Stephen P. King (stephenk1@home.com)
Sat, 24 Jul 1999 18:50:18 -0400
Dear Matti,
Matti Pitkanen wrote:
>
> Here begins my reply to your second email about parallel
> translations etc...
>
> On Fri, 23 Jul 1999, Stephen P. King wrote:
snip
[SPK]
> > OK, on this point let me be clear: The Universe "just exists"! It is
> > the experiences that are computed by the interactions (observations) of
> > the finite subsets (LSs) of the Universe.
[MP]
> I can agree here in the following sense. Each quantum jump
> is quantum computation in the manner I explained in
> part IV of my reply to earlier posting. Infinitely large
> quantum computer performing infitely long quantum computation
> and halting: Psi_i--Z UPsi_i-->Psi_f.
>
> Actually the sequences of computations of this kind represent thoughts
> which generate cascades of selves. Infnite number of
> simultaneous experiences by the hierarchy of dynamical selves
> forming abstractions about the experiences of their subselves.
>
> NP-computability is replaced by quantum computability in this
> sense in TGD framework.
Yes, but can you see that physics needs a model wherein n-observers are
participating to generate each others local framings ("reality",
Schommers calls them "pictures of reality")? The fact that so many
observers are involved, is, I believe why we must use statistics very
carefully. Peter's Secondary Observer Conjecture is an expression of
this.
snip
[SPK]
> > Perhaps I am not understanding how the "definite sector D_p of the
> > configuration space" is selected. I say that the act of observation is
> > the act of selection, in the sense that a given transition A -> B on the
> > material configuration involved in the particular observation is allowed
> > iff the information content of B implies the information content of A.
> > This is the essence of an infomorphism!
[MP]
> Configuration space decomposes into sectors D_p allowing effective
> p-adic topology with prime p. The localization of state
> to D_p is forced by Generalized Unitarity.
I need a link to a definition of "generalized unitarity"!
> The requirement that quantum jump corresponds to measurement
> which is local at the level of configuration space sharpens
> localization hypothesis: localization occurs to definite
> values of zero modes characterizing the classical features of
> spacetime.
I believe that the "volume" involved in the localization process is
related to the \epsilon of accuracy of bisimulational predictability
(perhaps also to the "log-likelyhood" of the prediction). I see the
Planck constant as an expression of this, it is a "mean" of the
observers that are participating in our little corner of the Universe!
> One could say that selection is involved at the level of zero modes.
Yes!
> Our volition probably corresponds to selection between degenerate
> absolute minima of Kahler action characterized by *discrete* zero
> modes: no experience selection in continous zero modes
> since it is not possible to experience what it is to select
> between continuum of alternatives.
Yes, thus we do not experience the 'objective' continuity of spectra
that the W^n has! Weyl has right!
> I do not assume quantum jump A-->B means that information content
> of B implies information content of A. This is too strong requirent.
> p-Adic evolution however implies that information gains tend to increase.
Yes, I weaken the strict binary implication (Chu_2 = {0,1} =>
Chu_[0,1]) to the fuzzy "similarity" of B's content to that of A. The
"more similar" the contents are to each other, the closer to binary
isomorphism they become! It is interesting to note that the constant Phi
found though out Nature is smallest scaling that maintains the
invariance with respect to arbitrary scale transformations!
> Note also that there are infinitely many types of informations
> and each is characterized by its own information measure:
> not only single abstract information.
Yes, I think that each LS has for its own one of these measures! I also
believe that they are all related to Fisher Information! (pg. 32 of
Physics from Fisher Information)
[MP]
> > One can even consider the primordial chaos obtained formally by putting
> > p=1: effective topology is roughest possible: distance between two
> > points is zero or one. I have essentially you picture but
> > at the level of effective experienced topology.
> > **
[SPK]
> > This is modeled by the Chu_{0,1} that Pratt discusses in ratmech.ps! I
> > am using the generalization that would be modeled by a Chu_[0,1], it
> > allows the modeling of \epsilon accuracy involved in dissipative
> > transitions of the configurations, e.g. memory fades, spectra shift to
> > red, entanglements decohere, etc. I wish I had a better grasp of the
> > formal language needed to communicate this precisely, but I guess that
> > that it why I am a philosopher, not a physicist. :-)
[MP]
> I have the feeling that Chu spaces might enter TGD in description of
> cognition as cascades of selves created with selves.
Me too! :-) To be specific, in the way that that causality is
defined...
[SPK]
> > > Is there any relationship between "zero modes" and "null geodesics"?
> > > Could there exist an infinity of almost disjoint hull hypersurfaces?
[MP]
> > All curves in zero modes are null geodesics formally. I do not
> > believe that this is however a useful concept. The space of zero
> > modes is infinite-dimensional. And each surface in this space
> > as formally vanishing metric. Or better to say: no metric at all.
> > Only symplectic structure making integration possible.
[SPK]
> > Interesting! Is it true that we could find every possible set of null
> > geodesic somewhere "in" this space of zero modes? Could you elaborate
> > about the role of this "symplectic structure"?
[MP]
> All curves would be null geodesics since line element vanishes:
> thefore the concept of geodesics becomes useless.
Yes, but does it vanish identically for all LSs, or just all but a
finite number of them? This allows for the use of interaction (or
connection matrices) that are inverse (?) functions of Hamming distance
(http://www-dept.cs.ucl.ac.uk/staff/S.Bhatti/D51-notes/node30.html) or
"dissimilarity", I think. Thus we avoid Olber's paradox and explain why
only a finite number of observers can interact at any (subjective)
moment! This gives each observer an asymptotically decreasing causal
influence on any other when considering Real values, and upon mapping to
p-adics, we get cut-offs. This gives a p-adic definition to a black-hole
event horizon! Wow!
> Symplectic structure is defined by antisymmetric tensor J^kl.
> One can define J_kl by the condition
>
> J^kr J_rl = -delta^k_l, Kronecker delta.
>
> Note that metric is not needed: it emerges
> only when one wants to define J^k_l by index raising operation
> applied to J_kl.
>
> J^kl defines Poisson bracket in the space of functions define
> on manifold
>
> {f,g}= J^{kl}f_lg_k
>
> _l means partial derivative. Poisson bracket is antisymmetric and makes
> function algebra infinite-dimensional Lie-algebra. Jacobi identities are
> indeed satisfied. Functions generate canonical transformations generated
> by the vector fields
>
> X^k = J^{kl}f_l, f arbitrary function.
I am not a mathematician :-( Words, please?
> Canonical transformations preserve all 2n dimensional integrals
> defined as integrals of J^J...^(n J:s ) over 2n-dimensional
> submanifolds.
>
> Canonical transformations are the isomorphisms of canonical
> formalism of classical mechanics. The are crucial also for
> canonical quantization. Quantization in standard QM means
> the replacement of function algebra with the algebra
> of Hilbert space operators and the replacement of Poisson
> bracket with operator commutator AB-BA.
>
Little by little! :-)
Onward!
Stephen
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