Re: Re: Is consciousness just an emergent property of overly complexcomputations ?

2012-10-17 Thread Roger Clough
Hi Craig Weinberg 

By sense do you mean Firstness, Secondness or Thirdness?
Or all three as a process ?


Roger Clough, rclo...@verizon.net 
10/17/2012  
Forever is a long time, especially near the end. -Woody Allen 


- Receiving the following content -  
From: Craig Weinberg  
Receiver: everything-list  
Time: 2012-10-16, 14:11:14 
Subject: Re: Is consciousness just an emergent property of overly 
complexcomputations ? 




On Tuesday, October 16, 2012 8:54:10 AM UTC-4, yanniru wrote: 
On Tue, Oct 16, 2012 at 8:29 AM, Craig Weinberg  wrote:  
 Computation is an overly simplified emergent property of sense. If you could  
 have computation without sense, then there would be no consciousness.  
 Craig  
  
Could you provide a link where you more fully explain what sense is  
and how it relates to comp and consciousness? You probably already  
have. But I missed it.  


This post http://s33light.org/post/24159233874 talks about why I use the word 
sense. I am saying that the only thing that the universe can be reduced to 
which is irreducible is sense, and by that I really mean sense in every sense, 
but in particular sensation, intuition, subjective feeling, pattern 
recognition, and categorization or discernment. 

Craig 
  

Richard  
  
 On Tuesday, October 16, 2012 7:50:17 AM UTC-4, rclough wrote:  
  
 Is consciousness just an emergent property of overly complex computations  
 ?  
  
 The short answer is that I am proposing that :  
  
 1) Penrose's noncomputability position is equivalent to the position  
 that consciousness emerges at such a level of complexity.  
  
 2) In addition, that while Godel's incompleteness theorem may make  
 such calculations incomplete, it does not make them beyond the  
 range of computabilitlity.  Instead, it exposes these halted  
 upward-directed  
 calculations to the possibility of continuing downward-directed platonic  
 reason,  
 the numbers themselves, and plato's geometrical forms. I do not know  
 enough  
 mathematics to be more specific.  
  
 If you would like a more complete discussion, read below.  
  
  
  
  
 ===  
 A MORE COMPLETE ANSWER:  
 Contemporary thinking on consciousness is that it is an emergent  
 property  
 of computational complexity among neurons. This raises some questions:  
  
 A. Is the emergence of consciouness simply a another name for Penrose's  
 condition of non-computability ?  
  
 http://www.quantumconsciousness.org/presentations/whatisconsciousness.html  
  
 Conventional explanations portray consciousness as an emergent property  
 of classical  
 computer-like activities in the brain's neural networks.  
 The prevailing views among scientists in this camp are that  
  
 1) patterns of neural network activities correlate with mental states,  
 2) synchronous network oscillations in thalamus and cerebral cortex  
 temporally bind information,  
 and  
 3) consciousness emerges as a novel property of computational complexity  
 among neurons.  
  
  
  
 B. Or is there another way to look at this emergence ?  
  
 Now my understanding of emergent properties is that they appear or  
 emerge through looking at a phenomenon  
 at a lower degree of magnification from above.  Thus sociology is an  
 emergent property of  
 the behavior of many minds.  
  
 IMHO from above means looking downward from Platonia. From a wiser  
 position.  
  
 Penrose seems to take take two views of Platonia:  
  
 http://cognet.mit.edu/posters/TUCSON3/Yasue.html  
  
 One is his belief that there is a realm of non-computability, presumably  
 that of Platonia as experienced.  
 All art and insight comes from such an experience.  
  
 On the other hand, if I am not mistaken, Penrose seems to believe that the  
 universe is made up of  
 quantum spin networks, which presumably can model even the most complex  
 entities.  
 He does not seem to deny that the non-computational calculations belong  
 to the realm  
 of spin networks.  
  
 This casts some doubt on his belief in the possibility of  
 non-computability,  
 and may even allow his spin networks, which are presumably complete,  
 to escape intact from Godel's incompleteness limitation.  
  
 Instead, I propose the following:  
  
 1) Penrose's noncomputability position is equivalent to the position  
 that consciousness emerges at such a level of complexity.  
  
 2) In addition, that while Godel's incompleteness theorem may make  
 such calculations incomplete, it does not make them beyond the  
 range of computabilitlity. Instead, it exposes these halted  
 upward-directed  
 calculations to the possibility of continuing downward-directed platonic  
 reason,  
 the numbers themselves, and plato's geometrical forms. I do not know  
 enough  
 mathematics to be more specific.  
 =  
  
  
  
 Roger Clough, rcl...@verizon.net  
 10/16/2012  
 Forever is a long time

Re: Re: Is consciousness just an emergent property of overly complexcomputations ?

2012-10-17 Thread Craig Weinberg


On Wednesday, October 17, 2012 6:33:15 AM UTC-4, rclough wrote:

 Hi Craig Weinberg 

 By sense do you mean Firstness, Secondness or Thirdness? 
 Or all three as a process ? 

 Using these as a guide:

(from http://www.helsinki.fi/science/commens/terms/thirdness.html)
  Firstness is the mode of being of that which is such as it is, 
positively and without reference to anything else. 
  Secondness is the mode of being of that which is such as it is, with 
respect to a second but regardless of any third. 
  Thirdness is the mode of being of that which is such as it is, in 
bringing a second and third into relation to each other. 

I would say that sense is primordial Sixthness. The meta juxaposition of 
all three modalities. Sense is the totality within which Firstness, 
Secondness, and Thirdness are defined and directly experienced. Fourthness 
could be thought of as the change that thirdness brings to firstness and 
Fifthness could be perhaps the juxtaposition of that change with it's 
canonical conjugate in Secondness. There is no Firstness without Sixthness. 
In quantitative terms, the universe doesn't begin with 0 or 1, it 'begins' 
with the instantaneous/perpetual division of 1 into infinite fractions. 
Timespace is only real at the periphery/circumference of that division.

Craig


 Roger Clough, rcl...@verizon.net javascript: 
 10/17/2012   
 Forever is a long time, especially near the end. -Woody Allen 


 - Receiving the following content -   
 From: Craig Weinberg   
 Receiver: everything-list   
 Time: 2012-10-16, 14:11:14 
 Subject: Re: Is consciousness just an emergent property of overly 
 complexcomputations ? 




 On Tuesday, October 16, 2012 8:54:10 AM UTC-4, yanniru wrote: 
 On Tue, Oct 16, 2012 at 8:29 AM, Craig Weinberg  wrote:   
  Computation is an overly simplified emergent property of sense. If you 
 could   
  have computation without sense, then there would be no consciousness.   
  Craig   

 Could you provide a link where you more fully explain what sense is   
 and how it relates to comp and consciousness? You probably already   
 have. But I missed it.   


 This post http://s33light.org/post/24159233874 talks about why I use the 
 word sense. I am saying that the only thing that the universe can be 
 reduced to which is irreducible is sense, and by that I really mean sense 
 in every sense, but in particular sensation, intuition, subjective feeling, 
 pattern recognition, and categorization or discernment. 

 Craig 
   

 Richard   

  On Tuesday, October 16, 2012 7:50:17 AM UTC-4, rclough wrote:   

  Is consciousness just an emergent property of overly complex 
 computations   
  ?   

  The short answer is that I am proposing that :   

  1) Penrose's noncomputability position is equivalent to the position   
  that consciousness emerges at such a level of complexity.   

  2) In addition, that while Godel's incompleteness theorem may make   
  such calculations incomplete, it does not make them beyond the   
  range of computabilitlity.  Instead, it exposes these halted   
  upward-directed   
  calculations to the possibility of continuing downward-directed 
 platonic   
  reason,   
  the numbers themselves, and plato's geometrical forms. I do not know   
  enough   
  mathematics to be more specific.   

  If you would like a more complete discussion, read below.   




  ===   
  A MORE COMPLETE ANSWER:   
  Contemporary thinking on consciousness is that it is an emergent   
  property   
  of computational complexity among neurons. This raises some questions: 
   

  A. Is the emergence of consciouness simply a another name for Penrose's 
   
  condition of non-computability ?   

  
 http://www.quantumconsciousness.org/presentations/whatisconsciousness.html  

  Conventional explanations portray consciousness as an emergent 
 property   
  of classical   
  computer-like activities in the brain's neural networks.   
  The prevailing views among scientists in this camp are that   

  1) patterns of neural network activities correlate with mental states, 
   
  2) synchronous network oscillations in thalamus and cerebral cortex   
  temporally bind information,   
  and   
  3) consciousness emerges as a novel property of computational 
 complexity   
  among neurons.   



  B. Or is there another way to look at this emergence ?   

  Now my understanding of emergent properties is that they appear or   
  emerge through looking at a phenomenon   
  at a lower degree of magnification from above.  Thus sociology is an 
   
  emergent property of   
  the behavior of many minds.   

  IMHO from above means looking downward from Platonia. From a wiser   
  position.   

  Penrose seems to take take two views of Platonia:   

  http://cognet.mit.edu/posters/TUCSON3/Yasue.html   

  One is his belief

Re: Re: Is consciousness just an emergent property of overly complexcomputations ?

2012-10-16 Thread Roger Clough
Hi Richard Ruquist  

I'm well aware of that, except you don't need
Godel to reach an impossibly complex state of
calculations.  My own position is that if you 
can't calculate upward any more, you calculate 
downward. From Platonia, except that you begin
to use the forms, numbers, reason, all of that
stuff. Consciousness is created from Platonia,
probably more form philosophy than math.
After some study, it turns out that 
Leibniz's substances are not based on
physical materials but on their forms. 
Just like Plato except that there are an
infinite types of materials.




Roger Clough, rclo...@verizon.net 
10/16/2012  
Forever is a long time, especially near the end. -Woody Allen 


- Receiving the following content -  
From: Richard Ruquist  
Receiver: everything-list  
Time: 2012-10-16, 08:33:45 
Subject: Re: Is consciousness just an emergent property of overly 
complexcomputations ? 


Roger, 
Philosophers such as Lucas, Hofstadter and Chalmers as well as Penrose 
and Godel suggest that consciousness may be due to incompleteness 
itself allowing for emergence... 
See http://vixra.org/pdf/1101.0044v1.pdf 
Richard 

On Tue, Oct 16, 2012 at 7:48 AM, Roger Clough  wrote: 
 Is consciousness just an emergent property of overly complex computations ? 
 
 The short answer is that I am proposing that : 
 
 1) Penrose's noncomputability position is equivalent to the position 
 that consciousness emerges at such a level of complexity. 
 
 2) In addition, that while Godel's incompleteness theorem may make 
 such calculations incomplete, it does not make them beyond the 
 range of computabilitlity. Instead, it exposes these halted upward-directed 
 calculations to the possibility of continuing downward-directed platonic 
 reason, 
 the numbers themselves, and plato's geometrical forms. I do not know enough 
 mathematics to be more specific. 
 
 If you would like a more complete discussion, read below. 
 
 
 
 
 === 
 A MORE COMPLETE ANSWER: 
 Contemporary thinking on consciousness is that it is an emergent property 
 of computational complexity among neurons. This raises some questions: 
 
 A. Is the emergence of consciouness simply a another name for Penrose's 
 condition of non-computability ? 
 
 http://www.quantumconsciousness.org/presentations/whatisconsciousness.html 
 
 Conventional explanations portray consciousness as an emergent property of 
 classical 
 computer-like activities in the brain's neural networks. 
 The prevailing views among scientists in this camp are that 
 
 1) patterns of neural network activities correlate with mental states, 
 2) synchronous network oscillations in thalamus and cerebral cortex 
 temporally bind information, 
 and 
 3) consciousness emerges as a novel property of computational complexity 
 among neurons. 
 
 
 
 B. Or is there another way to look at this emergence ? 
 
 Now my understanding of emergent properties is that they appear or emerge 
 through looking at a phenomenon 
 at a lower degree of magnification from above.  Thus sociology is an 
 emergent property of 
 the behavior of many minds. 
 
 IMHO from above means looking downward from Platonia. From a wiser 
 position. 
 
 Penrose seems to take take two views of Platonia: 
 
 http://cognet.mit.edu/posters/TUCSON3/Yasue.html 
 
 One is his belief that there is a realm of non-computability, presumably 
 that of Platonia as experienced. 
 All art and insight comes from such an experience. 
 
 On the other hand, if I am not mistaken, Penrose seems to believe that the 
 universe is made up of 
 quantum spin networks, which presumably can model even the most complex 
 entities. 
 He does not seem to deny that the non-computational calculations belong to 
 the realm 
 of spin networks. 
 
 This casts some doubt on his belief in the possibility of non-computability, 
 and may even allow his spin networks, which are presumably complete, 
 to escape intact from Godel's incompleteness limitation. 
 
 Instead, I propose the following: 
 
 1) Penrose's noncomputability position is equivalent to the position 
 that consciousness emerges at such a level of complexity. 
 
 2) In addition, that while Godel's incompleteness theorem may make 
 such calculations incomplete, it does not make them beyond the 
 range of computabilitlity. Instead, it exposes these halted upward-directed 
 calculations to the possibility of continuing downward-directed platonic 
 reason, 
 the numbers themselves, and plato's geometrical forms. I do not know enough 
 mathematics to be more specific. 
 = 
 
 
 
 Roger Clough, rclo...@verizon.net 
 10/16/2012 
 Forever is a long time, especially near the end. -Woody Allen 
 
 -- 
 You received this message because you are subscribed to the Google Groups 
 Everything List group. 
 To post to this group, send email to everything-list@googlegroups.com. 
 To unsubscribe from this group

Re: Re: Is consciousness just an emergent property of overly complexcomputations ?

2012-10-16 Thread Roger Clough
Hi Craig Weinberg  

You said,

 Computation is an overly simplified emergent property of sense. 
If you could have computation without sense, then there would be no 
consciousness.

That sounds potent, I'm but not sure what it means.
Could you expand on it a little ?


Roger Clough, rclo...@verizon.net 
10/16/2012  
Forever is a long time, especially near the end. -Woody Allen 


- Receiving the following content -  
From: Craig Weinberg  
Receiver: everything-list  
Time: 2012-10-16, 08:29:38 
Subject: Re: Is consciousness just an emergent property of overly 
complexcomputations ? 


Computation is an overly simplified emergent property of sense. If you could 
have computation without sense, then there would be no consciousness.  

Craig 


On Tuesday, October 16, 2012 7:50:17 AM UTC-4, rclough wrote: 
Is consciousness just an emergent property of overly complex computations ?  

The short answer is that I am proposing that : 

1) Penrose's noncomputability position is equivalent to the position 
that consciousness emerges at such a level of complexity.  

2) In addition, that while Godel's incompleteness theorem may make  
such calculations incomplete, it does not make them beyond the 
range of computabilitlity.  Instead, it exposes these halted upward-directed 
calculations to the possibility of continuing downward-directed platonic 
reason, 
the numbers themselves, and plato's geometrical forms. I do not know enough 
mathematics to be more specific. 

If you would like a more complete discussion, read below. 




=== 
A MORE COMPLETE ANSWER: 
Contemporary thinking on consciousness is that it is an emergent property  
of computational complexity among neurons. This raises some questions:  

A. Is the emergence of consciouness simply a another name for Penrose's 
condition of non-computability ?  

http://www.quantumconsciousness.org/presentations/whatisconsciousness.html  

Conventional explanations portray consciousness as an emergent property of 
classical  
computer-like activities in the brain's neural networks.  
The prevailing views among scientists in this camp are that  

1) patterns of neural network activities correlate with mental states,  
2) synchronous network oscillations in thalamus and cerebral cortex temporally 
bind information,  
and  
3) consciousness emerges as a novel property of computational complexity among 
neurons.  



B. Or is there another way to look at this emergence ?  

Now my understanding of emergent properties is that they appear or emerge 
through looking at a phenomenon  
at a lower degree of magnification from above.  Thus sociology is an emergent 
property of  
the behavior of many minds.  

IMHO from above means looking downward from Platonia. From a wiser position.  

Penrose seems to take take two views of Platonia:  

http://cognet.mit.edu/posters/TUCSON3/Yasue.html  

One is his belief that there is a realm of non-computability, presumably that 
of Platonia as experienced.  
All art and insight comes from such an experience.  

On the other hand, if I am not mistaken, Penrose seems to believe that the 
universe is made up of  
quantum spin networks, which presumably can model even the most complex 
entities.  
He does not seem to deny that the non-computational calculations belong to 
the realm 
of spin networks.   

This casts some doubt on his belief in the possibility of non-computability, 
and may even allow his spin networks, which are presumably complete, 
to escape intact from Godel's incompleteness limitation. 

Instead, I propose the following:  

1) Penrose's noncomputability position is equivalent to the position 
that consciousness emerges at such a level of complexity.  

2) In addition, that while Godel's incompleteness theorem may make  
such calculations incomplete, it does not make them beyond the 
range of computabilitlity. Instead, it exposes these halted upward-directed 
calculations to the possibility of continuing downward-directed platonic 
reason, 
the numbers themselves, and plato's geometrical forms. I do not know enough 
mathematics to be more specific. 
= 



Roger Clough, rcl...@verizon.net  
10/16/2012  
Forever is a long time, especially near the end. -Woody Allen 

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Re: Re: Is consciousness just an emergent property of overly complexcomputations ?

2012-10-16 Thread Roger Clough
Hi Stephen P. King 

Thanks. My mistake was to say that P's position is that
consciousness, arises at (or above ?) 
the level of noncomputability.  He just seems to
say that intuiton does. But that just seems
to be a conjecture of his.


ugh, rclo...@verizon.net 
10/16/2012 
Forever is a long time, especially near the end. -Woody Allen 


- Receiving the following content - 
From: Stephen P. King 
Receiver: everything-list 
Time: 2012-10-16, 08:55:23 
Subject: Re: Is consciousness just an emergent property of overly 
complexcomputations ? 


Hi Roger, 

On 10/16/2012 7:48 AM, Roger Clough wrote: 

Is consciousness just an emergent property of overly complex computations ? 

No! 



The short answer is that I am proposing that : 

1) Penrose's noncomputability position is equivalent to the position 
that consciousness emerges at such a level of complexity. 

No! 



2) In addition, that while Godel's incompleteness theorem may make 
such calculations incomplete, it does not make them beyond the 
range of computabilitlity. 


No, it puts them beyond the domain of computability. Bruno has already 
shown this! 


 Instead, it exposes these halted upward-directed 
calculations to the possibility of continuing downward-directed platonic 
reason, 
the numbers themselves, and plato's geometrical forms. I do not know enough 
mathematics to be more specific. 

Look up Bruno's resent cartoon of L? property. This is also available from 
http://lesswrong.com/lw/t6/the_cartoon_guide_to_l%C3%B6bs_theorem/ 

L?'s Theorem shows that a mathematical system cannot assert its own soundness 
without becoming inconsistent. 

A slightly more technical discussion here: 
http://en.wikipedia.org/wiki/Curry's_paradox 



If you would like a more complete discussion, read below. 



I will! 




=== 
A MORE COMPLETE ANSWER: 
Contemporary thinking on consciousness is that it is an emergent property 
of computational complexity among neurons. This raises some questions: 

A. Is the emergence of consciouness simply a another name for Penrose's 
condition of non-computability ? 

http://www.quantumconsciousness.org/presentations/whatisconsciousness.html 

Conventional explanations portray consciousness as an emergent property of 
classical 
computer-like activities in the brain's neural networks. 
The prevailing views among scientists in this camp are that 

1) patterns of neural network activities correlate with mental states, 
2) synchronous network oscillations in thalamus and cerebral cortex temporally 
bind information, 
and 
3) consciousness emerges as a novel property of computational complexity among 
neurons. 



That is Stuart Hameroff's idea, not Penrose's per se... 




B. Or is there another way to look at this emergence ? 

Now my understanding of emergent properties is that they appear or emerge 
through looking at a phenomenon 
at a lower degree of magnification from above.  Thus sociology is an emergent 
property of 
the behavior of many minds. 


Sure, but the integrity or wholeness of an individual mind is only 
subject to a threshold in the sense of the requirement of closure under 
consistent self-reference (which is what L?'s Theorem is all about.) But this 
makes a mind solipsistic unless we can break the symmetry somehow! 



IMHO from above means looking downward from Platonia. From a wiser position. 

Penrose seems to take take two views of Platonia: 

http://cognet.mit.edu/posters/TUCSON3/Yasue.html 

One is his belief that there is a realm of non-computability, presumably that 
of Platonia as experienced. 
All art and insight comes from such an experience. 



No, that is what Kunio Yasue thinks that Penrose's position on Platonia! 
You might read The Emperor's New Mind for yourself and get it straight from the 
Horse's mouth. 

http://www.thiruvarunai.com/eBooks/penrose/The%20Emperors%20New%20Mind.pdf 

This quote might give us a flavor of Penrose's thinking: 

In Plato's view, the objects of pure geometry straight lines, 
circles, triangles, planes, etc. --were only approximately 
realized in terms of the world of actual physical things. Those 
mathematically precise objects of pure geometry inhabited, 
instead, a different world Plato's ideal world of 
mathematical concepts. Plato's world consists not of tangible 
objects, but of 'mathematical things'. This world is 
accessible to us not in the ordinary physical way but, instead, 
via the intellect. One's mind makes contact with Plato's 
world whenever it contemplates a mathematical truth, perceiving 
it by the exercise of mathematical reasoning and 
insight. This ideal world was regarded as distinct and more perfect 
than the material world of our external experiences, 
but just as real. 

Exactly how the contact is made between the realms remains to be 
explained! This, BTW, is my one bone of contention with Bruno's COMP program 
and I am desperately trying

Re: Re: Is consciousness just an emergent property of overly complexcomputations ?

2012-10-16 Thread Roger Clough
Hi Stephen P. King  

This may have little connection to what you said,
but in one of Brain Greene's talks (on time) he
made mention that the subjective state, the
experiential state, always just experiences now. 

Similarly calculations flow in time as they are made,
and the one being made is made now.

There seems to be a connection but I can't express what it is. 



Roger Clough, rclo...@verizon.net 
10/16/2012  
Forever is a long time, especially near the end. -Woody Allen 


- Receiving the following content -  
From: Stephen P. King  
Receiver: everything-list  
Time: 2012-10-16, 09:08:49 
Subject: Re: Is consciousness just an emergent property of overly 
complexcomputations ? 


On 10/16/2012 8:54 AM, Richard Ruquist wrote: 
 On Tue, Oct 16, 2012 at 8:29 AM, Craig Weinberg wrote: 
 Computation is an overly simplified emergent property of sense. If you 
 could 
 have computation without sense, then there would be no consciousness. 
 Craig 
  
 Could you provide a link where you more fully explain what sense is 
 and how it relates to comp and consciousness? You probably already 
 have. But I missed it. 
 Richard 
Hi Richard, 

 Unless you are a zombie, you are experiencing right now exactly  
what Sense is. Only you can know exactly what the Sense of Richard  
Ruquist and Craig can only experience (and thus know) what his Sense  
is. What you need to understand is that Sense is strictly 1p, it has no  
3p aspect. You either experience your own version of it or, like Dennett  
and the materialist, try to deny its existence. 

--  
Onward! 

Stephen 


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Re: Re: Is consciousness just an emergent property of overly complexcomputations ?

2012-10-16 Thread Alberto G. Corona
Magic emergence from magic enough complexity has been advocated for almost
anything. Most of the time as an excuse for  not saying I don´t know,
that is the prerequisite for thinking deeper about the problem. I prefer to
say I don´t know.

2012/10/16 Roger Clough rclo...@verizon.net

  Hi Stephen P. King

 Thanks. My mistake was to say that P's position is that
 consciousness, arises at (or above ?)
 the level of noncomputability.  He just seems to
 say that intuiton does. But that just seems
 to be a conjecture of his.



 ugh, rclo...@verizon.net +rclo...@verizon.net
 10/16/2012
 Forever is a long time, especially near the end. -Woody Allen


 - Receiving the following content -
 From: Stephen P. King
 Receiver: everything-list
 Time: 2012-10-16, 08:55:23
 Subject: Re: Is consciousness just an emergent property of overly
 complexcomputations ?


 Hi Roger,

 On 10/16/2012 7:48 AM, Roger Clough wrote:

 Is consciousness just an emergent property of overly complex computations
 ?

 No!



 The short answer is that I am proposing that :

 1) Penrose's noncomputability position is equivalent to the position
 that consciousness emerges at such a level of complexity.

 No!



 2) In addition, that while Godel's incompleteness theorem may make
 such calculations incomplete, it does not make them beyond the
 range of computabilitlity.


 No, it puts them beyond the domain of computability. Bruno has already
 shown this!


  Instead, it exposes these halted upward-directed
 calculations to the possibility of continuing downward-directed platonic
 reason,
 the numbers themselves, and plato's geometrical forms. I do not know
 enough
 mathematics to be more specific.

 Look up Bruno's resent cartoon of L? property. This is also available
 from http://lesswrong.com/lw/t6/the_cartoon_guide_to_l%C3%B6bs_theorem/

 L?'s Theorem shows that a mathematical system cannot assert its own
 soundness without becoming inconsistent.

 A slightly more technical discussion here:
 http://en.wikipedia.org/wiki/Curry's_paradox



 If you would like a more complete discussion, read below.



 I will!




 ===
 A MORE COMPLETE ANSWER:
 Contemporary thinking on consciousness is that it is an emergent
 property
 of computational complexity among neurons. This raises some questions:

 A. Is the emergence of consciouness simply a another name for Penrose's
 condition of non-computability ?

 http://www.quantumconsciousness.org/presentations/whatisconsciousness.html

 Conventional explanations portray consciousness as an emergent property
 of classical
 computer-like activities in the brain's neural networks.
 The prevailing views among scientists in this camp are that

 1) patterns of neural network activities correlate with mental states,
 2) synchronous network oscillations in thalamus and cerebral cortex
 temporally bind information,
 and
 3) consciousness emerges as a novel property of computational complexity
 among neurons.



 That is Stuart Hameroff's idea, not Penrose's per se...




 B. Or is there another way to look at this emergence ?

 Now my understanding of emergent properties is that they appear or
 emerge through looking at a phenomenon
 at a lower degree of magnification from above.  Thus sociology is an
 emergent property of
 the behavior of many minds.


 Sure, but the integrity or wholeness of an individual mind is only
 subject to a threshold in the sense of the requirement of closure under
 consistent self-reference (which is what L?'s Theorem is all about.) But
 this makes a mind solipsistic unless we can break the symmetry somehow!



 IMHO from above means looking downward from Platonia. From a wiser
 position.

 Penrose seems to take take two views of Platonia:

 http://cognet.mit.edu/posters/TUCSON3/Yasue.html

 One is his belief that there is a realm of non-computability, presumably
 that of Platonia as experienced.
 All art and insight comes from such an experience.



 No, that is what Kunio Yasue thinks that Penrose's position on
 Platonia! You might read The Emperor's New Mind for yourself and get it
 straight from the Horse's mouth.

 http://www.thiruvarunai.com/eBooks/penrose/The%20Emperors%20New%20Mind.pdf

 This quote might give us a flavor of Penrose's thinking:

 In Plato's view, the objects of pure geometry straight lines,
 circles, triangles, planes, etc. --were only approximately
 realized in terms of the world of actual physical things. Those
 mathematically precise objects of pure geometry inhabited,
 instead, a different world Plato's ideal world of
 mathematical concepts. Plato's world consists not of tangible
 objects, but of 'mathematical things'. This world is
 accessible to us not in the ordinary physical way but, instead,
 via the intellect. One's mind makes contact with Plato's
 world whenever it contemplates a mathematical truth, perceiving
 it by the exercise of mathematical reasoning