TY - JOUR

T1 - Formal model of internal measurement

T2 - Alternate changing between recursive definition and domain equation

AU - Gunji, Yukio Pegio

AU - Ito, Keisuke

AU - Kusunoki, Yoshiyuki

PY - 1997

Y1 - 1997

N2 - 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.

AB - 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.

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U2 - 10.1016/S0167-2789(97)00126-7

DO - 10.1016/S0167-2789(97)00126-7

M3 - Article

AN - SCOPUS:0001112719

VL - 110

SP - 289

EP - 312

JO - Physica D: Nonlinear Phenomena

JF - Physica D: Nonlinear Phenomena

SN - 0167-2789

IS - 3-4

ER -