From: Stephen P. King [] 
Sent: Thursday, August 05, 2010 4:17 PM
Subject: RE: 3-Brain <-> 1-Mind?


Hi Bruno,


            Thanks for pointing this out to me (again?)! I think that what I
have in mind in a bit more primitive than Galois connection in that I do not
assume a partial ordering or any ordering at all a priori. I am trying to
sketch out a structure that would have Galois connections as special cases.
I think that one difference in our approaches is at the metaphysical level,
in the set of basic ideas that we use. I do not assume a pre-existing
ordering as I found that this notion is problematic for computational
complexity reasons. I assume that Becoming is fundamental and that Being is
the automorphism in it. Here is my reasoning: consider the collection of all
possible minds (even those that are insane!) and the collection of all
possible brains (digital or otherwise). Is there a unique mapping between
these two collections such that there are multiple pairings that can
represent the brains/minds of each of us as we experience a common world? We
are not "frozen in time; we have the appearance of a stream of events that
we experience sequentially. Additionally we have Relativity which tells us
that there is no absolute frame of reference.

            We seem to assume that there is, but what worries me is that
there has not been much thought about the necessary and sufficient
conditions for such. I got the idea while studying the Monadology of
Leibnitz. His Theory of Everything depends on an all-knowing entity
generating a grand orchestration - a "pre-ordained harmony" - that would
match any event of within one Monad with any other such that a "best
possible world" would obtain. The problem is that there are at least a
countable infinity of possible events that have to be matched up to see
which concurrency is the "best". This is known to be a NP-Complete problem
as it is the same thing as the traveling salesman problem over an infinite
number of cities. What is the best route to take for such? Of course we can
assume a prior existing ordering or measure by labeling events with numbers
and using the natural ordering of the numbers, but this is cheating since
the events themselves are not such that they have a unique value, in effect
they are "fungible". This line of thinking takes us back to the discussions
of Observer Moments that we had.

            My alternative is to drop the insistence on a priori orderings
and use the idea of "local orderings" that emerge from interactions of
systems that have finite computational resources.  



Let me get back to the Brains and minds question. Your statement that "To a
mind, from the mind's point of view, we have to associate (from a third
person point of view) an infinity of brains (indeed all the virtual or
arithmetical brains in sufficiently similar states generated by the
Universal Dovetailer or by the proof of the relevant sigma_1 sentences in
(Robinson) Arithmetic (by UDA). This is what makes physics a sum on an
infinity of computations." is part of this but unless there is a measure
that would allow one mind to select its next state out of the collection of
all possible we wind up in a mess, because minds to themselves are fungible!
One is just as good as any other. The UD would have to run eternally to
generate the measure. Oh wait! Are you thinking of the "running the UD"
itself as the measure? 

Hmmmmmmm, this is very interesting, but I still think that it is problematic
if only because that would be equivalent to assuming a well ordering over a
set that is not well founded! Are we forgetting that a mind can emulate
itself emulating another mind? Isn't this exactly what we have when we
imagine the thoughts of some other person that is thinking of our thoughts?
Additionally, to identify an infinite process - the running of the UD - with
a unique string of numbers that "just exists" doesn't solve the problem, it
just pushes the problem off into a corner.


More soon.




Stephen P. King





[] On Behalf Of Bruno Marchal
Sent: Wednesday, August 04, 2010 3:17 AM
Subject: Re: 3-Brain <-> 1-Mind?


Dear Stephen,


I found your message in the Google archive here (thanks to Quentin). Your
messages in my mail box are indeed empty, except for the message that there
is no virus. I copy your message below:


On 04 Aug 2010, at 00:06, Stephen P. King wrote:


Dear Bruno, 

        This point is very important in my own research! I would like to 
point out that the ascription of a 1-mind to a 3-brain is such that it is 
not unique (as we have the example of multiple personality disorder!), it is

at least a many to one map just as ascribing 3-brains to a 1-mind. I claim 
that this is understandable in terms of a mathematical duality relation. The

trick is in figuring out how these mappings between the duals leads to a 
mechanism that selects individual pairs. This is what V. Pratt discovered in

his work on Chu Spaces. Current work is ongoing to see if this works in 
terms of Hilbert spaces. See:
NF-mtZo81VEo-12FTM_w5OWW9ZYRA> for the 
preliminary ideas. 

To associate a 1-mind to a 3-brain is the default option. But you are right,
digging deeper we can say that even ONE mind is is or may be an integrated
collection of different minds. I have collected all my dreams during more
than 30 years, and I have observed that sometimes I can do two different
dreams at once. Louis Jouvet has made the same observation and consider that
this happens when the corpus callosum is shut down, for some reason. The two
dreams involve arguably two minds, and after awakening we can remember the
two dreams.

Similar phenomena appear with the use of dissociative drugs like the toxic
analgesic Ketamine or the (non toxic) Salvia divinorum, which cut
momentarily connection between different part of the brain. I have many
conjectures about how to interpret the entities people met when consuming
salvia, including the perception, made possible by the remaining integrated
limbic system, of different parts of the brains to each others. 

I am not sure I can related this to Pratt's work on the Chu duality, which I
relate more to the usual Galois connection, but if you know better I wait
for your explanations of this. Well I may perhaps see the relation, by
abstracting a brain part from the others (OK then).

I don't think this is relevant for the 1-mind 3-brain connection point I was
recalling. I was talking about the usual integrated mind associate to an
ideal fully connected 3-brain. You can associate one mind to a brain, like
we do in everyday life when we talk to some person. The key and "new" point
bring by digital mechanism, is that the usual identity thesis fails in the
mind-brain direction. To a mind, from the mind's point of view, we have to
associate (from a third person point of view) an infinity of brains (indeed
all the virtual or arithmetical brains in sufficiently similar states
generated by the Universal Dovetailer or by the proof of the relevant
sigma_1 sentences in (Robinson) Arithmetic (by UDA). This is what makes
physics a sum on an infinity of computations.







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