Stephen P. King (stephenk1@home.com)
Sun, 18 Apr 1999 17:13:11 -0400
Dear Hitoshi and Friends,
I tried to organize this... ;)
Hitoshi Kitada wrote:
snip
> > > Let me propose a problem about the direction of time, which, at least
> > > seemingly, has a form that has not been considered before. That is partly
> > > a reminiscence of [time 199] and hinted by Ben's remark [time 198].
> > >
> > > Direction of time or Does the free will exist?
> > >
> > > Let us consider the following observation:
> > >
> > > Let an observer O observe a local system L'=(L1,L2,X) or L=(L1,L2). Here
> > > L1 and L2 is the direct objects of observation of O and X is some
> > > automatic apparatus that observes the system L=(L1,L2).
[SPK]
> > Here we have a choice of observables, L or L'; I am assuming that they
> > are observationally mutually exclusive, e.g. O observers L xor L'.
[HK]
> I think you are right. In my thought, Wheeler's discussion of his delayed
> choice experiments seems not to include all apparatuses related with the
> experiments into consideration. In his experiment, he regards the second
> semi-transparent mirror is inserted "after" the photon was emitted and
> incident on the first semi-transparent mirror. But the system the observer
> looks at should be the one that includes the first and second semi-transparent
> mirrors and also the two totally reflecting mirrors on the way as well as the
> photon itself. The distinction between this and another experiment with no
> second semi-transparent mirror inserted can be made by the difference of the
> existence/nonexistence of the second mirror. Then the systems the observer
> looks at are different and hence it is natural that there is a difference in
> what the observer sees in them.
As you say, Hitoshi, these are two distinct experiments, but is there a
way to transform one into the other formally? I wonder could we think of
changes in observational viewpoints in terms of changes in experimental
setups. David Finkelstein seems to be trying this in his work... How do
we formally think of experiments? Does it properties include spatial and
temporal properties? We might think, in the special case of this
experiment, of parametrizing a transformation from the first
experimental setup to the second by using the 'degree' to which the
second semi-transparent mirror is in alignment or the probability of
reflection by it.
> Also in his consideration of the example of the light from a quasar, he seems
> to exclude the galaxy that affects as a gravitational lens to the light
> emitted from the quasar, by the reason that the lens worked in the far past.
> Here is an assumption that what are very far from the apparatuses that the
> observer sees directly and now can be thought as being outside the system the
> observer sees right now. Even if the light was emitted from the quasar 10
> billion years ago, the quasar and the gravitational lens must be included in
> the observed, and the exclusion of these 'apparatuses' causes the
> misunderstanding of the situation.
The galaxy would be part of the experiment obviously! :) The tendency
to neglect certain aspects of a situation in order to simplify the model
is widespread. Many philosophers of science have commented on it…
> I think these unnatural exclusions lead his discussions to the extreme that
> the present affects the past. In other words, he introduces the distinction
> between the past and the present in such a way that the present looks like
> affecting the past, while the system the observer actually observes is the
> system that includes the past and the present at the same time.
>
> Here is the essence of the notion of time. The same time for one is the
> simultaneity for himself. I.e. in the above experiment, the components of the
> system consisting of two semi-transparent mirrors, two totally reflecting
> mirrors and the photon should be considered as existing at the same time when
> the observer observes the photon enters one of the detector after passing the
> second semi-transparent mirror. What constitute the system is the objects that
> construct the experiment including the second mirror. Even if the second
> mirror is inserted afterwards, it actually participate in the process, and
> must not be thought outside the apparatus. Or more exactly, what observer sees
> at the final stage is the collision between the photon and the second mirror
> that moves with some velocity to the delayed-choice region (DCR). Just to
> think this mirror appears suddenly at the DCR makes the experiment look
> magical. Here is no magic actually, if we consider the experiment at the
> position of the observer.
In my discussions with Paul Hanna, it appears that observations involve
entire light-cones simultaneously extending to the horizon, not just
that part that is infinitesimally neighboring the origin. There is a
mystery here as how light acts as if it had infinite velocity in the
sense that it instantly connects a multitude of events, that are
observed simultaneously by an observer; but at the same time we observe
a finite signal propagation 'speed'. Maybe the inside-outside relation
of LS can be used to deal with this… I do recall your mention of speeds
being infinite inside of the LS...
> Similar confusion or exclusion seems to be found in many problems of physics.
> This may be one of the main causes of physical problems.
>
> The contradiction resides in the notion of time itself. It distinguishes
> several events by their times, and we tend to think that after a long time
> passed, we can forget the events at those old times. But for one observer,
> these events constitute one simultaneous system, even if some elements of the
> system have already disappeared elsewhere at the time of the observation. More
> exactly, these disappeared elements still are travelling some place, but just
> outside the sight of the observer at the time of the observation. But to
> explain the experiment, it is necessary to consider all the elements that
> participate in the experiment.
I agree, this is an important notion! :) But, we do not need to
maintain a realism stance about the elements no longer in view. To say
that they "still are traveling some place" brings in the tacit
assumption that they have definite properties independent of
observations, what remains definite is the "memory" that is local of
such measurements. This is why I say that the LSs encode information and
that the dynamics of this information is a computation.
> Time is an apparatus of oblivion. This is also the case with the distance in
> space. It is usually assumed that the particles far away from the objects one
> considers right now can be neglected. This would cause the same confusion in
> physics.
I like that: "Time is an apparatus of oblivion." Bohm seems to think of
this in terms of unfolding -> enfolding. It is this very reason that I
think of time as intimately related to entropy. As time brings new
observations into view it demolishes those prior observations, but this
notion is a local one, each observer has its own "moving hologram
parade". The 'trick' is how observer can communicate among themselves
about their own observations. I am working with Paul on a formal way of
saying and proving this. :)
> The notion of local system is the one that clarifies this confusion. In
> Wheeler's experiment, if the observer does not insert the second
> semi-transparent mirror, it simply means that the mirror does not participate
> in the experiment, and thus there is difference from the case the mirror
> inserted.
>
> I think it would be possible to see the future by some techniques utilizing
> this illusory property of time. After all time is an artificial notion that
> puts an order on the objects one sees.
"If information about the future is possible, as it seems, then
information travels faster than the speed of light." Pg. 3 Information
Flow http://www.phil.indiana.edu/~barwise/kjbbooks.html
Hitoshi, perhaps you are beginning to understand the
information/computer science aspect of this. :)
[SPK]
> > How are O and X defined in terms of local systems?
[HK]
> X may be definable, but I think the subjective observer O may not be
> definable. Subjectivity seems to remain undefinable and/or unsolvable in any
> objective way, in the sense that we cannot identify ourselves by ourselves.
:) Strangely enough, I believe that it is this *"undefinability" given
"objective" data* that defined a fundamental aspect of subjectivity! The
incompleteness of provability of axiomatic systems (containing
arithmetic) is analogous. See section 5.2 of
http://www.cs.brown.edu/~pw/papers/bcj1.pdf
I would like to discus this more later! :)
[SPK]
> > They seem to be classical and, upon thinking further, X looks to be another
> > observer itself. Perhaps we can think of it as one of Peter's "secondary
> > observers"... ( cf. [time 191])
[HK]
> Yes, X would behave as a macroscopic apparatus, and has to be treated as a
> classical system. Nevertheless, the part of X which interacts with the objects
> L1 and L2 when X observes L1 and L2 would have to be treated as quantum
> mechanical objects if we try to explain the mechanism of observation of L1 and
> L2 by X.
So that 'part' of X is the 'interior' of X? Could this be seen as the
subjective component?
> In a larger context, X would be the same as Peter's secondary observer. But I
> am not sure how Peter would utilize his notion of secondary observer.
I think of secondary observers as other LSs that could potentially
communicate with a given LS but choose not to. They are quantum
mechanical versions of on-line "lurkers"! :) It is the mere possibility
of interaction that alters the situation. We see this in various more
conventional bench-top experiments involving the two slit experiment
involving, say, electrons. To me, Wheeler, in the delayed choice
experiment speaks to how the possibility of choice alters the situation.
To quote from Peter's paper http://www.cs.brown.edu/~pw/papers/cm.ps,
pg. 12:
"A MIM is a tool for studying the interaction of k+1 entities, where
one plays a special role as an observed system and the remaining
entities are observers, modeled by streams. For interacting SIMs, k = 1
and the observer with the observed system form a closed system. When the
observed system is a MIM, k is greater than 1 and a primary observer
representing the experimenter is distinshed from k - 1 secondary
observers. MIMs appear nondeterministic from the viewpoint of a primary
observer who cannot predict or control the effects of secondary
observers and may be unaware of their presence. Primary observer[s]
perceive MIMs as subjectively nondeterministic even when, view by an
omniscient multi-agent observer (God), they are objectively
detreministic."
I think that this is a way to 'relativize determinism' and thus an
aspect of the LS model.
[HK]
> > > If O looks at L', then what O sees in the future about L
> > > is different from what O sees when O looks only at L. (1)
[SPK]
> > Here it seems that the meaning of "past" and "future" needs to be
> > carefully examined.
[HK]
> I agree. The notion "past, present, future" is some subtle trick which is very
> convenient to explain the outside of us. What you write in your home page:
> "Time exists because everything can not happen at once" is another expression
> of this convenient aspect of the notion of time, but is not a definition of
> time. This sentence is as well an expression of the western wisdom that uses
> the tense as the crucial structure of their language. However, I think that
> everything exists at one instant. No future nor past would exist. For we
> cannot grasp the past and future by our hands. They are just imaginary
> existence that is convenient. The nonlocality could be the proof of the
> non-existence of the past and the future.
My aphorism "Time exists because…" is an attempt to illustrate how
local finite interactions can not be a priori defined. There are timing,
interleaving, concurrency, etc. situations involved. I need to better
explain my argument that the NP-Completeness aspect of optimization,
etc. that is implicit in the so-called 'principle of least action' (and
in Feynman's path integration!) can not be ab initio postulated to "just
exist", such an argument is the beginning of errors that we are trying
to overcome with this work.
Yes, all possibilities Exist at the ontological level of the Totality
U, but as such they are not perceivable by a finite subjective stance,
this is manifested in how U is defined as a 'pure' bound state. Finite
observers can only apprehend finite qualia and it is the context (finite
and bounded) of the observation that "selects" what is observed. We can
say that something is not *subjectively real* until it is experienced by
the observer. So the question becomes: "How does an LS experience a
world?"
[SPK]
> > Can we understand this term "sees" as meaning logically inference?
[HK]
> I mean by this "sees" a future tense that certainly happens in the future. I
> wanted to express like the following: If one looks at L', then the part of his
> results about L of his observation of L' in his future is different from what
> one looks just at L always.
That is what I mean by logical inference, it is a prediction like: if A
then A'obtains ...
[SPK]
> > I am trying to think of this in terms of Peter's
> > Interactive Machine paradigm. If we could show that a LS is equivalent
> > to a finite IM, we could easily bring in the power of Peter's analysis
> > in to play. :) http://www.cs.brown.edu/~pw/papers/bcj1.pdf
[HK]
> I downloaded the paper, but I could not find time to see it.
I will try hard to be patient. :)
[HK]
> > > We may regard this as an experimental fact (provided that the situation
> > > describes exactly Wheeler's quantum eraser).
> > >
> > > Wheeler's case may be rephrased:
> > >
> > > The present affects the future. (1')
[SPK]
> > Is this meaning strict material causation, in the sense that a
> > primitive lightcone structure could be constructed using an array of
> > Observers O_i exchanging signals.
[HK]
> In (1') I think within the subjective time of the observer. For him, the
> outside would look like Minkowskian. I did not consider the communications
> among many observers.
I understand that. I think that the difficulty can be better dealt with
if we consider a realistic model involving many-observer communications.
Then we only have two, the algebras would be symmetrical, as in the SR
situation of traveling twins. The situation is different when there are
more that 2 observers. This is the main subject of Paul's work…
In fact, my weird conjecture of subject-object symmetry only holds that
for a single pair of observers, it is 'broken' for multiple observers.
It is analogous to the fact that vectors are always commutative in R^2…
I was trying to introduce the ideas implicit in bisimulation… :)
[SPK]
> > It is the "thermodynamic arrow" that, I believe, holds the key to thinking
> > of an asymmetry between evolutions toward the past or future.
[HK]
> I think thermodynamical arrow of time is a physical word that assumes the
> consensus among many observers. However, I am skeptical about this kind of
> consensus: such a consensus seems to be just a dream of mere physicists.
> Stating the problem on the more fundamental level, I suspect that such
> objective arrow of time might be impossible to be defined. If it could be
> defined, it would belong to a part of common sense, not the subject of
> science.
>
> I feel that the present science seems to be trying to be out of its limit. The
> objective description seems to be meeting the boundary of its area where it
> works. My substitute for the objective arrow of time is the subjective arrow
> of time.
This is how science makes progress, like a man in a dark place figuring
out how to make a light far from the lamp posts of conventional
thinking… ;)
> > But on a side note, independent of any
> > observation, an LS's time arrow can only be considered as having a
> > superposition of directions. This relates to my earlier questions about
> > time vectors. :)
>
> I do not have clear image yet about your "time vectors." If I would use that
> phrase, I would use it as meaning some average of the directions of time among
> many people on the level of common sense.
That is close. Think of a space where every point is represents an
event of some kind. We do not impose an absolute metric or ordering on
it a priori. The concatenation of points X into an finite ordering x_1,
x_2, …, x_n can be seen as defining a vector in that space where the
direction is given by comparison to some arbitrary chosen unit basis
(2^X?) and its magnitude by the number n of points concatenated together
(the cardinality of {X}?). There are many such orderings and thus many
such vectors...
If we think of an additional finite ordering P such that p_1, p_2, …,
p_m that is orthogonal to X, we get a model of time's conjugate vector…
I do believe that this is very similar to a well-known mathematical
object, I am using it as a mental picture… (But I am thinking these as
constructions, they are generated by interactions...)
[HK]
> > > Let us consider the observation with time order reversed. The question in
> > > this case is if the following is correct or not:
> > >
> > > If O looks at L', then what O sees in the past about L
> > > is different from what O sees when O looks only at L. (2)
> > >
> > > This would be paraphrased:
> > >
> > > The future affects the present. (2')
[SPK]
> > We are starting to think seriously about the ontological question of
> > causation and temporal transitivity! :) It is well known, that systems
> > described by invertible dynamics do not have an "arrow of time" (cf. M.
> > C. Mackey "Time's Arrow: The Origins of Thermodynamic Behavior".
> > Springer-Verlag, 1992 http://www.cnd.mcgill.ca/bios/mackey/mackey.html);
> > we need to look at the scattering state dynamics of LSs to see if they
> > satisfy "f* exactness" or some equivalent.
[HK]
> Would you explain "f* exactness"?
I will quote Mackey book. There are issues that will get generalized
such as "initiality", as per Peter's work with non-well-founded set
theory, but for now this works as a starting point…
Pg. 89-91 ibid.
"In Chapter 3 we have shown that invertible system shave absolutely
constant entropy, namely H_c(P^t f|f*) = H_c(f|f*) for all times t
(theorem 3.2), while for noninvertible systems the entropy may increase
(Theorem 3.1) since H_c(P^t f|f*) >/= H_c(f|f*). Thus, noninvertibility
is absolutely necessary (though not sufficient) for the entropy of any
system to increase from its initial value."
and
"If S_t is an f* measure preserving transformation operating on a
normalized phase space X, then S_t is said to be <<f* exact>> if
lim µ_* (S_t(A)) = 1
t -> oo (infinity)
for all sets A of nonzero measure. If f* is the uniform density, f* =1,
then we say that S_t is <<uniformly exact>>.
To understand the nature of exactness, it is first important to realize
that invertible systems cannot be exact. To see this, note that for an
invertible f* measure preserving transformation S_t we have µ_*(S_t(A))
= µ_*(S_t^-1(S_t(A)) = µ_*(A). Thus the definition of exactness is
violated.
Example 7.1. An example, similar to that for ergodicity and mixing, is
helpful in showing how exact systems operate. Figure 7.1 shows the first
six iterates of 10^4 points randomly distributed in [0, 1/10] x [0,
1/10] under the action of the uniformly exact transformation:
S(x, y) = (3x + y, x + 3y) (mod 1). (7.1)
It is clear that the behaviour is quite different from a mixing
transformation. Under the action of an exact transformation an initial
set A is quickly dispersed throughout the entire phase space X. If one
interpreted this example in terms of many different particles moving
with dynamics given by Eq. (7.1) and each with a different pair of
initial conditions, then we would very soon find them uniformly
dispersed throughout the phase space.
Example 7.2 A second example of a uniformly exact transformation is
given by the tent map (3.5). The tent map preserves the Lebesque measure
and if we start with an initial set B = [0, b], then a simple geometric
argument (try it!) suffices to show that after a finite number of
iterations µL(S_t(B)) = 1 and the transformation is uniformly exact. A
more precise proof can be carried out using the behaviour of the
evolution of the densities by the Frobenius-Perron operator contained in
Theorem 7.1 below.
Example 7.3. Though not as well studied as discrete time systems, some
noninvertible continuous time systems have been shown to be exact … and
Loskot (1985) have also considered the properties of the solution u(t,
x) of the first partial differential equation
đu/đt + c(x) đu/đx = f(x, u) [were đ is the partial differential
symbol]
with the initial function
u(0, x) = v(x) for x \element [0, 1].
Both c and f are assumed to be continuously differentiable, and it is
further assumed that
(1) c(0) = 0, c(x) > 0 for x \element [0,1];
(2) f_u(0,u_0)< 0, f(0, u)(u - u_0) < 0 for u > 0, u =/= u_0; and
(3) 0 >/= f(x, 0), f(x, u) </= k_1 + k_2 for x \element [0, 1], u>/= 0
with constant k_1, k_2 > 0 and u_0 > 0.
With these conditions, whenever the initial function v(x) satisfies v(0)
= 0 then the semidynamical systems S_t (v(x)) \equivalent u(t, x) is f*
exact. If f* is the (Gaussian) density of the Wiener measure (see Lasota
and Mackey, 1985) on the function space V = {v \element C_+ ([0, 1]:
v(0) = 0} and C_+(A) is the set of all nonnegative continuously
differentiable functions on A."
[SPK]
> > I believe that there is there is an analogy between the difference
> > between "bound and scattering states" and Mackey's "dynamical systems
> > and traces" (pg. 111 ibid.) and thus there is a way of defining LSs as
> > having a define time arrow.
[HK]
> > > Turning to the direction of time, I think it may be understood as the
> > > direction of one's own time when he sees the outside. If we understand the
> > > direction of time in this way, we have two alternatives with (2):
> > >
> > > If (2) is true, then the observer's time is reversible,
> > >
> > > while
> > >
> > > if (2) is false, then the observer's time is irreversible.
> > >
> > > (2) may be tested by experiments, similarly to Wheeler's.
> > >
> > > If the direction of time is that of the observer's subjective time as I
> > > proposed, my claim is thus that we can find by experiments if time has the
> > > direction or not.
[SPK]
> > Of course, it is the act of observation that implies that a fixing of
> > frame has occurred and that such fixes a chronological ordering. But, we
> > can *not* assume such distributive orderings exist *ab initio*, since
> > the computation of such ...
[HK]
> What problem does "such" designate? I.e. what kind of computation do you think
> necessary for one to fix his frame?
This is at the heart of my argument: Experiences are interactive
computations and as such there is a finite duration implicit in a
subjective experience. We see this when we think of Wheeler's universe
sized two slit experiment. The local clock aspect of an LS is the
"timing device" of the computer, which I see as the internal scattering
propagator as seen from the view point of another LS. The way that the
"sequence t_m -> ±oo (as m -> ±oo)" in the "unitary group e^(-itH_nl) (t
\element R^1) on \H_nl" speaks to me of a model of how subjective
experience is constructed by a sequence of approximations.
You say "t_m is only asymptotically equal to ±|x_b|/|q_b| as m -> ±oo.
What happens is one were to "suspend" the approach to ±oo at some finite
amount of m? We see in finite computation the need for "round off" in
the n-ary bit expansions, why? There is a finite limitation in the
interface, e.g. the pixels, etc. can represent only so many digits.
Perhaps our study of the decomposition idea re: [time 202]. I believe
that finite observations are also representable in these terms and, thus
agree with Peter's thesis. :)
[SPK]
> > ... is an NP-Complete problem and thus is
> > irreducible to mere postulations of "microcausality".
> > http://www.uncg.edu/mat/avg/avgnp/node9.html
> >
snip
> > > In short, _if (2) is true_, O must choose one right way always, whichever
> > > direction he takes at the branch, if the data coincide with those that he
> > > will see the apparatus X. He _can_ choose one of the two at his will, but
> > > his choice has been determined in the sense that he has _no ability_ to
> > > change his fate to see the apparatus X.
> > >
> > > So if (2) is true, no free will exists,
> > >
> > > or
> > >
> > > if (2) is false, the free will may exist.
[SPK]
> > Are we defining free will as strictly contradicting determinism at all
> > levels, could we have free choice externally and determinism interiorly
> > to the LSs?
[HK]
> I intended to discuss the external free will, i.e. the problem if we can get
> ourselves out of the bondage of the fate when we meet the outside. My guess
> would be that this is impossible.
[SPK]
> > In Computer science we distinguish between "linear time" and "branching
> > time" computations. The former assume complete initiality ab initio
> > ("all choices made at the outset") and the latter eliminates initiality
> > requirements ("choices made on-the fly to take into account the latest
> > information")
> > http://boole.stanford.edu/chuguide.html#P3
> > http://boole.stanford.edu/chuguide.html#gupthes
> >
> > It seems that if we consider that LSs "evolve", then it is not trivial
> > to consider that we could think of them as "adaptive" systems, and such
> > adaptations can well represent branching time types of computations.
[HK]
> I feel you are considering here the process of our decision making. Namely you
> seem to want to solve the machinery of how we think.
Yes, in the sense that observations, as interactions, are an essential
aspect of "the machinery of how we think." Thinking without observation
and/or interaction is an contradiction...
[HK]
> > > I.e.
> > >
> > > if the direction of time does not exist, the free will does not exist,
> > >
> > > or
> > >
> > > if the direction of time exists, the free will may exist.
> > >
> > > This problem may relate with the Classical/QM features of our world: Even > > > if (2) is true, we have our free will at each stage (QM aspect), but the > > > fate as a whole is determined (Classical aspect). If (2) is not true, then > > > such restrictions do not exist and we might have true free will.
[SPK]
> > We are faced here with the ontological question of the "reality" of an
> > it-itself unknowable quantum mechanical Universe and whether its finite
> > subsets can be known.
[HK]
> Yes, the Universe might be the fate, and its finite part may be reachable for
> our hands.
I think so! :)
[SPK]
> > The method of how knowledge evolves is itself exposed to analysis.
[HK]
> Your problem seems to be to understand the mechanism of humans' recognition or
> machinery of consciousness. My position is that such knowledge could be useful
> e.g., in constructing AI, and may be gotten in some future to the extent that
> the knowledge would suffice to make AI, but I think the same problem cannot be
> a subject of science if we go down to the essential level of the problem, i.e.
> to the level of the recognition that one cannot know oneself. I.e. even if
> human could create AI creatures by their understanding of the _machinery_ of
> recognition and/or consciousness, that understanding of the machinery could
> not help us to understand ourselves more than the understanding of the
> machinery.
Umm, I understand your argument, but it is begging the question. The
measurement problem in QM seems to require a pragmatic model of
consciousness in order to "cut its Gordian knot". :) Have you read
Searle's work?
(http://cogsci.soton.ac.uk/~harnad/Hypermail/Explaining.Mind97/0030.html,
http://www.cas.ilstu.edu/PT/chinroom.htm) Penrose mentions it in his
Emperor's New Mind, I think… Your above argument seems to echo his
sentiment. I think that Peter's discussion of the interactive Turing
Machine is very relevant! ;)
Onward to the Unknown,
Stephen
This archive was generated by hypermail 2.0b3 on Sun Oct 17 1999 - 22:31:52 JST