Stephen P. King (stephenk1@home.com)
Sat, 24 Jul 1999 18:07:34 -0400
Dear Matti,
Matti Pitkanen wrote:
>
> This like Terminator, The return of Terminator I, II,....ad infinitum!
My brain is being stretched! :-)
> In part IV we end up with the proposal that
> the replament of NP-computability with quantum computatibility
> by a infinite computer (the universe) with infinite computing time
> might be the TGD:eish version of computability(;-)
Excellent! It woudl be helpful if we could at some point translate our
notions into Peter's language!
> > [MP]
> > > I undestand that you great idea is identify observations with geometrical
> > > structures, 'posets of points of space'. I also parametrize
> > > the set of all possible observations: not as posets but as
> > > allowed quantum history pairs: but this parametrization tells
> > > anything about content of observation: it is just labelling: the only
> > > thing that matters that this naming scheme is one-to-one. I believe
> > > that the content of observation/cs experience cannot be expressed by any
> > > mathematical formula.
[SPK]
> > Sure, but when we construct intricate geometrical model we are doing
> > just that! We are attempting to express the content of observations/cs
> > experience with a mathemathical formula! SO long as we understand that
> > the "model" is not the "thing" we are ok.
[MP]
> But what differentiates the model from the thing? Does this
> difference mean that mathematical formula does not characterize
> the observation completely?
The distiction is very subtle! My model of a thing, to me is the
"thing"! To you, it is only a description of something that you may or
may not be able to have as a "thing". [I am using the word "think" as a
shorthand representation of what is considered "real" and concrete for a
given individual.]
The information/matter duality is very strange in this way. What is my
Mind for me, is a Body [brain function] for you and vice versa, what is
a Mind for you is a Body for me. Bodies can only interact with bodies by
compution the local extremum over the coresponding dual minds, Minds
interact with each other in the same way, but minds compute the local
extremum over the corresponding dual bodies. This is better explained in
Pratt's ratmech.ps paper. I use the term "local extremum" to represent
the way effect of \epsilon bound on accuracy of prediction
(bisimulation).
A mathematical formula can not characterize the particular subjective
experience of the observation!!!! It only can model range of
possibilities of such and only with in the tacit implications of the
mathematical model. Finite mathematical models can only represent finite
sets of possible experiences. Mathematicians cheat and introduce
concepts like limits, integrations, differentiations, etc. Computer
science has revealed these limitations and is busy trying to fix it.
This is why people like Pratt, Wegner, Calude, Chiatin, Svozil, etc. are
linked on my web page and talked about...
[MP]
> > > But there is the notion of observer. You take it as granted. I take
> > > observation fundamental.
[SPK]
> > No! I, like you, take observation as fundamental! I just am being
> > explicit about the fact that what each observer has a framing of their
> > observations is not an a priori given, it is a construction! Thus, with
> > Pratt I say "cognito, ergo eram", I think therefore I was....
[MP]
> I express it more technically: cogito, sequence of quantum jumps
> without any gap between existed (;-). Or even more precisely:
> a cascade like generation of selves within me occurred.
Yes! Your word are much better that mine! That I am trying to think
about it how an infinite number of selves are all doing this quantun
jumping concurrently! It is easy to model just one observer interacting
with a fixed background, but when we are trying to be realistic and see
that the "backgroung" is really "all of the other selfs doing something
similar", it gets really complicated!
snip
> > > It was paper by my 'boss' Masud-Chaichian and Peter Presnajder and third
> > > theoretician. They constructed noncommutative QFT in two-dimensional case.
> > > For cylinder it worked but for more general case they found infinities.
> > > They also suggested generalization of results to higher dimensional case.
> > > I do not have the paper here but I could ask for bibliodata.
This reminds me of Alan Connes' work... Umm, what kind of infinities? I
have not problem with infinities iff we can have infinite almost
disjoint observers! This solves many problems ranging from cosmological
constant to renormalization!
snip
MP]
> > > Also that. But the real blunder is the identification
> > > is the assumption that *contents of cs experience correspond to
> > > time=constant snapshot*.
> > > Neurophysiologists tell us that this is not the case. Consdier music
> > > as example. We are able to experience frequencies, which
> > > is nonlocal concept with respect to time.
[SPK]
> > Yes, that is why I use an M^4 to frame an observation, there are both
> > spatial and temporal non-localities involved. This is also why we can
> > use a RW metric to model how the space-time configurations of a single
> > observation are distributed! This speaks to concurrence, we are not able
> > to experience points, we experience hyper-surfaces! So, we agree here!
> > :-)
[MP]
> Not quite! Experiencing of mere hypersurfaces would not make possible
> experiening of frequencies: complete localization in time means
> by uncertainty principle of Fourier Analysis means that there is not
> frequency information. Cognition must be time nonlocal if it
> is to give some information about what will happen and happened.
> This is why cognitive spacetime sheets made possible by the classical
> nondeterminism of Kahler action are so crucial for TGD.
Remember the discussion by Robert Fung about the Fourier relationship
between frequency and time? It is relevant to your question, also:
http://gamma.magnet.fsu.edu/htmldox/super/classes/ACQUIRE1.fm48.html
Schommers discusses pairs of spaces that are Fourier transforms of each
other, and quess what, Chu spaces have the Pontyagin duality included!
(http://boole.stanford.edu/chuguide.html#gamut,
http://math.ucr.edu/home/baez/harmonic.html,
http://loki.sacredheart.edu/cas/math/lothp/cag.html)
from: http://www.ou.dk/nat/fak/kurser/matemati/mm45e.html
"For every locally compact Abelian group G one associates a dual group
G^ (also locally compact and Abelian) and defines the Fourier transform
as a linear transformation from L1(G) to C0(G^). We have G = G^
(Pontrjagin's duality theorem). For G = T we get G^ = Z and usual
Fourier series; for G = R we get G^ = R and obtain the usual Fourier
transformation."
This is a literal gold mine that we must explore! :-)
snip
[MP]
> > > I have studied Peter's papers (rather technical!). My view is that cannot
> > > start from so technical concept like NP-completeness in building model
> > > for universe: the reason is that I do not believe that universe computes
> > > itself into existence: it just exists! Even more, it is able to replace
> > > itself with a new one again and again and do also some computation
> > > besides that!
[SPK]
> > Matti, NP-Completeness is not merely a technical concept! It is a
> > fundamental problem! How does the Universe calculate the minimum energy
> > configuration of a protein molecule? How does the Universe figure out
> > the most stable orbits in a stellar system? How is it that soap bubbles
> > always cover the most volume with the least surface? How is it that a
> > quasi-crystal can grow at all? How is it that Lagrangians are calculated
> > by the Universe? All of these questions are aspects of the
> > NP-Completteness problem!
[MP]
> But why universe should calculate it? Even for modelling
> purposes in some remote psychological future and even at subjective
> distance of infinitely many quantum jumps? And how should universe
> calculate itself to existence: does the hardware
> used belong to universe. This like Munchausen trick: logical
> impossibility.
Munchausen trick? What I am saying is that what is experienced by an LS
is the "result" of a (interactive) computational process. This holds
equally if we think of the information as generated or "retrevied" from
a data base. Fact is that free energy was dissipated (Thermodynamic
entropy maximized and Fisher Information minimized!) in the process,
IFF, it is irreversable encoded in matter. This last is a caveat, to
deal with the situation of "delayed choice" experiments!
This follow from the bisumulation concept!
> Quantum jump replaces the computation (in classical sense as I
> understand). Quantum jump is what allows quasi-chrystal to grow!
> In the initial universe quasi-chrystal cannot grow but by
> quantum jumps one ends up to the universe where quasi-christal
> has grown.
Yes! :-) This is what I mean by computation.
> > What is interesting is that it has been proven that if there
> > exists a
> > finite computational scheme that can compute a given example of an
> > NP-complete problem, this scheme or algorithm can be transformed in
> > polynomial time into a scheme to compute any other NP-Complete problem.
> > But this, I think, only works for situations that can be modeled (or
> > "simulated") by Turing Machines. Peter's work shows us that most of the
> > computations that occur are not TM simulatable and thus we need to look
> > at this more closely.
>
> Perhaps it is not an accident that quantum jump can be regarded
> at general level as infinitely long quantum computation.
Indeed! The Turing Machine type of computation take undecidable
infinity to halt and produce result... Quantum computation has infinite
TM's acting as nodes in a network, this is true concurrency...
(http://boole.stanford.edu/~rvg/352.html)
> Psi_i corresponds to initial state of quantum computer. UPsi_i
> corresponds to the final state of qcomputer after infinitely long
> calculation and UPsi_i-->Psi_f means halting of quantum computation
> and emerges of the result of computation as conscious experience.
Yes, umm, perhaps the differences in "infinite primes" is what
distinguishes selves from each other!
> What about NP completeness problem when one introduces
> infinitely large quantum computers calculating infinitely long time?
> Can nondeterministic computations help.
I don't think so. We could use the example of the traveling salesman
problem to find out for sure!
http://home.wxs.nl/~onno.waalewijn/tspfast.html
http://www.mathsource.com/Content22/Enhancements/Interfacing/InterCall/0203-432
http://home.hiwaay.net:8000/~kdunn/problems/tsp.shtml
> What about sequences of quantum computations each lasting infinitely
> long time?: these are suggested by the notion of self. Thought
> as a cascade of quantum jumps creating hierarchy of subselves of
> self?
YES! I think that that is the minimum requirement for arbitrary value
of \epsilon!
> [To avoid confusions: the calculation time has nothing to do with
> the experience psychological time].
Indeed, since it is the "solution of the calculation" that defines each
quantum jump, it is an instant for the observer!
snip
[SPK]
> > Umm, I do not say that "the universe computes itself into
> > existence"! I
> > say that the individual experiences of Local Systems (using Hitoshi's
> > definition of LSs) are given in terms of space-times framings. This
> > follow from the distinction that I make between "existence" (qua CE) and
> > "actuality" which is a "local notion" that represents the subjective
> > experiences (observations, measurements, etc.) of an LS given any
> > particular moment of their local time. Thus I say that the Universe
> > experiences itself by the acts of observation of the finite LSs, which
> > are considered computations of NP-complete problems.
>
> OK. I see. What is your view about quantum computationalism?
> LS:s as computationas of quantum-computable problems? This
> would be TGD inspired computationalism!(;-).
We are converging to resonace! :-)
> > The key argument is that nothing can "happen" unless a price is paid.
> > Existence in-itself does not require the generation of equilibria. It
> > *is* at equilibria with respect to itself, that is why it merely exists.
> > It does not change, it has no duration or extension or any other
> > properties other that mere existence. It is the grundlagen! I do not
> > associate any space or time properties to it, those are the properties
> > of the observations of Local Systems, not the Universe itself.
snip
[MP]
> > > Funny thing, reading this I find that I agree completely. But
> > > somewhere the differences emerge: computationalism is one of the division
> > > lines.
[MP]
> > And this is exactly why we must discuss the notions we have about
> > computation!
> >
>
> Well. Replacing NP-computability with quantum-computability is
> what TGD would suggest.
I agree! Excellent! Next! :-)
Onward,
Stephen
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