Formal model of internal measurement

Alternate changing between recursive definition and domain equation

Yukio Gunji, Keisuke Ito, Yoshiyuki Kusunoki

Research output: Contribution to journalArticle

35 Citations (Scopus)

Abstract

We sketch a paradox generally resulting from recursivity, and propose a novel model to express evolutionary processes that requires identification of an interaction with internal measurement. In this model, a paradox is not resolved and the notion of relativity of any resolution is implicit. In a dynamical system a certain transition rule is used recursively along time. If one takes the foundation (or context) of recursivity into consideration, one obtains a fixed point or one confronts a paradox. In order to resolve this paradox, we adopt Scott's technical way to identify the form of a fixed point with a domain equation and to obtain a reflective domain, however we simultaneously show that any resolution is destined to be relative. In utilizing this notion, we construct a model of dynamical process by embedding a measurement process in one time step. Any time transition involves the process of doubting the foundation of a transition rule leading to a fixed point. Solving it and obtaining a reflexive domain is used as a new transition rule. Also, this process perpetually proceeds along time, and then the system perpetually proceeds while any solution is destined to be relative. We illustrate this type of model by using a dynamically changing contraction mapping as the interface of state and transition rule. Finally, we show that one can formalize emergent properties by using this model and discuss the relationship between endo-physics and internal measurement.

Original languageEnglish
Pages (from-to)289-312
Number of pages24
JournalPhysica D: Nonlinear Phenomena
Volume110
Issue number3-4
Publication statusPublished - 1997
Externally publishedYes

Fingerprint

Formal Model
Alternate
paradoxes
Paradox
Internal
Fixed point
Contraction Mapping
Relativity
Model
dynamical systems
embedding
contraction
relativity
Resolve
Identification (control systems)
Dynamical systems
Express
Physics
Dynamical system
physics

ASJC Scopus subject areas

  • Applied Mathematics
  • Statistical and Nonlinear Physics

Cite this

Formal model of internal measurement : Alternate changing between recursive definition and domain equation. / Gunji, Yukio; Ito, Keisuke; Kusunoki, Yoshiyuki.

In: Physica D: Nonlinear Phenomena, Vol. 110, No. 3-4, 1997, p. 289-312.

Research output: Contribution to journalArticle

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