[time 1121] Re: [time 1120] Interactions, windows and Monads (Re: [time 1105])

Stephen Paul King (stephenk1@home.com)
Wed, 15 Dec 1999 13:11:50 -0500

Dear Hitoshi,

Hitoshi Kitada wrote:
> Stephen Paul King <stephenk1@home.com> wrote:
> > > Could you explain what inconsistencies arise in more detail?
> > If we consider that the allowance of "windows" through which causal
> > connections could occur, e.g. the exchange of substances, it would seem
> > to be tantamount to allowing iterations (e.g. observations) to occur
> > between quantum mechanical systems that are by definition in a "pure"
> > state, we would be causing ourselves problems.
> I understand this. No observation is possible if the observer's local system is
> separated from the observed system.

        So, does this mean that observation, at a minimum, involves some
connection, or as you say "a merging" between the pair? I am trying to
think of a situation were we have a pair of observers, such as you and
I, and that each of us, when considered as an LS, is separate in one
sense and "merged" in another. More below... :-)
> > It seems that one is
> > trapped in the tar pit of mechanistic explanations. :-( For a possible
> > alternative see: http://www.hpl.hp.com/techreports/97/HPL-97-122.html
> > Is it necessary to have actual physical contacts between Local Systems?
> In a sense, I think so: Your message through e-mails would come to my eyes as
> emission of photons from CRT. No communication would be possible without
> physical contacts or with complete separation between the observer and the
> observed.

        Yes, but this is type of situation that is modeled in Peter's papers
and "Information Flow"! If we look carefully at the chain of exchange
between the message as I composed it in my mind to the message as it
registered in your mind we do see what appears to be a series of
physical connections. This could be used as support the tentative axiom
that a unique configuration X of classical particles connects a given
pair of LSs A and B. X would define a space-time manifold, correct?
        But, if we go on to ask about the possible relationships between the X
connecting A and B and Y connecting C and D, we find something strange.
There is no unique diffeomorphism that can transform X into Y and vise
versa; if there is, that would be a counterexample to your claim that
there is no parallel transport connection between the LSs fibering some
Riemannian manifold. Umm, I am not sure that of the mathematical details
of the definition of a connection. I will have to study this more
carefully! :-)

> > The idea I have is to consider that the interaction of minds is more of
> > a sort of "morphic-resonance" type of interaction.
> A local system as a sum of the observer's system and the observed system is the
> interaction itself between them. In this sense, I agree that interaction is a
> kind of "morphic-resonance."

        Ok, now we need to look at the situation were we have two or more
observers interacting!
> > Yes, this is one reason why I was very happy that I found this article
> > on-line. :-) Leibniz may have been very happy with the implications of
> > Quantum Mechanics as it allows for "acausal" behavior in the classical
> > local sense...
> > But, is this "acausality" truly randomness or is it perhaps merely the
> > local trace of a global causal situation such as illustrated by the
> > "secondary observers" that discussed by Peter Wegner?
> I think the latter is the case. I.e. the "acausality" would be the "local trace
> of a global causal situation" in your words.

> > > > If we are to mind the consequences of the Uncertainty Principle (UP),
> > > > we must dismiss this assumption on absolute initiality.
> > > I did not find time to see the pages you quoted below (I might have seen
> > > them
> > > before but am not sure). But if the initiality were an "absolute"
> > > initiality, it might be free from UP.
> > Umm, I disagree.
> I agree with your disagreement :-) I just thought the usage of the word
> "absolute" seemed to be inappropriate here in your context :-)

        Well, considering the way that the UP is defined in LS theory, I think
that I understand your thought here. :-) Is it correct that the UP
disappears in the limit of the bound state, e.g. the LS's infinite time?

> > The finitude of the "actuality" that any given LS could experience
> The "actuality" may be finite, but at the same time any LS is infinite in the
> sense that the LS is connected to the whole universe.

        Yes, but here I am looking for the subtle differences between the
information involved in the LS's scattering state and the bound state.
In the limit defined by the bound state, the LS is strictly bisimilar to
the total universe by what I understand of the definition given below.

> > is tied, I believe, to the finite scattering dynamics of the LS and,
> > specifically, the amount of information that it can encode.
> Any LS has an infinite amount of information as it can have it as the
> information that the complement of the LS can have. Any LS is equivalent to its
> complement by the stationary nature of the total universe.

        Yes, but like I said above, the complement of an LS when it is in a
scattering state would be different from the complement of the LS in the
bound state. The difference disappears as the exponential decay of the
scattering state evolves, correct?
        The "self-dual" nature of the equivalence of any LS to its complement,
is, I believe, the key property that makes any LS strictly bisimilar to
the total universe when and only when it is in the bound state.
        So, my question remains after this correction :-) : How do we quantify
the information content of an LS in a scattering state?

> > I am trying to find a better definition! Section 3.4 of
> > http://www.cs.brown.edu/~pw/papers/math1.ps has the best definition.
> >
> > "3.4 Bisimulation
> >
> > Equivalence is a subtle concept that may be progressively specialized
> > from equality (of all properties) to similarity (equivalence of some
> > properties) and simulation (dynamic equivalence of behavior). Symmetry
> > of equivalence gives rise to bisimilarity and bisimulation that capture
> > two-way step$B%e(Bby$B%e(Bstep simulation of processes. Bisimulation captures
> > mutual two$B%e(Bway dynamic behavior simulation between two systems,
> > and is the natural extension of static equivalence to dynamic sequential
> > interaction. Bisimulation is a coinductive equivalence relation between
> > non$B%e(Bwell$B%e(Bfounded sets that models the behavioral equivalence of
> > streams. The mathematical question ``when do two equations have the same
> > solution?'' models the computational question ``when do two systems have
> > the same behavior?''. For coalgebras, this question becomes
> > ``when do two coalgebras have the same final coalgebra?''
> > Equivalence for sets is specified by the $principle of extensionality$.
> > Two sets S, T are equal (S = T) if:
> >
> > a) for every s \element S there is a t \element T such that s = t
> > b) for every t \element T there is an s \element t S such that s = t
> >
> > Equality of sets is recursively defined in terms of equality of subsets
> > down to an arbitrary recursive level. This recursion always terminates
> > for well$B%e(Bfounded sets, giving us an inductive approach to proving set
> > equality. For non$B%e(Bwell$B%e(Bfounded sets, extensionality yields a circular,
> > coinductive form of extensionality called strong extensionality [BM]
> > that transcends inductive extensionality of finite structures. Strong
> > extensionality of non$B%e(Bwell$B%e(Bfounded sets determines equivalence of
> > infinite structures by interactive dynamic simulation processes.
> > Two sets S, T are equivalent if there exists a $bisimilarity relation$
> > R \subset S x T involving all members of S and T; R is recursively
> > defined as follows:
> > for all s \element S and t \element T, R(s,t) iff s and t are atomic and
> > s=t, or
> > a) for every s' \element s there is a t' \element t such that R(s',t')
> > b) for every t' \element t there is an s' \element s such that R(s',t')
> >
> > The primary difference between bisimilarity and the earlier definition
> > of equivalence is the replacement of extensional (inductively defined)
> > equality "='' by a coinductively defined relation R. More than one
> > bisimilarity R \subset S x T may exist for a given pair of sets S,T.
> > However, the union of all such R is unique, and is the greatest
> > bisimilarity. When bisimilarity is interpreted as equivalence of system
> > behavior for all states s \element S and t \element T, the greatest
> > bisimilarity includes all pairs of states that preserve behavior for
> > every possible action a \element A. This greatest bisimilarity expresses
> > coinductive maximality and specifies coinductive equivalence for
> > non$B%e(Bwell$B%e(Bfounded sets and the systems that they model.
> > When S and T are state sets of systems and R(s, t) means that s and t
> > have equivalent behavior, then bisimilarity expresses simulation of each
> > system by the other, and bisimilarity of sets becomes bisimulation of
> > systems. Bisimulation relations R model mutual on-line simulation of
> > sequences of actions in one system by sequences of actions in the other.
> > Bisimulation of systems is a specialized form of bisimilarity for
> > behavior equivalence between evolving systems about which we have
> > incomplete knowledge.
> > Bisimulation for coalgebras is defined by mutual simulation of their
> > system evolution functions.
> > Bisimulation of coalgebras: Two coalgebras CS = (S, m:S$B%e(B>\Lamda(S)) and
> > CT = (T, m':T$B%e(B>\Lamda(T)) are related by a bisimulation relation R
> > \subset S x T if for each s \element S and each evolution step of CS
> > there is a t \element T and evolution step of CT that preserves R, and
> > conversely."
> I see the equivalence or equality itself requires a careful argument in
> non-well-founded set theory, although it is elementary.

        So, does this help us in our work? :-)

> > Interactive systems can handle nonenumerable environments while
> > noninteractive systems can handle only enumerable environments. The
> > existence of a mathematical foundation for interactive computing
> > provides a mathematical basis for interactive models of objects and
> > distributed systems."
> > from: http://www.cs.brown.edu/people/pw/papers/ecoop99_speech.pdf
> This problem may not be a problem: As mentioned any finite LS can cope with
> nonenumerable observables by the existence itself of those nonenumerable
> observables. Any LS can use the total universe as its "memory" by the stationary
> nature of the total universe.

        Yes, but it seems that the part of the total universe that any LS has
"access" to depends on the extent to which it is bisimilar to the total
universe. When an LS is in a scattering state, far from the equilibrium
of the bound state, would there be a variable that would quantify the
information content that is the function of this "distance" from the
bound state?

> > Is it possible for LSs to observe each other without the perturbation?
> > They can not! So what is they merely are "guessing" or "simulating" each
> > the state other's inner world?
> I understand the difficulties and I agree with you on the fundamental nature of
> observation. But I do not think it necessary that an LS needs calculate or
> simulate the outside only by the "tools" inside itself; It can use the outside
> as its tools as well.
        Yes, but I am thinking that the "control" that the LS would have over
those "tools" that are outside would depend on its ability to encode and
manipulate the informational representations of such tools. This is part
of my thinking of how an LS is conscious of an external "world". This
relates to the notion that our minds are aware of only finite aspects of
the total universe.
        What we might look at for clues as to what determines the particular
set of observables that this entails is the notion of a morphic
resonance or bisimulation between the structure of the brain and the
structure of the world that it observes. Gerald Edelman's notion of
"re-entrant maps" is of particular interest to me in this regards. See:

> > > > It appears to me that the habituation of Western thought following a
> > > > materialistic and reductionistic paradigm is one root of this problem.
> > > I am interested in how this "materialistic and reductionistic paradigm" came
> > > into the western thoughts.
> > Perhaps the emphasis on the replication and implementation of
> > industrial mechanisms... We see the concepts of "time is money" and
> > "consumerism" as exemplifying this idea...
> I think industrial mechanism came after the introduction of the spirit of Modern
> age in the 17th century or around. "Time is money" and "consumerism" may be
> just the result of that spirit and express almost the final state of the Modern
> age, a final stage in the sense that it is the beginning of the next age.

        That makes sense to me. :-)

> > > Given the problem this may be a solution, but I need to understand how the
> > > western philosophy comes to the problem of mind and matter, without
> > > understanding which I think we could not go further.
> >
> > This will take some effort that may be beneficial to all of us! Is the
> > key question: "How do remote objects, situations and events carry
> > information about one another without any substance moving between
> > them?"
> This question is explained, in my opinion, due to the stationary nature
> of the total universe.

        Yes, but this holds only in the situation of the bound state of the
total universe, does it not?

Kindest regards,


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