Stephen Paul King (stephenk1@home.com)
Fri, 19 Nov 1999 01:30:45 -0500
Dear Prof. Matsuno,
I have combined your last two post to reply to them in a coherent
fashion. ;^) Please forgive the brevity of my responses. By the way, are
you familiar with the work of Howard Pattee?
(http://www.c3.lanl.gov/~rocha/pattee/)
I am reading your paper
(http://bio.nagaokaut.ac.jp/~matsuno/preprints/krakow99.html) to
understand better your mode of thinking...
koichiro matsuno/7129 wrote:
>
> Dear Stephen
>
> Thanks for your remarks. Since I am now in a trip, my response to
> yours to the Time List will be sent a little bit later.
>
> > About the work of Vaughan Pratt: Perhaps it would be better to go to
> >Pratt's site (http://boole.stanford.edu/chuguide.html) and start reading
> >with a paper that strikes your fancy. Perhaps
> >http://boole.stanford.edu/chuguide.html#ph94 would be good.
>
> I shall examine it after I return to my office.
[SPK]
> > One small request. I would like it if you could give us a definition of
> >the terms "present progressive", "present perfect" "universal singular"
> >and "universal general" that you use in your writings. I wish to be sure
> >that we understand your ideas and I believe, with Hitoshi, that you have
> >many important ideas to communicate. :-)
[KM]
> To define something indefinite definitely is a funny endeavor, but
> let me give it a try. The present progressive is about an agency of
> making distinctions in progress, and any material body is such an agency.
Could we go so far as using this statement as a formal theorem? It is
interesting in that it focuses on the capacity of "making distinctions
in progress" as a fundamental property of material bodies. The notion of
Local Systems (LS) as clocking agents follows a very similar vein. :-)
> The inevitable consequence is that both the temporal and spatial horizons
> towards the agency remain finite. Conversely, the present progressive is
> inevitable to such an observer or any mateiral agency having only the
> finite horizons for both space and time. At the least, time is upon the
> relational activity between a clock of whatever sort and another agency
> which reads it as such. (I suspect that Hitoshi is saying almost the
> same thing.) The present progressive is about the activity of
> synchronizing a whole bunch of clocks. If the universe consists of more
> than three clocks, the synchronization, once started, would neither stop
> nor be completed. Of course, one attribute of a clock is to read other
> clocks nearby.
The relationship between the finiteness of an observers spatial and
temporal horizons and its ability to make distinctions is, I agree, very
important! I have been thinking of the computational "simulation"
capacities of a LS as being a measure of this finiteness toward the
goal of a "bisimulational model of LS interaction.
We might consider this metaphorically as being a measure of how much
can be "held consistent simultaneously". I think that we could agree
that the complement of migrating inconsistencies is a moving locus of
consistency.
The capability of moving the boundary of the collection of
mutually consistent statements or representations has a very good
pedagogical explanation in the notion of synchronizing a whole bunch of
clocks.
> The present perfect is about the record of distinctions completed.
> The record must be consistent internally, otherwise no such record. The
> principle of the excluded middle applies there. However, it intrinsically
> lacks the capacity of making further distinctions. The factor driving the
> present progressive is the migrating inconsistencies among the concurrent
> mateiral agencies. The migrating inconsistencies violating the principle
> of the excluded middle are universally singular in the sense that if the
> whole is cut into pieces, the inconsistencies would be destroyed because
> of the forced halting of their migrations.
The idea of selectively applying the principle of the excluded middle
(PEM) reminds me of my silly idea of constructing a set theory that is
analogous to Riemannian geometry, the latter has a variable local
geometry while the former would have a variable membership and/or
subsethood...
The way that records "freeze" consistencies, I believe, is important to
note. But we should also note that the material in which the consistent
record of distinctions is "engraved" is by no means eternal, it to
degrades in the thermodynamic sense...
Umm, the notion that we could halt migrating inconsistencies by
"cutting the whole into pieces" is
interesting! It looks like the situation where a geometrical manifold
where cut into small enough pieces, each piece would have zero
curvature, while the whole could have non-zero curvature. This situation
is exploited in General Relativity! The problem that I see is that the
infinitesimal pieces can not contain clocks or rulers, as Hitoshi
explains, so inconsistency is avoided by default!
What I propose is that we consider each LS as an observer having a
large but finite space-time framing at any given "instant" of their
subjective measure of time, the migrating inconsistencies come into the
picture when we consider any acceleration as a change of the total
framing.
In this regard I am in complete agreement with Matti's thinking! The
"geometric time" is not the subjective time, it is a record of the
precedence ordering within the frozen record. In other words, the flow
of time in the subjective experiential sense is a shifting from one
frozen Minkowskian manifold to another. This idea is still in a very
primitive state and requires discussion! :-)
> The present progressive is about an ongoing negotiation among material
> agencies, the present perfect is about what has been agreed upon so far
> among the concerned parties, and the singular universal is an unsettled
> agenda on the negotiating table formed and shared by all of the
> participating parties.
I like this thought! I tend to think of our common world as being
"generated" by an ongoing conversation ("negotiation" is a better word!)
between quantum mechanical systems. (This is part of my periodic
gossiping idea) What we can agree upon, in the consistency sense, is
what is called the "classical" world! The Universe as the totality of
Existence would be the grundlagen from which and into which the "ideas"
rise. I confess to being influenced by David Bohm's thought here! :-)
> This has been a note from a hotel room out of town.
>
> All the best,
> Koichiro
>
koichiro matsuno/7129 wrote:
>
> Dear Stephen and All,
>
> Stephen Paul King <stephenk1@home.com> wrote:
[SPK]
> >How familiar are you with the ideas involved in the computer science,
> >particularly the work on distributed computing? Your idea "Any local act
> >for a consistency turns out to be a cause for disturbing the preceding
> >consistency in the neighborhood" looks to me to be a very good starting
> >point for the construction of a formal model! :-)
[KM]
> Although I am only an amateur in distributed computing, the extent the
> computing could really succeed in processing migrating inconsistencies so
> far would seem to remain quite limited. What has been bothering me is that
> once a set-theoretic framework is taken seriously, the tradeoff between
> reliability and flexibility would become a tough issue.
I hope that you understand my interest in mathematical models, I
wholeheartedly agree with your thinking with regards to the difficulties
that it inherently creates. I am merely trying to generate a template or
dictionary upon with to communicate effectively with our folks. :-)
It is interesting to note that Peter Wegner has written a paper that
deals with this very issue! See Wegner, P. Trade-offs Between Reasoning
and Modeling, in Research Directions in Concurrent Object Oriented
Programming, Eds: Agha, G.; Wegner, P.; Yonezawa, A. MIT Press (1993) pp
22-41.
[SPK]
> >We need to have
> >generic definitions for "consistency" and "neighborhood" that we could
> >use to generate a set theoretic equivalent to Riemannian geometry. Are
> >you familiar with fuzzy set theory and its logic? Are you familiar with
> >the Hausdorff property
> >(http://www.cut-the-knot.com/do_you_know/Hausdorff.html)?
[KM]
> Fuzzy set theory is quite rigid and artificial in saying how the
> membership function should be defined. In other words, the theory is
> extremely competent in coping with a fuzziness as a general universal.
> By general universal, I mean a universal but not concrete enough. The
> notion of a class is a representative case of general universals. The
> definition of a class is an artifact at its best, for instance, by
> finding a commonality among those pieces obtained by dissecting
> something singularly unique.
Can this be fixed? Pun intended :-)
> >I am reminded of the notion of symmetry breaking with the visual image
> >of a moving front of crystallization and also the ideas that David Bohm
> >discusses in his many books and papers, e.g. enfolding and unfolding
> >orders...
>
> The point is how Bohm viewed his implicate order. So far, I have
> failed in finding in his writings a positive reference to migrating
> inconsistencies.
Bohm tended to focus on the moving point/field of explication, which we
can see as the complement of migrating inconsistencies...
> >I recall a paper "Anholonomic deformations in the ether: a significance
> >for the electrodynamic potentials" [by P. R. Holland and C. Philippidis
> >in Quantum Implications: Essays in honour of David Bohm, B.J. Hiley and
> >F. David Peat, eds. Routledge & Kegan Paul, 1987.] that gets close to
> >this idea but does not specifically address Mach's Principle. The work
> >of Wolfram Schommers discusses Mach's Principle, but I do not have my
> >copies on hand... Umm, I believe that the tacit assumption of absolute
> >initiality in mathematical thinking in general (see Peter Wegner's
> >discussion of this in his papers) is the chief source of the problem.
>
> The set-theoretic framework must be vulnerable to your charge. Once
> one takes the most basic irreducible fundamentals to be static, the set-
> theoretic sort of stipulations must, however, be inevitable.
Yes!
> >I think that the notion of "branching time" used in distributed
> >computing is more useful. It considers the behavior of systems such that
> >the state of the system is able to consider input as it becomes
> >available instead of being restrained to follow a priori given input. We
> >see the latter situation in the way that the Hamiltonians of classical
> >systems require the a priori definition of a Cauchy hypersurface of
> >initial positions and momenta. Since Uncertainty considerations prohibit
> >the definition of a crisp Cauchy hypersurface, would it not make sense
> >to dispense with the notion of initiality (minimality condition in
> >induction) except for very special conditions?
> >(http://arXiv.org/find/gr-qc/1/abs:+Cauchy/0/1/0/all/0/1)
>
> This is an important point. Boundary conditions, in which initial
> conditions are the special case, are about the intensities making the
> underlying dynamics concrete enough. The mechanistic dynamics is
> wonderfully peculiar in that the law of motion as a general universal
> is claimed to be supplemented by non-dynamic boundary conditions as a
> concrete particular. It cannot address dynamic boundary conditions as
> dismissing the latter simply by declaration. In contrast, the dynamics
> of migrating inconsistensies is intrinsically intensive in exercising
> the capacity of leaving none of those inconsistencies behind in the
> completed record.
This clearly reveals the shortcomings of the conventional inductive
models that assume universal initiality. By operating within
asynchronous "windows" of consistency, we can have boundary conditions
that are subjective (in that they apply to individual LSs) and not
independent of context and history.
I need to understand your notion of intensities better!
> >> Although I am not familiar with what you have talked about, I
> >> deliberately avoided referring to the notion of classes in the above.
> >> Classes are associated with general universals.
>
> >Yes. But is this necessarily so, could we define "quasi-classes" that
> >have finite or "relative" identities? I believe that the formalism of
> >Non-wellfounded sets may already do this, but I am not sure. I think
> >that the association of the membership of the class with the set of
> >greatest fixed points may be what we need here.
>
> What are classes must be an empirical issue rather than a theoretical
> one. This is my tentative bid.
Ok, but is it not an empirical model of time that we are seeking?
Perhaps I am confused... :-)
> >> Now, here is one exception. That is the first law of thermodynamics. It
> >> states the transformation of energy, say, between thermal and mechanical
> >> energy while its total quantity is conserved. The first law already
> >> incorporates into itself both activities of experiencing and transforming.
> >> Precisely for this reason, we can expect to approach its representation even
> >> for a very short while before its inevitable next updating without
> >> committing ourselves to unnecessary abstractions, .
>
> > Umm, this seems to me to connect the notion of potential energy to the
> >"non-frozen leftover"! Am I reading it correctly? :-)
>
> The issue is again about the nature of time. If globally synchronous time
> is sanctioned from the start, the mechanistic scheme would survive there.
> Potential and kinetic energies complete their whatever transactions
> instantaneously in the globally consistent manner. On the other hand,
> potential energy as a non-frozen leftover of migrating inconsistencies could
> survive only when time is taken to be locally asynchronous on the spot.
Yes, I agree! Hitoshi's model, in showing that there can be no time
associated with the Universe as a whole, denies globally synchronous
time a priori. The best we can get is an asymptotic approximation of
such in the limit od infinite interactions among the LSs! ;^)
> >Do you think that there is a more concrete relationship between the
> >"non-frozen leftover" in terms of information and potential energy? This
> >seems to connect with what B. Roy Frieden is thinking about.
> >(http://members.home.net/stephenk1/Outlaw/fisherinfo.html )
>
> Energy in general or potential energy in particular in locally
> asynchronous time incorporates into itself the capacity of constraining
> or cocretization. This attribute is nothing other than what we know under
> the banner of information, though I do know I have to do a lot of homework
> to convince our folks on this point.
I don't need much convincing of this idea, I think that it is correct.
:-)
We do, on the other hand, need to flesh out our thinking and notions so
that we can work toward implementation of the physics that is implied.
:-)
> Cheers,
> Koichiro Matsuno
Kindest regards,
Stephen
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