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 language | English |
|---|---|
| Pages (from-to) | 289-312 |
| Number of pages | 24 |
| Journal | Physica D: Nonlinear Phenomena |
| Volume | 110 |
| Issue number | 3-4 |
| Publication status | Published - 1997 |
| Externally published | Yes |
Fingerprint
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 journal › Article
}
TY - JOUR
T1 - Formal model of internal measurement
T2 - Alternate changing between recursive definition and domain equation
AU - Gunji, Yukio
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.
UR - http://www.scopus.com/inward/record.url?scp=0001112719&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=0001112719&partnerID=8YFLogxK
M3 - Article
VL - 110
SP - 289
EP - 312
JO - Physica D: Nonlinear Phenomena
JF - Physica D: Nonlinear Phenomena
SN - 0167-2789
IS - 3-4
ER -