koichiro matsuno/7129 (kmatsuno@vos.nagaokaut.ac.jp)
Thu, 18 Nov 1999 18:09:46 +0900 (JST)
Dear Stephen and All,
Stephen Paul King <stephenk1@home.com> wrote:
>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! :-)
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.
>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)?
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.
>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.
>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.
>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.
>> 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.
>> 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 eve
n
>> 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.
>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.
Cheers,
Koichiro Matsuno
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