by Hugh M. Lewis

One would be hard pressed to determine whether a totally randomized system represented one that is entirely simplified or complicated in the extreme. It would really depend upon one's primes and one's primary point of view. In detail, accounting for every detail of occurrence, a totally randomized system would appear almost infinitely complicated. 

In sum, as a whole albeit orderless, meaningless system, lacking any informational patterning except the pattern of randomness itself, such a system would be construed as simplified in a nearly absolute sense. On the other hand, a totally determined system (a physical impossibility, by the way) in which every relationship between every component is completely predictable and ordered, would represent a picture of a system that is maximally complicated if seen from a holistic point of view, where every component relationship must be specified as a unique definition of the whole system as an integrated system and a problem of integration, and a picture that is maximally simplified if understood from the standpoint of the specific relationships occurring between the determined components of the system--every variable is specified and every relationship encompassed by the system, made known.

Systems change. This is inherent to the definition of systems--they change in form and content, they develop along a given state path trajectory through a rather expectable sequence of stages. Systems structurally also remain resistant to change, and remain in structural ways consistent over time, unchanging in a relative sense. This change/stasis aspect of system is the heart of the paradox of understanding systems, their organization and behavior.

If systems change, we may state that in general they will change in terms of the relative overall degree of complexity, and they will tend towards either greater complication or, on the other hand, in the case of randomization, in the direction toward simplification of structure.

A stable system may be said to be one that maintains its overall structural profile over the long term, and though may fluctuate within a range varying about some complex set of means, will not tend overall towards greater simplification or complication over time. But in the larger scheme of things, all systems will tend toward greater complication first, and then towards greater simplification in the long run before they fall apart as systems at the given level of integration.

The tendency of any developing system to increase in complexity over time is apparent in all of nature. Associated with this increase in complexity are many factors of growth, development, progressive evolution, extension, elaboration, etc. In biological systems we associate all these processes under the rubric of "growth."

The tendency for any developing system, as a system to achieve some plateau or arc in their trajectory, which plateau may be represented by a relatively long lived and stable configuration, in which change towards complexity tends to be balanced by factors of change towards simplicity.

In the long run, changes towards simplification win out and come to predominate over a system, leading to the eventual demise of the system as such, and the return of the components of the system, to the environment in which they are situated.

This trajectory of all natural systems is well represented by a general logistic curve that is bell shaped--it may be platykurtic or fairly sharp and angular in reaching a critical changing point, but overall all natural systems, in their state-path trajectory, follow this three stage process of development, whether it be a tornado forming from a confluence of winds and large storm cloud formations, or it be a large population of rodents in a city or the development and life-cycle of the human brain.

The level of complication and complexity achieved by natural systems can be truly astounding. Because all natural systems are inherently underdetermined, such systems exhibit processes of simplicity & complexity at the same time. When we refer to chaos theory, the popular misconception of chaos is that of the total randomization of systems rather than the inherent order and simplification underlying otherwise complicated and highly elaborated systems that are undetermined in terms of their final output states.

Stable complexity or relative simplicity may be understood as the relative even ratio of input states over final input states--a static system overall would have a ratio of one or close to one. A system that has an overall trend towards complication would have a tendency towards a greater number of output states in relation to the number of input states in any given period. A system that has an overall trend towards simplification would have a tendency towards a greater number of input states in relation to the number of output states. If we set up the arbitrary rule of output over input, then we can see that as output shrinks and input grows, the denominator will grow larger and the numerator smaller, and the system value will tend to shrink as a decimal number to smaller and smaller fractions. As the output grows and the input shrinks, the net system will increase and grow larger in value. I would call this the value of relative complication of a system.

It can be seen that in very complex systems, sub-cycles occur or develop that may tend in one direction or the other in terms of their value of simplification/complication. Some sub-cycles can be in a trend towards complexity, counteracting the trend of other sub-cycles toward simplification. The net balance of these cycles of complexity/simplicity would thus be a measure of the overall stability/instability of the system as a whole.

It should be noted that such measures would in theory be independent of the size of the system, and hence these are scale-free measures of systems. We may further speculate that if we take a ratio of the net measure of complication over the net measure of simplification of the system, we would have an estimate of the value of stability or "K" of the system over a given period of time. We would expect, according to the principles above, that as K approximates 1, it would tend towards stable equilibrium, and as it moved higher or lower in value, it would tend towards increasing instability, either in terms of complication or growth of the system, or towards simplification and demise of the system as such.

One more set of points seem worthwhile to highlight at this point, and this concerns the definition of systems in terms of the emergent properties associated with systems and used to generally characterize and classify such systems in nature. An emergent property or set of properties may be said to be the non-linear consequence of the interaction of the components of the system acting in a state of equilibrium. Properties that are stable and attributed to systems as characteristic of such systems must be properties that arise and are maintained primarily during the intermediate period of stasis of such a system, during which process of complication/simplification tend to be balanced in equilibrium.

From the standpoint of set theory, we can characterize any system as a special kind of set, defined by emergent properties that are shared by the members of the set, and that arise from the interaction of the component variables within the set. The analogy of the set to a system is not completely appropriate I believe, because a system implies relational interactions between components that do not necessarily occur in a population of a set that may be merely a collection of otherwise unrelated entities. 

The emergent properties that are associated with a particular kind of system and that are used to typify that kind of system in a general manner, regardless of the possible state variations occurring in a larger population of similar systems, may be said to be isomorphic or a synergistic consequence of the relational patterns occurring between variables of the system, and that serve to structurally stabilize the system over the long term of its trajectory. In this case, we have a clear means of deriving what amounts to a qualitative, discontinuous statement of the general emergent property associated with and typical to a certain kind of system, with the quantitative and continuous variables that underlie and account for that property or composite set of properties.

If we consider the problem for instance of anthropogenesis, or the rise of Homo sapiens in evolutionary history, we must attribute to the condition of modern human beings a complex, composite set of attributes (bipedality, language, manual dexterity, large brain, post-partum infant dependency, etc.) that cannot be isolated or taken to independently account for the human condition or for the human capacity for cultural construction and intelligent behavior. But we analytically consider each of the set of variables, both independently and in relation to all the other variables, to account specifically for those properties emergent in Homo sapiens that are used to distinguish his species as unique, and uniquely special, compared to all other life-forms on earth. Thus we have the dilemma of evolutionary explanation of the "gradual rise" of humankind on one hand or the sudden "bio-cultural miracle" of the rapid emergence of a uniquely human species. This kind of dilemma is more a hen & egg type problem that fails to see the systemic relationships between the variables involved in the explanation.

It follows that because all real or natural systems are by fact of their occurrence complex systems, then the general trend towards theoretical solution of explanation of such systems will be towards simplification. This is known in a loose way as parsimony or Occam's razor in scientific explanation. All models represent simplified versions of the real counterpart. Models are themselves real, but in simplified and reduced form, whether they are scalable or not. Inherent measures of complexity should be in theory at least scale free, hence applicable to any size model--but there are practical working limits to model construction which determines the achievable level of complexity we may obtain in such a manner. Any model is only a rough approximation of the system it seeks to represent, and it follows logically that any "system" represented by a model, or alternatively by the structural patterning of a real system, is an abstracted theoretical model of a system that is largely simplified in ideal terms in order to be as broadly generalizable as possible. In other words, any "system" as a symbolic representation of a real pattern that is somehow structured is in essence an ideal model, simplified, of the real thing or class of things and relations that it purports to represent. The difference between ideology and scientific theory in this regard is the necessary reference of the latter system of thinking and abstract representation to criteria of measurable, objective, empirical substantiation. Scientific theory must be capable of yielding sufficient explanations for phenomena that is empirically based, and that is at least partly determinative of the outputs of systems they purport to represent. The ability to informatively predict the outputs of systems, albeit in an experimental manner or through naturalistic behavioral observation, leads to the ability to physically manipulate and modulate the behavior of such systems to increase their complexity and to further determine their actual outcomes.

Solutions to complex problems always solve the Von Neumann bottleneck of the information explosion that is created by unresolved complications of systems. They lead logically to formulaic, syllogistic simplification of information in a general sense that applies to all related systems as part of larger general set that can be described taxonomically in terms of their associated characteristic attributes and emergent behavioral properties.

Of course, this does not mean that all scientific explanation must be simple and uncomplicated and that complex scientific theories cannot exist and be as equally valid as simpler models. Descriptive explanations, particularly of surface phenomena of systems, tend towards extreme complexity, and some fields that deal more directly with complexity in systems, like ecology, tend towards this kind of theoretical elaboration and complication of explanation on a descriptive level. Such fields tend to lack paradigmatically unifying, formulaic generalizations or comprehensive theories that would serve to contextualize and frame various descriptive explanations in a consistent manner. This is not because such paradigms are not possible, but only, given the inherent complexity of the systems involved, highly unlikely and very difficult to achieve. 

Supercomputing models have helped in the challenges of descriptive explanation of such complex systems, for instance and in particular in meteorology and description of weather patterns. But even with such ability to handle large amounts of information quickly and systematically, we remain little closer to actually predicting weather in a reliable manner in the long run. Weather can be modeled on the basis of a very small number of key variables, but these variables interact in complicating ways over the structure of the long run to produce extremely complex patterns with a great deal of inherent indeterminancy and chaos associated with its patterning.

General Systems Essays, Vol. I