A PARADIGM FOR COMPLEX SYSTEMS

As we can see from the writers we have reviewed, while hierarchies play an important role in each description of complexity, the definition of hierarchy is influenced by the field of the writer, and so is his conception of complexity. Partly, as Kenneth Boulding warned, we must be careful not to expect too much from a single theory. "General System Theory does not seek to establish a single, self-contained general theory of practically everything." Such an attempt would be absurd. "All wúe can say about practically everything is almost nothing," Instead, he suggests, that general systems theorists search for an "optimum degree of generality" for each level of abstraction. This optimum degree is not normally reached in classical scientific approaches. His contribution to hierarchy theory is a set of what he calls "levels of theoretical discourse,"

1. The first level is that of the static structure. It might be called the level of "framework". The patterns of electrons around the nucleus, the patterns of atoms in a molecular formula, the arrangement of atoms in a crystal, the anatomy of a gene, the cell, the plant, the animal, the mapping of the earth, the solar system, the astronomical universe.
2, The next level of systematic analysis is that of the simple dynamic system with pre-determined motions. This must be called the level of "clockworks", The solar system, of course, is the great clock of the universe from mans point of view, and the deliciously exact predictions of the astronomers are a testimony to the excellence of the clock which they study.
3 The next level is that of the control mechanism or cybernetic system which might be nicknamed the level of the "thermostat" This differs from the simple stable equilibrium system mainly in the fact that the transmission and interpretation of information is an essential parút of the system.
4, The fourth level is that of the open system or self-maintaining structure. This is the level at which life begins to differentiate itself from non-life. It might be called the level of the cell.
5. The fifth level might be called the "genetic-societal" level. It is typified by the plant and it dominates the empirical world of the botanist. The outstanding characteristics of these systems are, first a division of labor among cells to form a cell-society with differentiated and mutually dependent parts (roots, leaves, seeds, etc.). And second, a sharp differentiation between the genotype and the phenotype, associated with the phenomena of "equifinal", or "blueprinted" growth.
6. As we move upward from the plant world toward the animal kingdom, we gradually pass into a new level, the "animal" level, characterized by increased mobility, teleological behavior, and self-awareness
7. The next level is the "human" level, that is of' the individual human being considered as a system, In addition to all, or nearly all, of the characteristics of animal systems man possesses self-consciousness, which is something different from mere awareness.
8. Because of the vital importance for the individual of symbolic images and behavior based on them, it is not easy to separate clearly the level of the individual human organism from the next level, that of the " social organizations". In spite of' the occasional stories of feral children raised by animals, man isolated from his fellowús is practically unknown.
9. To complete the structure of the systems we should add a final turret of "transcendental systems", even if we may be accused at this point of having built Babel to the clouds. There are, however, the ultimates and absolutes and the inescapable unknowables and they also exhibit systematic structure and relationship,

The level of the "clockwork", Boulding said, is the level of' classical science. Beyond this level adequate theoretical models get scarcer. "The theory of control mechanisms (thermostats) has established itself as the newú discipline, or (cybernetics) and the theory of self-maintaining systems, or (open systems), likewise has made rapid strides, We could hardly maintain, however, that much more than a beginning has been made in these fields."

Boulding is a mathematician and economist, Robert Rosen approached the same questions from a different view. Whether because he was a biologist or just from looking at things in a different perspective

The levels of organization we perceive in a system, I would like to suggest, refer primarily to the multiplicity of ways in which we can interact with the system. If a system is "rich and complex" (as opposed to simply being complicated) it wúill generally happen that different kinds of state descriptions will be appropriate to describe the different activities which we can perceive. In this is the essence of the dissection of a complex system, like a living organism, into levels of structure and function. Even simple physical systems can look hierarchical to us if we can interact with them in essentially different ways.

A recurrent theme, you might have noticed, is the relationship between hierarchies that exist in a system such as structural or functional hierarchies, and those that we might apply to the system either for simplification or for pedagogical reasons. In the case of biological systems, however, structural and functional hierarchies play roles that are sufficiently obvious that they stand on their own merit. Rosen went into more detail on hierarchical levels in biological systems.

If we look at each hierarchical level as a dynamical system in its own right (which we can surely do) we begin to discern an unexpected stratum. Namely, the organization characteristics of specific levels of biological organization seem to be the same; independent of the level of organization we are concerned with. That is, there is a dictionary which will allow us to translate between the dynamical organization manifested in one biological level and the corresponding organization manifested in another level. By definition, then, this means simply that the dynamic systems arising from the intrinsic description of different levels of biological organization are models of each other.

But, as in this next quotation from Rosen, it is the interface between hierarchical levels and between separate systems on the same level that gives life its most important distinction, This interface, as he says, can be modeled using neural networks, suggesting a homology of processes.

The "on" response of a gene, mirrored in synthesis of a specific catalytic protein (enzyme) or in the appearance of the product of the reaction catalyzed by that enzyme, is the result of the interplay of two antagonistic processes, one of which facilitates the response (in this terminology called an inducer) and the other of which inhibits the response (in this terminology called a repressor). The molecules appearing as products catalyzed by gene products can play inductive or repressive roles for other genes in the cell, just as in a network of neurons any neuron can serve to excite or inhibit any other through a synapse. Using these simple ideas it turns out that there is an exact dynamical correspondence between a network of formal neurons and a network of genetic control; by using the appropriate dictionary, it is possible to apply what we know about neural nets to study developmental phenomena in a powerful way. Thus neural nets and genetic nets obey the same formal dynamical laws; they are models of each other, Yet, they represent biological organizations presenting themselves to us at completely different levels of structure and function.

This formal relationship between network and level systems might be paramount in a discussion of hierarchical biological systems, but wúhat is most important in ecological systems, is quite different. D. D. Siljak says that, "The essential characteristics of ecological models which distinguishes them from dynamic models used extensively in other natural, physical, and social sciences is the importance of interaction structure." Jackson Webster, in developing a description of' hierarchical organization in ecosystems points out that descriptions of hierarchies in other fields include statements that members of a single level structure are members of a specific class, He made the important point that this is not necessarily accurate.

In many interesting examples of hierarchies this is not so. In a structural hierarchy each element of U is composed of other elements of U. A book is a good example, A book is made up of chapters, pages, paragraphs, sentences, words, and letters. Each chapter, page, etc., may be considered an element of U, the set of all things that are part of the book. R may be interpreted as "consists of"'. A book (level 1) consists of chapters (level 2), chapters consist of pages, and so forth. R is antisymmetric -- a sentence does not consist of paragraphs, and transitive -- a book consists of letters.
Two important properties of structural hierarchies must be noted. First, the entire structure, the book, exists completely at all levels. The levels represent only different perspectives on the book. Consider the different ways a reader, publisher, printer, copy editor, and typesetter view a book. Each sees the book at a different level, yet each ultimately sees the entire book.

Another descriptive point made by some systems theorists is that the elements of one level are made exclusively of elements of the next lower level. Webster considers this a generality, "Taken out of context, a book consists not only of words, or sentences, or paragraphs, but also of the paper on which they are printed." In taxonomy a class consists of orders, not some orders, some families, etc. The relationship that defines a level structure need not even deal with physical objects it might be defined as "is more complex than". An abstract object might be defined by its dynamic behavior.

History exemplifies such a dynamic hierarchy in which R is based on behavioral frequencies. If we are interested in a very brief period of history, we might concentrate on day-to-day occurrences. However, in a comparison of political administrations. such day-to-day happenings would be glossed over in monthly or yearly generalities. At higher levels even these behaviors would be lost, such as in comparison of the Greek and Roman Empires.

We can also combine our dynamic and structural descriptions. One method in particular combines "consists of" and "behaves at a lower frequency than".

This hierarchy, known as levels of organization or: levels of integration hierarchy, is both a structural and dynamic hierarchy, Each element, that is each natural system, consists of systems of' the next lower level and is characterized by behaviors occurring more slowly than behaviors at the next lower level. Behaviors of atoms and subatomic particles occur in fractions of milliseconds. Organismic behaviors occur over hours, days, and years, possibly even hundreds of millions of years.

The usual ecological levels in levels of organization hierarchy are organisms, populations, communities, and ecosystems, Each system, to qualify as a level, should show stronger interactions among their own subsystems than between members of the same level. At the ecosystem level there is more interaction within the systems than between ecosystems. Similarly there are stronger interactions within an organism than between organisms. But in the case of populations and communities this is not necessarily true. "Phytophagous insects of a forest canopy insect community do not interact more strongly with each other than with the forest tree community. Organisms of the phytoplankton community do not interact more among themselves than with the abiotic and zooplankton components," A community is not a subsystem, it is a conceptual part of an ecosystem. Whether populations interact more with each other than with other populations depends on which you feel is a stronger activity, procreation orú feeding. You can find ecologists aligned either way. Webster resolved this when he said:

The only satisfactory subdivision of an ecosystem is into smaller physical subunits which exhibit a high level of internal interaction. A forest might be divided into canopy, forest floor, and soil subsystems; a lake might be divided into littoral, pelagic, and benthic subsystems. Within these systems the inter acting subsystems must be recognized as organisms.