Stephen Paul King (stephenk1@home.com)
Wed, 29 Dec 1999 13:20:19 -0500
Dear Koichiro and Folks,
I am attempting to jump start our discussions. :-) This conversation that
you are having with Hitoshi is of keen interest to me!
Koichiro Matsuno wrote:
> Dear Hitoshi and All,
>
> At 22:58 on 15 Dec 1999, Hitoshi Kitada <hitoshi@kitada.com> wrote:
>
> >Then may I ask what do you think a right way to realize consistency and the
> >completeness simultaneously?
>
> A tough question, indeed. I don't know the answer.
Perhaps the very nature of information and representations prohibits the
simultaneous realization of consistency and completeness, something akin to an
Uncertainty principle for mathematical models.
> May I add a small footnote here? Most often, we do both syntactic
> integration and semantic concretization when we try to say anything.
> Consistency is for syntactic integration, and completeness for semantic
> concretization. If both syntactic consistency and semantic completeness are
> literally synchronized with each other, Leibniz' Monadology must be the best
> buy. However, once it is legitimately noticed that semantic concretization
> proceeds in the empirical or practical domain while syntactic integration
> does in the abstract domain, the literal synchronization between the two
> would come to get into trouble.
I agree, the monadology seems to assume a perfect circumstance, like Pratt's
K=2 Chu space interpretation of Mind and Body interactions as having an lossless
involution: Mind -> Body -> Mind and Body -> Mind -> Body. This assumes that no
inconsistencies can arise in the transformation.
The synchronization between semantic concretization and syntactic
integration that you speak of here implies, to me, the strong demand of a
"pre-ordained harmony" between Mind and Body that is the weak link of the
monadology. We can think of this a trying to demand the a priori existence for a
complete mathematical model for the physical universe. LaPlacean deterministic
demon is based on this assumption.
> The second best one could imagine might be
> to let semantic concretization drive the subsequent syntactic integration
> while being driven by the necessary failure in the preceding consistent
> integration. An example of this endeavor is Karl Popper's falsification in
> the practice of empirical sciences. Any sound model conceived for an
> empirical phenomenon must be concrete enough to be falsified later. A
> positive implication of the falsification business is seen in that
> concretization persistently goes beyond syntactic integration since possible
> concretizations constantly remain innumerable.
Ah, are you echoing the property of nonenumerable that shows up in Peter
Wegner's model of interactional computation? :-) When we try to take into
account the fact that the particular structure given by any concretization (or
dually, integration) will only be finitely representable, e.g. it will always
have an epsilon of error that can not be neglected, since the requirement of a
"pre-ordaind harmony" is untenable as it tacitly assumes that infinite
information can be computed in arbitrarily small amounts of time. Basically, it
assumes the existence of a Maxwellian type of demon that can differentiate a
pair of semantic and syntactic structures that will be consistent under
arbitrary conditions without having any thermodynamic restrictions!
The role of the observer of the Universe is deeply involved in this! Both
the concrete and integrated aspects of an observer are a priori nonenumerable.
> >I do not see your "model" of the update. Could you describe it more
> >concretely?
>
> Just for the sake of argument, consider the law of action and reaction in
> classical mechanics. The third law of mechanics is about syntactic
> integration. However, implementing each action and reaction is about
> semantic concretization. If there is no synchronization between the two, the
> concretization process will have no model of making itself concrete enough
> in advance. Despite that, one likelihood of having a model on the semantic
> concretization might be to let the law in the abstract domain be fulfilled
> if each concretization in the empirical domain is properly abstracted. One
> advantage of this strategy is to enable one to say that movements in the
> empirical domain proceed so as to fulfill the third law of mechanics,
> instead of saying that movements already fulfilling the third law should
> proceed. I have a few concrete examples of this sort.
John Cramer's Interactional Interpretation of QM
(http://mist.npl.washington.edu:80/npl/int_rep/ti_over/ti_over.html) points this
out in a subtle way. The use of both advanced and retarded "signals" in the
exchange of bosons between particles within the framing of a single Minkowskian
manifold highlights that even the law of action and reaction has subtle
requirements that involve the notion of migrating inconsistencies.
> Our problem is this: Once measurement or observation as a concretization
> process enters, contradictions or inconsistencies would become inevitable.
> One way to live with these inconveniences is to let the abstraction of
> syntactic integration also be part of empirical activities.
>
> >So you set the basis on our existence?
>
> Right.
The concretization process, such as occurs in a measurement involving
pointer readings or bubbles in the bubble chamber, breaks the symmetry of the
Universe as a totality, thus only a finite consistency is manifested. The
complementary inconsistencies are "pushed" outward, as it were, away from the
locus of manifestation (both concretization and integration together). The
effect of this process, I believe, is deeply connected with the notion of
entropy!
> >Completeness is implicitly assumed in our daily life: We always think we
> >said
> >what we want to express fully well, but it is usually an illusion. This is
> >the
> >case also in sciences, which is the cause that we need to make
> >communications
> >forever. If completeness had been realized, we need not exist.
>
> Surely.
Yes, this is the subtle notion behind my statement that Time exists because
everything can not happen at once.
> Cheers,
> Koichiro
Kindest regards,
Stephen
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