On 16 Oct 2012, at 14:55, Stephen P. King wrote:
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 Löb property. This is also
available from http://lesswrong.com/lw/t6/the_cartoon_guide_to_l%C3%B6bs_theorem/
"Löb's Theorem shows that a mathematical system cannot assert its
own soundness without becoming inconsistent."
I get only "page not found".
Bruno
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 Löb'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 to find a solution.
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.
The "physical universe" yes, he believes that... He has shown
how one can derive a crude version of space-time using spin
combinatorials.
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.
Not even wrong!
Instead, I propose the following:
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. 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.
=================================================================
We must study the math, there are no short-cuts!
Roger Clough, [email protected]
10/16/2012
"Forever is a long time, especially near the end." -Woody Allen
--
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Onward!
Stephen
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