Matti Pitkanen (matpitka@pcu.helsinki.fi)
Sat, 24 Jul 1999 11:47:49 +0300 (EET DST)
Here continues the answer to your second posting.
>
> [MP]
> > > b) *Spacetime* are dynamical and not unique and quantum states
> > > are superpositions of classical spacetime surface. The localization
> > > in zero modes associated with every quantum jump localizes quantum
> > > history to the set of spacetime surfaces which are identical in
> > > macroscopic aspects characterized by zero modes.
> [SPK]
> > Does this implicitly assume a unique set of measuring "tools"
for all
> > possible observers?
> [MP]
> No. I think that measuring tools is not fundamental concept: it is
> too 'classical'. Quantum measurement is more promising starting point.
> Localization in zero modes obviously can be regarded as
> *quantum measurement* of zero modes: this of course does not mean
> that contents of conscious experience would contains values of
> zero mode coordinates(:-)!
> **
>
> Why not? If the causal connective structure of the space-time
framing
> of an experience is given by a set of null rays (this is what the light
> cone structure is after all!)
Good question. I belive that sensory information is to large extend
information about zero modes but that finite p-adic p characterizing
the self=observer, in particular finite size of self, gives limits for
this information: at most p*log(p)/log(2)
bits. There are infinity of zero modes so that
there is no hope of compressing the information contained by the
values of zero modes to finite number of bits.
"Localization in the zero modes" is
> equivalent to my concept of "constructing a space-time"! The "values of
> zero mode coordinates" is a strictly relative notion! This is why
> tensors are needed to model the movement of objects in space-time. The
> particular values used are irrelevant, what matters is that the
> information content can be communicated.
Yes. The values of zero modes coordinates is relative notion:
as such these number contain no information. Unless of course, one
can identify preferred coordinates fixed by symmetry considerations.
Perhaps it is the direct experience about localization which represents
what it is to have these values of zero modes.
> Perhaps it would help me to explain that I believe that motion is
point
> to point teleportation rather than the classical motion of a
> transposition of a rigid object or wave within an independently existing
> space.
Intesting idea! This would be quantum level concept involving quantum
jump whereas ordinary classical motion is purely geometric concept.
By the way, motion in zero modes occurs as hopping quantum jump by quantum
jump:
x1-->x2--x3---
Just like Brownian motion. In fact, I believe that Brownian motion
indeed corresponds to this kind of motion. The possibility to
Brownian motion to move faster than light would not be a
result of nonrelativistic approximation but real physical
effect.
>
> [SPK]
> > If so, how? I am very aware that the usual
> > explanation involves the notion that numbers "exist" a priori, but,
> > really, how can it be affirmed that something is knowable just by
> > postulating its existence?
> [MP]
> By no means! Objective realities exists and quantum jumps
> between them make it possible to learn more and more about the
> nature of objective realities. Sooner or later with respect to
> subjective time these quantum jumps begin to make claims
> about what these existences are and at some quantum the discovery
> of the importance of the internal mathematical consistency occurs.
>
> Subjective reality is doomed to make hypothesis about nature of
> objective existences and test them. It can never be certain.
> **
[SPK]
>
> Yes on both counts! This is why I say that the Universe can only
> experience itself via the interactions of its subsets! Only in the limit
> of Eternity is absolute certainty possible! Absolute Boolean certainty
> is impossible within the domain of experience because of the
> NP-Completeness problem! The material resources available to a subset
> LS_i of the Universe to compute the solution to the n-body problem (that
> is the Langrangian of the complement of the LS_i) increase exponentially
> slower that the number of subsets that become modelable by the
> computation. This is Malthus in the Large!
>
> [SPK]
> > CE does not imply necessity of knowledge or
> > experienciability! In order to allow for the uniqueness of the
> > individual self, it is necessary and sufficient that there is at least
> > one attribute that can be unique to such. The mere CE postulate is not
> > enough, we need a dynamical difference. When one posits a pre-given
> > metric for all and assumes that all observer exist *in* the same
space,
> > it is the postulation of a prison for the self from which there is no
> > escape.
> [MP]
> I do not assume observer: self is closest to observer I can get.
> Sequence of quantum jumps during which informational time development
> operator does not generate p-adic entanglement. Observers
> do not exist anywhere! They, or selves, correspond to sequences of
> p-adically unentangling quantum jumps. This is extremely deep and
> important point.
> **
>
> Umm, Yes, but, just because any given observer can not interact
with
> all others, does not imply that they are not "out there". I am saying
> that there must exist an observer for every possible experience. Not all
> experiences can be communicated within a world (remember how I define
> such!). This is why we can not observer objects traveling faster than
> light; we can not measure such motions because the observations of the
> observers can not be logically infered within our \epsilon of accuracy.
> Logic contrains observations, not some a priori defineteness! Please
> recognize the failure of naive realism! Please!
[MP]
I realize the failure of naive realism. I have given up the notion
of single objective reality, I have given up the notion of
observer as continous stream of consciousness! I have given
up the standard notion of psychological time! I have given up
many standard dogmas to avoid paradoxes.
What I am suggesting that communication cannot be modelled as mapping
between observers. Much more delicate process occurs: not
at the geometric level but at quantum level. Informational
time development U during quantum computation (that is U)
is what gives rise to communication between selves.
Quantum nondeterminism implies that conscious logic is
not sharp, it is erratic but extremely flexible.
>
> snip
> [MP]
> > > Each quantum jump changes the macroscopic characteristics of these
> > > spacetimes in quantum superposition and they seem to naturally
correspond
> > > to our sensory information: localization in zero modes is quantum
> > > measurement of zero modes and sensory experiences seem indeed to
give
> > > information about zero modes. Perception is quantum measurement in
this
> > > sense.
> >
> > Sure, I can agree with that. Each person's sensory experiences
can be
> > explained a unique integration of many almost disjoint quantum
> > measurements, thus I think of posets...
> [MP]
> Actually the measurement can be said to be disjoint in well
> defined sense. Separate selves mutually unentangled.
> **
>
> Yes! This is why separate selves have separate indentities! I say
that
> experiences are "almost disjoint" since they differ in at least the
> "point of identity". The notion of a fixed point under a given set of
> transformations is what I considered before I has educated by Peter's
> work. The Self, within Peter's formalism, is a greatest fixed point, I
> think. Umm, I need to review his paper:
> http://www.cs.brown.edu/~pw/papers/math1.ps
>
Quantum entanglement is what destroys selves. For instance, could
it be that the separate notes in chord correspond to
frequency-selves which have entangled to form chord-self?
This would explain why we do not hear separate notes but entire
chord.
By the way, the attempt to understand music in terms of self hierarchy
seems to be exciting. Metaphor for harmonious co-existence
seems to have direct translation to quantum self organization.
Harmoniously co-existing selves personal subselves to generate
higher 'enlightened' self having no decomposition into subselves
and having experience of oneness!(;-). Chords as enlightened
groups of notes in a state of Nirvana!
> [SPK]
> > But what is troubling me is the
> > notion that the localization is somehow independent of what it is that
> > makes the poset different for each person.
> [MP]
> There is big localization in entire configuration space which decomposes
> into sublocalizations for selves.
> **
>
> How is the information content of this localization given? This is
an
> infinite NP-Complete problem that requires ETERNITY to compute! It can
> not be given a priori!
TGD generously provides this eternity! The quantum computation defined
by informational time development operator lasts infinite amount
of lightcone proper time (not our psychological time which
is quite different thing).
Each moments of cs, meaning increment of psychological time by something
like 10^4 Planck times, involves single quantum computation
lasting this infinite period of lightcone proper time. It seems that
NP-completeness is not a problem in TGD:eish Universe!
Despite all this: I do not believe that universe exists by computing
itself.
> This is my whole point as to why naive realism
> fails! "It is not even wrong"! Think of the ability to predict the
> weather on Earth, the computational power needed to predict with
> arditrary accuracy (limit \epsilon -> 0) instantly exceeds the available
> matter in the observable world!
Predicting is simulation, not existence! One must make sharp
distinction between these notions. As I already noticed
the idea of universe as computing itself seems to lead to
Munchausen paradox. Where is the hardware and software, can they
belong to the universe?
If it can not be predicted, it can not
> be said to be determined, thus can not be observed either.
> The self is actualized within its own time as the interactions
among
> the LSs carry out the computation of "what will happen next"! We
> construct our reality by interacting with each other. Read the
> introduction to Frieden's book again, he is saying what I am saying!
>
I understand what you are saying. This is probably the only possible
consistent philosophy in the framework in which one does not introduce
quantum jump and replace single objective reality with all
possible objective realities allowed by physical theory.
> [SPK]
> > I think that if we start out
> > with the notion that each measurement is informative only in
comparison
> > to some aspect of the measuring device, here a person, we could
perhaps
> > avoid the trap of classically. The idea of a pre-existing classical
> > world or space-time in which all observers are "embedded" is the
error,
> > but it is very hard to escape it! It must be done. We need a radical
> > shift in paradigm!
>
> [MP]
> I agree that the assumption about pre-existing objective reality is
> error. But I do not identify objective reality as spacetime
> with observers imbedded but as quantum history. Imbedding space
> has nothing to do with observers nor objective realities: it
> only emerges as structure related to the configuration space which
> is also pregiven.
> **
>
> Umm, perhaps I am misinterpreting what you mean by "pregiven"! I
use a
> notion identical to what Peter uses in the definition of Interaction
> Machines! What is "pregiven" by one LS is not necessarily "pregiven" by
> another! There is no way of entablishing absolute precedence, we only
> have finite "windows" within which an LS can have a configuration as
> actual.
I think that a lot of confusion is created by different views about
imbedding space. I do not regard its points as reprsentations of events:
it is quite too simple thing for that.
> This is another reason why the naive realism of Newton et al is
just
> plain wrong! The fact is that the concurrent ordering of events is an
> infinite NP-Complete problem! Laplace and Minkowski's vision of the
> Universe as a static 4-manifold is just a hallucination!
>
> [MP]
> You want to give up pre-existing spacetime and replace it with something
> dynamical whereas I want to give
> up the notion of observer and replaced it with something quantum
> dynamical.
> **
>
> YES! Matti, this is exactly what Hitoshi's model of Local Systems
does!
> Please read his papers again! The observer *IS* a quantum mechanical
> system. Hitoshi does not get into the nitty-gritty details of the
> composition of sub-LSs, but this is what your p-adic acomplish. I firmly
> believe that your work is the needed generalization and extension of
> Hitoshi's idea! Tis is why I get so emotional when I participate in
> discussions with you! :-)
I am well aware of the similarities. The notion of self
as sussystem able to remain unentangled and characterized by
p-adic prime p is much analogous to the notion of self.
But there is big difference: I do not build mappings between observers.
My mapping corresponds to the mapping of real structures
to their p-adic counterparts, reality is mnapped to p-adicity'. The view
of self about world is determined by his personal p-adicity:
for instance, information gains are limited to be below
p*log(p)/log(2) bits.
> [MP]
> We are locating evolution at different levels. Otherwise we agree.
> **
>
> No, we just have complementary view points! :-)
>
Best,
MP
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