[time 509] Re: [time 504] Observation models

Matti Pitkanen (matpitka@pcu.helsinki.fi)
Sun, 1 Aug 1999 08:51:43 +0300 (EET DST)

On Sat, 31 Jul 1999, Stephen P. King wrote:

> Dear Matti,
> I am taking a little break to think and read...
> Matti Pitkanen wrote:
> >
> > On Thu, 29 Jul 1999, Stephen P. King wrote:
> > > Matti Pitkanen wrote:

> >
> > Or some aspects of computationalism. Symbols, representations,
> > hierarchical, modular language like structures, program like
> > structures as cascades of selves generaated with self.
> > Computing defined as deterministic symbol manipulation by fixed
> > rules is not in question. I refuse from honour of being robot!(;-)
> But is it not true that symbols are information when we think of them
> as having a "meaning" but are material configurations when we think of
> quantities such as charge, mass, spin, etc. ? A robot has all of its
> behavior predetermined, it has not free-will!

I would say that symbols are more: they are conscious subselves
representing someting (in external world). Selves as robots
is of course the great failure of AI. The capture of basic
hierarchical structures of cognitive processing and mechnization
of logical thinking is its victory and also quantum theories
of cs must be able to reproduce this part of computationalism
(neuroscience and cognitive psychology rely strongly on computational

> [MP]
> > I did not get intuitive grasp about the arrow diagram. Just why
> > should the directions of time arrow and logical arrow be different while
> > I directly experience them to be same when I think a conscious thought A
> > implies B?
> Think of how logical implication works. Think of what "precedence"
> means in terms of logic...
> snip

> [MP]
> > I would see this as follows: each item in sequence A-->B--> ...means
> > wakeupe of subself. A or some larger self containing A experiences all
> > these wakeups consciously. Depending on what kind of quantum jump is
> > involved, conscious experience is that of A implies B .. or object B
> > is contained inside object A or something else.
> The q-jumps define the forward flow of observer's time. I do not
> believe that time has any meaning independent of an observer... The
> arrow of logical precedence (entailment) goes the other direction...

> [MP]
> > In TGD approach LS would see those sub-LS:s, which are awake as
> > representations for objects of external world or internal world.
> Ok, but I don't fully understand what you are thinking here...
> snip
> [SPK]
> > > The problem I see is that the assumed identification of a self with a
> > > set must be considered very carefully!
> [MP]
> > Actually identification as quantum subsystem 'able to stay awake' in in
> > question. Tensor factor of state state. This identification is induced
> > from definition relying on the identification of spacetime sheet as
> > subsystem. This problem is very intricate and I do not claim of having
> > understood all of it. I wants to pretend that all is understood but
> > I do not believe it(;-).
> Let's discuss it further...

> [MP]
> > I am not sure what you meant with 'the ordering of quantum jumps is not an
> > a priori given'. It is! There is only ordered heap of ticks with new
> > tickes added on this heap 'all the time'. What is not given except in
> > statistical sense, is the ordering of psychological times associated with
> > quantum jumps for a given self: psychological time can also decrease
> > occasionally. The ordering of quantum jumps is what gives subjective
> > time absolute arrow and induces arrow of psychological time.
> > In second time scale this arrow is absolute. 10^40 events make
> > statistics excellent!
> I am talking about the order of the "ticks", like how would they be
> labeled 1, 2, 3, ... The "heap" of then "exists" for sure, but the order
> in which individual q-jumps are taken from the heap is, I am arguing,
> not a priori given.

[MP] It is. The point is that jumps are pairs

m-->n n--p p--> s.

Since the *initial* state of next jump is the *final* state of previous
jump natural ordering of quantum jumps is unavoidable.

> Umm, my thinking of this is "weird" since the
> ordering is "fixed" only within a finite "window" that constitutes an
> observer (with is why I cal an observer a poset of observations), is is
> dissipative... Umm, nothing is truly fixed, only relatively fixed...

> [MP]
> > Yes. The question is: which is the correct framework for
> > discussing logical implication in physics. In Einstein's times it would
> > have been considered at the level of spacetime and this is what you are
> > suggesting.
> Not really, I am saying that space-time is a subjective notion, a
> framing within which the particular observations are related for each
> other. This is very different from the classical thinking.


> > I suggests that neither statespace or spacetime is the correct
> > framework. Logic is aspect of mind and consciousness and therefore it
> > is *quantum jump* which defines the correct framework.
> > This suggests that connection with lightcone causality comes only
> > through the concept of psychological time. Already the phenomenon
> > of quantum tunneling (breaking of lightcone causality) suggests that this
> > is the case.
> Yes! We are so close! Because of the mathematical duality between the
> dynamics of the logical entailment of information contained in q-jumps
> and the light-cone causality defining material motions, the change in
> one of these "complementary" aspect is reflected in the other. More on
> this later...

> [MP]
> > This would be true if you would quantize metric of spacetime just as it
> > is quantized in GRT. In TGD nothing like this is attempted.
> >
> > a) Association X^3-->X^4(X^3) *fixing geodesics* but is by no means in
> > conflict with uncertainty principle since the construction of
> > configuration space spinor fields reduces to the construction of their
> > values on the space of 3-surfaces located on lightcone boundary times
> > CP_2. Values of configuration space spinor fields elsewhere are fixed
> > by Diff^4 invariance.
> But, what about the problem that Hitoshi points out that Diff^4
> invariance prohibits the construction of clocks, and without clocks it
> is impossible to measure time.

Why would one need this highly idealized continuous network of clocks? I
think that it is quite too much! All what is needed that theory allows
conscious selves able to have sensory experience about how some purely
classical oscillatory processes proceed. Cognitive spacetime sheets allow

If one requires that spacetime has magic ability to measure the
coordinates of its points (not only time) one encounters also the problem:
which coordinates it uses?

> > b) One can construct representations of Diff^4 invariant Poincare
> > algebra parametrized by lightcone proper time parameter a and these
> > representations reduce to representations of ordinary Poincare
> > algebra for a---> infty.
> >
> > c) Uncertainty principle forces states to be *superpositions of
> > spacetime surfaces X^4(X^3)* but does not make the concept of
> > classical goeodesic nonsensical.
> After reading Prigogine's work I am not so sure! He points out that it
> is impossible to define individual trajectories, e.g. geodesics...
Certainly true in standard quantization of general relativity.
If metric become operator of second quantized theory then
also the notion of geodesic line becomes very fuzzy. Of course,
the operator formalism fails down: the highly nonlinear
formulas of GRT simply do not make sense as operator formulas.

The key question is: is classical theory only approximation
of quantum theory or essential part of it. In standard physics
answer is 'only approximation', in TGD the answer is 'essential
part of it'. That TGD answer is possible relates directly to
the hypothesis that spacetimes are 4-surfaces. This
hypothesis also solves the energy problem of GRT.

> [MP]
> > Yes. Let me see this from my viewpoint. I have definition of self as
> > quantum subsystem: the geometric definition
> > underlies it. The event horizons associated with wormholes (metric
> > determinant vanishes since metric changes from 1-1-1-1 to -1-1-1-1
> > signature are natural boundaries of selves.
> I do not understand your thinking here. How do you know that it is a
> metric chance involved in the boundary of a self?

The surface at which signature changes is natural candidate
for a boundary of self. All what remains inside boundary forms kind of
causal closure *classically*: geodesics do not lead out.

> [MP]
> > Reading Pinker it becomes clear that AI people also have realized
> > the importance of competion: otherwise everything would be drowned
> > floodwave caused by by combinatorial explosion. The most interesting
> > conscious experiences are experienced: this is the fundamental
> > dynamics of conscious information processing. The decision of winner
> > in TGD framwork is simple: quantum jumper with maximum entanglment
> > negentropy gain is the winner.
> Yes, I agree. Is the number of players competing (in the q-jump)
> restricted to a finite number?

In principle no.

> > Why I regard it as so important is that it gives direct connection
> > with quantum measurement theory and is consistent with it. Any principle
> > which one postulates, must be consistent with QMT: this is highly
> > nontrivial requirement.
> The only difficulty is that we must be very careful how we interpret
> QMT!
QMT reduces in practice to simple rules: final states are eigenstates of
observables and probabilities for various outcomes are given by Born's
rule. Every generalization shold produce these well tested rules.

> > > It is here that I see both Pratt and Frieden pointing us to the
> > > notion of "information aquisition" games and the use of pay-off
> > > matrices to define the before-mentioned criteria.
> > >
> >
> > The concept of pay-off matrix is new to me.
> Can we discuss it?

Of course.

> >
> > CP_2 Kahler form is projected to generic spacetime surface. One must
> > scan over all spaceteime surfaces to identify absolute minimum X^4(X^3) of
> > Kahler action= Maxwell action for induced Kahler form going
> > through given X^3 on lightcone boundary (this restriction
> > for X^3 is possible by Diff^4 invariance).
> This is still a bit too idealistic for my taste. :-( I do not like
> having to postulate a priori ensembles and "generic" structures... But I
> can see how it is useful in the model. I have to be sure that we do not
> use these "non-observables" to much...

Any action principle does this and without action principles
there is no physics! It is quite possible that absolute minimization
problem can be solved exactly. Construction of configuration
space geometry leads to very strong constraints on initial
values giving absolute minima. The situation is very much analogous
to that in Euclidian YM theories, which absolutely minimize
Euclidian YM action.

> [MP]
> > No. Induction procedure and projection of CP_2 Kahler
> > form to spacetime surface is completely unique. The map of
> > real spacetime surface to p-adic spacetime
> > surface defines observer dependent spacetime as a p-adic version of
> > spacetime surface satisfying p-adic field equation (absolute minimization
> > of Kahler action).
> Ok, On this I agree, but it is not what I am asking about! I am
> thinking about how the minimization of the Kaehler action is not a
> global action, it is local to the particular observer, thus each
> observer would have their own "absolute minimization of the Kaehler
> action", since every observer has their own light-cone structure. I
> point to a generalization of the principle of equivalence: "every
> observer always is at rest with respect to their local framing". When
> interaction occurs between observers the space-time framing is changed
> by the q-jump, and thus the particular minimization configuration of
> changed. This is the act of computation that I am thinking of!

In good approximation this is indeed the case. Kahler function
reduces in good approximation to a sum of Kahler functions associated
with spacetime sheets representing individual observers. There
are however small interaction terms involved.

The more or less implicit assumption of all physical theories is
that one can build more complicated solutions from simpler ones
somehow and that quantities like energy and action are additive
in this process in good approximation. In linear theories one just
sums solutions. In nonlinear solvable models one 'sums'
single soliton solutions. In TGD this building recipe is to glue
spacetime sheets on spacetime sheets.

> [SPK]
> > > I do not understand this! :-) Is it really necessary to have "unique"
> > > canonical monentum densities? What is the conjugate of this quantity?
> > > Does this have to do with the lack of a time-energy operator in QM? If
> > > so, Schommers outlines one that works also for the Frieden method, I
> > > think! :-)
> [MP]
> > The uniqueness of canonical momentum densities is absolutely crucial
> > for the approach. Without this you do not have unique Hamiltonian
> > and quantization fails down totally!
> >
> > Canonical momentum densities are canonical conjugates of dynamical
> > variables: now 4 suitably chosen imbedding space coordinates as
> > function of spacetime coordinates. Actually situation becomes
> > completely catastrophic for vacuum extremals, in particular
> > M^4_+ imbedded as surface for which CP_2 coordinates are constant.
> > Canonical momentum densities vanish identically for them!
> >
> > This problem is purely TGD:eish and due to the extreme nonlinearity of the
> > action and vacuum degeneracy which corresponds to Abelian U1 gauge
> > invariance and gives rise to spin glass analogy and cognitive spacetime
> > sheets and padicity and.... The failure of canonical formalism
> > reflects all new concepts and new mathematics characteristic for
> > quantum TGD.
> >
> > Well, I am not sure what you mean with time-energy operator...
> > Even the unique existence of energy operator, Hamiltonian
> > fails.
> We need to study Schommers work! He shows how to deal with this!
> [MP]
> > There is infinite hierarchy of p-adic number fields and topologies
> > labelled by primes. p-Adic prime p of observer fixes the
> > effecitive p-adic topology obeyed by this observer spacetime sheet
> > and, as I assume, the effective topology of the spacetime,
> > and universe, as experience by the observer. The larger the value of p,
> > the more intelligent observer (maximum information gain in cs experience
> > behaves as log(p)*p). Everything is experienced as 'grainy' and p
> > and pinary cutoff defines the degree of 'graininess'. 2-adic
> > observers are the most 'grainiest' selves. Amusingly, computer technology
> > works with bits and all engineering acievements are very squareish:
> > just like the 2-adic fractals in my homepage. This would suggests
> > that our technology reflects the lowest possible level of p-adic
> > evolution(;-)!
> Have you ever heard of "relative primes"?
> (http://www.askdrmath.com/problems/athena11.24.97.html,
> http://www.dacafe.com/Book/CH02/CH02.17.htm,
> http://www.cs.washington.edu/homes/gjb/doc/philmath.htm)

Yes, they are familiar for me.



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