organismic sets

organismic sets

0.1

Organismic Set Theory and Relational Biology

Organismic sets

(

O

⁢

S

n

) were defined by Nicolas Rashevsky as simple set-theoretical models of organization in living organisms at discrete

integer

or zero levels by means of sets of several distinct types or order beginning at the zeroth order, and having an upper limit as the fifth or sixth order of roganization. Thus, in the case of organismic sets of zero-th order,

S

0

, the

elements

correspond to genes, and a concrete

S

0

⁢

c

is defined as the set of all genes

[

G

n

]

of a specific organism or organism type (understood as a stable biological species).

Alternatively,

S

0

⁢

c

can be defined as a set representation of any organismic genome,

G

O

, consisting of the complete set of active,

functional

genes of an organism together with controlling genes/operons. The latter are then also considered together with inputs

e

i

from the environment, as well as their activities

a

i

and

relations

R

i

⁢

j

among organismic set elements (genes in the case of

S

0

), where

i

,

j

are indices in a

countable

,

index set

I

. Thus, Rashevsky’s organismic set (OS) theory is part of

abstract relational biology

(

http://planetmath.org/AbstractRelationalBiology

), but unlike organismic networks,

metabolic-replication systems

and

organismic supercategories

, Rashevsky’s OS are only endowed with the discrete topology, and are thus the simplest model whose only connectivities to organization are through the hierarchical

lattice

structure

of the different types of OS, from

G

O

to (

O

⁢

S

n

), with

n

>

1

.
At the next level of biological organization, cells are considered as

first order

organismic sets

,

S

1

, whereas multi-cellular organisms are modeled by organismic sets of

second order

,

S

2

, whose ‘elements’ are the first order organismic sets, or cells,

S

1

. Attempts were then made by Rashevsky to expand his theory of organismic sets to organizational models of human societies. Results from such studies of

relations

between sets were considered to be far more important than the numerical or

quantitative

aspects that play such important roles in physics and chemistry. A number of interesting results were obtained by means of standard (

Boolean

) logic

predicates

applied to organismic sets and their relations. Further details can be found in the publications listed below and the references cited therein. Subsequently, autopoietic theories have enlarged upon, and also extended, the application of organismic sets to biological and ecological systems.

References

1

Rashevsky, N.: 1965, The Representation of Organisms in Terms of
Predicates,

Bulletin of

Mathematical Biophysics

27

: 477-491.

2

Rashevsky, N.: 1969, Outline of a Unified Approach to Physics, Biology and Sociology.,

Bulletin of Mathematical Biophysics

31

: 159–198.

Title

organismic sets

Canonical

name

OrganismicSets

Date of creation

2013-03-22 18:11:20

Last modified on

2013-03-22 18:11:20

Owner

bci1 (20947)

Last modified by

bci1 (20947)

Numerical id

28

Author

bci1 (20947)

Entry type

Topic

Classification

msc 92C30

Classification

msc 92B99

Classification

msc 92B20

Classification

msc 92B05

Synonym

lattices or sets of organismic structures

Related topic

OrganismicSet

Related topic

NicolasRashevsky

Related topic

AbstractRelationalBiology

Related topic

GeneticNetsOrNetworks

Related topic

ComplexSystemsBiology

Related topic

OrganismicSetTheory

Related topic

FunctionalBiology

Defines

organismic set

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