Principles of biological organization: Local-global negotiation based on "material cause"

Yukio Gunji, Taichi Haruna, Koji Sawa

Research output: Contribution to journalArticle

18 Citations (Scopus)

Abstract

Organization of living things is characterized by dynamical hierarchical structures inheriting discrepancy among levels. It can be expressed as a system consisting of two layers; the microscopic perspective (Extent) defined by a collection of elements and the macroscopic perspective (Intent) defined by the property as a whole, and the interplay between them. First we show that if the microscopic and macroscopic perspectives are consistent with each other (an ideal case), then the operation between the two layers can be expressed as a sheaf between a lattice and a quotient lattice, where a sheaf is a mathematical operation representing the gluing process. Second, we introduce an observer who cannot look out over the whole world, and this reveals a discrepancy between the two layers. Third, we introduce a new mathematical construction, called skeleton, that is derived by the sheaf operation. The skeleton reduces the discrepancy between the micro- and macroscopic perspectives, and that reveals the perpetual transition between the perspectives. This process yields a basic framework of biological organizations. Finally, we argue that the skeleton mediating between the two levels is a particular expression for the material cause.

Original languageEnglish
Pages (from-to)152-167
Number of pages16
JournalPhysica D: Nonlinear Phenomena
Volume219
Issue number2
DOIs
Publication statusPublished - 2006 Jul 15
Externally publishedYes

Fingerprint

musculoskeletal system
Gluing
Sheaves
Skeleton
causes
Discrepancy
quotients
Hierarchical Structure
Thing
Observer
Quotient

Keywords

  • Endo-physics
  • Hierarchy
  • Lattice
  • Sheaf

ASJC Scopus subject areas

  • Applied Mathematics
  • Statistical and Nonlinear Physics

Cite this

Principles of biological organization : Local-global negotiation based on "material cause". / Gunji, Yukio; Haruna, Taichi; Sawa, Koji.

In: Physica D: Nonlinear Phenomena, Vol. 219, No. 2, 15.07.2006, p. 152-167.

Research output: Contribution to journalArticle

@article{91ff8f58209e44138fdc4289de2b0ec1,
title = "Principles of biological organization: Local-global negotiation based on {"}material cause{"}",
abstract = "Organization of living things is characterized by dynamical hierarchical structures inheriting discrepancy among levels. It can be expressed as a system consisting of two layers; the microscopic perspective (Extent) defined by a collection of elements and the macroscopic perspective (Intent) defined by the property as a whole, and the interplay between them. First we show that if the microscopic and macroscopic perspectives are consistent with each other (an ideal case), then the operation between the two layers can be expressed as a sheaf between a lattice and a quotient lattice, where a sheaf is a mathematical operation representing the gluing process. Second, we introduce an observer who cannot look out over the whole world, and this reveals a discrepancy between the two layers. Third, we introduce a new mathematical construction, called skeleton, that is derived by the sheaf operation. The skeleton reduces the discrepancy between the micro- and macroscopic perspectives, and that reveals the perpetual transition between the perspectives. This process yields a basic framework of biological organizations. Finally, we argue that the skeleton mediating between the two levels is a particular expression for the material cause.",
keywords = "Endo-physics, Hierarchy, Lattice, Sheaf",
author = "Yukio Gunji and Taichi Haruna and Koji Sawa",
year = "2006",
month = "7",
day = "15",
doi = "10.1016/j.physd.2006.06.001",
language = "English",
volume = "219",
pages = "152--167",
journal = "Physica D: Nonlinear Phenomena",
issn = "0167-2789",
publisher = "Elsevier",
number = "2",

}

TY - JOUR

T1 - Principles of biological organization

T2 - Local-global negotiation based on "material cause"

AU - Gunji, Yukio

AU - Haruna, Taichi

AU - Sawa, Koji

PY - 2006/7/15

Y1 - 2006/7/15

N2 - Organization of living things is characterized by dynamical hierarchical structures inheriting discrepancy among levels. It can be expressed as a system consisting of two layers; the microscopic perspective (Extent) defined by a collection of elements and the macroscopic perspective (Intent) defined by the property as a whole, and the interplay between them. First we show that if the microscopic and macroscopic perspectives are consistent with each other (an ideal case), then the operation between the two layers can be expressed as a sheaf between a lattice and a quotient lattice, where a sheaf is a mathematical operation representing the gluing process. Second, we introduce an observer who cannot look out over the whole world, and this reveals a discrepancy between the two layers. Third, we introduce a new mathematical construction, called skeleton, that is derived by the sheaf operation. The skeleton reduces the discrepancy between the micro- and macroscopic perspectives, and that reveals the perpetual transition between the perspectives. This process yields a basic framework of biological organizations. Finally, we argue that the skeleton mediating between the two levels is a particular expression for the material cause.

AB - Organization of living things is characterized by dynamical hierarchical structures inheriting discrepancy among levels. It can be expressed as a system consisting of two layers; the microscopic perspective (Extent) defined by a collection of elements and the macroscopic perspective (Intent) defined by the property as a whole, and the interplay between them. First we show that if the microscopic and macroscopic perspectives are consistent with each other (an ideal case), then the operation between the two layers can be expressed as a sheaf between a lattice and a quotient lattice, where a sheaf is a mathematical operation representing the gluing process. Second, we introduce an observer who cannot look out over the whole world, and this reveals a discrepancy between the two layers. Third, we introduce a new mathematical construction, called skeleton, that is derived by the sheaf operation. The skeleton reduces the discrepancy between the micro- and macroscopic perspectives, and that reveals the perpetual transition between the perspectives. This process yields a basic framework of biological organizations. Finally, we argue that the skeleton mediating between the two levels is a particular expression for the material cause.

KW - Endo-physics

KW - Hierarchy

KW - Lattice

KW - Sheaf

UR - http://www.scopus.com/inward/record.url?scp=33746323049&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=33746323049&partnerID=8YFLogxK

U2 - 10.1016/j.physd.2006.06.001

DO - 10.1016/j.physd.2006.06.001

M3 - Article

AN - SCOPUS:33746323049

VL - 219

SP - 152

EP - 167

JO - Physica D: Nonlinear Phenomena

JF - Physica D: Nonlinear Phenomena

SN - 0167-2789

IS - 2

ER -