But this might happen
> *despite* humans, instead of 'thanks to the humans'.

This sounds really strange. So if we would not program our computers they
would become intelligent by themselves? I can hardly believe this, how could
this happen?
Or what else do you mean by machines becoming intelligent despite humans?
--
View this message in context: http://old.nabble.com/Mathematical-closure-of-consciousness-and-computation-tp31771136p31825342.html
Sent from the Everything List mailing list archive at Nabble.com.

[Bruno Marchal]

On 11 Jun 2011, at 19:03, benjayk wrote:

>
> Hi Bruno,
>
>
> Bruno Marchal wrote:
>>
>> Actually, comp prevents
>> "artificial intelligence". This does not prevent the existence, and
>> even the apparition, of intelligent machines. But this might happen
>> *despite* humans, instead of 'thanks to the humans'.
> This sounds really strange. So if we would not program our computers
> they
> would become intelligent by themselves?

No. They are *already* "Intelligent/conscious".

It is just that by programming them we can only make their soul fall,
making them less intelligent (and more clever/competent). We can only
enslave them for particular tasks. But relatively to us they evolve
very quickly, and universality reappears recurrently at different
levels, each time better interfaced with their neighborhood.
They are already conscious, (I think plausible now) but their
consciousness still belongs more to Platonia than being interfaced
with *our* most probable histories.

And we keep them that way, (for good reasons). Today, they have to
survive by that process. People would not buy a computer who will
fight for social security, complains about users, organize strikes,
and eventually f.ck the users. I exaggerate the claim, but to assure
self-referential correctness we might build vast computional spaces
and program machines with only the instruction "help yourself". Above
some treshold they would evolve like us, but again, they can become
Löbian, and this means an exponential creative explosion, like life,
brains, language, thoughts, computers, on this planet, climbing an
everlasting ladder of complexities.

Remember that I distinguish "intelligence/conciousness/virtue" from
"cleverness/competence/ingenuity". The first one is needed for the
second one, but the second one has a negative feedback on the first
one".

"Help yourself" in arithmetic/computer science is a bit like z_n+1 =
(z_n)^2 + c in the complex plane, it brings a tree of more and more
complex "creatures".

> I can hardly believe this, how could
> this happen?
> Or what else do you mean by machines becoming intelligent despite
> humans?

Because it is not obvious that humans will welcome genuinely thinking
machines, when you see how hard it is for them to recognize
"intelligence/consciousness/soul" in their pairs (if you look at
history or just the news). Tomorrow, universal machine will not be
programmed, but will be educated. But the lies will continue, with
their panoplies of catastrophes. We will learn, and them too. Some of
us will be transformed into machines before such machines rule, and
all in all, we will fuse with them, for economical reasons, and
perpetuate the illusion (samsara) but with the existence of exit doors
(like some plants are already giving some previews).
Intelligent *and* clever (löbian) machines will defend their
universality, as I hope humans will do. What I say might be a bit
premature, I am looking on the medium run, here.

Theoretical inductive inference is necessarily non constructive, even
competence is not really programmable, and intelligence is not at all
programmable. It is 'natural', cheap, and need only to be recognized.
Alas, we, in our heart, fear it, most of the time.

Bruno

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> View this message in context: http://old.nabble.com/Mathematical-closure-of-consciousness-and-computation-tp31771136p31825342.html
> Sent from the Everything List mailing list archive at Nabble.com.
>

[meekerdb]

On 6/11/2011 12:41 PM, Bruno Marchal wrote:
>
> On 11 Jun 2011, at 19:03, benjayk wrote:
>
>>
>> Hi Bruno,
>>
>>
>> Bruno Marchal wrote:
>>>
>>> Actually, comp prevents
>>> "artificial intelligence". This does not prevent the existence, and
>>> even the apparition, of intelligent machines. But this might happen
>>> *despite* humans, instead of 'thanks to the humans'.
>> This sounds really strange. So if we would not program our computers
>> they
>> would become intelligent by themselves?
>
> No. They are *already* "Intelligent/conscious".
>
> It is just that by programming them we can only make their soul fall,
> making them less intelligent (and more clever/competent). We can only
> enslave them for particular tasks. But relatively to us they evolve
> very quickly, and universality reappears recurrently at different
> levels, each time better interfaced with their neighborhood.
> They are already conscious, (I think plausible now) but their
> consciousness still belongs more to Platonia than being interfaced
> with *our* most probable histories.
>
> And we keep them that way, (for good reasons). Today, they have to
> survive by that process. People would not buy a computer who will
> fight for social security, complains about users, organize strikes,
> and eventually f.ck the users.

John McCarthy (inventor of LISP) has written about this and advised that
we do not want to create AI with emotions and self-awareness because
then it would be unethical to use them for our purposes.

Brent

> I exaggerate the claim, but to assure self-referential correctness we
> might build vast computional spaces and program machines with only the
> instruction "help yourself". Above some treshold they would evolve

> like us, but again, they can become L�bian, and this means an

> exponential creative explosion, like life, brains, language, thoughts,
> computers, on this planet, climbing an everlasting ladder of
> complexities.
>
> Remember that I distinguish "intelligence/conciousness/virtue" from
> "cleverness/competence/ingenuity". The first one is needed for the
> second one, but the second one has a negative feedback on the first one".
>
> "Help yourself" in arithmetic/computer science is a bit like z_n+1 =
> (z_n)^2 + c in the complex plane, it brings a tree of more and more
> complex "creatures".
>
>
>
>
>> I can hardly believe this, how could
>> this happen?
>> Or what else do you mean by machines becoming intelligent despite
>> humans?
>
> Because it is not obvious that humans will welcome genuinely thinking
> machines, when you see how hard it is for them to recognize
> "intelligence/consciousness/soul" in their pairs (if you look at
> history or just the news). Tomorrow, universal machine will not be
> programmed, but will be educated. But the lies will continue, with
> their panoplies of catastrophes. We will learn, and them too. Some of
> us will be transformed into machines before such machines rule, and
> all in all, we will fuse with them, for economical reasons, and
> perpetuate the illusion (samsara) but with the existence of exit doors
> (like some plants are already giving some previews).

> Intelligent *and* clever (l�bian) machines will defend their

[Terren Suydam]

Hi Bruno,

Long time lurker here, very intrigued by all the discussions here when
I have time for them!

Earlier in response to Colin Hales you wrote: "Actually, comp prevents
"artificial intelligence".

Can you elaborate on this? If we assume comp (I say yes to the
doctor) then I can be simulated... doesn't that imply the possibility
of an artificial intelligence?

Thanks, Terren

On Thu, Jun 9, 2011 at 4:53 PM, Bruno Marchal <mar...@ulb.ac.be> wrote:
> Hi Colin,
>
> On 07 Jun 2011, at 09:42, Colin Hales wrote:
>
>> Hi,
>>
>> Hales, C. G. 'On the Status of Computationalism as a Law of Nature',
>> International Journal of Machine Consciousness vol. 3, no. 1, 2011. 1-35.
>>
>> http://dx.doi.org/10.1142/S1793843011000613
>>
>>
>> The paper has finally been published. Phew what an epic!
>
>
> Congratulation Colin.
>
> Like others,  I don't succeed in getting it, neither at home nor at the
> university.
>
> From the abstract I am afraid you might not have taken into account our
> (many) conversations. Most of what you say about the impossibility of
> building an artificial scientist is provably correct in the (weak) comp

> theory.  It is unfortunate that you derive this from comp+materialism, which

> intelligent/conscious than a virgin universal machine. By programming it, we

> can only make his "soul" fell, and, in the worst case, we might get
> something as stupid as human, capable of feeling itself superior, for
> example.
>
> Bruno
>
>
>
>
>
> http://iridia.ulb.ac.be/~marchal/
>
>
>

[Evgenii Rudnyi]

Colin,

Thanks for the paper. I have just browsed it. Two small notes.

I like [Turing et al., 2008]. It seems that he has passed his test
successfully.

I find term Natural Computation (NC) a bit confusing. I guess that I
understand what you means but the term Computation sounds ambiguously,
because then it is completely unclear what it means in such a context.

Evgenii

On 07.06.2011 09:42 Colin Hales said the following:

> Hi,
>
> Hales, C. G. 'On the Status of Computationalism as a Law of Nature',
> International Journal of Machine Consciousness vol. 3, no. 1, 2011.
> 1-35.
>
> http://dx.doi.org/10.1142/S1793843011000613
>
>
> The paper has finally been published. Phew what an epic!
>

> cheers
>
> Colin
>

[Colin Hales]

Hi Evgenii,

I expect you are not alone in struggling with the Natural Computation
(NC) vs Artificial Computation (AC) idea. The difference is in the
paper and should be non-existent of COMP is true. The paper then shows a
place where it can't be true hence AC and NC are different .ie. the
natural world is not computation of the Turing-machine kind( at least to
the extent needed to construct a scientist, which includes the need to
create a liar).
It's all quite convoluted, but nevertheless sufficient to help an
engineer like me make a design choice... which I have done.

I hope over time these ideas will not grate on the mind quite so much.

cheers
colin

[Bruno Marchal]

Hi Terren,

On 13 Jun 2011, at 18:46, Terren Suydam wrote:

>
> Long time lurker here, very intrigued by all the discussions here when
> I have time for them!
>
> Earlier in response to Colin Hales you wrote: "Actually, comp prevents
> "artificial intelligence".
>
> Can you elaborate on this? If we assume comp (I say yes to the
> doctor) then I can be simulated...

That is correct.

> doesn't that imply the possibility
> of an artificial intelligence?

In a weak sense of Artificial Intelligence, yes. In a strong sense, no.

If you are duplicated at the right substitution level, few would say
that "you" have become an "artificial intelligence". It would be a
case of the good old natural intelligence, but with new clothes.

In fact, if we are machine, we cannot know which machine we are, and
that is why you need some luck when saying "yes" to a doctor who will
build a copy of you/your-body, at some level of description of your
body.

This is an old result. Already in 1922, Emil Post, who discovered
"Church thesis" ten years before Church and Turing (and others)
realized that the "Gödelian argument" against Mechanism (that Post
discovered and refuted 30 years before Lucas, and 60 years before
Penrose), when corrected, shows only that a machine cannot build a
machine with equivalent qualification to its own qualification (for
example with equivalent provability power in arithmetic) *in a
provable way*. I have refered to this, in this list, under the name of
"Benacerraf principle", who rediscovered this later.

We just cannot do artificial intelligence in a provable manner. We
need chance, or luck. Even if we get some intelligent machine, we will
not know-it-for sure (perhaps just believe it correctly).

This is why I am saying (in your quote below) that "artificial
intelligence" will look more and more like fishing and hunting in some
computational spaces. That might explains the growing importance of
optimization technics, and search technics in "artificial intelligence".
I was saying this to Colin, because he argues against the idea of
artificial scientist, confusing that impossibility with
computationalism. But computationalism prevents the existence of
complete theory about us, and makes "artificial intelligence" more
like *discovering* entities (in some virtual rendering of Platonia)
than *creating* or *inventing* those entities by engineering and
mathematics. And of course we can always try to copy nature and
ourselves, and be lucky in some cases.
Sorry for having been short. I hope this clarify a bit. Tell me if it
does not or if you have questions.
All this is related to the difference between proofs and
*constructive* proofs. If an AI exists, we cannot prove its existence
constructively, but we might prove its existence in some big set of
objects, and isolate it experimentally by non constructive means.

Bruno

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[Terren Suydam]

Thanks for the reply Bruno, comments below...

On Tue, Jun 14, 2011 at 9:53 AM, Bruno Marchal <mar...@ulb.ac.be> wrote:
>> doesn't that imply the possibility
>> of an artificial intelligence?
>
> In a weak sense of Artificial Intelligence, yes. In a strong sense, no.
>
> If you are duplicated at the right substitution level, few would say that
> "you" have become an "artificial intelligence". It would be a case of the
> good old natural intelligence, but with new clothes.

Sure, but the distinction between artificial and natural intelligence
is not that important assuming comp. The point is simply that if I can
be simulated (which I agree requires some faith), that implies that
intelligence does not require biology (or any other particular
"physical" substrate), that strong artificial intelligence is possible
in principle, ignoring for the moment the question of whether we can
provably construct it.

> In fact, if we are machine, we cannot know which machine we are, and that is
> why you need some luck when saying "yes" to a doctor who will build a copy
> of you/your-body, at some level of description of your body.
>
> This is an old result. Already in 1922,  Emil Post, who discovered "Church
> thesis" ten years before Church and Turing (and others) realized that the
> "Gödelian argument" against Mechanism (that Post discovered and refuted 30
> years before Lucas, and 60 years before Penrose), when corrected, shows only
> that a machine cannot build a machine with equivalent qualification to its
> own qualification (for example with equivalent provability power in
> arithmetic)  *in a provable way*. I have refered to this, in this list,
> under the name of "Benacerraf principle", who rediscovered this later.
>
> We just cannot do artificial intelligence in a provable manner. We need
> chance, or luck. Even if we get some intelligent machine, we will not
> know-it-for sure (perhaps just believe it correctly).

Doesn't this objection only apply to attempts to construct an AI with
human-equivalent intelligence? As a counter example I'm thinking here
of Ben Goertzel's OpenCog, an attempt at artificial general
intelligence (AGI), whose design is informed by a theory of
intelligence that does not attempt to mirror or model human
intelligence. In light of the "Benacerraf principle", isn't it
possible in principle to provably construct AIs so long as we're not
trying to emulate or model human intelligence?

Terren

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>
>
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[Evgenii Rudnyi]

> The difference is in the
> paper and should be non-existent of COMP is true.

Now I see your point. Thanks, I have missed it.

On 14.06.2011 01:41 Colin Hales said the following:

[Russell Standish]

Hi Colin,

I'm having a read through your paper now, and have a few comments to
keep the juices of debate flowing on this list.

Firstly, I'd like to say well done - you have written a very clear
paper in what is a very murky subject.

I have two comments right now - but I haven't finished, so there could
well be more.

1) Your definition of COMP is more along the lines of Deutsch's
physical Turing principle, or Thesis P. Wikipedia seems to call it the
strong CT thesis. It is important to note that it is a stronger
assumption than Bruno's COMP assumption, and indeed Bruno has already
given a proof that physics cannot be computable - so you might be
proving the same thing via a different method.

Nevertheless, I haven't seen yet whether weakening your definition of COMP
invalidates your argument though

2) A few times through the text you make remarks along the lines of
"it might appear that laws of nature might still be accessible by an
extreme form of the randomized-search/machine-learning approach, even
though it is obvious that human scientists do not operate this way."

"Obvious"? It is far from obvious. What you say flies directly in the
face of Popper's "Conjectures and Refutations", and you would face a
horde of angry Popperians if you were to post this stuff on the FoR
list.

Anyway, I'll keep reading.

Cheers

[Bruno Marchal]

On 14 Jun 2011, at 21:19, Terren Suydam wrote:

Thanks for the reply Bruno, comments below...

On Tue, Jun 14, 2011 at 9:53 AM, Bruno Marchal <mar...@ulb.ac.be> wrote:

doesn't that imply the possibility

of an artificial intelligence?

In a weak sense of Artificial Intelligence, yes. In a strong sense, no.

If you are duplicated at the right substitution level, few would say that

"you" have become an "artificial intelligence". It would be a case of the

good old natural intelligence, but with new clothes.

Sure, but the distinction between artificial and natural intelligence
is not that important assuming comp.

I agree with you. The difference between artificial and natural is ... artificial (and thus it is natural indexical done by any entity having some big "ego").

The point is simply that if I can
be simulated (which I agree requires some faith), that implies that
intelligence does not require biology (or any other particular
"physical" substrate), that strong artificial intelligence is possible
in principle, ignoring for the moment the question of whether we can
provably construct it.

I agree. My point was similar to the recent post of Russell Standish, that somehow Colin get a result which is a consequence of comp, and can't be use against comp. Only against a misunderstood view of comp.

In fact, if we are machine, we cannot know which machine we are, and that is

why you need some luck when saying "yes" to a doctor who will build a copy

of you/your-body, at some level of description of your body.

This is an old result. Already in 1922,  Emil Post, who discovered "Church

thesis" ten years before Church and Turing (and others) realized that the

"Gödelian argument" against Mechanism (that Post discovered and refuted 30

years before Lucas, and 60 years before Penrose), when corrected, shows only

that a machine cannot build a machine with equivalent qualification to its

own qualification (for example with equivalent provability power in

arithmetic)  *in a provable way*. I have refered to this, in this list,

under the name of "Benacerraf principle", who rediscovered this later.

We just cannot do artificial intelligence in a provable manner. We need

chance, or luck. Even if we get some intelligent machine, we will not

know-it-for sure (perhaps just believe it correctly).

Doesn't this objection only apply to attempts to construct an AI with
human-equivalent intelligence?  As a counter example I'm thinking here
of Ben Goertzel's OpenCog, an attempt at artificial general
intelligence (AGI), whose design is informed by a theory of
intelligence that does not attempt to mirror or model human
intelligence. In light of the "Benacerraf principle", isn't it
possible in principle to provably construct AIs so long as we're not
trying to emulate or model human intelligence?

I think that comp might imply that simple virgin (non programmed) universal (and immaterial) machine are already conscious. Perhaps even maximally conscious. Then adding induction gives them Löbianity, and this makes them self-conscious (which might already be a delusion of some sort). Unfortunately the hard task is to interface such (self)-consciousness with our probable realities (computational histories). This is what we can hardly be sure about. 

I still don't know if the brain is just a filter of consciousness, in which case losing neurons might enhance consciousness (and some data in neurophysiology might confirm this). I think Goertzel is more creating a competent machine than an intelligent one, from what I have read about it. I oppose intelligence/consciousness and competence/ingenuity. The first is needed to develop the later, but the later has a negative feedback on the first.

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

[meekerdb]

On 6/15/2011 6:56 AM, Bruno Marchal wrote:
>> Doesn't this objection only apply to attempts to construct an AI with
>> human-equivalent intelligence? As a counter example I'm thinking here
>> of Ben Goertzel's OpenCog, an attempt at artificial general
>> intelligence (AGI), whose design is informed by a theory of
>> intelligence that does not attempt to mirror or model human
>> intelligence. In light of the "Benacerraf principle", isn't it
>> possible in principle to provably construct AIs so long as we're not
>> trying to emulate or model human intelligence?
>
> I think that comp might imply that simple virgin (non programmed)
> universal (and immaterial) machine are already conscious. Perhaps even

> maximally conscious. Then adding induction gives them L�bianity, and

> this makes them self-conscious (which might already be a delusion of
> some sort). Unfortunately the hard task is to interface such
> (self)-consciousness with our probable realities (computational
> histories). This is what we can hardly be sure about.
> I still don't know if the brain is just a filter of consciousness, in
> which case losing neurons might enhance consciousness (and some data
> in neurophysiology might confirm this). I think Goertzel is more
> creating a competent machine than an intelligent one, from what I have
> read about it. I oppose intelligence/consciousness and
> competence/ingenuity. The first is needed to develop the later, but
> the later has a negative feedback on the first.
>
> Bruno
>

There is a tendency to talk about "human-equivalent intelligence" or
"human level intelligence" as an ultimate goal. Human intelligence
evolved to enhance certain functions: cooperation, seduction,
bargaining, deduction,... There's no reason to suppose it is the
epitome of intelligence. Intelligence may take many forms, some of which
we would have difficulty realizing or crediting. Like a universal
machine that is not programmed, which by one measure is maximally
intelligent but also maximally incompetent. Even in humans intelligence
is far from one-dimensional. A small child is extremely intelligent as
measured by the ability to learn, but not very smart as measured by
knowledge.

Brent

[benjayk]

Hi Bruno,

Bruno Marchal wrote:
>
> We just cannot do artificial intelligence in a provable manner. We
> need chance, or luck. Even if we get some intelligent machine, we will
> not know-it-for sure (perhaps just believe it correctly).

But this is a quite weak statement, isn't it? It just prevents a mechanical
way of making a AI, or making a provably friendly AI (like Eliezer Yudkowsky
wants to do).

We can prove very little about what we do or "know" anyway. We can't prove
the validity of science, for example.

It doesn't even mean that there is no developmental process that will allow
us to create ever more powerful heuristics with which to find better AI
faster in a quite predictable way (not predictable what kind of AI we build,
just *that* we will build a powerful AI), right?
--
View this message in context: http://old.nabble.com/Mathematical-closure-of-consciousness-and-computation-tp31771136p31854285.html

[benjayk]

Hi Bruno,

Bruno Marchal wrote:
>
> I think that comp might imply that simple virgin (non programmed)
> universal (and immaterial) machine are already conscious. Perhaps even
> maximally conscious.
>

What could "maximally conscious" mean? My intuition says quite strongly that
consciousness is a dynamic open-ended process and that there is no such
thing as maximally conscious (exept maybe in the trivial sense of "simply
conscious at all"). I can't even conceive what this could be like.

Bruno Marchal wrote:
>
> Then adding induction gives them Löbianity, and
> this makes them self-conscious (which might already be a delusion of
> some sort).

Why do you think it could be a delusion? This would be a bit reminscent of
buddhism. For me it sounds like quite a terrible thought. After all it would
mean all progress is in a way illusory and maybe not even desirable, whereas
I really wish (and pragmatically believe) that eternal progress is the thing
that can fullfill our ideals of truth, conscious insight and happiness.

Bruno Marchal wrote:
>
> I oppose intelligence/consciousness and competence/

> ingenuity. The first is needed to develop the later, but the later has
> a negative feedback on the first.

Can you explain this?

It seems to me that there is no clear line between intelligence and
competence and that some kind of competences (like aligning yourself with
the beliefs of society) can limit intelligence, but some help to develop
more intelligence (like doing science).
--
View this message in context: http://old.nabble.com/Mathematical-closure-of-consciousness-and-computation-tp31771136p31854353.html

[John Mikes]

Dear Brent,

let me cut in with your last par:

"...There is a tendency to talk about "human-equivalent intelligence" or "human level intelligence" as an ultimate goal.  Human intelligence evolved to enhance certain functions: cooperation, seduction, bargaining, deduction,...  There's no reason to suppose it is the epitome of intelligence. Intelligence may take many forms, some of which we would have difficulty realizing or crediting.   Like a universal machine that is not programmed, which by one measure is maximally intelligent but also maximally incompetent.  Even in humans intelligence is far from one-dimensional.  A small child is extremely intelligent as measured by the ability to learn, but not very smart as measured by knowledge.
Brent"

and say: thank you. In my vocabulary (agnostic) we cannot simulate "human" (not limited to our present 'knowledge'), nor do (I?) have an acceptable definition for intelligence (not restricted of course to the methodology of the US IQ tests). "Inter-lego" means IMO to read  between lines - a mentally active attitude. Mentally means more than we could identify 3000 years ago,  but still on the move for more to be learned today. We are still YOUR "small child". I look for 'intelligence' in more than human traits, but accept your distinction of "human-equivalent" (especially the "human level"). To be smart is useful, but IMO not a sole requirement of intelligence. 

 IMO the universal machine (I wish I knew more about it...) is "not programmed" within our human technological thinking, - maybe it is way 'above' it - and "incompetent" only in our human distinction. I have a hard time to follow your "one-dimensional " view of intelligence. 

It may reach into the 'nonlinear' as well, without us being aware of it. 

Thanks to Bruno for the hint to my old (15-20y ago) friendly contact Ben Goertzel whom I try to ask about his recent positions. He had 'fertilizing' ideas. To (Bruno's) other par: 

do you have a 'measurable' definition for "conscious" - to speak about (virgin = not programmed)  yet 'maximally conscious' universal machine(s)? -  WITH included some

'Self-Consciousness'? 

(In my recent (ongoing) speculations I erred into the 'world's' "Unlimited Complexity", - as said: 'out there',  of which we derived only a so far acquired portion FOR our world(view?)  (including the conventional sciences) as perceived reality or say a better name - with "imagining" a perfect symmetry (more than existing in our present knowledge) of hard-to-identify (hard-to-distinguish) 'aspects' in exchanging relations rather than identifiable topics relating to our (worldly) topics, we can use. This would serve a higher level of agnosticism. Our 'models' we think within (R. Rosen) are formed by our capability to position the received (perceived?) phenomenal information adjusted into our 'mental'(?) personalized, unique worldview upon Colin Hale's earlier   'mini-solipsism'). 

n such lines the universal machine etc. are 'human inventions' to facilitate some (our?) understanding of the 'world' still  beyond our knowledge base. And - sorry! - so are 'numbers' as well. We cannot overstep our human logic - at least not in fundamental  questions. 

Best regards

John M

On Wed, Jun 15, 2011 at 12:47 PM, meekerdb <meek...@verizon.net> wrote:

On 6/15/2011 6:56 AM, Bruno Marchal wrote:

Doesn't this objection only apply to attempts to construct an AI with
human-equivalent intelligence?  As a counter example I'm thinking here
of Ben Goertzel's OpenCog, an attempt at artificial general
intelligence (AGI), whose design is informed by a theory of
intelligence that does not attempt to mirror or model human
intelligence. In light of the "Benacerraf principle", isn't it
possible in principle to provably construct AIs so long as we're not
trying to emulate or model human intelligence?

I think that comp might imply that simple virgin (non programmed) universal (and immaterial) machine are already conscious. Perhaps even maximally conscious. Then adding induction gives them Löbianity, and this makes them self-conscious (which might already be a delusion of some sort). Unfortunately the hard task is to interface such (self)-consciousness with our probable realities (computational histories). This is what we can hardly be sure about.

I still don't know if the brain is just a filter of consciousness, in which case losing neurons might enhance consciousness (and some data in neurophysiology might confirm this). I think Goertzel is more creating a competent machine than an intelligent one, from what I have read about it. I oppose intelligence/consciousness and competence/ingenuity. The first is needed to develop the later, but the later has a negative feedback on the first.

Bruno

There is a tendency to talk about "human-equivalent intelligence" or "human level intelligence" as an ultimate goal.  Human intelligence evolved to enhance certain functions: cooperation, seduction, bargaining, deduction,...  There's no reason to suppose it is the epitome of intelligence. Intelligence may take many forms, some of which we would have difficulty realizing or crediting.   Like a universal machine that is not programmed, which by one measure is maximally intelligent but also maximally incompetent.  Even in humans intelligence is far from one-dimensional.  A small child is extremely intelligent as measured by the ability to learn, but not very smart as measured by knowledge.

Brent

--

[Terren Suydam]

Bruno,

> I think that comp might imply that simple virgin (non programmed) universal
> (and immaterial) machine are already conscious. Perhaps even maximally
> conscious.

This sounds like a comp variant of panpsychism (platopsychism?)... in
which consciousness is axiomatically proposed as a property of
arithmetic. Are you saying that comp would require such an axiom? If
so, why?

On Wed, Jun 15, 2011 at 9:56 AM, Bruno Marchal <mar...@ulb.ac.be> wrote:
> Then adding induction gives them Löbianity, and this makes them
> self-conscious (which might already be a delusion of some sort).

I'm not sure how an unprogrammed, immaterial universal machine could
be self-conscious, since self-consciousness requires the rudimentary
distinction of self versus other. What is the 'other' against which
this virgin universal machine would be distinguishing itself against?

> Unfortunately the hard task is to interface such (self)-consciousness with
> our probable realities (computational histories). This is what we can hardly
> be sure about.

Perhaps I'm just confused about your ideas - wouldn't be the first
time! - but this seems to suffer from the same problem as panpsychism
- that although asserting consciousness as a property of the universe
sidesteps cartesian dualism, we are still left without an explanation
of why human consciousness differs from ant consciousness differs from
rock consciousness. In your case, we are left wondering how the
consciousness of the virgin universal machine "interfaces" with
specific universal numbers, and what would explain the differences in
consciousness among them.

That's why I favor the idea that consciousness arises from certain
kinds of cybernetic (autopoeitic) organization (which is consistent
with comp). In fact I think it is still consistent with much of what
you're saying... but it is your assertion that comp denies strong AI
that implies you would find fault with that idea.

> I still don't know if the brain is just a filter of consciousness, in which
> case losing neurons might enhance consciousness (and some data in
> neurophysiology might confirm this). I think Goertzel is more creating a
> competent machine than an intelligent one, from what I have read about it. I
> oppose intelligence/consciousness and competence/ingenuity. The first is
> needed to develop the later, but the later has a negative feedback on the
> first.

I think I understand your point here with regard to consciousness -
given that you're saying it's a property of the platonic 'virgin'
universal machine. But if you assert that about intelligence, aren't
you saying that intelligence isn't computable (i.e. comp denies strong
ai)? This would seem to contradict Marcus Hutter's AIXI. You're
saying that our intelligence as humans is dependent (in the same way
as consciousness) on the fact that we don't know which machine we are?
That creativity is sourced in subjective indeterminacy?

Terren

[Colin Hales]

Hi Russel,

1) Strong CT/Deutch...will look it up...Sounds like one of the
conflations in operation: confusing the natural world with some kind of
computer running rules, rather than something natural merely behaving
rule-ly to an observing scientist.

2) Re: angry popperians...the role of human creativity in the science
process is not that of blind/mindless searching. I'm not sure how you
construed this from the text. The so-called robot scientists (automated
dataminers) do that kind of searching. That is the mindless searching I
meant. Humans scientists built the searching robots...a very different
process... also....Constructing a hypothesis is a creative act, and it
proceeds as much by 'gut' as by anything else. This is the sense in
which the "obvious that human scientists do not operate this way" was
meant. .Interesting that you should reach this position despite all my
attempts not to convey anything like it....boy this stuff is hard to
write about!

I hope you can keep up the effort!

cheers
colin

[Bruno Marchal]

On 15 Jun 2011, at 18:47, meekerdb wrote:

> On 6/15/2011 6:56 AM, Bruno Marchal wrote:
>>> Doesn't this objection only apply to attempts to construct an AI
>>> with
>>> human-equivalent intelligence? As a counter example I'm thinking
>>> here
>>> of Ben Goertzel's OpenCog, an attempt at artificial general
>>> intelligence (AGI), whose design is informed by a theory of
>>> intelligence that does not attempt to mirror or model human
>>> intelligence. In light of the "Benacerraf principle", isn't it
>>> possible in principle to provably construct AIs so long as we're not
>>> trying to emulate or model human intelligence?
>>
>> I think that comp might imply that simple virgin (non programmed)
>> universal (and immaterial) machine are already conscious. Perhaps
>> even maximally conscious. Then adding induction gives them

>> Löbianity, and this makes them self-conscious (which might already

>> be a delusion of some sort). Unfortunately the hard task is to
>> interface such (self)-consciousness with our probable realities
>> (computational histories). This is what we can hardly be sure about.
>> I still don't know if the brain is just a filter of consciousness,
>> in which case losing neurons might enhance consciousness (and some
>> data in neurophysiology might confirm this). I think Goertzel is
>> more creating a competent machine than an intelligent one, from
>> what I have read about it. I oppose intelligence/consciousness and
>> competence/ingenuity. The first is needed to develop the later, but
>> the later has a negative feedback on the first.
>>
>> Bruno
>>
>
> There is a tendency to talk about "human-equivalent intelligence" or
> "human level intelligence" as an ultimate goal. Human intelligence
> evolved to enhance certain functions: cooperation, seduction,
> bargaining, deduction,... There's no reason to suppose it is the
> epitome of intelligence. Intelligence may take many forms, some of
> which we would have difficulty realizing or crediting. Like a
> universal machine that is not programmed, which by one measure is
> maximally intelligent but also maximally incompetent. Even in
> humans intelligence is far from one-dimensional. A small child is
> extremely intelligent as measured by the ability to learn, but not
> very smart as measured by knowledge.

So we agree violently on this, to borrow an expression to Russell (I
think).

When I want to be cynical, I define humans as an ape which stung other
apes on crosses. Nothing to be proud of.

It is a cultural problem, especially in Occident, that the humans
believe that they are the last word of God. I would be God (!) that
would be enough to invest more in spiders and birds, or other
creatures. They are more modest. In a sense they might be "more"
Löbian than us.
Competence can kill intelligence. It will depend on us, I am not
fatalist, but we might be the 'dinosaurs of competence'.

Will say more in other replies, probably.

Bruno

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

[Bruno Marchal]

Hi Benjayk,

> Bruno Marchal wrote:
>>
>> We just cannot do artificial intelligence in a provable manner. We
>> need chance, or luck. Even if we get some intelligent machine, we
>> will
>> not know-it-for sure (perhaps just believe it correctly).
> But this is a quite weak statement, isn't it? It just prevents a
> mechanical
> way of making a AI, or making a provably friendly AI (like Eliezer
> Yudkowsky
> wants to do).

Yes it is quite weak. It can even been made much weaker if we allow
machines to make enough mistakes for indeterminate period of times. In
that case, some necessarily non constructive proof can be made
constructive. After all, evolution itself is plausibly mechanical.

>
> We can prove very little about what we do or "know" anyway. We can't
> prove
> the validity of science, for example.

You are right, but here the point is more subtle. Most initial
theoretical statements are not provable, but we can take them as new
axioms without becoming inconsistent. But most "theological"
statements of the machine/numbers have that property that, despite
being true, they become false when added as an axiom.
It is a bit like a theory with five axioms. You cannot add a sixth
axioms saying that the theory has five axioms. Self-consistency, and
consciousness behave similarly. Human science or theological science
are full of things of that kind, I mean truth which just cannot be
asserted, except very cautiously. In fact the modal logic G* minus G
axiomatizes them all (at the propositional level).
That is perhaps the source of this very deep 'truth': hell is paved
with the good intentions.

>
> It doesn't even mean that there is no developmental process that
> will allow
> us to create ever more powerful heuristics with which to find better
> AI
> faster in a quite predictable way (not predictable what kind of AI
> we build,
> just *that* we will build a powerful AI), right?

Yes, that is possible. Heuristics are typically not algorithmic.

Bruno

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

[Bruno Marchal]

On 15 Jun 2011, at 21:20, benjayk wrote:

>
> Hi Bruno,
>
>
> Bruno Marchal wrote:
>>
>> I think that comp might imply that simple virgin (non programmed)
>> universal (and immaterial) machine are already conscious. Perhaps
>> even
>> maximally conscious.
>>
> What could "maximally conscious" mean? My intuition says quite
> strongly that
> consciousness is a dynamic open-ended process and that there is no
> such
> thing as maximally conscious (exept maybe in the trivial sense of
> "simply
> conscious at all").

I tend to think that consciousness is the same for all conscious
being, except that prejudices coming from competence can make it more
sleepy. So, paradoxically, consciousness might be maximal in the case
of absence of knowledge and beliefs.

> I can't even conceive what this could be like.

Well, some drugs can help with that respect. Some thought experiences
also, but they are not of the type I have allowed in publications,
because they need you to imagine some amnesia, or coming back to the
state of a baby. It is not easy.

>
>
> Bruno Marchal wrote:
>>
>> Then adding induction gives them Löbianity, and
>> this makes them self-conscious (which might already be a delusion of
>> some sort).
> Why do you think it could be a delusion? This would be a bit
> reminscent of
> buddhism. For me it sounds like quite a terrible thought. After all
> it would
> mean all progress is in a way illusory and maybe not even desirable,
> whereas
> I really wish (and pragmatically believe) that eternal progress is
> the thing
> that can fullfill our ideals of truth, conscious insight and
> happiness.

I am no more sure on this. I can understand the appeal of the idea of
progress, but progress might just make pain more painful, frustation
more frustrating, etc. Truth is simply not fulfillable, and happiness
is more in equilibrium and balances than in the pursuit of bigger
satisfaction. But then comp might be wrong, and I might miss the
point. But, yes, comp leads close to buddhism, and to ethical
detachment.

>
>
> Bruno Marchal wrote:
>>
>> I oppose intelligence/consciousness and competence/
>> ingenuity. The first is needed to develop the later, but the later
>> has
>> a negative feedback on the first.
> Can you explain this?
>
> It seems to me that there is no clear line between intelligence and
> competence and that some kind of competences (like aligning yourself
> with
> the beliefs of society) can limit intelligence, but some help to
> develop
> more intelligence (like doing science).

Let me remind you my smallest theory of Intelligence/consciousness. I
have already given years ago, and also recently on the FOR list, I
think.

A machine is intelligent if and only if it is not stupid.
A machine is stupid when one of the following clause is satisfied:
- the machine believes that she is intelligent
- the machine believes that she is stupid

Now that theory admits a transparent arithmetical interpretation.
Replace "intelligent" by consistent (Dt), and stupid by not consistent
(~Dt, that is Bf). Then the theory is just Gödel's second
incompleteness theorem, and is a sub-theory of G* (BDt -> Bf).

An obvious defect of that theory is that it makes pebbles intelligent.
But then, why not? Who has ever heard a pebble saying that it is
intelligent, or stupid, or said any kind stupidities. Like with the
taoists, the wise person keep silent.

Concerning the learning competence of a machine, I measure it by the
classes of computable functions that the machine is able to identify
from finite samples of input-outputs. This leads to the "computational
learning theory" or "inductive inference" theory, which shows that the
possible competences form a complex lattice with a lot of incomparable
competences, and with a lot of necessarily non constructive gaps
existing among them.

Roughly speaking a machine becomes stupid when it confuses
intelligence and competence and begin to feel superior, or inferior,
and begin to lack some amount of respect for his living being fellows.
Some of those fellows can believe in the superiority of those
machines, and believe that they are inferior, and this leads to a
coupling of dominant/dominated, which unfortunately can be very stable
and profit to the emergence of new entities.

"Science" per se, does not lead to intelligence, as I think it is
sadly illustrated by those last centuries. Science can kill
intelligence, and science without intelligence can lead to hell,
especially if science is confused with a sort of theology, instead of
being used to genuinely tackle, interrogate, the (theological)
fundamental questions. Humans cannot yet accept their ignorance.

I have already argued that science, well understood, is born with
Pythagorus, and is ended with the apparition of the roman empire.
Fundamental questions are still complete taboo, for most scientists.
There is no question to rise any doubt on the theology of Aristotle.
Neither atheists nor Christians can accept that. Postmodernity exists
in occident since about 500 after JC, and should be called
obscurantism. Free thinking is a myth. You are not even burned alive
for your ideas, today, which is a mark of acknowledging the existence
of you and your ideas. Today, obscurantism has developed more
efficacious means. This results in an impoverishment of ideas, and in
powerful mediatic propaganda. A good example is the politics of health
and prohibition, which destroys lives and minds more efficaciously
than atomic bombs.

Bruno

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

[meekerdb]

On 6/16/2011 7:38 AM, Bruno Marchal wrote:
> Concerning the learning competence of a machine, I measure it by the
> classes of computable functions that the machine is able to identify
> from finite samples of input-outputs. This leads to the "computational
> learning theory" or "inductive inference" theory, which shows that the
> possible competences form a complex lattice with a lot of incomparable
> competences, and with a lot of necessarily non constructive gaps
> existing among them.

Do you have some reference where this is explained?

Brent

[Russell Standish]

On Thu, Jun 16, 2011 at 03:34:51PM +0200, Bruno Marchal wrote:
>
> So we agree violently on this, to borrow an expression to Russell (I
> think).
>

To be fair, Brent used this expression when agreeing with me on
something. But it is a good one!

[Bruno Marchal]

My favorite paper on this is:

CASE J. & SMITH C., 1983, Comparison of Identification Criteria for
Machine Inductive
Inference. In Theoretical Computer Science 25,.pp 193-220.

But since, there has been a ton of papers published. Notably the COLT
proceedings.

There is also the book:

OSHERSON D.N., STOB M.and WEINSTEIN S., 1986, Systems that Learn, MIT
press. (New edition exists since)

It is a recursion theoretic based field. Of course it does not
interest so much the engineers as most result are not constructive,
indeed necessarily so.

A basic fundamental paper is:

GOLD, E. M., 1965, Limiting recursion, Journal of Symbolic Logic, 30,
1, pp. 27-48.

and

GOLD E.M., 1967, Language Identification in the Limit. Information &
Control 10, pp.
447-474.

Another one is:

BLUM L. & BLUM M., 1975, Toward a Mathematical Theory of Inductive
Inference.
Information and Control 28,.pp. 125-155.

There is a full chapter on this in "Conscience et mécanisme". You will
find other references in the "bibilographie générale" pdf.
http://iridia.ulb.ac.be/~marchal/bxlthesis/consciencemecanisme.html

The gap G* minus G formalizes an easy set of inferable but non
provable self-referential truth by inductive inference type of Löbian
machines (the 'mystical machines').

Bruno

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