Matti Pitkanen (matpitka@pcu.helsinki.fi)
Sat, 24 Jul 1999 10:35:58 +0300 (EET DST)
This is realy long message!
>
> > >I see them as constructed
> > > dynamically in the act of observation in that they are aspect of the
> > > framing. Thus I do not see them as a priori givens! Is it not
enough to
> > > show that the "shadow" is a construction of the mapping between LSs?
Do
> > > we really have to suppose that the "statue" exists "out there" prior
to
> > > the sculptor's work?!
> >
> > This is a good question. Your point of view makes possible to avoid
> > dualism: observations contra world out there.
>
> Could you elaborate? I don't understand? I thought that I was
> saying that there is a duality, Level 2?!
I understood with duality the materialistic idea that there is single
objective universe out there independently of our observations.
If this independent objective reality does not exist there is no duality.
But of course, if you assume sculptor exists you have the duality
but in weaker sense! So you must not assume the existence of sculptor
but only the moments of creation and self of scultor(;-).
>
> > But so does also my approach. I see painting and landscape as one and
the
> > same thing! Painter exists only in the moment of consciousness when
> > painting/landscape is replaced with a new one. Painter experiences
some
> > of the beauty of painting and, by artst's vanity concludes that he did
> > it!
>
> Sure, Pratt says that Chu spaces are both the player of the Game
and
> the Game itself. The Duality is in the complementarity! I agree with you
> completely here! But notice that the "painting" and the "landscape" are
> instances of "information" and "matter" structures! Their relationship
> is the infomorphism! The Stone-Birkhoff duality!
> (http://www.mcs.newpaltz.edu/faculty/clark.html)
LOGOS= COSMOS is what I indeed assume.
> The construction of a material symbol [painting] within is only
the
> construction of an information carrying structure [beauty] iff a similar
> material symbol [print] elsewhere/when could be constructed from a
> description of a similar information carrying structure [beauty]. We
> must understand that [beauty] is a local notion and is not a priori
> given. All properties are given only in relation to a finite subset of
> all possible. Plato was wrong!
>
There is important point here. Beauty, ugliness etc. are *qualities*.
Length, duration, mass... are *quantities*. Quantities are properties
of quantum histories/objective realities/ideas. Qualities
are properties of quantum jump and one cannot number to them.
Universes are not beutiful, beauty is in the quantum jump
replacing universe with a new one where also the life is.
> > I see as the difficulty of your approach the necessity to provide
> > formula for the contents of consciousness: this indeed seems to be the
> > case if you identify reality as observations.
> > *********
>
> Yes. But, a model that gives us a way to predict what will be
> experienced under an arbitrary conditional is what a physics is all
> about! Thus, my attempt to identify "reality as observations" is a local
> only notion, local in the sense that they are constructed within finite
> M^4 framings which I am identifying with piece-wise constructed
> Riemannian maifolds from the "bricks" that are posets of points in a
> W^n.
>
Theory *alone* is not enough since it cannot give formula for contents
of cs expeience. But theory and experience can be combined: if one has
good enough model for observer and external world and memories about
previous experiences, one can indeed predict experiences and imagine what
they will be! Theory *alone* is unable to say anything about
what it is to experience this or that quantum jump.
> > > It "exists" only in the sense of being a
> > > possibility! The metric or related properties are given by the act
of
> > > observation which is determined by the local logical entailment
aspect
> > > of the informorphism that is the interaction between LSs.
> > > To be sure, I need to discuss the "compactness" notion that
you
> > > mentioned before with regards to the W(r)...
> > >
> > This leads to the problems in the following sense. Our observations
give
> > extremely limited information about spacetime. I do not experience
> > all the values of the metric tensor or classical gauge fields defined
> > on it. Does this mean that one should give up entirely the notion
> > of spacetime and what should be left? Some set discrete points
perhaps:
> > but how can you understand in this kind of context how observes
> > invent concepts like moral and freedom and how the idea of infinity
> > arises?
>
> Good questions! The limitation of the information content involved
in
> our observations is due to the finiteness of the material configurations
> available to encode information within the local "reality" of the
> particular observer. We note that this local reality has the form of a
> space-time as noted by Kant and other philosophers.
> We can not experience all possible values of the metric tensor (or
all
> of the energy spectra, which range over -/+ R) simultaneously because of
> the above restriction!
> We only give up the notion of an independently pre-given
space-time.
> Instead we have the understanding that individual's observations and
> measurements are not "absolutes given from above" but are local
> constructions that are selected from the set of all possible by an act
> of finite and discrete act of interaction.
> While the concepts of "morals" and "freedom" are very important, I
an
> not addressing them directly, I see them as concepts that can be
> communicated about within the interactions that are infomorphisms
> between local systems. My idea here is very similar to Leibnitz's
> monadology, except that I do not require that an external Divine entity
> create them ab inition ex nihilo!
>
These isomorphisms between local systems are replaced in my approach
by mappings of real geometric structure to their p-adic counterparts:
there is ineed 'reality' (realities) and this reality is mapped
to p-adicity of particular self. There is no direct mapping
between selves.
You could counterargue that there is no communciation between selves
in my approach: communciation is contained in quantum jump:
Psi_i--> UPsi_i --Psi_f
U is the informational time development giving rise to informational
currents modelling the communication. Selves can hence
communicate by forming cognitive representations about other
selves as subselves. This is only mimicry but it is enough!
> > > > d) Thus everything is classical mathematics: even induction
> > > > procedure which is standard mechanism of building new bundles
> > > > by mapping manifolds to base spaces of bundles but not noticed
> > > > by say string model people.
> > >
> > > Umm, I an missing something! :-( I say that each LS observes a
> > > classical like world, thus can be approximated and modeled by
classical
> > > math, but we need to consider co-induction, not just classical
> > > induction... Perhaps I am misunderstanding you!
> [MP]
> > This induction is not induction in the sense as co-induction defines
it.
> > Induction in the sense of Faraday! When you have metric in some space
> > you have also natural metric for its submanifolds: distances are
measured
> > using the length units of imbedding space.
>
> Since I consider the Universe as having to definite properties in
> itself, and the notion of an embedding space, as Level 2, has all
> possible "length units", (not an absolute ONE, but MANY) but such are
> not given independent of interactions, they are only defined within
> particular interactions.
>
Yes. Here our view points differ. Induction procedure brings in dynamics
when imbedding space is nondynamical.
BTW, this is also how dynamics enters in string models basically.
The need to get spacetime from this picture however led to the
introduction of dynamical imbedding space and
spontaneous compactification. Tragic accident which stopped
the development of theoretical physics for decades(;-)!
> snip
> [SPK]
> > > The way that M^4s are constructed "piece-by-piece" is well
illustrated
> > > in Penrose's discussion of quasi-crystals and it highlighted in by
> > > Forbidden Symmetry paper:
> > > http://members.home.net/stephenk1/Outlaw/forbiden.html
> >
> > [MP]
> > I agree that this what you are saying applies to how our ideas about
> > spacetime evolve.
>
> Not quite how I see it, our knowledge (relationships between
> information) evolves along with our space-times (relationships between
> matter).
Yes. I see the difference.
>
> snip
> > > [MP]
> > > > The mere existence fixes that which exist essentially uniquely
> > > > in infinite-dimensional context: this is the basic idea. One
cannot
> > > > construct dynamics for the metric of infinite-dimensional
configuration
> > > > space because it is fixed already by the requirement that it
> > > > exists! The existence of Cauchy hypersurface poses problems when
> > > > one assumes dynamical spacetime and tries to quantize metric.
> > > > Now imbedding space is given and these problems disappear.
> [SPK]
> > > But how do we derive particular actual properties by merely
evoking the
> > > fact that they exist? Existence is "outside of time", it is
tenseless.
> > > The dynamics that define sharp properties only occur "in time", in
fact,
> > > I propose that in a subtle sense, they ARE time, but since each LS
has
> > > its own unique dynamics (defined by its internal QM propagator),
each
> > > has their own time and thus their own length scale or gauge. Thus I
say
> > > that each LS constructs its space-time M^4 framings by interaction
with
> > > other LSs.
> [MP]
> > We have articulated rather precisely the differences in our
philosophy.
> > For you LS:s are all that is. For me LS:s could represent models for
> > contents of conscious experiences of selves but besides this
> > the realities behind these experiences would exist.
>
> No, LS are not "all that is". They are "all that can experience
> anything" or "can have a subjective self". The "realities" "behind these
> experiences would exist" is given, but as I said before, existence does
> not imply experienceability!
So we agree also in this aspect!
> In order to experience something that
> exists it is necessary to construct a finite structure that can encode
> the descriptive information about it, this allows for the information to
> be communicated. The brain's structure of interconnected neurons is what
> allows for the information content of our experiences to be communicated
> and to be used to apprehend new information. Thus information requires
> matter to be encoded in as symbols and matter requires information to
> give it actual meaning. The existence property is mute with regard to
> meaning or configurations!
>
Objective existence has nothing to with meaning, would I say.
Qualities and meaning are involved with quantum jump between objective
existences. Matter does not give meaning: it is change
of material configuration which contains the meaning.
And also change of informational configuration: in quantum
jumps conscious information gain is the difference
between initial and final informations. Selves are eaters
of information and U generates it in every quantum jump: we
live in an information-prosperous world.
> [SPK]
> > > The Cauchy problem holds in the static case since the
Uncertainty
> > > principle prohibits the a priori definite "sharp" properties!
> [MP]
> > This is true if one consdier QFT in Minkowski space. One can fix
> > only E or B. Similar conclusion holds for the components of
> > spacetime metric regarded as small perturbation of Minkowski metric.
> > It is nonsensical to speak about entire spacetime metric as given.
>
> Yes, this is part of my reasoning!
>
> > Only some of its components commute at given time =constant section.
>
> Can you elaborate on this?
I state this somewhat inprecisely. I should have said that
only some components of curvature tensor commute.
This relates to the canonical quantization of metric as quantum field.
a) The components of 3-metric are commuting physical
quantities. g_ij: 6 alltogether. The remaining
components of metric are nondynamical since general coordinate
invariance (4 coordinates) implies that 4 components of metric
are nondynamical and can be fixed: this gauge condition
fixes the coordinates used. g_00 and g_0i are indeed
good candidates for components of metric tensor fixed by some
coordinate conditions. For instance g_0i could vanish.
b) In quantization one constructs Hamiltonian formalism and
identifies the canonical momentum densities as
partial derivatives of Lagrangian density (curvature scalar
times sqrt(g) with respect to time derivatives of metric
components g_ij. Canonical momentum densities and g_ij commute
to delta function as operators: this is microlocal causality
stating that gravitons are point like particles.
This is how it should roughly work. Unfortunately it does not.
>
> > But as we know, this approach to quantum gravitation does not work!
> > TGD approach is quite different and in complete accordance with
> > uncertainty principle. There is no quantization of
> > metric or other classical gauge fields.
>
> Topological Geometro-Dynamics, to me is a model of how the worlds
> (given by the intersection of a finite number of local "realities")
> behave. This is well within the preview of Hitoshi's LS theory. He has
> worked out how the LS itself can be modeled consistently, but the model
> needs to be extended with regard to the way LS observe each other.
> Hitoshi's remarks about GR's field equations and the role of connections
> is important in comsidering this.
>
Some people are promiting the idea that realities are intersections
of higher-dimensional realities. Interesting idea but I do not know how
to realize it.
> > > It is for
> > > this reason that Einstein was very opposed to QM! His statement "GOD
> > > does not play with dice" [to determine the properties of the world]
> > > speaks directly to this!
> >
> > Einstein's argument relied on spacetime concept he had invented: the
> > idea about quantum jump occurring at definite value of time is in
violent
> > conflict with space-time democracy. It breaks general coordinate
> > invariance and it breaks the hypothesis about deterministic
> > field equations. Quantum jump between quantum histories concept was
> > originally forced by the requirement of General Coordinate Invariance
and
> > the avoidance of determism-nondeterminism paradox.
>
> OK. Could you discuss your thoughts on the
"determism-nondeterminism
> paradox" sometime soon?
>
Certainly.
Best,
MP
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