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1.
N. Rashevsky 《Bulletin of mathematical biology》1969,31(1):159-198
The theory of organismic sets, introduced by N. Rashevsky (Bulletin of Mathematical Biophysics,29, 139–152, 1967;30, 163–174, 1968), is developed further. As has been pointed out, a society is a set of individuals plus the products of their
activities, which result in their interactions. A multicellular organism is a set of cells plus the products of their activities,
while a unicellular organism is a set of genes plus the products of their activities. It is now pointed out that a physical
system is a set of elementary particles plus the product of their activities, such as transitions from one energy level to
another. Therefore physical, biological and sociological phenomena can be considered from a unified set-theoretical point
of view. The notion of a “world set” is introduced. It consists of the union of physical and of organismic sets. In physical
sets the formation of different structure is governed preponderantly by analytical functions, which are special type of relations.
In organismic sets, which represent biological organisms and societies, the formation of various structures is governed preponderantly
by requirements that some relations, which are not functions, be satisfied. This is called the postulate of relational forces.
Inasmuch as every function is a relation (F-relation) but not every relation is a function (Q-relation), it has been shown previously (Rashevsky,Bulletin of Mathematical Biophysics,29, 643–648, 1967) that the physical forces are only a special kind of relational force and that, therefore, the postulate of
relational forces applies equally to physics, biology and sociology. By developing the earlier theory of organismic sets,
we deduce the following conclusions: 1) A cell in which the genes are completely specialized, as is implied by the “one gene—one
enzyme” principle, cannot be formed spontaneously. 2) By introducing the notion of organismic sets of different orders so
that the elements of an organismic set of ordern are themselves organismic sets of order (n−1), we prove that in multicellular organisms no cell can be specialized completely; it performs, in addition to its special
functions, also a number of others performed by other cells. 3) A differentiated multicellular organism cannot form spontaneously.
It can only develop from simpler, less differentiated organisms. The same holds about societies. Highly specialized contemporary
societies cannot appear spontaneously; they gradually develop from primitive, non-specialized societies. 4) In a multicellular
organism a specialization of a cell is practically irreversible. 5) Every organismic set of ordern>1, that is, a multicellular organism as well as a society, is mortal. Civilizations die, and others may come in their place.
6) Barring special inhibitory conditions, all organisms multiply. 7) In cells there must exist specially-regulatory genes
besides the so-called structural genes. 8) In basically identically-built organisms, but which are built from different material
(proteins), a substitution of a part of one organism for the homologous part of another impairs the normal functioning (protein
specificity of different species). 9) Even unicellular organisms show sexual differentiation and polarization. 10) Symbiotic
and parasitic phenomena are included in the theory of organismic sets. Finally some general speculations are made in regard
to the possibility of discovering laws of physics by pure mathematical reasoning, something in which Einstein has expressed
explicit faith. From the above theory, such a thing appears to be possible. Also the idea of Poincaré, that the laws of physics
as we perceive them are largely due to our psychobiological structure, is discussed. 相似文献
2.
I. Băianu 《Bulletin of mathematical biology》1971,33(3):339-354
The representation of biological systems by means of organismic supercategories, developed in previous papers (Bull. Math. Biophysics,30, 625–636;31, 59–71;32, 539–561), is further discussed. The different approaches to relational biology, developed by Rashevsky, Rosen and by Băianu
and Marinescu, are compared with Qualitative Dynamics of Systems which was initiated by Henri Poincaré (1881). On the basis
of this comparison some concrete result concerning dynamics of genetic system, development, fertilization, regeneration, analogies,
and oncogenesis are derived. 相似文献
3.
Cull P 《Bio Systems》2007,88(3):178-184
N. Rashevsky (1899-1972) was one of the pioneers in the application of mathematics to biology. With the slogan: mathematical biophysics : biology :: mathematical physics ; physics, he proposed the creation of a quantitative theoretical biology. Here, we will give a brief biography, and consider Rashevsky's contributions to mathematical biology including neural nets and relational biology. We conclude that Rashevsky was an important figure in the introduction of quantitative models and methods into biology. 相似文献
4.
Transformations of dynamical systems are discussed in terms of adjoint, simple adjoint and weak adjoint functors. The relevance
of this approach to interpretations of nuclear transplant experiments is suggested, and three new theorems concerning the
development of biological systems are presented. Another three theorems concerning adjoint dynamical systems are proved. The
connection of these results with the theory of organismic sets developed by Rashevsky (1966, 1967a-c, 1968a-c, 1969a-c, 1971a,
b) is also investigated. 相似文献
5.
Alvin M. Weinberg 《Bulletin of mathematical biology》1939,1(1):19-22
The approximation method, recently developed by N. Rashevsky, is applied to a problem of periodic cell reactions, studied
exactly in a previous publication. The fundamental features of that previous investigation are thus obtained in a rather simple
way. 相似文献
6.
N. Rashevsky 《Bulletin of mathematical biology》1972,34(4):439-441
It is shown that from the definition of organismic sets (Rashevsky,Organismic Sets. Some Reflections on the Nature of Life and Society, Holland, Michigan, Mathematical Biology, Inc. and Grosse Pointe, Michigan, J. M. Richards Laboratory) a complete sensory
deprivation of an organismic set of ordern=2 should result in malfunctioning of the set. A generalization to higher order sets is suggested. 相似文献
7.
N. Rashevsky 《Bulletin of mathematical biology》1971,33(4):555-559
In combining the author's theories of organismic sets (Rashevsky,Bull. Math. Biophysics,31, 159–198, 1969a) and Robert Rosen's theory of (M, R)-systems (Bull. Math. Biophysics,20, 245–265, 1958), a conclusion is reached that the number of either normal or pathological phenomena in organismic sets may
occur. Those phenomena are characterized by occurring spontaneously once in a while but are not exactly periodic. Some epilepsies
are an example of such pathological phenomena in the brain. 相似文献
8.
N. Rashevsky 《Bulletin of mathematical biology》1967,29(1):139-152
The discussion as to whether societies are organisms andvice versa has been going on for a long time. The question is meaningless unless a clear definition of the term “organism” is made.
Once such a definition is made, the question may be answered by studying whether there exists any relational isomorphism between
what the biologist calls an organism and what the sociologist calls society. Such a study should also include animal societies
studied by ecologists. Both human and animal societies are sets of individuals together with certain other objects which are
the products of their activities. A multicellular organism is a set of cells together with some products of their activities.
A cell itself may be regarded as a set of genes together with the products of their activities because every component of
the cell is either directly or indirectly the result of the activities of the genes. Thus it is natural to define both biological
and social organisms as special kinds of sets. A number of definitions are given in this paper which define what we call here
organismic sets. Postulates are introduced which characterize such sets, and a number of conclusions are drawn. It is shown
that an organismic set, as defined here, does represent some basic relational aspects of both biological organisms and societies.
In particular a clarification and a sharpening of the Postulate of Relational Forces given previously (Bull. Math. Biophysics,28, 283–308, 1966) is presented. It is shown that from the basic definitions and postulates of the theory of organismic sets,
it folows that only such elements of those sets will aggregate spontaneously, which are not completely “specialized” in the
performance of only one activity. It is further shown that such “non-specialized” elements undergo a process of specialization,
and as a result of it their spontaneous aggregation into organismic sets becomes impossible. This throws light on the problem
of the origin of life on Earth and the present absence of the appearance of life by spontaneous generation. Some applications
to problems of ontogenesis and philogenesis are made. Finally the relation between physics, biology, and sociology is discussed
in the light of the theory of organismic sets. 相似文献
9.
N. Rashevsky 《Bulletin of mathematical biology》1967,29(2):389-393
It is shown that the principle of biological epimorphism (Rashevsky,Mathematical Principles in Biology and Their Applications, Springfield, Ill.: Charles Thomas, 1960) is contained in the theory of organismic sets (Bull. Math. Biophysics,29, 139–152, 1967) if an additional postulate not directly connected to mappings is made. 相似文献
10.
N. Rashevsky 《Bulletin of mathematical biology》1971,33(3):321-338
After giving a brief review of the theory of organismic sets (Bull. Math. Biophysics,29, 139–152, 1967;31, 159–198, 1969), in which the concept of relational forces, introduced earlier (Bull. Math. Biophysics,28, 283–308, 1966a) plays a fundamental role, the author discusses examples of possible different structures produced by relational
forces. For biological organisms the different structures found theoretically are in general agreement with observation. For
societies, which are also organismic sets as discussed in the above references, the structures can be described only in an
abstract space, the nature of which is discussed. Different isomorphisms between anatomical structures, as described in ordinary
Euclidean space, and the sociological structures described in an abstract space are noted, as should be expected from the
theory of organismic sets. 相似文献
11.
Joslyn C 《Bio Systems》2001,60(1-3):131-148
We provide a conceptual analysis of ideas and principles from the systems theory discourse which underlie Pattee's semantic or semiotic closure, which is itself foundational for a school of theoretical biology derived from systems theory and cybernetics, and is now being related to biological semiotics and explicated in the relational biological school of Rashevsky and Rosen. Atomic control systems and models are described as the canonical forms of semiotic organization, sharing measurement relations, but differing topologically in that control systems are circularly and models linearly related to their environments. Computation in control systems is introduced, motivating hierarchical decomposition, hybrid modeling and control systems, and anticipatory or model-based control. The semiotic relations in complex control systems are described in terms of relational constraints, and rules and laws are distinguished as contingent and necessary functional entailments, respectively. Finally, selection as a meta-level of constraint is introduced as the necessary condition for semantic relations in control systems and models. 相似文献
12.
Arthur Bierman 《Bulletin of mathematical biology》1953,15(4):509-522
A model based on enzyme localization is developed which gives rise to an apparent active transport of a metabolite into or
out of cells. The model is applied to three simple situations, using Fick's equation and the Rashevsky approximation. It is
shown that the apparent efficiency can be made as large as desired if, for constant reaction, the outer cell region is made
sufficiently small, or, for autocatalytic reaction, if the metabolite concentration in the outer region is sufficiently small.
The physical limitations imposed by this mechanism are developed for all three situations. 相似文献
13.
14.
N. Rashevsky 《Bulletin of mathematical biology》1969,31(1):199-203
Henri Poincaré (Derniere Pansées, Paris, Flamerion, 1920) makes the interesting suggestion that our space is three-dimensional
because ourvoluntary movements are those of quasi-rigid bodies in three dimensional space. Inasmuch as according to the theory of organismic sets
(Rashevsky,Bulletin of Mathematical Biophysics,31, 159–198, 1969) organisms are conceivable, perhaps in some remote parts of the universe, for which the primary voluntary
changes may be not spatial movements but changes of other physical qualities, it is pointed out that the acceptance of Poincaré's
hypothesis will require an invariance of the physical laws in an abstractn-hyperspace with respect to the choice ofm<n coordinates as the basic frame of reference. 相似文献
15.
John Z. Hearon 《Bulletin of mathematical biology》1953,15(1):23-31
The approximation method of N. Rashevsky is discussed and reviewed. It is shown that in addition to theexplicit assumptions and approximations there is involved the assumption that the rate of metabolism is the same at every point in
the cell and that theaverage rate of metabolism is different from zero. An expression is given for the error in the approximate method when the rate of
metabolism is any function of the concentration. It is also shown that a solution in theform of that obtained by the approximate method is not possible if the generalized laws of diffusion are assumed to apply.
A portion of this work was performed while the author was a research participant, Oak Ridge Institute of Nuclear Studies,
assigned to the Mathematics Panel, Oak Ridge National Laboratory. 相似文献
16.
N. Rashevsky 《Bulletin of mathematical biology》1968,30(3):501-518
The author’s theory of imitation or mass behavior (N. Rashevsky:Mathematical Biology of Social Behavior, chapter xii, revised edition. Chicago: The University of Chicago Press, 1959; also Rashevsky:Looking at History through Mathematics, Cambridge, Mass.: The MIT Pres, 1968), when society chooses one of two mutually exclusive behaviors, is applied to the interaction
of two social groups, an oppressor group and an oppressed one. Using crude approximations, conditions are derived as to when
the oppressed group will revolt or riot, when the revolt will be suppressed, and when the oppressors will completely give
in and oppression will end. Even in the simple approximation used, the situation depends on 14 parameters showing that a simplistic
view on riots such as mere strong punishments is utterly inadequate. It is also shown that situations may exist in which revolution-like
changes from one type of behavior of a society to another cannot be prevented by any measures. 相似文献
17.
H. D. Landahl 《Bulletin of mathematical biology》1939,1(1):1-17
The recent approximate method developed by N. Rashevsky in his bookMathematical Biophysics is shown to lead to results equivalent to those obtained in the preceding paper on cell respiration. An estimate is made
of the value of the total diffusion resistance to lactic acid for unfertilizedArbacia eggs. Several more general reactions are treated to illustrate the effect of intermediate products. Expressions for the glycolytic
coefficient are derived in terms of the parameters of the cell. 相似文献
18.
H. G. Landau 《Bulletin of mathematical biology》1950,12(3):221-235
The discussion given by N. Rashevsky (1949) on the effect of imitation in the mathematical biology of social behavior is generalized
by assuming the distributions involved to be normal rather than Laplace distributions, and also by showing how most of the
results can be derived without assuming any specific form for the distributions. In particular, it is demonstrated that it
is possible, in a sufficiently large population, to have a stable behavior pattern which is quite independent of the desires
of the population or of their inherent pattern of response. 相似文献
19.
N. Rashevsky 《Bulletin of mathematical biology》1961,23(3):233-235
With a view to future applications in relational biology, the notion of relations between sets is introduced and several theorems
are demonstrated. 相似文献
20.
John Z. Hearon 《Bulletin of mathematical biology》1965,27(3):265-269
When an experimenter determines the “internal concentration” of a substance in a cell (or cell suspension) it is in general the average concentration (quantity of substance divided by cell volume or volume of cell water) which is measured. When this concentration is less than that in the ambient medium but there is either no flow into the cell or flow from the cell into the medium, then (under the usually tacit assumption of spatial uniformity in the cell) the possibility of active transport is considered. The possibility that lack of spatial uniformity could lead to apparent active transport was early proposed by A. Bierman and later examined quantitatively by N. Rashevsky for a special case. In this paper spherical cells are treated but under quite general conditions regarding the metabolic aspects of the problem. It is shown that apparent active transport can result for a metabolite which is a reactant in one set of reactions and a product in another provided the sites of these sets of reactions are spatially separated in the cell. 相似文献