Models, models …
perhaps they are the poetry of mathematics or,
the other way around,
mathematics is poetry
The term Organismic Sets described a puzzling and difficult area of research that apparently appears nowadays forgotten, for recent publications cannot be pinpointed. The objective here intends to find out what this subject deals with, not trying to go deeper in its intrincacies, for it would exceed by far the possibilities of the article. Instead, the article only calls the attention and perhaps stimulates the young mathematically oriented researcher.
The word organismic is defined by the Free Dictionary as something related to or belonging to an organism considered as a whole. Immediately thereafter, it adds a short sentence: the organismic theory of the state [1]. In fact, such sentence instead of clarifying brings confusion. Thus, the origin of these words needs to be better determined.
Who first came up with these terms?
Soon, one gets into organismic theories in psychology, defined as a family of holistic theories that tend to stress the organization, unity, and integration of human beings expressed through each individual’s inherent growth or developmental tendency. Holistic, as an adjective, means encompassing the whole of a thing, and not just the part. In philosophy, it is characterized by the belief that the parts of something are intimately interconnected and explicable only by reference to the whole. In medicine, it is characterized by the treatment of the whole person, taking into account mental and social factors, rather than just the symptoms of a disease.
Well, new terminology shows up quickly giving the impression of complexity. The idea of an explicitly organismic theory dates at least back to the publication of a book by Kurt Goldstein in 1934. It deals with psychology and neurology, first published under the title, in German, Der Aufbau des Organismus: Einführung in die Biologie unter besonderer Berücksichtigung der Erfahrungen am kranken Menschen. After the rise of Hitler, Goldstein escaped to Amsterdam, where he presented his ideas. Soon they became his magnum opus. Its first English version, with only minor revisions, appeared in 1939. Another English translation was published in 1995: The Organism: A Holistic Approach to Biology Derived from Pathological Data in Man. Observe that the translation of the title does not exactly follow its German counterpart.
Goldstein (1878–1965), a German neurologist and psychiatrist, created the holistic theory of the organism. Educated in medicine, his clinical work inspired the establishment of the Institute for Research into the Consequences of Brain Injuries. As a Jew, Goldstein was forced to leave Germany when Hitler came to power. The book Goldstein wrote in 1934 was focused on patients with psychological disorders, particularly cases of schizophrenia and war trauma, and their ability to readjust to substantial losses in central control. He produced the principle of self-actualization, defined as the driving force that maximizes and determines the path of an individual, i.e., the tendency to update itself as fully as possible. It is a basic drive, the drive of self-actualization.
Other contributions and terms followed suit
The rather long and detailed article by Walter M. Elsasser [2], based on a series of other articles published previously in 1961, 1962, and 1963, represents no doubt a remarkable contribution from which we have here drawn considerable information. He gives a sequence of definitions, assumptions, and propositions, with connecting and explanatory text. Organismic theory is not identical with biological theory. It inquires into the possible modes of behavior of inhomogeneous systems recalling the differences from the behavior of the macroscopic homogeneous systems usually considered in physics and chemistry. This author recognizes the validity of the laws of quantum physics in the organism but, at the same time, also realizes that novel methods of analysis are required to take into account the tremendous complexity and inhomogeneity that is found in living organisms. They are in no way comparable to those encountered in the inorganic world.
Nicolas Rashevsky (1899–1972) was a Russian-born physicist who was one of the pioneers of mathematical biology and is also considered the father of mathematical biophysics and theoretical biology. He came to the USA in 1924, settling down at the University of Chicago, where he headed the unforgettable Committee on Mathematical Biology. Before, he had worked for some time in other places. He delved also in organismic sets, which he defined as a simple set of theoretical models of organization in living organisms at discrete integer or zero levels by means of sets of several distinct types at the zeroth order, and having an upper limit at the fifth or perhaps sixth order, too. Thus, in the case of organismic sets of zeroth order, the elements correspond to genes. Thereafter, he defined the set of all genes of a specific organism or organism type [3]–[5].
New concepts, new terminology
This new area of science brought a number of words as, for example, the organic metaphor, which understands organizations as organisms that go through continuous change along its life cycle in the face of internal or external challenges. It represents a significant concept recognizing a direct influence from inside psychology, in turn, from gestalt psychology. Gestalt, in German, is more or less equivalent to overall shape, configuration, or appearance. Gestalt psychology refers to perception and behavior from the standpoint of an individual’s response to configurational wholes underlining psychological and physiological events and rejection of discrete events of stimulus, perception, and response. This approach is often contrasted with mechanistic and reductionist perspectives in psychology [6]. Holism and reductionism appear as opposite concepts, as mentioned before. For the reductionist the simple is the source of the complex. In other words to explain a complex phenomenon (like human behavior) one needs to reduce it to its constituent elements. For the holist, instead, the whole is more than the sum of the parts [7]. Besides, the discussion as to whether societies are organisms and vice versa has been going on for a long time. The question requires a clear definition of the term organism trying to find any relational isomorphism, that is, is there a one-to-one correspondence between two mathematical sets? Then arises the question intending to understand 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 the products of their activities. Complex the subject, indeed. The net idea states, we emphasize by repeating what was said above, that organismic theory is not identical with biological theory.
The laws of quantum theory hold in the organism without any modifications, as they do in theoretical chemistry, in the physics of solids, and other areas of the physical sciences. In statistical mechanics, one considers the number of ways in which systems can be assigned to available states. The simplest combinatorial problem of this type consists in determining the number of ways in which N different objects can be ordered, this number being
Z = N ! ~ NN
thus, log2(Z) = N log2 N. If here N is taken as of the order of the number of molecules in a body the size of a small cell, say, N will be a very large number, and so will be its logarithm. The number Z, above, is an immense number. There exists no common convention as to when a number is to be considered large, this being usually a matter of day-to-day convenience. For example, infinite distance many times means only a few meters. The definition of an immense number may reduce to that of a large number. In practice, we may assume that a number is large if it is of the order of a few hundred. The number of organisms, or cells, of any class existing on the earth while it may be extremely large, is not immense. Every organism changes its internal chemical and electrochemical configuration all the time. We can assume, for example, that a cell changes its internal configuration every microsecond. This is a system event. The number of system events is equal to the lifetime of the object measured in an appropriately small unit. System events in any class of organisms may be very large, but it is a finite number, perhaps a number between 1060 and 1080 as a possible upper limit. This number, however, is immensely small compared to the number of quantum states. In organismic theory, the mathematical tool of description is an abstract structure designated as Finite Universe of Discourse (FUD), another concept that must be kept in mind. So far, so good, for stating basic general ideas.
Discussion
Herein, only a very simple and incomplete notion of organismic sets is given. The reader may become attracted by the subject even considering its great complexity. One question easily comes up: Are there people still working in this area? A search carried out by the author did not produce satisfactory results. Does this mean that the subject has been abandoned or forgotten?
References
- [Online]. Available: https://www.thefreedictionary.com/organismic
- W. M. Elsasser, “Synopsis of organismic theory,” J. Theoret. Biol., vol. 7, no. 1, pp. 53–61, Jul. 1964.
- N. Rashevsky, “Organismic sets: Outline of a general theory of biological and social organisms,” Bull. Math. Biophys., vol. 29, no. 1, pp. 139–152, Mar. 1967.
- N. Rashevsky, Organismic Sets: Some Reflections on the Nature of Life and Society, Grosse Point Park, Holland, MI: Richards Laboratory, 1972.
- N. Rashevsky, “Organismic sets. Scientific creativity, its spread and applications,” Bull. Math. Biol., vol. 35, pp. 339–344, Feb.–Apr. 1973.
- [Online]. Available: https://en.wikipedia.org/wiki/Organismic_theory
- [Online]. Available: https://www.simplypsychology.org/reductionism-holism.html