**Stephen Paul King** (*stephenk1@home.com*)

*Mon, 15 Nov 1999 07:47:32 -0500*

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Dear Prof. Matsuno,

Koichiro Matsuno wrote:

*>
*

*> Dear Stephen and All,
*

*>
*

*> At 6:36 on 12 Nov 99, Stephen Paul King <stephenk1@home.com> wrote:
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*>
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*> >Have you considered a slightly more
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*> >mathematical treatment of this picture?
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*>
*

*> I did some work on cell motility in biology to see how the leftover or
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*> the moving obstacle develops in time. What I tried was to retrieve the
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*> movement in the past progressive mode from the video-taped record of a
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*> flagellar movement registered in the present perfect mode. The non-frozen
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*> leftover driving the subsequent progressive movement is in a form of
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*> constantly migrating inconsistencies. Of course, there is no room of
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*> inconsistencies in stasis, otherwise no descriptive or mathematical endeavor
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*> for representation would be feasible. Any local act for a consistency turns
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*> out to be a cause for disturbing the preceding consistency in the
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*> neighborhood. This migration process of local inconsistencies can be
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*> formalized on a paper and concretized at least on a computer.
*

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! :-) 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)?

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...

*> >I see Mach's Principle and true concurrency
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*> >hiding here!
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*>
*

*> Agreed. Mach's principle dressed with constantly migrating
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*> inconsistencies, that are real in progress but remain virtual in the
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*> product, is the picture I have in mind. Is there any serious attempt
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*> supplementing general relativity by Mach's principle carrying such migrating
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*> 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.

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)

*> >The distinction between general and singular universals is, I also
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*> >think, important. I would like to better understand your thinking about
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*> >the relationship and differences between concrete particulars and
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*> >singular universals. I tend to think of experiences as particular
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*> >observations that could be considered in an abstract sense as
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*> >measurements, or following D. Finkelstein, experiments.
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*>
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*> Right. Measurement is about the material process of one party being
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*> constrained by another in whatever way. Thus, one party can identifiy
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*> another to the extent of being constrained by the latter. However,
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*> measurement as a movement distinguishes between measurement in progress and
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*> measurement in the product. Representation is always associated with the
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*> latter measurement in the product. At this point, migrating inconsistencies
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*> come to the surface again. If migrating inconsistencies remain in
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*> measurement in the product, there would be no hope of expecting
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*> representation since any representation remains consistent in itself and
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*> passively immobile on its own. Perhaps, we may require a underlying scheme
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*> of experiencing and transforming that further upholds measurement. What is
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*> implied is that any material body experiencing migrating inconsistencies
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*> comes to transform itself into a consistent body even for a very short
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*> while. Measurement in progress on any material body is about experiencing
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*> migrating inconsistencies and then transforming itself into a consistent
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*> body, while measurement in the product is nothing but the transformed body
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*> serving as a representation to be presented to any material bodies in the
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*> neighborhood. Nonetheless, every material body subsequently comes to
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*> experience those representaitons presented from its neighborhood again in
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*> the form of migrating inconsistencies because there is no global coordinator
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*> beforehand. Representation is destined to be updated. Measurement in the
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*> product is only part of what measurement is all about.
*

This "updating of representations" seems to be a key notion!

*> > The making of a universal statement in the present tense by any finite
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*> >entity seems to indicate automatically that the entity considers his
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*> >statement as an accurate representation of the universal and this seems
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*> >to follow the way that observers in general always have their own
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*> >standards with which to make observations. It seems to me that there
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*> >exists a tacit solipsism inherent in this notion that is not problematic
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*> >if we remember that there exists more than a single observer. The
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*> >"crowd" metaphor is applicable!
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*>
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*> Right. There is no representation unless the updating scheme is equipped.
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*>
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*> >The crowd is not an individual at the
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*> >same level as any person that makes it up, but crowds of persons can be
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*> >considered as individuals in comparison with each other.
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*> > Perhaps this line of thinking will help deal with a difficulty that
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*> >Lance and I have encountered with the mathematical notions of sets and
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*> >classes!
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*>
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*> Although I am not familiar with what you have talked about, I
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*> deliberately avoided referring to the notion of classes in the above.
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*> 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.

*> > A question: Are conservation laws necessarily general universals in the
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*> >sense that they apply equally to all possible agents/observers in a
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*> >strict quantitative sense or merely qualitatively? For example, in the
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*> >case of the conservation laws that involve time reversal symmetry, is
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*> >this only absolute in the limit of all possible clockings?
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*>
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*> Briefly, conservation law in stasis or in representation is an
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*> abstraction and accordingly, a general universal. This is in fact an
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*> abstraction in the sense that migrating inconsistencies are abstracted out.
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*> If we understand whatever conservation law in the form of a representation,
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*> there would be no possibility of appreciating constantly migrating
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*> inconsistencies. A supreme example dismissing those migrating
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*> inconsistencies is time-reversal conservation laws, in which globally
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*> synchronous time is introduced as a global coordinator for the purpose.
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I agree! There does seem to be a relationship between static

consistency and a "global coordinator".

*> Now, here is one exception. That is the first law of thermodynamics. It
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*> states the transformation of energy, say, between thermal and mechanical
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*> energy while its total quantity is conserved. The first law already
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*> incorporates into itself both activities of experiencing and transforming.
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*> Precisely for this reason, we can expect to approach its representation even
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*> for a very short while before its inevitable next updating without
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*> 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? :-)

*> > Peter Wegner would say that "observers perceive only the observational
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*> >equivalence classes to which objects belong and not the objects
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*> >themselves". I think that the notion of a record as it relates to it
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*> >remaining in present perfect mode needs to considered carefully. Perhaps
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*> >Barbour's ideas about "time capsules" can seed this thinking... so long
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*> >as we recognize the error of assuming that the subsets of the Universe
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*> >can have time even if the whole has none...
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*>
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*> I believe I can understand your caution. If we consider a particular
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*> representation without paying much attention to its inevitable updating, the
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*> sturdy problem surrounding a thing-in-itself, its representation and
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*> classification may become unavoidable. My strategy at this moment is to keep
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*> a distance as much as possible from this tough question.
*

Ok.

*> > It looks like the "non-frozen leftover" is analogous to the "missing
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*> >information" that is always needed to complete in the Goedelian sense
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*> >any model of the Universe.
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*>
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*> I can follow you on this point.
*

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 )

*> >The idea of a perpetual indefiniteness
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*> >driving time "forward" is very close to my thinking that there is a deep
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*> >relationship between the "tendency of closed system to go to
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*> >equilibrium" and the asymptotic approach to Goedelian completeness by
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*> >logical systems. I see this implicit in Pratt's thinking
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*> >(http://boole.stanford.edu/chuguide.html#ratmech), but am still having
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*> >trouble articulating this idea clearly.
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*> >
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*> Thanks for your info. Give me some time to catch up with.
*

Sure! :-)

*> Cheers,
*

*> Koichiro Matsuno
*

Kindest regards,

Stephen

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