**Stephen P. King** (*stephenk1@home.com*)

*Sun, 04 Apr 1999 12:35:42 -0400*

**Messages sorted by:**[ date ] [ thread ] [ subject ] [ author ]**Next message:**Ben Goertzel: "[time 142] Re: [time 136] Re: [time 123] RE: [time 69] Spacetime & consciousness"**Previous message:**Ben Goertzel: "[time 140] Re: [time 81] Discreteness and p-adics"**In reply to:**Matti Pitkanen: "[time 139] Re: [time 81] Discreteness and p-adics"

Hitoshi Kitada wrote:

*>
*

*> Dear Stephen,
*

*>
*

*> The parts you quoted from Prugovecki are all well-known in math, and do not
*

*> reflect the special features of the dualism of Chu spaces.
*

*>
*

*> Best,
*

*> Hitoshi
*

Dear Hitoshi,

The fact that they are "all well-known in math" is what makes my task

so difficult. It is only because something is so close and "obvious"

that blinds us to the implications. As a philosopher, it is the

implications of these mathematical formalisms that matters. When we

think of causality, what is it that we mean? We say A causes B; but if

we look past the "fact" and look to the "how" of this fact, we are

forced to face the difficulty of explaining them in a way that is

logically consistent with all other facts available, thus I say: A

causes B iff Y implies X, A encodes information X and B encodes

information Y.

When we recognize that the Universe is not fixed ab initio by some

divine act, but is constructed by the interactions of finite subsets of

it, we cannot just say "it is so because we observe it to be so", even

though this statement is undeniably true.

When we come to the problem of consciousness within the Universe, we

have many ideas available with which to construct models. Pratt has

found that the original Cartesian proposal of Mind-body dualism can be

corrected so that it does provide a viable paradigm with which to make

sense of how it is that information and matter can influence each other.

Perhaps a little toy model would help. I have been working on a

gedankenexperiment for a long time now and am lacking making it

mathematically rigorous. :( We start with the now infamous Maxwell Demon

who attempts to bypass the laws of thermodynamics. We substitute a

computer for the imaginary demon. The computer's "power" is supplied by

using the difference in temperature/pressure/gravitational

curvature/charge/etc. between the two closed and isolated chambers, and

it opens and closes the valve/wormhole/switch/etc. between the two using

a string of bits. For a binary sting reading computer, we think of the

1s as open and 0s as closed. We can easily generalize this to a [0, 1]

n-ary stream, where the binary is a mere special case.

What makes this idea concrete is that we can think of the two Chambers

as closed manifolds that differ in their clock readings. Thus we can

think of the Demon as "connecting" together two separate instants "in

time". Alternatively, we can think of the pair of spaces that are dual

to each other in the manner "that is well know in mathematics". There is

also a duality existing between the information content of the pair!

If the two manifolds/spaces are identical, or that there is a complete

bijective mapping between the two (or totally orthogonal : A x X = 0 <->

B x Y = 0), then the computer is unable to derive any power to operate.

The Totality Universe, being a bound state has this property between any

of its proper subsets, thus we arrive to the conclusion that no time

exist at that level. What is interesting, is that if there is no time

there is also no consciousness possible and vise versa!

Pratt's residuations between Chu spaces and Wegner et al's

infomorphisms between classifications are connections of the same type

but they explicitly take information content into account. We can say

that information entropy *is* thermodynamic entropy, but we are very

wrong! They are only identical (bisimilar/bisimulational equivalence

becomes isomorphism) at the Universe level, were we have infinite

completeness and Eternity to compute the bijection, the problem is that

such a computation is IMPOSSIBLE. In Eternity, there is no free energy,

no differences on matter to encode bits on/in, no shifts, no nothing!

http://boole.stanford.edu/chuguide.html

http://www.cs.brown.edu/~pw/papers/math1.ps

other sources

http://www.i.kyushu-u.ac.jp/~seki/P-complete/all/node103.html

http://wrcm.dsi.unimi.it/DSI/Rapporti_Interni_DSI/1995/%237631403

http://wwwis.win.tue.nl/~wsinmarc/abstracts/spne.html

http://www.dcs.ed.ac.uk/lfcsreps/EXPORT/92/ECS-LFCS-92-218/index.html

http://www.inrialpes.fr/vasy/pub/COST247/cost111.html

http://www.risc.uni-linz.ac.at/courses/ss98/parsem/ccs2/

etc.

In Maxwell's original model the "survival" of the demon was not

dependent on the existence of a difference of some kind between the two

chambers/space/manifolds/etc.. But, here it is obvious that any demon,

being a "real" computer operating over some n-ary stream or a

supernatural entity, has to exist "within" the Universe and thus we see

that its survival does depend on the fact that there exist subsets of

the Universe that are

scattering/evolving/non-static/far-from-equilibrium from each other.

If there is no way at all allowed to "connect" subsets (LSs) to each

other, then we are back to were Newton started: A Universe at

equilibrium between itself and all of its subsets. When we postulate

that there is no uniquely a priori defined connection, language,

wormhole, mapping, parallel transport, etc. We are allowing for

consciousness and time to be concrete and real. "All is allowed that is

not Forbidden" (Peter Wegner)

Wegner and Pratt's ideas, for me, speak to this Connection. The

Universe is Both Information and Matter, it is their interaction that is

us. :)

Onward to the Unknown,

Stephen

PS, Robert's discovery of Phi is a direct manifestation of a fundamental

principle involved here!

http://www.bestweb.net/~ca314159/

*> ----- Original Message -----
*

*> From: Stephen P. King <stephenk1@home.com>
*

*> To: Hitoshi Kitada <hitoshi@kitada.com>; Time List <time@kitada.com>; Vaughan
*

*> Pratt <pratt@CS.Stanford.EDU>
*

*> Sent: Sunday, April 04, 1999 1:58 PM
*

*> Subject: [time 129] Re: [time 128] On Pratt's Duality
*

*>
*

*> > Dear Hitoshi,
*

*> >
*

*> > I don't think that he knows Pratt's work, but...
*

*> >
*

*> > page 33.
*

*> >
*

*> > "An M-coordinate-independent definition of 'covariant vectors'... can be
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*> > obtained by introducing the *cotangent space* T_x^*M above x as the
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*> > algebraic dual of T_xM. -i.e.as consisting of real-valued linear
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*> > functionals w over T_xM. An equivalent definition of cotangent space can
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*> > also be given in terms of the family of all smooth real-valued functions
*

*> > defined on some neighborhood N_x of x, which forms the basis of the
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*> > definition (1.5), by introducing for each element f in that family the
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*> > following linear maps:
*

*> >
*

*> > df: X |-> Xf \element R^1, X \element T_xM. (1.8)"
*

*> >
*

*> > ...
*

*> >
*

*> > Page 63. Note 11
*

*> > "Note that, in the case that g is a matrix that acts by matrix
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*> > multiplication on the elements of R^n, for its action from the
*

*> > rightthose elements have to be viewed as one-row matrices, whereas for
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*> > its action on the left they have to be viewed as one-column matrices, so
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*> > that one mode of such action can be related to the other by taking the
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*> > transposes of the matrices in question."
*

*> >
*

*> > These properties are consistent with a Chu space. I may have gotten a
*

*> > bit exited and missed something... :) There is much to cover and I am a
*

*> > bit tired. :)
*

*> >
*

*> > Later,
*

*> >
*

*> > Stephen
*

*> >
*

*> > Hitoshi Kitada wrote:
*

*> > >
*

*> > > Dear Stephen,
*

*> > >
*

*> > > ----- Original Message -----
*

*> > > From: Stephen P. King <stephenk1@home.com>
*

*> > > To: Hitoshi Kitada <hitoshi@kitada.com>
*

*> > > Cc: Time List <time@kitada.com>
*

*> > > Sent: Sunday, April 04, 1999 11:19 AM
*

*> > > Subject: [time 127] Re: [time 121] RE: [time 115] On Pratt's Duality
*

*> > >
*

*> > > > Dear Hitoshi,
*

*> > > >
*

*> > > > I apologize for the length of this... :) BTW, I think that Prugovecki's
*

*> > > > formalism already has Chu_2 spaces built in, he just does not understand
*

*> > > > the implications! More on this later... ;)
*

*> > >
*

*> > > At which points or where in the book does Prugovecki include Chu spaces?
*

*> > >
*

*> > > Best,
*

*> > > Hitoshi
*

*> >
*

**Next message:**Ben Goertzel: "[time 142] Re: [time 136] Re: [time 123] RE: [time 69] Spacetime & consciousness"**Previous message:**Ben Goertzel: "[time 140] Re: [time 81] Discreteness and p-adics"**In reply to:**Matti Pitkanen: "[time 139] Re: [time 81] Discreteness and p-adics"

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