Matti Pitkanen (matpitka@pcu.helsinki.fi)
Fri, 20 Aug 1999 20:20:55 +0300 (EET DST)
> > Everything is static in 4-dimensional view.
> > With respect to subjective time the temporal position of CS at MS is
> > not
> > static. In each quantum jump it changes and this gives rise
> > to arrow of psychological time.
[SPK]
> Sure, each observation in a "moment" is 4-dimensional. Hitoshi's
> discussion of the apparent Hubble expansion involves this!
>
[MP]
> > Think just a sphere, CS, 'glued' to planar surface (MS). Call
x-axis
> > time axis. In each quantum jump this world is replaced by a new one
and
> > x-coordinate of the sphere increases on the average.
>
> But, this is inherently problematic as it tacitly suggests that
the
> "increases on the average" are just stochastic. How do we consistently
> represent the alteration of the quantum history due to interactions
> (measurements)? This picture of yours is too a priori synthetic for my
> taste... :-(
[MP] I do not see anything bad in statistical nature of time's arrow. The
statistical nature of arrow of psychological time is in principle testable
prediction. In practice the statistics is so excellent (10^40 quantum
jumps per second!) that there are probably no hopes of
observing the actual nondeterminism. One should be able to do
experimentation in time scale of 10^(-40) seconds: BTW, the time scale at
which all symmetries are expected to unify!
Most colleagues would believe that this time scale is scale where
standard spacetime concept breaks down: I claim that it is psychological
time=geometric time idealization, which breaks down at this time scale.
> [MP]
> > No!! The whole point of the argument is that quantum jump replaces
> > spacetime surface containing material and cognitive spacetime sheets
> > with a new one.
>
[SPK]
> Sure, we agree; but it difficult for me to understand how... I
believe
> that space-times are defined by the range of motions and transformations
> of cm points of LSs, space-times that "contain" no matter are impossible
> to define. They are, to me, like "free particles", just convenient
> mental fictions.
>
[MP] Also cognitive spacetime sheets contain classical fields and energy
but energies are extremely tiny. Cognitive spacetime sheets
take small sample of material spacetime sheet: they are measurement
instruments.
[MP]
> > The temporal position of cognitive spacetime sheet changes in this
quantum
> > jump, material spacetime sheet does not change much. Therefore
cognitive
> > spacetime sheet 'sees' different small temporal portion
> > of material spacetime sheet, for instance a new reading of purely
> > classical clock ticking on the wall. I suggest direct visualization
> > of the idea: it is extremely simple.
> >
> > Cognitive spacetime sheet gives actually about small time interval,
> > I was just simplifying things to make the connection with standard
> > picture clear.
>
[SPK]
> Umm... :-( I see the "standard picture" as deeply wrong. We must
> consider the subject-object relation as fundamental in physics, we can
> not maintain that the world just exists. It does, indeed, exist, but in
> what particular state and what particular event? That is not an
> existent. We could say that the specific content of an experience does
> not precede the experience itself!
>
[MP] Standard picture IS deeply wrong. What I wanted is to show
how TGD picture differs from it.
> [SPK]
> > > Ok, we agree that "time is in our mind"! The problem is that
there
> > > seems to exist more that one mind, and there does not seem to be any
> > > particular a priori ordering of space-time "slices" "out there"!
What to
> > > do?
> [MP]
> > I think that you misunderstood my argument.
> > There is no ordering of geometric time and no ordering of geometric
time
> > is needed. The ordering of geometric time is misconception
> > induced from the failure to distinguish between subjective and
geometric
> > time.
>
> So why do we have a geometric time at all? Is it because of your use of
> a "M^4_+ future light cone"? I must say that I have a serious problem
> with this! All that an observer can "see" is within a M^4- past light
> cone, the M^4+ is not "out there" any more than "tomorrow" is out there
> waiting for me to get to it. Actually, the "past" only is actual in that
> records can be found of its events, it is not "out there" either! The
> events that are experience by observers are "put together" by their
> observations, each observer's acts select from the infinite potential
> (of Existence) to actualize an observation. The recording of such is
> dual to the selection.
[MP] Without geometric time one loses practically all known physics.
For instance, there would be no concept of energy
(invariance of laws of physics with respect to time translations),etc...
Main stream physics do not even mention the notions of
psychological time or subjective time: as far as predictions are
considered only geometric time is needed. Of course this all
is just play with formulas. They are not understood but they work
magically. For instance, scattering rates involve integrals over entire
geometric spacetime: taking literally this is nonsense from standard
physics view but the formulas work.
The problem is to understand the triplet subjective time-psychological
time-geometric time: how they relate to each other.
[MP]
> > The apparent ordering of geometric time induced from ordering of
> > subjective time measured by quantum jumps. In statistical sense the
> > geometric time observed by cS=temporal position of CS, increases by
> > 10^4 Planck times in single quantum jump. In hope of making things
clear
> > I use the phrase 'psychological time' instead of geometric time
> > when I talk about time experienced by us.
> >
> > Each cognitive spacetime sheet experiences its own psychological
time.
> > Cognitive spacetime sheets are perhaps a realistic version for
> > a continuous distribution of clocks around spacetime, which, at least
> > to me, is too hard an idealization.
>
[SPK]
> The idea of a "continuous distribution of clocks around spacetime" is
> impossible if we require the spacetime to be Diff^4 invariant! This is
> one of the key points that led Hitoshi to his model.
> "a cause of the problem of time seems to lie in associating time to
> each point which has no positive size. No clocks can reside in a
> sizeless point. At the stage of special theory of relativity, this
> difficulty does not appear: Time is associated to each inertial frame
> which can accommodate actual clocks. At the stage of general theory of
> relativity, the field equation with the invariance postulate with
> respect to diffeomorphisms requires one to eliminate the size of the
> frames in which clocks reside." http://www.kitada.com/#pre
[MP] About the overidealization we agree.
> [MP]
> > I think that you might catch the idea just by looking the
illustrations
> > of cognitive spacetime sheets on my homepage. The idea trivializes in
> > whole-body consciousness mode and this mode communicates with
> > figures(;-).
>
> I am having a hard time interpreting your illustrations... :-( I have
> pictures of my own that give me fits! I think I understand this
> whole-body consciousness. :-) I have pictures, more like immersion
> experiences that overwhelm me. I had one the other day about loop spaces
> defined by CTL's (closed timelike loops) and was looking at the behavior
> of electromagnetic fields and light rays...
[SPK]
> Umm... why then do people identify the reals with temporal events? Your
> idea of "values seem to increase" is usually associated with "the
> thermodynamic arrow" in the literature...
[MP] Perhaps because Einstein talked about events. Just thinking
carefully what Riemann geometry really is one realizes that
there are no time arrow involved. Time and space are in same position.
There is no preferred time coordinate to measure. If one introduces
clock measuring geometric time, one should introduce also clocks measuring
all three spatial coordinates.
The map assigning definite temporal cm coordinate of cognitive spacetime
sheet maps subjective time to geometric time and then we make the error of
projecting the irreversiblity and clockability of subjective time
to properties of geometric time.
[SPK]
> Thinking further as I talked to Al last night, I can see geometric time
> as the M^4- lightcone structure of events that is illustrated by looking
> out into the night sky and considering that the further away a point of
> light is from my "moment of now" the "further back in time" it is. SO I
> think that I am softening my thinking about geometric time, but with the
> caveat that each observer has a version of geometric time (M^4-) thus
> making it subjective. The idea of an "objective geometric time" can be
> derived from the overlapping of subjective geometric times. The
> discussion of the Robertson-Walker metric by Hitoshi as giving an
> appearance of a expanding 'universe' follows logically...
>
> [MP]
> > I would say something resembling this: subjective existence is in
> > quantum jump. Universes/quantum histories themselves are LOGOS=COSMOS
> > but without consciousness.
>
[SPK] To me LOGOS is a verb, an act... I do agree that Universes/quantum
> histories themselves have no consciousness, but only when we are
> considering them from the perspective of observations. The
> Object-Subject relation is, I believe, symmetrical. Every object that I
> can perceive is, in a sense of interactions, perceiving me.
>
[MP] I would have agreed about symmetry for half a year ago but I
do not know anymore. Strong NMP did not
tell whether it is subsystem or its complement which is measured.
The notion of self forced different interpretation: experiencer
is self whose subsystem and its complement
inside self define the quantum measurement.
> > [MP] But the problem is that classical Turing machine is too
restricted
> > model for computation as conscious beings do it.
> > That one can model classical physics by Turing machines (forgetting
> > now the problems caused by initial value sensitivity) does not
> > mean that classical time development is actually a computation.
[SPK]If any classical system's behavior can be modeled by a UTM and a UTM
> can be implemented in a classical system, I see a connection between
> time and computation! (Noting that this particular model assumes unique
> initiality conditions) Now that we have good models of quantum
> computation, such as Peter's, we can understand better how time works in
> a quantum context... It is just a model, a way of thinking after all...
>
[MP]
Problems are caused by noncomputability in classical context.
> [MP]
> > The point is that the values of function are set of reals with
> > cardinality or reals, call it C. You should put C infinitely long
> > decimal expansions to row and get still real, is this possible?
>
>[SPK] Yes, I think so. A diagonalization of a R x R matrix is within R,
> unlike the integers...
>
> > Calude speaks of *rows of integers* having finite expansion.
> > Also rationals have periodic decimal expansion and information
> > about rational can be coded by finite number of decimals (right?).
>
[SPK]
> Let me see... "Any finite sequence [of symbols] can be
unambiguously
> coded in binary (or decimal) and thus corresponds exactly to some
> rational number." What I am making noise about is that "symbols" are
> matter codings of information. (Without matter it would be impossible to
> make records, thus disproving Idealism...) Umm, another thing about
> Calude's Lexicons are like programs, they need material configurations
> to be read, e.g. reading heads - tape, etc.
[MP] This is perfectly understandable if symbols carry finite bits of
information to us. What fascinates me that characterization
of quantum jump by bit sequence, integer leads to characterization
of infinite sequence of quantum jumps by real and since most
reals are lexicons this means that every quantum jump (classified
in pinary resolution) appears infinitely many times in sequence.
This means complete information about all possible quantum jumps.
The infinite p systems with infinitely long subjective memory
have all the data needed to build a physical theory and communicate
it to us(;-)!
[MP]
> > I generalize integers by starting from the decomposition to a product
> > of powers of prime.
> >
> > N= Prod_k p^(n_k).
>
[SPK]
> Could you give me a specific numerical example? The algebra symbols
> give me no pictures. :-(
>
[MP]
Examples of prime decompositions of finite integers:
9=3^3, 14=2*7, 28= 2^2*7, 60= 2^2*5*3, etc...
What I allow is also infinite primes in these product decompositions:
single example.
Denote by X=2*3*7*... the product of all finite primes. I do not bother
to write it to the marginal since my computer memory is rather limited
but
it is purely mechanical task and I leave it as an exercise(;-).
P = X+1 is infinite prime since P modulo p is 1 modulo p =1
for any finite prime so that no finite p divides P.
2*3*P is infinite integer.
[MP]
> > Usually only finite primes appear in this product. Now I allow also
> > infinite primes and their powers and get infinite integers. I believe
> > that the construction for all infinite primes exists.
>
[SPK]
> What cardinality does the set of these primes have? Umm, this looks
> like a alternative to the continuum hypothesis...
> http://www.ii.com/math/ch/faq/
[MP] I wrote something about the cardinalities but I cannot
recall the argument. The cardinaly of basic primes at first level
is at least the cardinality of possible subsets of primes
since simplest infinite primes correspond physically to many-fermions
states formed from fermions labelled by primes. This would
mean at least the cardinality of reals since the cardinality
of subsets of integers is that of reals (OK?).
There are also other infinite primes that the basic ones so that
cardinality at the first level is *at least* the cardinality of
reals. At the next level of infinity the cardinality is at
least the cardinality of all subsets of reals, etc...
Perhaps this goes like
C= cardinality of integers (primes).
C1>= 2^C,
C2>=2^C1, ......
[MP]
> > Then I define generalized rationals as
> >
> > R= M/N.
> >
> > Depending on M and N they can be infinite, infinitesimals or
> > also finite as real numbers.
>
[SPK]
> Interesting! I like to think of this as a reason why we only
> experience rational values. :-)
[MP]
And those enlightened souls above us would think in terms
of super-rational values(;-).
> [MP]
> > I really do not know the position of Dennett but as a physicist and
> > dedicated tripartist(;-) I see a problem.
>
[SPK]
> I agree with your assessment of Dennett, he is a bit too smug...
> > I admit of course, that I do not understand the delicacies of the
> > dualistic approach: perhaps dualist sees software and hardware as
> > duals
> > of each other: in this kind of situation itw ould make sense to
> > replace
> > reading head with a program. But is our world dualistic?
>
[SPK]
> Exactly! software and hardware behave dualistically. We can replace the
> reading head with a program but we are merely swapping the duality
> around.
>
[MP]
> > Probably I do not understand what computation really means in
> > dualistic
> > approach and how it differs from my intuitive notions. Could one
> > consider
> > a model of Turing machine as a challenge for dualistic approach?
>
> No. The Turing Machine is dualism's best witness! Mind is dynamics of
> information, software, in the usual sense, is just a linear version of a
> mind. Body is the dynamics of matter, hardware... The interaction of the
> two is given not by exchange mechanisms but by bisimulation, e.g. the
> behavior of matter and mind simulate each other. It is in the actions of
> each that they make contact, mental states via logical precedence
> chaining and matter events via impression of configurations.
[MP]
Chalmers represented in his books arguments stating that the basic
problem of dualism is that consistency with the determinism of physics
leads to conclusion that mind is one-one image of matter and can be
eliminated as un-necessary so that one has materialistic
monism. Or that in interactive dualism there is no
basic difference between matter and mind like degrees of freedom
and one could quite well call them just matterlike. Have you studied
these arguments?
> [MP]
> > I understand. Sarfatti is dualist and my bitter enemy, he
> > not-even-wrongizes me in every possible instance: what do you
> > think about Sarfatti?
>
{SPK]
> I find Sarfatti to be abrasive and close minded. I do not
>understand Sarfatti's version of dualism.
[MP] The idea is to regard some fields as matter like and some fields
as mind like obeying determistic dynamics. The dynamics of matter fields
looks nondeterministic if one forgets the presence of mind like fields.
The problem is that the decomposition into matter and mind like fields
is completely ad hoc.
Pilot wave would be mind like field and classical particles would
represent matter.
[SPK]
> ok. I am very interested in this notion of statistical
determinism. :-)
> Could you elaborate on your thinking about it?
[MP]
This is the basic hypothesis of QM. In ensemble of identical systems
under identical conditions the probabilities of outcomes are what
Born rule gives for them.
For temporal sequence of quantum jumps the same holds. This is crucial
for the concept of self. 10^40 quantum jumps means that self of
age of one second experiences kind of average experience and this
experience is reliable although the outcomes of individual quantum jumps
are not predictable.
The great surprise for me was that quantum statistical determinism
seems to be present directly at the level of our own experiencing:
not only in the analysis of quantum measurements made for
atomic systems.
Best,
MP
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