The concepts just indicated have often been considered to describe characteristics only of living beings, or even to be a proof of vitalism. In actual fact they are formal properties of systems.
(1) Let us assume again that the equations (3.1) can be developed into Taylor series:
We see that any change in some quantity, Q1 is a function of the quantities of all elements, Q1 to Qn. On the other hand, a change in a certain Qi causes a change in all other elements and in the total system. The system therefore behaves as a whole, the changes in every element depending on all the others.
(2) Let the coefficients of the variables Qj (j # i) now become zero. The system of equations degenerates into:
This means that a change in each element depends only on that element itself. Each element can therefore be considered independent of the others. The variation of the total complex is the (physical) sum of the variations of its elements. We may call such behavior physical summativity or independence.
We may define summativity by saying that a complex can be built up, step by step, by putting together the first separate elements; conversely, the characteristics of the complex can be analyzed completely into those of the separate elements. This is true for those complexes which we may call “heaps,” such as a heap of bricks or odds and ends, or for mechanical forces, acting according to the parallelogram of forces. It does not apply to those systems which were called Gestalten in German. Take the most simple example: three electrical conductors have a certain charge which can be measured in each conductor separately. But if they are connected by wires, the charge in each conductor depends on the total constellation, and is different from its charge when insulated.
Though this is trivial from the viewpoint of physics, it is still necessary to emphasize the non-summative character of physical and biological systems because the methodological attitude has been, and is yet to a large extent, determined by the mechanistic program (von Bertalanffy, 1949a, 1960). In Lord Russell’s book (1948), we find a rather astonishing rejection of the “concept of organism.” This concept states, according to Russell, that the laws governing the behavior of the parts can be stated only by considering the place of the parts in the whole. Russell rejects this view. He uses the example of an eye, the function of which as a light receptor can be understood perfectly well if the eye is isolated and if only the internal physico-chemical reactions, and the incoming stimuli and outgoing nerve impulses, are taken into account. “Scientific progress has been made by analysis and artificial isolation. … It is therefore in any case prudent to adopt the mechanistic view as a working hypothesis, to be abandoned only where there is clear evidence against it. As regards biological phenomena, such evidence, so far, is entirely absent.” It is true that the principles of summativity are applicable to the living organism to a certain extent. The beat of a heart, the twitch of a nerve-muscle preparation, the action potentials in a nerve are much the same if studied in isolation or within the organism as a whole. This applies to those phenomena we shall define later as occurring in highly “mechanized” partial systems. But Russell’s statement is profoundly untrue with respect exactly to the basic and primary biological phenomena. If you take any realm of biological phenomena, whether embryonic development, metabolism, growth, activity of the nervous system, biocoenoses, etc., you will always find that the behavior of an element is different within the system from what it is in isolation. You cannot sum up the behavior of the whole from the isolated parts, and you have to take into account the relations between the various subordinated systems and the systems which are super-ordinated to them in order to understand the behavior of the parts. Analysis and artificial isolation are useful, but in no way sufficient, methods of biological experimentation and theory.
(3) Summativity in the mathematical sense means that the change in the total system obeys an equation of the same form as the equations for the parts. This is possible only when the functions on the right side of the equation contain linear terms only; a trivial case.
(4) There is a further case which appears to be unusual in physical systems but is common and basic in biological, psychological and sociological systems. This case is that in which the interactions between the elements decrease with time. In terms of our basic model equation (3.1), this means that the coefficients of the Qi. are not constant, but decrease with time. The simplest case will be:
In this case the system passes from a state of wholeness to a state of independence of the elements. The primary state is that of a unitary system which splits up gradually into independent causal chains. We may call this progressive segregation.
As a rule, the organization of physical wholes, such as atoms, molecules, or crystals, results from the union of pre-existing elements. In contrast, the organization of biological wholes is built up by differentiation of an original whole which segregates into parts. An example is determination in embryonic development, when the germ passes from a state of equipotentiality to a state where it behaves like a mosaic or sum of regions which develop independently into definite organs. The same is true in the development and evolution of the nervous system and of behavior starting with actions of the whole body or of large regions and passing to the establishment of definite centers and localized reflex arcs, and for many other biological phenomena.
The reason for the predominance of segregation in living nature seems to be that segregation into subordinate partial systems implies an increase of complexity in the system. Such transition towards higher order presupposes a supply of energy, and energy is delivered continuously into the system only if the latter is an open system, taking energy from its environment. We shall come back to this question later on.
In the state of wholeness, a disturbance of the system leads to the introduction of a new state of equilibrium. If, however, the system is split up into individual causal chains, these go on independently. Increasing mechanization means increasing determination of elements to functions only dependent on themselves, and consequent loss of regulability which rests in the system as a whole, owing to the interrelations present. The smaller the interaction coefficients become, the more the respective terms can be neglected, and the more “machine-like” is the system—i.e., like a sum of independent parts.
This fact, which may be termed “progressive mechanization,” plays an important role in biology. Primary, it appears, is behavior resulting from interaction within the system; secondarily, determination of the elements on actions dependent only on these elements, transition from behavior as a whole to summative behavior takes place. Examples are found in embryonic development, where originally the performance of each region depends on its position within the whole so that regulation following arbitrary disturbance is possible; later on, the embryonic regions are determined for one single performance—e.g., development of a certain organ. In the nervous system, similarly, certain parts become irreplaceable centers for certain—e.g., reflex—performances. Mechanization, however, is never complete in the biological realm; even though the organism is partly mechanized, it still remains a unitary system; this is the basis of regulation and of the interaction with changing demands of the environment. Similar considerations apply to social structures. In a primitive community every member can perform almost anything expected in its connection with the whole; in a highly differentiated community, each member is determined for a certain performance, or complex of performances. The extreme case is reached in certain insect communities, where the individuals are, so to speak, transformed into machines determined for certain performances. The determination of individuals into workers or soldiers in some ant communities by way of nutritional differences at certain stages amazingly resembles ontogenetic determination of germinal regions to a certain developmental fate.
In this contrast between wholeness and sum lies the tragical tension in any biological, psychological and sociological evolution. Progress is possible only by passing from a state of undifferentiated wholeness to differentiation of parts. This implies, however, that the parts become fixed with respect to a certain action. Therefore progressive segregation also means progressive mechanization. Progressive mechanization, however, implies loss of regulability. As long as a system is a unitary whole, a disturbance will be followed by the attainment of a new stationary state, due to the interactions within the system. The system is self-regulating. If, however, the system is split up into independent causal chains, regulability disappears. The partial processes will go on irrespective of each other. This is the behavior we find, for example, in embryonic development, determination going hand in hand with decrease of regulability.
Progress is possible only by subdivision of an initially unitary action into actions of specialized parts. This, however, means at the same time impoverishment, loss of performances still possible in the undetermined state. The more parts are specialized in a certain way, the more they are irreplaceable, and loss of parts may lead to the breakdown of the total system. To speak Aristotelian language, every evolution, by unfolding some potentiality, nips in the bud many other possibilities. We may find this in embryonic development as well as in phylogenetic specialization, or in specialization in science or daily life (von Bertalanffy, 1949a, 1960, pp. 42 ff.).
Behavior as a whole and summative behavior, unitary and elementalistic conceptions, are usually regarded as being an-titheses. But it is frequently found that there is no opposition between them, but gradual transition from behavior as a whole to summative behavior.
(5) Connected with this is yet another principle. Suppose that the coefficients of one element, ps, are large in all equations while the coefficients of the other elements are considerably smaller or even equal to zero. In this case the system may look like this:
if for simplicity we write the linear members only.
Then relationships are given which can be expressed in several ways. We may call the element ps a leading part, or say that the system is centered around ps. If the coefficients ais of ps in some or all equations are large while the coefficients in the equation of ps itself are small, a small change in pt will cause a considerable change in the total system. ps may be then called a trigger. A small change in ps will be “amplified” in the total system. From the energetic viewpoint, in this case we do not find “conservation causality” (Erhaltungskausalitat) where the principle “causa aequat effectum” holds, but “instigation causality” (Anstosskausalitat) (Mittasch, 1948), an energetically insignificant change in ps causing a considerable change in the total system.
The principle of centralization is especially important in the biological realm. Progressive segregation is often connected with progressive centralization, the expression of which is the time- dependent evolution of a leading part—i.e., a combination of the schemes (3.25) and (3.26). At the same time, the principle of progressive centralization is that of progressive individualization. An “individual” can be defined as a centralized system. Strictly speaking this is, in the biological realm, a limiting case, only approached ontogenetically and phylogenetically, the organism growing through progressive centralization more and more unified and “more indivisible.”
All these facts may be observed in a variety of systems. Nicolai Hartmann even demands centralization for every “dynamic structure.” He therefore recognizes only a few kinds of structures, in the physical realm, those of smallest dimensions (the atom as a planetary system of electrons around a nucleus) and of large dimensions (planetary systems centralized by a sun). From the biological viewpoint, we would emphasize progressive mechanization and centralization. The primitive state is that where the behavior of the system results from the interactions of equipoten- tial parts; progressively, subordination under dominant parts takes place. In embryology, for example, these are called organizers (Spemann); in the central nervous system, parts first are largely equipotential as in the diffuse nervous systems of lower animals; later on subordination to leading centers of the nervous system takes place.
Thus, similar to progressive mechanization a principle of progressive centralization is found in biology, symbolized by time- dependent formation of leading parts—i.e., a combination of schemes (3.25) and (3.26). This viewpoint casts light on an important, but not easily definable concept, that of the individual. “Individual” stands for “indivisible.” Is it, however, possible to call a planarian or hydra an “individual” if these animals may be cut up into any number of pieces and still regenerate a complete animal? Double-headed hydras can easily be made by experiment; then the two heads may fight for a daphnia, although it is immaterial on which side the prey is caught; in any case it is swallowed to reach the common stomach where it is digested to the benefit of all parts. Even in higher organisms individuality is doubtful, at least in early development. Not only each half of a divided sea urchin embryo, but also the halves of a salamander embryo develop into complete animals; identical twins in man are, so to speak, the result of a Driesch experiment carried out by nature. Similar considerations apply to the behavior of animals: in lower animals tropotaxis may take place in the way of antagonistic action of the two halves of the body if they are appropriately exposed to stimuli; ascending the evolutionary scale, increasing centralization appears; behavior is not a resultant of partial mechanisms of equal rank but dominated and unified by the highest centers of the nervous system (cf. von Bertalanffy, 1937; pp. 131ff., 139ff.).
Thus strictly speaking, biological individuality does not exist, but only progressive individualization in evolution and development resulting from progressive centralization, certain parts gaining a dominant role and so determining behavior of the whole. Hence the principle of progressive centralization also constitutes progressive individualization. An individual is to be defined as a centered system, this actually being a limiting case approached in development and evolution so that the organism becomes more unified and “indivisible” (cf. von Bertalanffy, 1932; pp. 269ff.). In the psychological field, a similar phenomenon is the “centeredness” of gestalten, e.g., in perception; such centered- ness appears necessary so that a psychic gestalt distinguishes itself from others. In contrast to the “principle of ranklessness” of association psychology, Metzger states (1941, p. 184) that “every psychic formation, object, process, experience down to the simplest gestalten of perception, exhibits a certain weight distribution and centralization; there is rank order, sometimes a derivative relationship, among its parts, loci, properties.” The same applies again in the sociological realm: an amorphous mob has no “individuality”; in order that a social structure be distinguished from others, grouping around certain individuals is necessary. For this very reason, a biocoenosis like a lake or a forest is not an “organism,” because an individual organism always is centered to a more or less large extent.
Neglect of the principle of progressive mechanization and centralization has frequently led to pseudoproblems, because only the limiting cases of independent and summative elements, or else complete interaction of equivalent elements were recognized, not the biologically important intermediates. This plays a role with respect to the problems of “gene” and “nervous center.” Older genetics (not modern genetics any more) was inclined to consider the hereditary substance as a sum of corpuscular units determining individual characteristics or organs; the objection is obvious that a sum of macromolecules cannot produce the organized wholeness of the organism. The correct answer is that the genome as a whole produces the organism as a whole, certain genes, however, preeminently determining the direction of development of certain characters—i.e., acting as “leading parts.” This is expressed in the insight that every hereditary trait is co-determined by many, perhaps all genes, and that every gene influences not one single trait but many, and possibly the total organism (polygeny of characteristics and polypheny of genes). In a similar way, in the function of the nervous system there was apparently the alternative of considering it either as a sum of mechanisms for the individual functions, or else as a homogeneous nervous net. Here, too, the correct conception is that any function ultimately results from interaction of all parts, but that certain parts of the central nervous system influence it decisively and therefore can be denoted as “centers” for that function.
(6) A more general (but less visualizable) formulation of what was said follows. If the change of Qi be any function Fi of the Qi and their derivates in the space coordinates we have:
(7) The system concept as outlined asks for an important addition. Systems are frequently structured in a way so that their individual members again are systems of the next lower level. Hence each of the elements denoted by Q1, Q2 , …, Qn, is a system of elements Oi1, Oi2 … Oin, in which each system O is again definable by equations similar to those of (3.1):
Such superposition of systems is called hierarchical order. For its individual levels, again the aspects of wholeness and sum-mativity, progressive mechanization, centralization, finality, etc., apply.
Such hierarchical structure and combination into systems of ever higher order, is characteristic of reality as a whole and of fundamental importance especially in biology, psychology and sociology.
(8) An important distinction is that of closed and open systems. This will be discussed in Chapters 6-8.
Source: Bertalanffy Ludwig Von (1969), General System Theory: Foundations, Development, Applications, George Braziller Inc.; Revised edition.