Deterministic and Stochastic Models of Biological Systems
49
the body and for the S's certain geometric or analytic idealizations, obtained by analogy with simple physical or engineering systems, to represent
the lungs, heart, arteries, capillaries, veins, etc.
c. Environment E. Conceptually, a distinction or separation between a
biological system and its "environment", because of the open nature of
biological processes and their activities, seems neither desirable nor possible.
For this reason, we include it alongside the composition and structure of a
system, as an additional component of a biosystem 6. It is particularly
a relative and arbitrary matter, depending on the degree to which it is biologically interpretable and reasonable in a given situation, to distinguish
between, in effect, a target "subsystem" and a larger system which contains
it. Perhaps the biological situation can be compared to certain mathematical
situations. Thus, topology may be said to be concerned with global properties of surf aces (or "topological systems") of two kinds: 1. intrinsic topological
properties entirely confined to a given surface and 2. extrinsic or imbedding
properties that depend on the relationship of that surface to its spatial environment. Many biological systemic properties by analogy might be called "extrinsic" and hence dependent on their "environment" in any sense of the term.
In general, it seems that one could only safely say that included in
environment E of a system 6 are all other biological, chemical and physical
systems that can in some sense be regarded as secondary or supportive to
those aspects of all living matter which have been arbitrarily included in
the enumeration of parts C und S of a biosystem 6. Thus for greatest
clarity we might write out the notation 6 (C, 5, E, F, t) for a biosystem
more completely as 6 (C, 5, F, I: E (C', 5', F', I')) to indicate that the total
biosystem 6 includes the "target system" (C, 5, F, t) and its associated
environmental system E (C', 5', F', t'). Further remarks on the environment are included in section e.
d. The Functions F, or Activities of a Biological Syslem 6. It is also considered that associated with a given biological system 6 is a set of biological,
physical or chemical activities F which, in molecular- or biomathematicalset theoretic terms, are representable as transformations T with domains and
ranges in the C-, 5-, or E-sets of 6. The set F of such transformations
includes simple and complex chemical and biochemical reactions, metabolic
activities, the events of protein synthesis, cellular and other growth and
development processes, struggles for existence between different populations of organisms, epidemic processes, etc.-in short, all the dynamic aspects
of a system taking place within and between its various components and
associated also with interactions and exchanges between that system and
its environment.
As noted in previous papers [4, 8, 9], it would appear possible to infer
an algebra of such functions and activities which translates directly into
appropriate mathematical models.
4 3. Symp. Quant. BioI.
49
the body and for the S's certain geometric or analytic idealizations, obtained by analogy with simple physical or engineering systems, to represent
the lungs, heart, arteries, capillaries, veins, etc.
c. Environment E. Conceptually, a distinction or separation between a
biological system and its "environment", because of the open nature of
biological processes and their activities, seems neither desirable nor possible.
For this reason, we include it alongside the composition and structure of a
system, as an additional component of a biosystem 6. It is particularly
a relative and arbitrary matter, depending on the degree to which it is biologically interpretable and reasonable in a given situation, to distinguish
between, in effect, a target "subsystem" and a larger system which contains
it. Perhaps the biological situation can be compared to certain mathematical
situations. Thus, topology may be said to be concerned with global properties of surf aces (or "topological systems") of two kinds: 1. intrinsic topological
properties entirely confined to a given surface and 2. extrinsic or imbedding
properties that depend on the relationship of that surface to its spatial environment. Many biological systemic properties by analogy might be called "extrinsic" and hence dependent on their "environment" in any sense of the term.
In general, it seems that one could only safely say that included in
environment E of a system 6 are all other biological, chemical and physical
systems that can in some sense be regarded as secondary or supportive to
those aspects of all living matter which have been arbitrarily included in
the enumeration of parts C und S of a biosystem 6. Thus for greatest
clarity we might write out the notation 6 (C, 5, E, F, t) for a biosystem
more completely as 6 (C, 5, F, I: E (C', 5', F', I')) to indicate that the total
biosystem 6 includes the "target system" (C, 5, F, t) and its associated
environmental system E (C', 5', F', t'). Further remarks on the environment are included in section e.
d. The Functions F, or Activities of a Biological Syslem 6. It is also considered that associated with a given biological system 6 is a set of biological,
physical or chemical activities F which, in molecular- or biomathematicalset theoretic terms, are representable as transformations T with domains and
ranges in the C-, 5-, or E-sets of 6. The set F of such transformations
includes simple and complex chemical and biochemical reactions, metabolic
activities, the events of protein synthesis, cellular and other growth and
development processes, struggles for existence between different populations of organisms, epidemic processes, etc.-in short, all the dynamic aspects
of a system taking place within and between its various components and
associated also with interactions and exchanges between that system and
its environment.
As noted in previous papers [4, 8, 9], it would appear possible to infer
an algebra of such functions and activities which translates directly into
appropriate mathematical models.
4 3. Symp. Quant. BioI.