Re: Interesting paper on consciousness, computation and MWI

2011-10-07 Thread Bruno Marchal


On 07 Oct 2011, at 01:59, Brian Tenneson wrote:


Thanks Bruno for patiently explaining things.

It's interesting that you bring up computer science as I am doing a
career change right now and am going into computer science.  I
eventually want to work in brain simulation.  A lot of the ideas in
this group are relevant.


Thanks.




From the paper, I'll quote again (mainly for myself when I look back
at this message)
From page 17
It is my contention that the only way out of this dilemma is to  
deny the
initial assumption that a classical computer running a particular  
program can

generate conscious awareness in the first place.

If the author is correct that would seem to drive a nail in the coffin
for the digital generation of conscious awareness though in some way
that might not prove that brain simulation is impossible.


Yes. the expression is ambiguous.




Perhaps
brain simulation would occur in such a way that the simulation is
never consciously self-aware but if that were the case, how good is
that simulation??


That would lead to zombie. Still, I don't believe any particular  
implementation of a computation generates awareness by itself  
(neither in a physical universe, nor in a immaterial arithmetical  
dovetailing). Awareness needs all implementation of all computations,  
as it follows from the step 8 in UDA.


When I say yes to the doctor, I might survive in the usual sense, but  
this does not mean that the artificial brain generates my  
consciousness (which is more an heaven kind of object). but the  
artificial brain, if well done enough, might make it possible for my  
mind (existing only in hevan) to continue to manisfest itself here (on  
earth), like my brain seems to already be able to do.
It is a subtle point, but if our bodies are machine, we provably have  
an independent soul, and machines (silicon or carbon based) just makes  
it possible fro a soul to manifest itself with respect to other souls  
with reasonable probabilities.





If my doctor wanted to replace my brain with an artificial brain, I
think I'd be scared out of my mind if LINUX wasn't an option hehe...
Thanks Bruno.


All right, but then everyone can get your code source, and your fist  
person indeterminacy might grow a lot. Expect to find your self in the  
nightmarish fantasy of your neighbors. Be careful :)








I know this might seem like a naive observation but the Bolshoi
universe simulation recently done on a supercomputer at UC Santa Cruz
in California produced some images of an early universe that had an
uncanny resemblance to the human brain.


It is the filamentous web of cluster of galaxies, using information  
from Hubble and COBE, I think. It is very impressive and shows how big  
the physical cosmos is.


I think that comp implies that the cosmos is infinite. The cosmos is  
the border of an infinite universal mind, and an infinity of  
computations plays some role. But this is hard to prove, because comp  
can also collapse, from the first person views, or renormalize, many  
infinities. The cosmos is a priori infinite, but some weird  
computational phenomenon collapsing infinities are hard to avoid  
especially before we understand better why the 'white rabbits' are so  
rare in our neighborhoods.




It gives me hope that it is
possible to simulate a brain on a classical computer.  Perhaps the
details would involve highly complex neural networks;


Don't forget the glial cells. They are 20 times more numerous than  
neurons, and we know that they don't not only communicate (by chemical  
waves instead of ionic electricity) between themselves, but they do  
communicate with the neurons also (this plays a role notably in the  
chronic pains). They might be needed for the conscious background.





the hope would
be to rival the complexity of an actual brain.


Good luck. It will be easier to copy highly plastic brain (like  
baby's brain) and let them organize themselves that to actually copy  
an adult brain, which contains tremendous amount of distributed  
information.





Here is a link that includes video
http://hipacc.ucsc.edu/Bolshoi/


It is beautiful.
Have you look to this nice video (by SpaceRip):

http://www.youtube.com/watch?v=CEQouX5U0fc

Ah, but you can find impressive filamentous structure in the  
Mandelbrot set too, and even without digging deep:


http://www.youtube.com/watch?v=9G6uO7ZHtK8




(Then of course we might get into some ethical quandaries regarding
the personhood of a simulated brain such as can we run any experiment
on it that we feel like running... is simulated suffering ethically
equivalent to actual suffering... and that sort of thing.)


With comp, simulated suffering is the same as suffering, and should be  
forbidden, unless someone accept it for its own brain, and this before  
doing the copy. (Like I think you have the right to kill or even  
torture yourself, as far as you are not making other suffering).
The very complex case, is when 

Re: Interesting paper on consciousness, computation and MWI

2011-10-06 Thread Bruno Marchal


On 04 Oct 2011, at 23:14, Brian Tenneson wrote:


Hmm... Unfortunately there are several terms there I don't understand.
Digital brain.  What's a brain?  I ask because I'm betting it doesn't
mean a pile of gray and white matter.


Suppose that you have a brain disease, and you doctor propose to you  
an artificial brain, and he does not hide that this mean he will copy  
your brain state at the level of the molecules, processed by a  
computer. he adds that you can choose between a mac or a pc.
Comp assumes that there is a level such that you can survive in the  
usual clinical sense with such a digital brain like you can already  
survive with an artificial pump at the place of the heart.





Then you mention artificial brain.  That's different from digital?


Well, it could be for those studying an analog version of comp. But  
unless the analog system use actual infinities, it will be emulable by  
a digital machine. The redundancy of the brains and its evolution  
pleads for the idea that the brain is indeed digitally emulable.





Is
digital more nonphysical than artificial?


Not a priori, at all. Sellable computers are digital and physical.  
Today the non physical universal machines are still free, and can be  
found in books or on the net. You might find a lot by looking toward  
yourself, but the study of computer science can accelerate that  
discovery a lot.


Bruno






On Tue, Oct 4, 2011 at 7:31 AM, Bruno Marchal marc...@ulb.ac.be  
wrote:


On 04 Oct 2011, at 05:33, Brian Tenneson wrote:


From page 17
It is my contention that the only way out of this dilemma is to  
deny the
initial assumption that a classical computer running a particular  
program

can
generate conscious awareness in the first place.

What about the possibility of allowing for a large number of  
conscious

moments that would, in a limit of some sort, approximate continuous,
conscious awareness?  In my mind, I liken the comparison to that  
of a
radioactive substance and half-life decay formulas.  In truth,  
there are

finitely many atoms decaying but the half-life decay formulas never
acknowledge that at some point the predicted mass of what's left  
measures
less than one atom.  So I'm talking about a massive number of  
calculated
conscious moments so that for all intents and purposes, continuous  
conscious

awareness is the observed result.

Earlier on page 17...
its program must
only generate a finite sequence of conscious moments.


I think I agree with you. I think that such a view is the only  
compatible

with Digital Mechanism, but also with QM (without collapse).

Consciousness is never generated by the running of a particular  
computer.
If we can survive with a digital brain, this is related to the fact  
that we
already belong to an infinity of computations, and the artificial  
brain
just preserve that infinity, in a way such that I can survive in my  
usual

normal (Gaussian) neighborhoods.

Bruno




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



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Re: Interesting paper on consciousness, computation and MWI

2011-10-06 Thread Brian Tenneson
Thanks Bruno for patiently explaining things.

It's interesting that you bring up computer science as I am doing a
career change right now and am going into computer science.  I
eventually want to work in brain simulation.  A lot of the ideas in
this group are relevant.

From the paper, I'll quote again (mainly for myself when I look back
at this message)
From page 17
It is my contention that the only way out of this dilemma is to deny the
initial assumption that a classical computer running a particular program can
generate conscious awareness in the first place.

If the author is correct that would seem to drive a nail in the coffin
for the digital generation of conscious awareness though in some way
that might not prove that brain simulation is impossible.  Perhaps
brain simulation would occur in such a way that the simulation is
never consciously self-aware but if that were the case, how good is
that simulation??

If my doctor wanted to replace my brain with an artificial brain, I
think I'd be scared out of my mind if LINUX wasn't an option hehe...
Thanks Bruno.

I know this might seem like a naive observation but the Bolshoi
universe simulation recently done on a supercomputer at UC Santa Cruz
in California produced some images of an early universe that had an
uncanny resemblance to the human brain.  It gives me hope that it is
possible to simulate a brain on a classical computer.  Perhaps the
details would involve highly complex neural networks; the hope would
be to rival the complexity of an actual brain.

Here is a link that includes video
http://hipacc.ucsc.edu/Bolshoi/

(Then of course we might get into some ethical quandaries regarding
the personhood of a simulated brain such as can we run any experiment
on it that we feel like running... is simulated suffering ethically
equivalent to actual suffering... and that sort of thing.)


On Thu, Oct 6, 2011 at 11:04 AM, Bruno Marchal marc...@ulb.ac.be wrote:

 On 04 Oct 2011, at 23:14, Brian Tenneson wrote:

 Hmm... Unfortunately there are several terms there I don't understand.
 Digital brain.  What's a brain?  I ask because I'm betting it doesn't
 mean a pile of gray and white matter.

 Suppose that you have a brain disease, and you doctor propose to you an
 artificial brain, and he does not hide that this mean he will copy your
 brain state at the level of the molecules, processed by a computer. he adds
 that you can choose between a mac or a pc.
 Comp assumes that there is a level such that you can survive in the usual
 clinical sense with such a digital brain like you can already survive with
 an artificial pump at the place of the heart.



 Then you mention artificial brain.  That's different from digital?

 Well, it could be for those studying an analog version of comp. But unless
 the analog system use actual infinities, it will be emulable by a digital
 machine. The redundancy of the brains and its evolution pleads for the idea
 that the brain is indeed digitally emulable.



 Is
 digital more nonphysical than artificial?

 Not a priori, at all. Sellable computers are digital and physical. Today the
 non physical universal machines are still free, and can be found in books or
 on the net. You might find a lot by looking toward yourself, but the study
 of computer science can accelerate that discovery a lot.

 Bruno





 On Tue, Oct 4, 2011 at 7:31 AM, Bruno Marchal marc...@ulb.ac.be wrote:

 On 04 Oct 2011, at 05:33, Brian Tenneson wrote:

 From page 17
 It is my contention that the only way out of this dilemma is to deny
 the
 initial assumption that a classical computer running a particular
 program
 can
 generate conscious awareness in the first place.

 What about the possibility of allowing for a large number of conscious
 moments that would, in a limit of some sort, approximate continuous,
 conscious awareness?  In my mind, I liken the comparison to that of a
 radioactive substance and half-life decay formulas.  In truth, there are
 finitely many atoms decaying but the half-life decay formulas never
 acknowledge that at some point the predicted mass of what's left
 measures
 less than one atom.  So I'm talking about a massive number of calculated
 conscious moments so that for all intents and purposes, continuous
 conscious
 awareness is the observed result.

 Earlier on page 17...
 its program must
 only generate a finite sequence of conscious moments.

 I think I agree with you. I think that such a view is the only compatible
 with Digital Mechanism, but also with QM (without collapse).

 Consciousness is never generated by the running of a particular
 computer.
 If we can survive with a digital brain, this is related to the fact that
 we
 already belong to an infinity of computations, and the artificial brain
 just preserve that infinity, in a way such that I can survive in my usual
 normal (Gaussian) neighborhoods.

 Bruno




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



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 You received this message because you are subscribed to the 

Re: Interesting paper on consciousness, computation and MWI

2011-10-04 Thread Bruno Marchal


On 04 Oct 2011, at 01:00, Russell Standish wrote:


On Mon, Oct 03, 2011 at 05:31:21PM +0200, Bruno Marchal wrote:


The states are countable, but not the (3-)states + the neighborhhood
of (infinite) computations that you are mentioning yourselves.
Not sure if I see where is the problem. It seems that you have
answered it. The 1-OMs *are* set of histories, but with a particular
3-state, single out in the indexical way, and which will play the
role of the Bp. The  p will force the logic of the
computational extensions to be different.


The way I was talking about it, there is a 1:1 correspondence between
the 3-states and the sets of histories making up the 1-OM. In that
case the cardinality of 1-OM is the same as that of the 3-states -
which you have already admitted is countable.


OK, I see your point. You are right on this, and I should have  
perhapssaid set of sets of histories. This is related to the  
possible semantics of the first person logics (S4Grz1).


The 1-OMs are mutiplied by the computations going through it, making  
it as great as the continuum of those computations going through, and  
that can be understood intuitively by UDA-like reasoning. This come  
from the rule Y = I. To have the measure on the 1-OMs, we have to  
count the computations going through, not the states themselves. So an  
1-OMs can be defined just by one computations (perhaps infinite), but  
this does not entirely work, and that is why we have to take into  
account the structure imposed by the logic to which the first person  
obeys.





Perhaps I'm missing something? I don't quite get the indexical bit
for instance.


Examples of  indexical are terms like now, me, here, I, there.  
Their meaning or referent depends on the locutor or of its current  
(also an indexical) situation.


The 3-I of a machine, is an indexical, rather well handled by the  
description of the machine as handled by the machine, like with  
Gödel's beweisbar B. The precise (arithmetical contento of B  
varies from one machine to another, but if the machine verifies some  
conditions (rich, ideally correct, etc.) it obeys the same modal  
logics (G, G*).


The 1-I is similarly well captured by the conjunction of the 3-I and  
truth (Bp  p). This is a drastic change, because that I is no  
describable by the machine, it is *not* arithmetical, and it changes  
the logic of self-reference (which becomes a logic of evolving states).


Sorry for having been unclear, but I continue to doubt about the  
relevance of the term OMs terms. It did mislead me in my answer too  
you, and I should stick on the person-views and their modalities.


Ask for any clarification. Nothing is really simple here. I will add  
some info in my reply to Brent.


Bruno



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



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Re: Interesting paper on consciousness, computation and MWI

2011-10-04 Thread Bruno Marchal


On 04 Oct 2011, at 05:33, Brian Tenneson wrote:


From page 17
It is my contention that the only way out of this dilemma is to  
deny the
initial assumption that a classical computer running a particular  
program can

generate conscious awareness in the first place.

What about the possibility of allowing for a large number of  
conscious moments that would, in a limit of some sort, approximate  
continuous, conscious awareness?  In my mind, I liken the comparison  
to that of a radioactive substance and half-life decay formulas.  In  
truth, there are finitely many atoms decaying but the half-life  
decay formulas never acknowledge that at some point the predicted  
mass of what's left measures less than one atom.  So I'm talking  
about a massive number of calculated conscious moments so that for  
all intents and purposes, continuous conscious awareness is the  
observed result.


Earlier on page 17...
its program must
only generate a finite sequence of conscious moments.


I think I agree with you. I think that such a view is the only  
compatible with Digital Mechanism, but also with QM (without collapse).


Consciousness is never generated by the running of a particular  
computer. If we can survive with a digital brain, this is related to  
the fact that we already belong to an infinity of computations, and  
the artificial brain just preserve that infinity, in a way such that I  
can survive in my usual normal (Gaussian) neighborhoods.


Bruno




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



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Re: Interesting paper on consciousness, computation and MWI

2011-10-04 Thread Brian Tenneson
Hmm... Unfortunately there are several terms there I don't understand.
Digital brain.  What's a brain?  I ask because I'm betting it doesn't
mean a pile of gray and white matter.
Then you mention artificial brain.  That's different from digital?  Is
digital more nonphysical than artificial?



On Tue, Oct 4, 2011 at 7:31 AM, Bruno Marchal marc...@ulb.ac.be wrote:

 On 04 Oct 2011, at 05:33, Brian Tenneson wrote:

 From page 17
 It is my contention that the only way out of this dilemma is to deny the
 initial assumption that a classical computer running a particular program
 can
 generate conscious awareness in the first place.

 What about the possibility of allowing for a large number of conscious
 moments that would, in a limit of some sort, approximate continuous,
 conscious awareness?  In my mind, I liken the comparison to that of a
 radioactive substance and half-life decay formulas.  In truth, there are
 finitely many atoms decaying but the half-life decay formulas never
 acknowledge that at some point the predicted mass of what's left measures
 less than one atom.  So I'm talking about a massive number of calculated
 conscious moments so that for all intents and purposes, continuous conscious
 awareness is the observed result.

 Earlier on page 17...
 its program must
 only generate a finite sequence of conscious moments.

 I think I agree with you. I think that such a view is the only compatible
 with Digital Mechanism, but also with QM (without collapse).

 Consciousness is never generated by the running of a particular computer.
 If we can survive with a digital brain, this is related to the fact that we
 already belong to an infinity of computations, and the artificial brain
 just preserve that infinity, in a way such that I can survive in my usual
 normal (Gaussian) neighborhoods.

 Bruno




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



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Re: Interesting paper on consciousness, computation and MWI

2011-10-03 Thread Bruno Marchal


On 02 Oct 2011, at 01:55, Russell Standish wrote:


On Sat, Oct 01, 2011 at 05:15:34PM +0200, Bruno Marchal wrote:


On 01 Oct 2011, at 09:31, Russell Standish wrote:


On Thu, Sep 22, 2011 at 07:02:28PM +0200, Bruno Marchal wrote:


OK. But note that in this case you are using the notion of 3-OM (or
computational state), not Bostrom notion of 1-OM (or my notion of
first person state).
The 3-OM are countable, but the 1-OMs are not.


Could you explain more why you think this? AFAICT, Bostrom makes no
mention of the cardinality of his OMs.


I don't think that Bostrom mentions the cardinality of his OMs,
indeed. I don't think that he clearly distinguish the 1-OMs and the
3-OMs either. By 3-OM I refer to the computational state per se,
as defined relatively to the UD deployment (UD*). Those are clearly
infinite and countable, even recursively countable.

The 1-OMs, for any person, are not recursively countable, indeed by
an application of a theorem of Rice, they are not even
3-recognizable. Or more simply because you cannot know your
substitution level. In front of some portion of UD*, you cannot
recognize your 1-OMs in general. You cannot say I am here, and
there, etc. But they are (non constructively) well defined. God
can know that you are here, and there, ... And the measure on the
1-OMs should be defined on those unrecognizable 1-OMs.



I'm still struggling to understand what you mean by 1-OM here. Are you
talking about the infinite histories making up UD*? There are an
uncountable number of these, it is true.


Only those going through some computational state being mine, from my  
points of view. It looks like a relativistic cone, except that futures  
might be more numerous than past. Now the 1-OM is the subjective part  
of this: it is an indexical, whose logics will obey the modalities  
having a connection with truth (like Bp  p, and Bp  Dy  p).






But then, I wouldn't call these OMs. An OM must surely be related to
the set of all such histories passing through your current here and
now.


Yes. And there are non countably many such histories.




Such things, I am convinced, must be countable, implying that
each such sets histories is a continuum.


The states are countable, but not the (3-)states + the neighborhhood  
of (infinite) computations that you are mentioning yourselves.
Not sure if I see where is the problem. It seems that you have  
answered it. The 1-OMs *are* set of histories, but with a particular 3- 
state, single out in the indexical way, and which will play the role  
of the Bp. The  p will force the logic of the computational  
extensions to be different.


Bruno

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



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Re: Interesting paper on consciousness, computation and MWI

2011-10-03 Thread Russell Standish
On Mon, Oct 03, 2011 at 05:31:21PM +0200, Bruno Marchal wrote:
 
 The states are countable, but not the (3-)states + the neighborhhood
 of (infinite) computations that you are mentioning yourselves.
 Not sure if I see where is the problem. It seems that you have
 answered it. The 1-OMs *are* set of histories, but with a particular
 3-state, single out in the indexical way, and which will play the
 role of the Bp. The  p will force the logic of the
 computational extensions to be different.

The way I was talking about it, there is a 1:1 correspondence between
the 3-states and the sets of histories making up the 1-OM. In that
case the cardinality of 1-OM is the same as that of the 3-states -
which you have already admitted is countable.

Perhaps I'm missing something? I don't quite get the indexical bit
for instance.

Cheers

-- 


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


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Re: Interesting paper on consciousness, computation and MWI

2011-10-03 Thread Brian Tenneson

From page 17
It is my contention that the only way out of this dilemma is to deny the
initial assumption that a classical computer running a particular 
program can

generate conscious awareness in the first place.

What about the possibility of allowing for a large number of conscious 
moments that would, in a limit of some sort, approximate continuous, 
conscious awareness?  In my mind, I liken the comparison to that of a 
radioactive substance and half-life decay formulas.  In truth, there are 
finitely many atoms decaying but the half-life decay formulas never 
acknowledge that at some point the predicted mass of what's left 
measures less than one atom.  So I'm talking about a massive number of 
calculated conscious moments so that for all intents and purposes, 
continuous conscious awareness is the observed result.


Earlier on page 17...
its program must
only generate a finite sequence of conscious moments.

Cheers
Brian

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Re: Interesting paper on consciousness, computation and MWI

2011-10-02 Thread Bruno Marchal


On 01 Oct 2011, at 22:23, meekerdb wrote:


On 10/1/2011 8:15 AM, Bruno Marchal wrote:


On 01 Oct 2011, at 09:31, Russell Standish wrote:


On Thu, Sep 22, 2011 at 07:02:28PM +0200, Bruno Marchal wrote:


OK. But note that in this case you are using the notion of 3-OM (or
computational state), not Bostrom notion of 1-OM (or my notion of
first person state).
The 3-OM are countable, but the 1-OMs are not.


Could you explain more why you think this? AFAICT, Bostrom makes no
mention of the cardinality of his OMs.


I don't think that Bostrom mentions the cardinality of his OMs,  
indeed. I don't think that he clearly distinguish the 1-OMs and the  
3-OMs either. By 3-OM I refer to the computational state per se,  
as defined relatively to the UD deployment (UD*). Those are clearly  
infinite and countable, even recursively countable.


The 1-OMs, for any person, are not recursively countable, indeed by  
an application of a theorem of Rice, they are not even 3- 
recognizable. Or more simply because you cannot know your  
substitution level. In front of some portion of UD*, you cannot  
recognize your 1-OMs in general. You cannot say I am here, and  
there, etc. But they are (non constructively) well defined. God  
can know that you are here, and there, ...


Wouldn't that require that all the infinite UD calculations be  
completed before all the you could be indentified?


The infinite UD calculations are just number relations, which are out  
of space and time.






And the measure on the 1-OMs should be defined on those  
unrecognizable 1-OMs.


Are the 1-OMs countable? In the quote above, I say that they are  
not countable. What I meant by this is related to the measure  
problem, which cannot be made on the states themselves, but, I  
think, on the computational histories going through them, and,  
actually,  on *all* computational histories going through them.  
This includes the dummy histories which duplicate you iteratively  
through some processes similar to the infinite iteration of the WM  
self-duplication. Even if you don't interact with the output (here:  
W or M) or the iteration, such computations multiplies in the non- 
countable infinity. (I am using implictly the fist person  
indeterminacy, of course). Those computation will have the shape:


you M
you M
you W
you M
You W
You W
You W
You M
ad infinitum

This gives a white noise, which is not necessarily available to  
you, but it still multiplies (in the most possible dumb way) your  
computational histories. Such infinite computations, which are  
somehow dovetailing on the reals (infinite sequence of W and M)  
have a higher measure than any finite computations and so are good  
candidates for the winning computations. Note that such an  
infinite background noise, although not directly accessible through  
your 1-OMs,  should be experimentally detectable when you look at  
yourselves+neighborhood below the substitution level, and indeed QM  
confirms this by the many (up + down) superposition states of the  
particles states in the (assumed to be infinite) multi-universes.


But aside from the quantum level, doesn't the measure problem have  
the same drawback and Boltzman's brains.  Shouldn't I find myself in  
a world where everyone is Brent Meeker?


Well, if you prove this, then you refute comp (and most of its super- 
Turing weakenings).
The big difference between Boltzman brains and UD*, is that the first  
are not well defined and depends on physical assumption, the second is  
well defined and depends only of the addition and multiplication laws  
of non negative integers.


Bruno






This might be also confirmed by some possible semantics for the  
logic of the first person points of view (the quantified logic  
qS4Grz1, qX1* have, I think, non countable important models).


3-OMs are relatively simple objects, but 1-OMs are more  
sophisticated, and are defined together with the set of all  
computations going through their correspondent states.


To be sure, I am not entirely persuaded that Bostrom's 1-OMs makes  
sense with digital mechanism, and usually I prefer to use the label  
of first person experiences/histories. With the rule Y = II, that  
is: a bifurcation of a computations entails a doubling of the  
measure even on its past (in the UD steps sense), this makes  
clear that we have a continuum of infinite histories.
Again, this is made more complex when we take amnesia and fusion of  
histories) into consideration.


I hope this helps a bit. In my opinion, only further progress on  
the hypostases modal logics will make it possible to isolate a  
reasonable definition of 1-OMs, which obviously is a quite  
intricate notion.


Bruno






--


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Principal, High Performance Coders
Visiting Professor of Mathematics  hpco...@hpcoders.com.au
University of New South 

Re: Interesting paper on consciousness, computation and MWI

2011-10-01 Thread Russell Standish
On Thu, Sep 22, 2011 at 07:02:28PM +0200, Bruno Marchal wrote:
 
 OK. But note that in this case you are using the notion of 3-OM (or
 computational state), not Bostrom notion of 1-OM (or my notion of
 first person state).
 The 3-OM are countable, but the 1-OMs are not.

Could you explain more why you think this? AFAICT, Bostrom makes no
mention of the cardinality of his OMs.

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Re: Interesting paper on consciousness, computation and MWI

2011-10-01 Thread Bruno Marchal


On 01 Oct 2011, at 09:31, Russell Standish wrote:


On Thu, Sep 22, 2011 at 07:02:28PM +0200, Bruno Marchal wrote:


OK. But note that in this case you are using the notion of 3-OM (or
computational state), not Bostrom notion of 1-OM (or my notion of
first person state).
The 3-OM are countable, but the 1-OMs are not.


Could you explain more why you think this? AFAICT, Bostrom makes no
mention of the cardinality of his OMs.


I don't think that Bostrom mentions the cardinality of his OMs,  
indeed. I don't think that he clearly distinguish the 1-OMs and the 3- 
OMs either. By 3-OM I refer to the computational state per se, as  
defined relatively to the UD deployment (UD*). Those are clearly  
infinite and countable, even recursively countable.


The 1-OMs, for any person, are not recursively countable, indeed by an  
application of a theorem of Rice, they are not even 3-recognizable. Or  
more simply because you cannot know your substitution level. In front  
of some portion of UD*, you cannot recognize your 1-OMs in general.  
You cannot say I am here, and there, etc. But they are (non  
constructively) well defined. God can know that you are here, and  
there, ... And the measure on the 1-OMs should be defined on those  
unrecognizable 1-OMs.


Are the 1-OMs countable? In the quote above, I say that they are not  
countable. What I meant by this is related to the measure problem,  
which cannot be made on the states themselves, but, I think, on the  
computational histories going through them, and, actually,  on *all*  
computational histories going through them. This includes the dummy  
histories which duplicate you iteratively through some processes  
similar to the infinite iteration of the WM self-duplication. Even if  
you don't interact with the output (here: W or M) or the iteration,  
such computations multiplies in the non-countable infinity. (I am  
using implictly the fist person indeterminacy, of course). Those  
computation will have the shape:


you M
you M
you W
you M
You W
You W
You W
You M
ad infinitum

This gives a white noise, which is not necessarily available to you,  
but it still multiplies (in the most possible dumb way) your  
computational histories. Such infinite computations, which are somehow  
dovetailing on the reals (infinite sequence of W and M) have a higher  
measure than any finite computations and so are good candidates for  
the winning computations. Note that such an infinite background  
noise, although not directly accessible through your 1-OMs,  should be  
experimentally detectable when you look at yourselves+neighborhood  
below the substitution level, and indeed QM confirms this by the many  
(up + down) superposition states of the particles states in the  
(assumed to be infinite) multi-universes.


This might be also confirmed by some possible semantics for the logic  
of the first person points of view (the quantified logic qS4Grz1, qX1*  
have, I think, non countable important models).


3-OMs are relatively simple objects, but 1-OMs are more sophisticated,  
and are defined together with the set of all computations going  
through their correspondent states.


To be sure, I am not entirely persuaded that Bostrom's 1-OMs makes  
sense with digital mechanism, and usually I prefer to use the label of  
first person experiences/histories. With the rule Y = II, that is: a  
bifurcation of a computations entails a doubling of the measure even  
on its past (in the UD steps sense), this makes clear that we have a  
continuum of infinite histories.
Again, this is made more complex when we take amnesia and fusion of  
histories) into consideration.


I hope this helps a bit. In my opinion, only further progress on the  
hypostases modal logics will make it possible to isolate a  
reasonable definition of 1-OMs, which obviously is a quite intricate  
notion.


Bruno






--


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Principal, High Performance Coders
Visiting Professor of Mathematics  hpco...@hpcoders.com.au
University of New South Wales  http://www.hpcoders.com.au


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Re: Interesting paper on consciousness, computation and MWI

2011-10-01 Thread meekerdb

On 10/1/2011 8:15 AM, Bruno Marchal wrote:


On 01 Oct 2011, at 09:31, Russell Standish wrote:


On Thu, Sep 22, 2011 at 07:02:28PM +0200, Bruno Marchal wrote:


OK. But note that in this case you are using the notion of 3-OM (or
computational state), not Bostrom notion of 1-OM (or my notion of
first person state).
The 3-OM are countable, but the 1-OMs are not.


Could you explain more why you think this? AFAICT, Bostrom makes no
mention of the cardinality of his OMs.


I don't think that Bostrom mentions the cardinality of his OMs, indeed. I don't think 
that he clearly distinguish the 1-OMs and the 3-OMs either. By 3-OM I refer to the 
computational state per se, as defined relatively to the UD deployment (UD*). Those are 
clearly infinite and countable, even recursively countable.


The 1-OMs, for any person, are not recursively countable, indeed by an application of a 
theorem of Rice, they are not even 3-recognizable. Or more simply because you cannot 
know your substitution level. In front of some portion of UD*, you cannot recognize your 
1-OMs in general. You cannot say I am here, and there, etc. But they are (non 
constructively) well defined. God can know that you are here, and there, ... 


Wouldn't that require that all the infinite UD calculations be completed before all the 
you could be indentified?



And the measure on the 1-OMs should be defined on those unrecognizable 1-OMs.

Are the 1-OMs countable? In the quote above, I say that they are not countable. What I 
meant by this is related to the measure problem, which cannot be made on the states 
themselves, but, I think, on the computational histories going through them, and, 
actually,  on *all* computational histories going through them. This includes the dummy 
histories which duplicate you iteratively through some processes similar to the infinite 
iteration of the WM self-duplication. Even if you don't interact with the output (here: 
W or M) or the iteration, such computations multiplies in the non-countable infinity. (I 
am using implictly the fist person indeterminacy, of course). Those computation will 
have the shape:


you M
you M
you W
you M
You W
You W
You W
You M
ad infinitum

This gives a white noise, which is not necessarily available to you, but it still 
multiplies (in the most possible dumb way) your computational histories. Such infinite 
computations, which are somehow dovetailing on the reals (infinite sequence of W and M) 
have a higher measure than any finite computations and so are good candidates for the 
winning computations. Note that such an infinite background noise, although not 
directly accessible through your 1-OMs,  should be experimentally detectable when you 
look at yourselves+neighborhood below the substitution level, and indeed QM confirms 
this by the many (up + down) superposition states of the particles states in the 
(assumed to be infinite) multi-universes.


But aside from the quantum level, doesn't the measure problem have the same drawback and 
Boltzman's brains.  Shouldn't I find myself in a world where everyone is Brent Meeker?




This might be also confirmed by some possible semantics for the logic of the first 
person points of view (the quantified logic qS4Grz1, qX1* have, I think, non countable 
important models).


3-OMs are relatively simple objects, but 1-OMs are more sophisticated, and are defined 
together with the set of all computations going through their correspondent states.


To be sure, I am not entirely persuaded that Bostrom's 1-OMs makes sense with digital 
mechanism, and usually I prefer to use the label of first person experiences/histories. 
With the rule Y = II, that is: a bifurcation of a computations entails a doubling of the 
measure even on its past (in the UD steps sense), this makes clear that we have a 
continuum of infinite histories.
Again, this is made more complex when we take amnesia and fusion of histories) into 
consideration.


I hope this helps a bit. In my opinion, only further progress on the hypostases modal 
logics will make it possible to isolate a reasonable definition of 1-OMs, which 
obviously is a quite intricate notion.


Bruno






--


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Principal, High Performance Coders
Visiting Professor of Mathematics  hpco...@hpcoders.com.au
University of New South Wales  http://www.hpcoders.com.au


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Re: Interesting paper on consciousness, computation and MWI

2011-10-01 Thread Russell Standish
On Sat, Oct 01, 2011 at 05:15:34PM +0200, Bruno Marchal wrote:
 
 On 01 Oct 2011, at 09:31, Russell Standish wrote:
 
 On Thu, Sep 22, 2011 at 07:02:28PM +0200, Bruno Marchal wrote:
 
 OK. But note that in this case you are using the notion of 3-OM (or
 computational state), not Bostrom notion of 1-OM (or my notion of
 first person state).
 The 3-OM are countable, but the 1-OMs are not.
 
 Could you explain more why you think this? AFAICT, Bostrom makes no
 mention of the cardinality of his OMs.
 
 I don't think that Bostrom mentions the cardinality of his OMs,
 indeed. I don't think that he clearly distinguish the 1-OMs and the
 3-OMs either. By 3-OM I refer to the computational state per se,
 as defined relatively to the UD deployment (UD*). Those are clearly
 infinite and countable, even recursively countable.
 
 The 1-OMs, for any person, are not recursively countable, indeed by
 an application of a theorem of Rice, they are not even
 3-recognizable. Or more simply because you cannot know your
 substitution level. In front of some portion of UD*, you cannot
 recognize your 1-OMs in general. You cannot say I am here, and
 there, etc. But they are (non constructively) well defined. God
 can know that you are here, and there, ... And the measure on the
 1-OMs should be defined on those unrecognizable 1-OMs.
 

I'm still struggling to understand what you mean by 1-OM here. Are you
talking about the infinite histories making up UD*? There are an
uncountable number of these, it is true.

But then, I wouldn't call these OMs. An OM must surely be related to
the set of all such histories passing through your current here and
now. Such things, I am convinced, must be countable, implying that
each such sets histories is a continuum.


-- 


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Principal, High Performance Coders
Visiting Professor of Mathematics  hpco...@hpcoders.com.au
University of New South Wales  http://www.hpcoders.com.au


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Re: Interesting paper on consciousness, computation and MWI

2011-09-22 Thread Bruno Marchal


On 21 Sep 2011, at 12:41, Russell Standish wrote:


On Mon, Sep 19, 2011 at 01:14:04PM -0400, Stephen P. King wrote:


   Exactly why are there not a continuum of OMs? It seems to me if
we parametrize the cardinality of distinct OMs to *all possible*
partitionings of the tangent spaces of physical systems (spaces
wherein the Lagrangians and Hamiltonians exist) then we obtain at
least the cardinality of the continuum. It is only if we assume some
arbitrary coarse graining that we have a countable set of OMs.


I do not assume an arbitrary coarse graining, but do think that each  
OM

must contain a finite amount of information. This implies the set of
OMs is countable.


OK. But note that in this case you are using the notion of 3-OM (or  
computational state), not Bostrom notion of 1-OM (or my notion of  
first person state).

The 3-OM are countable, but the 1-OMs are not.









The problem with this argument is that all rational numbers, when
expressed in base2, ultimately end in a repeating tail. In decimal
notation, we write dots above the digits that repeat. Once the
recurring tail has been reached, no further bits of information is
required to specify the rational number. Another way of looking at  
it

is that all rational numbers can be specified as two integers - a
finite amount of information.


   I must dispute this claim because that reasoning in terms of
'two integer' encoding of rationals ignores the vast and even
infinite apparatus required to decode the value of an arbitrary pair
of 'specified by two integers' values.


Both the human brain, and computers are capable of handling rational
numbers exactly. Neither of these are infinite apparatuses. If you're
using an arbitrary precision integer representation (eg the software
GMP), the only limitation to storing the rational number (or decoding
it, as you put it) is the amount of memory available on the computer.

The amount of information needed to represent any rational number is
finite (although may be arbitarily large, as is the case for any
integer). Only real numbers, in general, require infinite
information. Such numbers are known as uncomputable numbers.


OK. This of course does not prevent a machine to discover and handle  
many non computable numbers. She can even generate them all, like in  
finite self-duplication experiences.






The same applies to the
notion of digital information. Sure, we can think that the observed
universe can be represented by some finite collection of finite bit
strings, but this is just the result of imposing an arbitrary upper
and lower bound on the resolution of the recording/describing
machinery. There is no ab initio reason why that particular
upper/lower bound on resolution exists in the first place.



It rather depends what we mean by universe. An observer moment, ISTM,
is necessarily a finite information object. Moving from one observer
moment to the next must involve a difference of at least one bit, in
order for there to be an evolution in observer moments. A history,  
or linear

sequence of observable moments, must therefore be a countable set of
OMs, but this could be infinite. A collection of such histories would
be a continuum.


OK. And they define the structure of the 1-OMs.



A world (or universe), in my view, is given by a bundle of histories
satisfying a finite set of constraints. As such, an infinite amount of
information in the histories is irrelevant (don't care bits).


It might be for the 1-OM measure problem.

Bruno





But if
you'd prefer to identify the world with a unique history, or even as
something with independent existence outside of observation, then
sure, it may contain an infinite amount of information.



I notice this paper is an 02 arXiv paper, so rather old. It hasn't
been through peer review AFAICT. There was a bit of a critique of it
on Math Forum, but that degenerated pretty fast.

Cheers


  Ideas are sometimes like vine or a single malt whiskey that must
age before its bouquet is at its prime.



Partly I was wondering how much effort to put into it. Unfortunately,
it appears that the author's email addresses are no longer valid, as
it would be very interesting to have him engage in our discussions.


Onward!

Stephen

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Re: Interesting paper on consciousness, computation and MWI

2011-09-21 Thread Russell Standish
On Mon, Sep 19, 2011 at 01:14:04PM -0400, Stephen P. King wrote:
 
 Exactly why are there not a continuum of OMs? It seems to me if
 we parametrize the cardinality of distinct OMs to *all possible*
 partitionings of the tangent spaces of physical systems (spaces
 wherein the Lagrangians and Hamiltonians exist) then we obtain at
 least the cardinality of the continuum. It is only if we assume some
 arbitrary coarse graining that we have a countable set of OMs.

I do not assume an arbitrary coarse graining, but do think that each OM
must contain a finite amount of information. This implies the set of
OMs is countable.

 
 
 The problem with this argument is that all rational numbers, when
 expressed in base2, ultimately end in a repeating tail. In decimal
 notation, we write dots above the digits that repeat. Once the
 recurring tail has been reached, no further bits of information is
 required to specify the rational number. Another way of looking at it
 is that all rational numbers can be specified as two integers - a
 finite amount of information.
 
 I must dispute this claim because that reasoning in terms of
 'two integer' encoding of rationals ignores the vast and even
 infinite apparatus required to decode the value of an arbitrary pair
 of 'specified by two integers' values. 

Both the human brain, and computers are capable of handling rational
numbers exactly. Neither of these are infinite apparatuses. If you're
using an arbitrary precision integer representation (eg the software
GMP), the only limitation to storing the rational number (or decoding
it, as you put it) is the amount of memory available on the computer.

The amount of information needed to represent any rational number is
finite (although may be arbitarily large, as is the case for any
integer). Only real numbers, in general, require infinite
information. Such numbers are known as uncomputable numbers.

 The same applies to the
 notion of digital information. Sure, we can think that the observed
 universe can be represented by some finite collection of finite bit
 strings, but this is just the result of imposing an arbitrary upper
 and lower bound on the resolution of the recording/describing
 machinery. There is no ab initio reason why that particular
 upper/lower bound on resolution exists in the first place.
 

It rather depends what we mean by universe. An observer moment, ISTM,
is necessarily a finite information object. Moving from one observer
moment to the next must involve a difference of at least one bit, in
order for there to be an evolution in observer moments. A history, or linear
sequence of observable moments, must therefore be a countable set of
OMs, but this could be infinite. A collection of such histories would
be a continuum.

A world (or universe), in my view, is given by a bundle of histories
satisfying a finite set of constraints. As such, an infinite amount of
information in the histories is irrelevant (don't care bits). But if
you'd prefer to identify the world with a unique history, or even as
something with independent existence outside of observation, then
sure, it may contain an infinite amount of information. 

 
 I notice this paper is an 02 arXiv paper, so rather old. It hasn't
 been through peer review AFAICT. There was a bit of a critique of it
 on Math Forum, but that degenerated pretty fast.
 
 Cheers
 
Ideas are sometimes like vine or a single malt whiskey that must
 age before its bouquet is at its prime.
 

Partly I was wondering how much effort to put into it. Unfortunately,
it appears that the author's email addresses are no longer valid, as
it would be very interesting to have him engage in our discussions.

 Onward!
 
 Stephen
 
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Re: Interesting paper on consciousness, computation and MWI

2011-09-21 Thread Stephen P. King

On 9/21/2011 6:41 AM, Russell Standish wrote:

On Mon, Sep 19, 2011 at 01:14:04PM -0400, Stephen P. King wrote:

 Exactly why are there not a continuum of OMs? It seems to me if
we parametrize the cardinality of distinct OMs to *all possible*
partitionings of the tangent spaces of physical systems (spaces
wherein the Lagrangians and Hamiltonians exist) then we obtain at
least the cardinality of the continuum. It is only if we assume some
arbitrary coarse graining that we have a countable set of OMs.

I do not assume an arbitrary coarse graining, but do think that each OM
must contain a finite amount of information. This implies the set of
OMs is countable.

[SPK]
Umm, how does the finiteness of the elements of a set X  induce 
finiteness of X? I may have missed this in my studies of set theory.



The problem with this argument is that all rational numbers, when
expressed in base2, ultimately end in a repeating tail. In decimal
notation, we write dots above the digits that repeat. Once the
recurring tail has been reached, no further bits of information is
required to specify the rational number. Another way of looking at it
is that all rational numbers can be specified as two integers - a
finite amount of information.

 I must dispute this claim because that reasoning in terms of
'two integer' encoding of rationals ignores the vast and even
infinite apparatus required to decode the value of an arbitrary pair
of 'specified by two integers' values.

Both the human brain, and computers are capable of handling rational
numbers exactly. Neither of these are infinite apparatuses. If you're
using an arbitrary precision integer representation (eg the software
GMP), the only limitation to storing the rational number (or decoding
it, as you put it) is the amount of memory available on the computer.

[SPK]
True, but that misses my point. Brains and Computers are not 
entities existing in an otherwise empty universe; we have to consider a 
multiplicity of mutually observing and measuring entities and the 
internal interpretational and representational structures thereof.  
Consider a simple digital camera. The images that the camera can capture 
are limited by the pixel resolution of the camera, this is a constraint 
induced by the physical design of the camera. The camera itself, as a 
physical object, is not limited in the detail of its properties by those 
intrinsic constraints. We must take care to not assume that the limits 
of the observational or measurement process is not assumed to be that of 
the system that is making the observations/measurement.


While a the measured properties of an object A as determined by 
object B is limited to the resolving abilities of B, this in no way is a 
constraint on the properties of A. To consider the properties of A one 
at least might consider the set of all possible measurements of A and 
one might notice that these involve real valued variations, say of 
relative position, and thus the total set of measurable information of A 
is infinite, at least in principle. BTW, this is one reason why the 
Hilbert space of a realistic QM system is infinite, even modulo linear 
superposition!



The amount of information needed to represent any rational number is
finite (although may be arbitarily large, as is the case for any
integer). Only real numbers, in general, require infinite
information. Such numbers are known as uncomputable numbers.

[SPK]
Surely Reality is not limited to the rationals! Are we to be 
crypto-Pythagoreans, claiming to believe that only the rationals exist, 
yet still using pi, e and other irrationals without question??? If 
Nature is computational, does it not make sense that its computations 
/information accessing and processing might not be limited to the rationals?



The same applies to the
notion of digital information. Sure, we can think that the observed
universe can be represented by some finite collection of finite bit
strings, but this is just the result of imposing an arbitrary upper
and lower bound on the resolution of the recording/describing
machinery. There is no ab initio reason why that particular
upper/lower bound on resolution exists in the first place.


It rather depends what we mean by universe. An observer moment, ISTM,
is necessarily a finite information object. Moving from one observer
moment to the next must involve a difference of at least one bit, in
order for there to be an evolution in observer moments. A history, or linear
sequence of observable moments, must therefore be a countable set of
OMs, but this could be infinite. A collection of such histories would
be a continuum.


[SPK]
I consider an Observer moment to be the content of experience on an 
ideal non-anthropomorphic observer that might obtain in a minimum 
quantity of time, thus there is a maximum quantity of energy involved, 
as per the energy-time uncertainty relation (which is controversial as 
time is not an observable per se!). If 

Re: Interesting paper on consciousness, computation and MWI

2011-09-21 Thread meekerdb

On 9/21/2011 7:08 AM, Stephen P. King wrote:

[SPK]
I consider an Observer moment to be the content of experience on an ideal 
non-anthropomorphic observer that might obtain in a minimum quantity of time, thus there 
is a maximum quantity of energy involved, as per the energy-time uncertainty relation 
(which is controversial as time is not an observable per se!). If we assume that this 
observer is constrained by the laws of QM then its ability to communicate its 
information/knowledge to another via emission and/or absorption events is finite, it is 
quantized, but its observational content is only constrained by the Heisenberg 
Uncertainty relation, a relation that does not put an upper bound on any single 
observable, it only constrains simultaneous measurement of pairs of canonically 
conjugate variables.


You seem to be invoking the Heisenberg uncertainty backwards.  What is says is:

delta-t*delta-E  hbar

not .  So if you make delta-t small then you force delta-E  hbar/delta-t.  The HUP 
puts a *lower* bound on E.  Or perhaps you are saying that since and observer has only a 
finite amount of energy there is a limit on how big delta-E can be and hence delta-t  
hbar/max[delta-E] and this provides a lower bound on the duration of an Observer Moment. 
?  Of course as you note time is not an observable in QM, but one can construct quantum 
mechanical clocks that provide a local measure of time and the HUP applies to them.


Brent

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Re: Interesting paper on consciousness, computation and MWI

2011-09-21 Thread Stephen P. King

On 9/21/2011 2:30 PM, meekerdb wrote:

On 9/21/2011 7:08 AM, Stephen P. King wrote:

[SPK]
I consider an Observer moment to be the content of experience on 
an ideal non-anthropomorphic observer that might obtain in a minimum 
quantity of time, thus there is a maximum quantity of energy 
involved, as per the energy-time uncertainty relation (which is 
controversial as time is not an observable per se!). If we assume 
that this observer is constrained by the laws of QM then its ability 
to communicate its information/knowledge to another via emission 
and/or absorption events is finite, it is quantized, but its 
observational content is only constrained by the Heisenberg 
Uncertainty relation, a relation that does not put an upper bound on 
any single observable, it only constrains simultaneous measurement of 
pairs of canonically conjugate variables.


You seem to be invoking the Heisenberg uncertainty backwards.  What is 
says is:


delta-t*delta-E  hbar

not .  So if you make delta-t small then you force delta-E  
hbar/delta-t.  The HUP puts a *lower* bound on E.  Or perhaps you are 
saying that since and observer has only a finite amount of energy 
there is a limit on how big delta-E can be and hence delta-t  
hbar/max[delta-E] and this provides a lower bound on the duration of 
an Observer Moment. ?  Of course as you note time is not an observable 
in QM, but one can construct quantum mechanical clocks that provide a 
local measure of time and the HUP applies to them.


Brent


Hi Brent,

Thank you for pointing this out. You are correct in that I was 
considering that since an observer has only a finite amount of energy 
... But the same situation would occur if the observer has only a finite 
duration within which to make an observation...


Onward!

Stephen

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Re: Interesting paper on consciousness, computation and MWI

2011-09-21 Thread Russell Standish
On Wed, Sep 21, 2011 at 10:08:55AM -0400, Stephen P. King wrote:
 On 9/21/2011 6:41 AM, Russell Standish wrote:
 On Mon, Sep 19, 2011 at 01:14:04PM -0400, Stephen P. King wrote:
  Exactly why are there not a continuum of OMs? It seems to me if
 we parametrize the cardinality of distinct OMs to *all possible*
 partitionings of the tangent spaces of physical systems (spaces
 wherein the Lagrangians and Hamiltonians exist) then we obtain at
 least the cardinality of the continuum. It is only if we assume some
 arbitrary coarse graining that we have a countable set of OMs.
 I do not assume an arbitrary coarse graining, but do think that each OM
 must contain a finite amount of information. This implies the set of
 OMs is countable.
 [SPK]
 Umm, how does the finiteness of the elements of a set X  induce
 finiteness of X? I may have missed this in my studies of set theory.

That is not what I said. Firstly, I said the set of OMs are countable, which
includes the lowest transfinite cardinal aleph_0. Also, there is more
to it. Perhaps I wasn't explicit about the fact that I consider two
OMs with the same information content to be identical. Ie, the
contained information uniquely identifies the OM.

In that case, the set of all OM can be mapped 1-1 to the set of finite
binary strings [0,1]* (I think that's how it is written). That set is
countable, so the set of all OMs must be too.

  I must dispute this claim because that reasoning in terms of
 'two integer' encoding of rationals ignores the vast and even
 infinite apparatus required to decode the value of an arbitrary pair
 of 'specified by two integers' values.
 Both the human brain, and computers are capable of handling rational
 numbers exactly. Neither of these are infinite apparatuses. If you're
 using an arbitrary precision integer representation (eg the software
 GMP), the only limitation to storing the rational number (or decoding
 it, as you put it) is the amount of memory available on the computer.
 [SPK]
 True, but that misses my point. Brains and Computers are not
 entities existing in an otherwise empty universe; we have to
 consider a multiplicity of mutually observing and measuring entities
 and the internal interpretational and representational structures
 thereof.  Consider a simple digital camera. The images that the
 camera can capture are limited by the pixel resolution of the
 camera, this is a constraint induced by the physical design of the
 camera. The camera itself, as a physical object, is not limited in
 the detail of its properties by those intrinsic constraints. We must
 take care to not assume that the limits of the observational or
 measurement process is not assumed to be that of the system that is
 making the observations/measurement.
 

Since the observable world is defined by the observer, one can't
really not take the observer into account. One can perhaps get higher order
cardinalities by looking at the boundary of that which is common to
all observers. For concreteness, consider the UD trace UD* in Bruno's
work. UD* is isomorphic to the reals - you would have to define
something like that to be your world to get uncountable things.

 
 The amount of information needed to represent any rational number is
 finite (although may be arbitarily large, as is the case for any
 integer). Only real numbers, in general, require infinite
 information. Such numbers are known as uncomputable numbers.
 [SPK]
 Surely Reality is not limited to the rationals! Are we to be
 crypto-Pythagoreans, claiming to believe that only the rationals
 exist, yet still using pi, e and other irrationals without
 question??? If Nature is computational, does it not make sense that
 its computations /information accessing and processing might not be
 limited to the rationals?
 

No, again, I didn't say that. I think of reality as being the set of
knowable things, which is necessarily countable. Various computable
numbers such as e, pi etc are definitely knowable.

John Eastmond was the one to bring up the rationals by means of a
bijection from a set of OMs. I was pointing to flaws in his use of
rational numbers (they're still countable, for instance).


-- 


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Principal, High Performance Coders
Visiting Professor of Mathematics  hpco...@hpcoders.com.au
University of New South Wales  http://www.hpcoders.com.au


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Re: Interesting paper on consciousness, computation and MWI

2011-09-21 Thread Stephen P. King

On 9/22/2011 1:05 AM, Russell Standish wrote:

On Wed, Sep 21, 2011 at 10:08:55AM -0400, Stephen P. King wrote:

On 9/21/2011 6:41 AM, Russell Standish wrote:

On Mon, Sep 19, 2011 at 01:14:04PM -0400, Stephen P. King wrote:

 Exactly why are there not a continuum of OMs? It seems to me if
we parametrize the cardinality of distinct OMs to *all possible*
partitionings of the tangent spaces of physical systems (spaces
wherein the Lagrangians and Hamiltonians exist) then we obtain at
least the cardinality of the continuum. It is only if we assume some
arbitrary coarse graining that we have a countable set of OMs.

I do not assume an arbitrary coarse graining, but do think that each OM
must contain a finite amount of information. This implies the set of
OMs is countable.

[SPK]
 Umm, how does the finiteness of the elements of a set X  induce
finiteness of X? I may have missed this in my studies of set theory.

That is not what I said. Firstly, I said the set of OMs are countable, which
includes the lowest transfinite cardinal aleph_0. Also, there is more
to it. Perhaps I wasn't explicit about the fact that I consider two
OMs with the same information content to be identical. Ie, the
contained information uniquely identifies the OM.

In that case, the set of all OM can be mapped 1-1 to the set of finite
binary strings [0,1]* (I think that's how it is written). That set is
countable, so the set of all OMs must be too.

[SPK]
Thank you for this explanation. There is just something about this 
that is still unsettling to me. I will ponder it further.



 I must dispute this claim because that reasoning in terms of
'two integer' encoding of rationals ignores the vast and even
infinite apparatus required to decode the value of an arbitrary pair
of 'specified by two integers' values.

Both the human brain, and computers are capable of handling rational
numbers exactly. Neither of these are infinite apparatuses. If you're
using an arbitrary precision integer representation (eg the software
GMP), the only limitation to storing the rational number (or decoding
it, as you put it) is the amount of memory available on the computer.

[SPK]
 True, but that misses my point. Brains and Computers are not
entities existing in an otherwise empty universe; we have to
consider a multiplicity of mutually observing and measuring entities
and the internal interpretational and representational structures
thereof.  Consider a simple digital camera. The images that the
camera can capture are limited by the pixel resolution of the
camera, this is a constraint induced by the physical design of the
camera. The camera itself, as a physical object, is not limited in
the detail of its properties by those intrinsic constraints. We must
take care to not assume that the limits of the observational or
measurement process is not assumed to be that of the system that is
making the observations/measurement.


Since the observable world is defined by the observer, one can't
really not take the observer into account. One can perhaps get higher order
cardinalities by looking at the boundary of that which is common to
all observers. For concreteness, consider the UD trace UD* in Bruno's
work. UD* is isomorphic to the reals - you would have to define
something like that to be your world to get uncountable things.

[SPK]
How do we extend this to a countable number of seperate observers 
and their interactions and communications with each other. It seems to 
me, and I may be wrong, that this generates a diagonalization. The 
bisimulation algebra that was developed is not closed in non-symmetric 
cases.


**
Summary of basic properties:

A  =  A ~ A real identity bisimulation rule

B ~ C not= C ~ B   non-commutativity rule; conjugate of 
bisimulation not equal to itself


A ~ A  =  A ~ B ~ Alaw of real identity bisimulation (when 
conjugate equal to itself)


Corollary:
A ~ A  not=  A ~ B ~ C ~ A  by law of real identity bisimulation

A ~ A  =  A ~ B ~ C ~ B ~ A retractable path independence; by law of 
real identity bisimulation



A ~ C  not=  A ~ B ~ C  non-closure
**
Am I missing something?



The amount of information needed to represent any rational number is
finite (although may be arbitarily large, as is the case for any
integer). Only real numbers, in general, require infinite
information. Such numbers are known as uncomputable numbers.

[SPK]
 Surely Reality is not limited to the rationals! Are we to be
crypto-Pythagoreans, claiming to believe that only the rationals
exist, yet still using pi, e and other irrationals without
question??? If Nature is computational, does it not make sense that
its computations /information accessing and processing might not be
limited to the rationals?


No, again, I didn't say that. I think of reality as being the set of
knowable things, which is necessarily countable. Various computable
numbers such as e, pi etc are definitely 

Re: Interesting paper on consciousness, computation and MWI

2011-09-19 Thread Russell Standish
On Wed, Aug 24, 2011 at 03:12:31PM -0700, David Nyman wrote:
 This paper presents some intriguing ideas on consciousness, computation and 
 the MWI, including an argument against the possibility of consciousness 
 supervening on any single deterministic computer program (Bruno might find 
 this interesting).  Any comments on its cogency?
 
 http://arxiv.org/abs/gr-qc/0208038
 
 David
 

I've done a partial read of this paper, and already in section 5 I see
a problem.

In section 5, Eastmond attempts to derive a paradox from the
assumption of an infinite number of observer moments in a lifetime (as
might be the case with quantum immortality, for example).

He starts with a mapping between the lifetime of OMs and the rational
numbers between 0  1. Then he argues that in observing one's current
observer moment, determining which half of the unit interval the OM is
mapped to gives 1 bit of information. Further subdividing the interval
gives, of course, more bits of information. He then concludes that an
infinite number of bits of information is needed to specify the OM.

The paradox is derived by using Cantor's argument to show that there
are an uncountable number of infinite length bitstrings, many more
than the OMs.

The problem with this argument is that all rational numbers, when
expressed in base2, ultimately end in a repeating tail. In decimal
notation, we write dots above the digits that repeat. Once the
recurring tail has been reached, no further bits of information is
required to specify the rational number. Another way of looking at it
is that all rational numbers can be specified as two integers - a
finite amount of information.

I notice this paper is an 02 arXiv paper, so rather old. It hasn't
been through peer review AFAICT. There was a bit of a critique of it
on Math Forum, but that degenerated pretty fast.

Cheers
-- 


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


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Re: Interesting paper on consciousness, computation and MWI

2011-09-19 Thread Stephen P. King

On 9/19/2011 3:20 AM, Russell Standish wrote:

On Wed, Aug 24, 2011 at 03:12:31PM -0700, David Nyman wrote:

This paper presents some intriguing ideas on consciousness, computation and
the MWI, including an argument against the possibility of consciousness
supervening on any single deterministic computer program (Bruno might find
this interesting).  Any comments on its cogency?

http://arxiv.org/abs/gr-qc/0208038

David


I've done a partial read of this paper, and already in section 5 I see
a problem.

In section 5, Eastmond attempts to derive a paradox from the
assumption of an infinite number of observer moments in a lifetime (as
might be the case with quantum immortality, for example).

He starts with a mapping between the lifetime of OMs and the rational
numbers between 0  1. Then he argues that in observing one's current
observer moment, determining which half of the unit interval the OM is
mapped to gives 1 bit of information. Further subdividing the interval
gives, of course, more bits of information. He then concludes that an
infinite number of bits of information is needed to specify the OM.

The paradox is derived by using Cantor's argument to show that there
are an uncountable number of infinite length bitstrings, many more
than the OMs.


Exactly why are there not a continuum of OMs? It seems to me if we 
parametrize the cardinality of distinct OMs to *all possible* 
partitionings of the tangent spaces of physical systems (spaces wherein 
the Lagrangians and Hamiltonians exist) then we obtain at least the 
cardinality of the continuum. It is only if we assume some arbitrary 
coarse graining that we have a countable set of OMs.




The problem with this argument is that all rational numbers, when
expressed in base2, ultimately end in a repeating tail. In decimal
notation, we write dots above the digits that repeat. Once the
recurring tail has been reached, no further bits of information is
required to specify the rational number. Another way of looking at it
is that all rational numbers can be specified as two integers - a
finite amount of information.


I must dispute this claim because that reasoning in terms of  'two 
integer' encoding of rationals ignores the vast and even infinite 
apparatus required to decode the value of an arbitrary pair of 
'specified by two integers' values. The same applies to the notion of 
digital information. Sure, we can think that the observed universe can 
be represented by some finite collection of finite bit strings, but this 
is just the result of imposing an arbitrary upper and lower bound on the 
resolution of the recording/describing machinery. There is no ab initio 
reason why that particular upper/lower bound on resolution exists in the 
first place.




I notice this paper is an 02 arXiv paper, so rather old. It hasn't
been through peer review AFAICT. There was a bit of a critique of it
on Math Forum, but that degenerated pretty fast.

Cheers


   Ideas are sometimes like vine or a single malt whiskey that must age 
before its bouquet is at its prime.


Onward!

Stephen

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Re: Interesting paper on consciousness, computation and MWI

2011-08-31 Thread Pierz
Sophistry has a smell. Sometimes an argument smells of it, but it may
be a lot harder to pin down where the specious logic is – especially
when it’s all dressed up in a mathematical formalism that may be
inaccessible to the non-mathematician/logician. However the problem
with the arguments relating to consciousness in this paper is not so
hard to pin down, and indeed Stephen King is on the right track with
his objection.

Eastmond argues that an infinite conscious lifetime is impossible
because, in ‘finding oneself’ at a particular point in that lifetime,
one would have to gain an infinite amount of knowledge, which is
absurd.  He concludes that such an infinite lifetime is in principle
impossible. The flaw lies in the way the author glosses over the
notion of “gaining information”. In examining the problem, he treats
this “gaining of information” as if it occurred magically the moment
one finds oneself at a certain point in a lifetime, but in fact such
information has to be acquired by a concrete computation. For example,
if I am to gain information about my current lifetime position, I need
to examine a calendar and compare this to stored or acquired knowledge
about my date of birth. In the case of an infinite lifetime, the size
of the computation required is arbitrarily large (but finite) in the
case of an infinite lifetime with a lower bound (a life time with a
starting point), or simply uncomputable in the case of an infinite
lifetime with no lower bound.  This is the same as saying that one
cannot calculate the age of a person who has always existed. The fact
that such a person’s age is uncomputable does not however mean that
such a person cannot exist.

The favoured theory in modern cosmology suggests that the universe is
spatially infinite. How then do we calculate the position of our
planet in this universe? If astronomers had infinite access to the map
of the universe, they could still never calculate our position,
because the calculation would be infinite. Given that time is known to
be interconvertible with space, it follows that the same logic would
apply to locating an event on an infinite timeline. The situations are
mathematically indistinguishable, yet this does not prove away the
spatially infinite universe theory.

In an infinite lifetime with no lower bound, we can never know our
age, and the amount of information ‘gained’ when we find ourselves at
a point of time in such a lifetime is a function of how much
information we can process (concrete processing limitations) and the
amount of information available to us about our position. Whichever is
smaller forms the limit.

There is also a flaw in the reasoning in relation to the proposed
conscious computer which resets itself in order to generate repeated
(and therefore infinite) conscious moments. We must remember that the
information gain is made by the conscious entity and must form part of
its conscious computation. Otherwise where is the supposed gain
occurring? All we would have is an objective description of a
perfectly mathematically conceivable situation – an infinite set of
values for the set of conscious moments, or an infinitely long string
to define a moment within that set.  So the computer must gain the
information. But it cannot do so if it continually resets. The
invocation of thermodynamics does not help if the computer cannot
access information about entropy. It can escape this problem with an
endless incrementing loop, but then it needs an infinite memory to
store this growing string. Its computational limitations inevitably
force its incrementing register to 'clock over' (like Y2K) at some
point, causing it to repeat itself.

So  unless we grant the possibility of an infinite mind/computer, an
infinite lifetime necessarily entails the repeat  of conscious
experience (just as cosmologists grant that the spatially infinite
universe with locally finite information must entail a Nietzschean
infinite recurrence). Such a lifetime is perfectly imaginable. Indeed,
theoretically an infinite lifetime with no repetition is possible with
infinite computational resources.
With these flaws the remaining argument regarding the impossibility of
a deterministic and conscious computer need not even be addressed,
since they are built on unsound foundations.


On Aug 25, 8:12 am, David Nyman david.ny...@gmail.com wrote:
 This paper presents some intriguing ideas on consciousness, computation and
 the MWI, including an argument against the possibility of consciousness
 supervening on any single deterministic computer program (Bruno might find
 this interesting).  Any comments on its cogency?

 http://arxiv.org/abs/gr-qc/0208038

 David

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Re: Interesting paper on consciousness, computation and MWI

2011-08-25 Thread Bruno Marchal

Hi David,

It looks not so bad :)
At first sight it is based on the ASSA (absolute self-samplings, like  
in the doomsday argument; may be Russell can comment on this). He  
seems naïve on the identity thesis, but that could be a reduction ad  
absurdum. The use of classical chaos is interesting, but not  
completely convincing, I might think on it. Will take a deeper look  
later. Thanks,


Bruno


On 25 Aug 2011, at 00:12, David Nyman wrote:

This paper presents some intriguing ideas on consciousness,  
computation and the MWI, including an argument against the  
possibility of consciousness supervening on any single deterministic  
computer program (Bruno might find this interesting).  Any comments  
on its cogency?


http://arxiv.org/abs/gr-qc/0208038

David

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Re: Interesting paper on consciousness, computation and MWI

2011-08-25 Thread Stephen P. King

Hi,

I have found what I believe is a flaw in the reasoning in the paper.

On pages 5-6 we find:

 In Section 5, I attempt to apply this reasoning to the case of an 
infinite lifetime. I find that, on the one hand, in discovering his 
current moment out of an infinite ensemble of moments, the observer 
should gain an infinite amount of information. But, on the other hand, I 
argue that such a state of affairs is not logically possible. Thus I 
conclude that an infinite conscious lifetime is not possible in principle.


I disagree with this conclusion because the ability to 'discover' 
ones current moment out of an infinite ensemble of moments would require 
the ability to access the computational resources needed to run the 
computation of the search algorithm on the infinite ensemble. In this 
case it is required that an infinite quantity of resources be available 
in a finite or infinitesimal duration. The author does mention some 
aspects of the problem in computational terms but the issue of resources 
does not seem to have been noticed. I find it strange that computations 
can be treated as if they are not subject to the laws of physics that 
included prohibitions on perpetual motion machines. There is no such 
thing as a free computation. The content of our Observer moments is 
finite due to computational resource limitations not because of some 
universal prior measure.


Onward!

Stephen



On 8/25/2011 5:32 AM, Bruno Marchal wrote:

Hi David,

It looks not so bad :)
At first sight it is based on the ASSA (absolute self-samplings, like 
in the doomsday argument; may be Russell can comment on this). He 
seems naïve on the identity thesis, but that could be a reduction ad 
absurdum. The use of classical chaos is interesting, but not 
completely convincing, I might think on it. Will take a deeper look 
later. Thanks,


Bruno


On 25 Aug 2011, at 00:12, David Nyman wrote:

This paper presents some intriguing ideas on consciousness, 
computation and the MWI, including an argument against the 
possibility of consciousness supervening on any single deterministic 
computer program (Bruno might find this interesting).  Any comments 
on its cogency?


http://arxiv.org/abs/gr-qc/0208038

David

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