A Contribution from the Theory of Hierarchies (1)

Hierarchy - "any arrangement of principles, things, etc., in an ascending or descending order."

A hierarchy is a system of organization, that organizes a number of unit members of the hierarchy into a multileveled structure consisting of a semiautonomous series of parts. Each semiautonomous part of the hierarchy, can be further divided into an additional lower-level series of semiautonomous parts. And each semiautonomous part of the hierarchy can equally be grouped with other similar parts at the same level, into a higher-level semiautonomous part. With the exceptions of units at the top or bottom of the hierarchy, each component of the hierarchy can be viewed and treated as both a small part of a higher-level part, and as consisting of a series of lower-level parts. At any random position in the hierarchy (again with the exception of the top and bottom), any particular unit exists as both a part of a higher-level unit, and as a grouping of a set of lower-level units.

Hierarchies can be closed systems, such as a Table of Organization, that have a defined top unit, and a defined bottom level of units. Alternatively, they can be open systems, where there is no clearly defined top or bottom, such as the hierarchy of physical and organizational structures of the brain. Any particular unit in an open hierarchy can be treated as the top or bottom depending on the purposes of the discussion in hand. Another popular example of an open-ended hierarchy, is the hierarchy of living things. An individual living thing, such as yourself, can be grouped into a higher-level unit of the structure called a family, and families can be grouped into societies, societies into species, species into families of species, and families of species into phyla, and so forth, until you get tired of the list, or reach a vaguely defined top that would be "All Living Things". Similarly, the same individual living thing could be regarded as a set of organs, the organs as a set of specialized cell groups, the cell groups as a set of cells, the cell as a set of cell organelles, and so forth until the vaguely defined bottom extends beyond things generally considered as living. I think you get the picture.

The term for any single unit of a hierarchy, at any arbitrary level, is "Holon". Every holon of any hierarchy, regardless of the subject of the hierarchy, will be characterized by two separate but related sets of properties. On the one hand, each holon exists as an individual, independent, and self-defining group entity whose characteristics and behaviour are determined by the interaction of its constituent parts. On the other hand, each holon exists as a defined, and dependent constituent part of a group of similar entities that constitute the higher level holon. The interactions between the members of any group, is what defines the membership in the group, and determines the characteristics and behaviour of the higher-level holon. The set of properties that establish a holon as a self-defining group entity, are termed its "Self-Assertive" properties. The set of properties that establish a holon as a dependent member of a group that makes up a higher-level holon, are termed its "Integrative" properties.

All hierarchies classify and organise things into holons defined by their self-assertive and integrative properties. Regardless of the subject matter of the hierarchy, each holon, or "pigeon-hole" in the structure will exhibit these two sets of properties. For passive entities or concepts and for static classifications, the two sets of properties will determine into which pigeon-hole a particular instance of the subject matter is classified. Consider the hierarchy of living things just mentioned. As a static classification of the concepts of living things, any particular living thing or group of living things at whatever level, can be accurately placed into the proper hierarchical classification by considering what the thing is part of, and what it consists of. In other words, by considering its integrative and self-assertive properties.

Let us consider placing into this structure, a thing labeled "Q". Now of course, we do not yet know what this "Q" is, so we can't yet place it in its proper slot. But suppose I tell you that "Q" is part of the collections of humans; that it consists of both male and female humans; that it also consists of children. You probably have a much better idea now of where to classify this thing "Q" than you did at the beginning. You know the rough area in the hierarchy, but perhaps not the exact holon. Suppose I now tell you that one of Q's Self-Assertive properties is that the constituent parts share a higher than average degree of family relationship; and there are between 20 and 200 individual parts in the group. You should now be able to pigeon-hole "Q" into the holon labeled "Tribe" that will appear in the hierarchy somewhere between "family" and "Species". The static hierarchy is most often employed to classify information and to act as a static representation of Reality at some instant in time. The holons in the hierarchy do not themselves behave. The self-assertive and integrative properties define what information is contained in each holon, and defines to which holon a particular piece of data belongs. Placing or finding an instance of the subject matter within any particular holon, will yield a large amount of information about that instance as a result of all of the integrative properties of the holons above it, and all the self-assertive properties of the holons below it in the structure.

Another, more common, kind of hierarchy is the dynamic or behaving hierarchy. Dynamic hierarchies are used to represent Reality over time, as the particular piece of Reality under discussion behaves and responds to the environment. In dynamic hierarchies, the self-assertive and integrative properties define the character of the behaviours displayed by the holon. Each holon in a dynamic hierarchy will function as an individual, independent, self-regulating and self-motivating unit, expressing its self-assertive properties. It will also function as a dependent, co-operating, and motivated member of some higher-level holon. Every holon of a dynamic hierarchy, no matter what the subject of the structure, will exhibit these two forms of behaviour. A department in a corporation, for example, will function as an integral part of the company, obeying the rules and striving for the objectives established by higher levels of management. It will also function as an independent unit, maintaining its own internal discipline and local objectives, interacting and competing in certain "legitimate" and possibly certain illegitimate ways with other departments of the company.

The rules that determine what interaction ("legitimate" or otherwise) takes place between holons at any level in a hierarchy, are part of the rules that establish the discipline and functional behaviour of the immediately higher holon. For any particular holon in a dynamic hierarchy, the internal structure of its constituent parts, the procedures for self-discipline among those parts, and the principles of self-regulation among those constituent parts determine how the holon will express its self-assertive properties. They will also determine how the holons that are its parts will express their integrative properties. At any level in the hierarchy, the objectives and constraints that a holon inherits from its parent holon, are subdivided and provided with more detail when translated down to the next lower level of holon. The objectives any holon inherits from its parent will determine the objectives of the holon's integrative behaviour. The rules for structure and discipline inherited from the parent, will define the scope within which the holon can express its self-assertive behaviour.

One of the most interesting characteristic of any hierarchy (static or dynamic), is that it is impossible to fully understand the behaviour of any particular holon by studying it in isolation. Nor is it possible to understand the behaviour of one level of the hierarchy, by studying levels other than those immediately adjacent. This is because every holon in any hierarchy possesses properties that are reflected in the rules governing the discipline, regulation, and cooperation between its parts that are not reflected in the rules operating internal to any of those parts. It is not possible, for example, to understand the full nature of a dictionary by studying only the words it contains. You must also understand the intermediate holon of the page. The intermediate "page" holon possesses characteristics not demonstrated by the "word" holons. The "page" holon, for example, possesses characteristics of size and type-font that will determine how many words will fit on the page. This will have an influence on the size of the dictionary, but is not reflected in any of the properties of the words themselves. The same sort of phenomenon exists in dynamic hierarchies. It is not possible, for example, to understand the behaviour of the human brain, by studying bio-chemistry. There are intermediate layers of the structure that possess properties governing the way in which the various parts work together. These properties will not be in evidence in hierarchical levels as far removed from each other as the mind and the molecules of the cells of the brain.

The combination of things that a holon inherits from its parent (the objectives and the rules of organisation, discipline, cooperation and competition) are termed the "Canon" of that holon. The canon that a holon will pass down to its constituent parts will consist of much of the canon inherited from its parent, but will be modified by the way in which that holon expresses its self-assertive properties. The degree to which the canon of a hierarchy will govern the behaviour of the hierarchy as a whole, depends on the "Tightness" of the hierarchy's restrictions on self-assertive behaviours. In some hierarchies (like the military for example) there is very little freedom permitted for the expression of self-assertive properties. In other hierarchies (a college for example) wide latitude is granted in the canon for the expression of self-assertive properties. In many colleges, the individual departments sometimes become almost totally independent fiefdoms of the department head. And the overall management of the college can sometimes find it very difficult to control these quasi-independent fiefdoms. The rules of behaviour, or canon, that is passed down from a parent holon to is constituent parts describe how those lower level holons will interact with each other and with other holons in other parts of the hierarchy. But they do not totally define the behaviour of each child holon. Each child holon's self-assertive behaviour is constrained by the integrative rules defined in the canon, but the child holon is free to explore the possibilities that are not specifically limited by the canon. So you cannot completely predict the full behaviour of the child holon by studying only the behaviour of the parent and the canon handed down.

And when studying any particular level or specific holon in a dynamic hierarchy, you will gain an understanding of how its parts interact, but you will not be able to understand how the next higher level in the hierarchy reacts. How each holon in a dynamic hierarchy interacts with other holons in the hierarchy can be understood in detail by examining the behaviour rules of that particular holon. But in most hierarchies, the number of possible interactions between holons is very large. And while it might be a simple problem to understand how a few of these holons interact with each other, the behaviour quickly becomes impossibly complex and effectively unpredictable when the numbers become large. In addition, it is a characteristic of dynamic hierarchies, that their behaviour is generally non-linear, especially in the more "interesting" examples. When the number of interacting holons in such a hierarchy rises beyond a very small number, the overall behaviour that is exhibited quickly becomes Chaotic. What started out as relatively simple rules of behaviour at the level of the single holon, quickly generates complex and unpredictable behaviour when the number of interacting holons becomes large.

Consider a part of a hierarchy that consists of a parent holon and four child holons in isolation. You can understand the behaviour of the parent holon in terms of the behaviour of the child holons, by examining the behavioural principles and modes of interaction of the four child holons. But to understand the behaviour of the grand-parent holon in the same terms, you would have to understand the principles and interactions of all sixteen child holons. The progression is geometric, with each layer of the hierarchy multiplying the total by the number of child holons below each parent at that level. And in the kinds of dynamic hierarchies that are encountered in Reality, sections of the hierarchies do not behave in isolation. There is almost always interactions between holons in widely separated sections of the hierarchy, and the hierarchies are almost always non-linear in their responses. Soon you will find that the holons at distant upper parts of the hierarchy you are studying, are exhibiting behaviours that are impossible to predict from an understanding of the principles and interactions of the particular lower layer of holons you are examining. The behaviour of these distant upper level holons "emerges" in an unpredictable and unexpected way from the detailed specifications of the behaviour of the hierarchy of holons that are its parts. In other words, it is impossible to understand the behaviour of the hierarchy that is the human mind, from a study of the behaviour of the nerve cells that are its parts.

At first encounter, the implications of these rather generic principles of the Theory of Hierarchies can be difficult to grasp, so lets look at a more concrete and familiar example than the Human Mind.

The Holonic Nature of Life

An individual cell is an excellent example of a hierarchical holon. As a unit of a hierarchy, the individual cell plays an important part in the cellular community that is a plant or animal. And also as a unit in a hierarchy, it is made up of a number of distinct, individual, and relatively autonomous parts (organelles). The cell, while co-operating and participating in the functioning of the total organism of which it is a part, is also efficiently self-regulating and has its own internal functions and rules. Similarly, the cell's various organelles, while co-operating and participating in the functioning of the cell, are largely independent self-regulating structures having their own internal functions.

According to current ideas in evolutionary theory, those parts of the cell that perform the most distinct functions were once individual life-forms in their own right. The mitochondria, for example, are thought to have once been similar to amoebae. The ribosomes are thought to have been bacteria. Each of these two organelles even have their own DNA, separate and distinct from the normal cellular DNA. It is thought that over the billions of years it took for life to develop to the cellular level, these once separate life-forms congregated together for mutual benefits, and developed a close symbiotic relationship. Now, of course, that symbiosis is so tight that they would not be able to survive on their own. It is from their probable origins as independent life-forms, that these and other cellular organelles inherited their self-assertive properties.

The superficial perception of Evolution as a series of random mutations at the molecular level of DNA, does not take into consideration the holonic nature of the many parts of the living cell. Nor does it consider the many holonic characteristics of the DNA molecule itself. Because many of the cellular parts are semiautonomous in nature, the vast majority of molecular mutations are corrected through the processes of self-regulation within the holons that make up the cell. Biochemical research has shown that the cell has a remarkable versatility for the correction of many kinds of malfunctions of it's parts.

Recent biochemical analysis of the nature of the DNA molecule reveals that the holonic nature of life extends even to the molecular level of the genetic coding in the genes. Analysis has shown that many genes contain repeated coding sequences to minimize the possibility of the message being scrambled through damage to one single sequence. Examination of the way that the genetic coding of the DNA molecule is translated into proteins and the other stuff of life, has shown that the procedures have extensive and remarkable capabilities for self-regulation, error correction, and damage removal.

The genetic coding structures of the cell also exhibit extensive redundancy of information. The evolution of sexual methods of reproduction was a significant contribution to genetic redundancy. For species employing the sexual method, the total set of genes present consists of two relatively independent and totally complete subsets. Each of these two subsets constitutes a complete recipe for an individual member of the species. Each of the two subsets is inherited from a different parent. Since the two recipes are never exactly the same, procedures have evolved to resolve any differences between the two messages. This process is evidenced by what is referred to as Dominant and Recessive genes. For any one particular gene-site, it takes the occurrence of two recessive DNA encodings to result in the expression of the recessive message. It only takes the occurrence of a single dominant encoding to result in the expression of the dominant message. The recessive message remains hidden and unexpressed. In this way, a malformed message in a recessive gene-site, would be less likely to be expressed to the detriment of the cell (or the organism).

In addition to the evidence for redundancy and self-correction, there is also considerable evidence for the close integration of function between the diverse parts of the genetic coding. This is the "Integrative" side of the holonic nature of the DNA. This property explains why small mutations in one part of the genetic message can result in major, but coherent alterations in the organism as a whole. Parts of the genetic message seem to adjust to changes in the other parts. Such changes have been observed to occur in the mutation of fruit flies for example. When the genes that code for larger wings are carefully transferred from one fly egg to another, the new fruit fly also develops the required larger musculature.

All of the evidence suggests that the entire genetic machinery and life system of the cell must be viewed as a dynamic hierarchy of inter-related and inter-dependent functions. Each part, down to the molecular level has its own characteristic properties of behaviour. Each holon possesses self-assertive properties that display behavioural characteristics unexplainable in terms of the properties of its parts. Yet each holon functions smoothly as an integral part in the proper functioning of the holon of which it is a part.

Viewing the evolution of the cell in this way, makes the processes hypothesized for "punctuated equilibrium" easier to grasp. The "punctuated equilibrium" theory of evolutionary progress hypothesizes that populations remain genetically stable for long periods of time, and then suddenly, over a short period of time, undergo rapid evolutionary changes. Regarding the processes of genetic interpretation as a hierarchical series of processes, we can suggest a logical methodology behind the evidence. Using the "Integrative" properties of the processes of genetic interpretation, the species accumulates a slowly increasing number of errors in the genetic material that are "hidden" because they are corrected for and suppressed. Then some threshold level of errors is reached. Once this threshold is passed, the combination of "Self-Assertive" and "Integrative" properties re-interpret the genetic code in a new but self-consistent way. What the evolutionary record then shows is a long stable period of very little morphological change, followed by a relatively short period of very rapid morphological change. What has actually happened is that a constant relatively low level of mutational changes, has suddenly been re-interpreted in a new way. A bio-chemical "paradigm shift" as it were. The error correction processes have been overwhelmed, and the self-organizational behaviour of the chemistry of the cell has been forced to interpret the genetic code in a new way. A chemical "paradigm shift" has taken place and all that shows in the fossil record is a sudden spurt of morphological change.

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Footnotes

(1) This section is a précis of the discussion of hierarchies presented in The Ghost in the Machine, by Arthur Koestler; Hutchinson Publishing Group Ltd., London, 1971; ISBN 0-330-02476-0.