Chapter XVIII

Advanced systems are fundamentally alternative abstract models and conceptual constructs rooted in mathematical theory and application, and serving primarily the heuristic function of facilitating our understanding and science about complex real systems. This heuristic function does extend systematically to general problem solving and experimental applications of alternative designs in reality, but the main purpose of this work is not such extension, but the explicit and general elaboration of the abstract representations that stand behind such applicability.

While I advance a grand prototypical model of a "metasystem" I see this as mostly a philosophical problem that serves as a central touchstone to the integration of advanced systems. It deals with a central philosophical problematic that underlies all our knowledge of reality, and that is the problem of the integration of reality. I can take the easy rode, suggested by the pressupposition of anthropological relativity of knowledge, and just say that human reality is symbolically integrated. But this sidesteps the central issues of truth and possibility, and presumes too much in the first place. From the standpoint of advanced systems sciences, this kind of answer is insufficient and unrevealing of the true complexity of the problem that brings to bear almost the whole breadth and scope of our philosophies, our mathematical knowledge systems and our sciences.

At this stage, it is quite apparent to me that solving the problem of the integration of reality require solving the implicit problem of the integration of our knowledge systems at a highly abstract, philosophical and theoretical level. In essence, I would say that both kinds of integration are two sides of the same central problem posed to us by our sense of reality in the first place. The two cannot be fundamentally alienated or dichotomized in our consideration of alternative central solutions.

The hypostatization of metasystems is therefore as much a paradigm as it is a central problem, based primarily upon a non-linear mechanical view of reality, as it is a functional model or general theory of integration of reality. I stake no claims as to its metaphysical validity or ontological status in regard to any particular real system, however large in scope or particular and finite in detail.

I seek to employ a diverse range of mathematical theories and methods to tackle an equally diverse range of problems that occur upon different levels of our knowledge and experience of reality. Within this range, the central problem of the integration of reality is approached and broached in many ways, but no where adequately solved. I deal only with those issues that I consider most important to our sense of reality and worldview, and which cannot be excluded if we are to entertain any illusions about being comprehensive. Though I make a stake in comprehensivity of perspective, I make no claims about being complete or exhaustive in this regard or in any other way. It is a beginning for other work, hopefully basic, ground breaking and foundational in some respects, but it does not stand in place of work that remains to be accomplished in the future.

It is apparent to myself at least, at this stage in my intellectual development, that if we are to make great strides in our understanding of the complexity and order presented to is at almost every point in our shared experience of reality, then we must strive to achieve a higher level of integration of our knowledge in systematic and, hopefully, nontrivial ways. This being said, it is easier said than done.

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I have approached Advanced Systems Science with the purpose of outlining a core set of theoretical structures that are hypothetically applicable to all identifiable and self-contained systems, what I call a metasystem, whether these are naturally occurring or artificially constructed and maintained systems. The potential value of such an abstracted model of advanced systems science is in its heuristic and creative application to the identification, understanding and construction of new systems in reality and to the resolution of complex problems created by actual systems. I believe that to effectively realize such a metasystem would be to allow us to better control both our sciences and the functional purposes to which science is put in the world. It serves as a touchstone for the theoretical, operational and functional integration of science at all levels and in all areas, whether this is pure or applied.

In the previous companion work Natural Systems I dealt mainly theoretically and constructively with the problem of natural systems at these primarily have been found to occur in some larger phenomenological sense, or what I would call the problem of Nature or Natural reality. In this work, I deal with a complementary set of problems that I would define as the general problem of Reality, and of how we come to know reality. This is a larger and more basic issue compared with the problem of nature. I call it in general the Reality Problem, and I propose herein the "Reality Principle" as the foundation for advanced systems science. The reality problem subsumes a larger set of problems that I call real problems, and these encompass as a subset the class of natural problems that normal science typically deals with. The implication of this is that science as a general knowledge system is tied and a part of a larger sytem of understanding reality. If we are to get at a clearer, more comprehensive, and more systematic science, then we must first get at this background system of understanding and knowledge in a more explicit manner.

Science, as this is conventionally construed, is in the birth throes of yet another revolution. This is a more general knowledge revolution than most people realize. It is an entire frameshift of our entire worldview. It encompasses the so-called Information revolution at its heart, but this information revolution is itself but one aspectual manifestation of this more general background movement. Scientific knowledge is rapidly transforming our world and our realities in ways we do not yet fully comprehend. We cannot know the long-term consequences of these kinds of tranformations, and they are as noetic and behavioral as they are tehnological and informational.

Scientific knowledge has as its central problematic the understanding of nature and natural systems, but science as a knowledge system is actually much larger in scope than this. It comes to embrace a broader range of applied fields that derive largely artificial and constructed systems that do not normally occur in nature. It then reflexively rebounds on itself at some point to attempt to understand itself as a natural system. If we are to understand and develop science as an advanced system of abstraction, inquiry and application to reality in the broadest senses of the term, then we must be willing to step beyond the normal boundaries of conventional scientific praxis. This is true especially as this has been rooted to a highly successful past, and be daring enough to explore new possibilities and new manifestations of its development and implication in our world.

The approach I take in advanced systems science is to see that for any given set of related phenomena, there is at least one possible hypothetical explanatory paradigm that works on two levels, generalistically, and applied or particularistically. These lead to construction and development of alternative working models of the system in question. The interaction between the two levels provides dialectical feedback enough to drive alternative model building in the area of concern. Underlying any coherent paradigm is in theory at least one or a set of related working models that defines the paradigmatic exemplars upon which substantiation of the theory rests. These models are generally defined in relation to some central problem upon which the parent paradigm is based.

The relationship of the paradigm to the model is that of the relationship between parent and child. Multiple models may share a single paradigm, but rarely will multiple paradigms share the same set of models unless they are competing for possession of the same space. Paradigms exist in mutually exclusive space to one another, and hence there is usually an intrinsic competition upon this level of theoretical integration & unification. Models may or may not be exclusive and hence competitive to one another. Models, I believe, exist at an intermediate level of theoretical construction and serve the purpose of mediating the very general with the phenomenal instantiation or particular events themselves. They are largely symbolic constructs that mediate our experience of reality in self-consistent ways. Models are approximate constructions rooted in our language of descriptive explanation, and lead to what can be called prototypical or archetypical exemplars that govern the articulation of paradigms. Paradigms in general define the theoretical and practical limits to systemic construction and knowledge--they are articulated and organized by means of models, and provide the ground plan and foundation for normal operationalization of scientific procedures.

While paradigms function in a manner that is comprehensive and all encompassing, tending to integrate diverse ranges of phenomena at multiple levels, models tend to be analytically particularizing and synthetically generalizaing in allowing us to recognize instances of problem sets and hence variations of phenomenal patterns. They permit is to extend the range and embrace of our understanding by systematic incorporation of new phenomena and by recognition and excoriation of new problem sets. They are an intrinsic part of the normal dialectic of scientific language and praxis by which integration of knowledge and progress in the sciences is achieved.

This dichotomization between paradigms and models may be more apparent than real, and more arbitrary than necessary, in our understanding of advanced systems science. A model may be a paradigm under some cases, especially if a paradigm is represented by a single model. A paradigm may be a model, or set of models, if it lacks a central or cohesive theoretical framework by which to interrelate the models in a more comprehensive manner. Thus paradigms can be represented by some class of models even if they lack clear or concise theoretical definition or outline. The paradigm would be said to be implicit to the class of models that are used to represent it.

But I believe that the distinction between a paradigm and a model in our theory building is important and critical in the development of our scientific understanding of systems. They do appear to be two clear and distinctive sets of entities in our theoretical constructions of science. Models can be said to represent prototypical exemplars in demonstration of a paradigmatic explanation. Paradigms can be set to define the theoretical boundaries and permutations of a hypothetical system to which models are related and by which they are themselves explained as exemplars.

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It can be said that advanced systems sciences are fundamentally and paradigmatically dialectical in their articulation and pattern of development. This is an important concept that has had an unfortunate history of misunderstanding and misappropriation. In a sense, all systems can be said to be dialectical in that there is intrinsic and extrinsic feedback both between the system and other systems, and between the system and our understanding of the system. The dialectical framework can be represented by the following kind of table:

This kind of table suggest that in our theoretical construction and reality testing processes there is in fact a complex set of relationships occurring that inform the discourse and development of models and ideas in different areas of science. I became first aware of this patterning of dialectic in my attempt to understand the paradigmatic aspects of the Anthropological sciences about a decade ago. I believe it has as much relevance of any area of scientific inquiry as it has had in the history of Anthropology or in its various sub-disciplines.

The point of emphasizing this dialectical structure of scientific inquiry is to point up its counter-paradigmatic possibilities. In whatever system of ideas we may posit, the dialectical approach allows us to step beyond the constraints of any such system, and to adopt critically and hermeneutically the antithetical viewpoints of alternative multiple systems. Thus, in the structure of our inquiry, we are able to fundamentally transcend the paradigmatic constraints of any system, and to embrace a more comprehensive synthetic understanding that allows us to understand the limited value of alternative systems.

Properly speaking, a dialectical approach that is itself non-paradigmatic, is inherently meta-paradigmatic in that it permits us to realistically weigh and compare alternative systems of understanding, while simultaneously to escape the ideological conundrums of adopting any one viewpoint exclusively.

I believe dialectical structure defines the structure of inquiry and systems as theoretical constructs, and is intrinsic to our systems sciences. Whatever point we may adopt or construe, there is always at least one contraposed counterpoint that serves to relativize our understanding, and therefore forces us to reconcile alternative realities.

The process of synthesis in dialectical development of idea systems allows our sciences to achieve the degree of transcendent integration of our understanding. It allows us to synthetically transcend analysis and to reconstruct our sense of reality in a holistic and synergistic sense. This is vital to the successful achievement of such inquiry.

It is apparent that in the sciences, as these have been formally and conventionally construed, there is a strong emphasis on analysis and often a devaluation of the role of synthesis in theoretical and operational construction. Overemphasis upon analysis to the exclusion of the role of synthesis in model building leads to a strong and pervasive form of reductionism that is quite common in research. Often times, holistic and synthetic approachs are regarded as beyond the purview of science, as essentially ascientific in character, especially when such approaches deal with mixed type problems. In general, applied fields that demands some degree of cross-disciplinary integration are construed as "impure" type sciences, or even as non-scientific approaches in engineering design. Sometimes, those who prefer to practice what they preach, often develop a negative antipathy or reaction against theory and the place of "pure" scientific activity, even to the detriment of their possible outcomes.

One of the main rationalizations of advanced systems science is the notion that this dichotomization between analytic and synthetic approaches to science can be transcended and reintegrated through the systematic achievement of both theoretical comprehensivity and functional integration of the fields of inquiry. Thus, those who do holistic and applied sciences, often regarded as impure, do not have to be segregated as non-scientists, from those who presume to pontificate on scientific theory and conduct pure research without having to be concerned with the problematics that science leads naturally to. I believe that a studied and built-in dialectical transcendence can accomplish this set of goals.

A systems approach inherently transcends and embraces the analytic-synthetic dichotomy that divides conventional science into contraposed camps of activity. Being "systems" they are both simultaneously analytically reducible as nothing but the sum of the parts and synthetically holistic and synergistic as something more than that mere sum. It can be seen that most systems actually operate or function at multiple levels simultaneously, and thus come to define a complex set of contextual relations at these different levels. To construe the functioning of a system at only one level to the neglect of its epiphenomenal patterning at other levels is to short-change the role of systems science as nothing but a hand-maiden of conventional scientific activity that is paradigmatically and somewhat dogmatically committed to narrow disciplinary interests.

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Certain basic principles of constraint seem to inform all systems. These are kinds of fundamental design features regarding all systems, as "knowledge" systems or as theoretical constructs about some set that phenomenally occurs in reality. These can be identified as the following:

Anthropological Relativity: We as subject knowers are at the center of knowledge of all systems. In general, it can be said that we can only know a system in a partial sense, and we can only infer the entire system from this partial knowledge. Our knowlege of any system is therefore by definition always incomplete and imperfect. Anthropological relativity conditions our knowledge at all levels. It is true that we are bound within our own human event horizon, which would be a solipsistic shell of objectivity if we did not have some sense of inter-subjective communication by which to test the objectivity of our constructs. But even then, often our standards of measurement themselves are bound within the same event horizon

There is more than a little bit of "Heisenbergian" uncertainty involved in all our knowledge, as it is quite true that there is a fundamental complementarity of our knowledge structures. The means we use to relate to and understand and measure our reality, affect the reality that is being measured in fundamental ways. Thus for each construct, there is always a hypothetical alternative construct available that might prove more accurate.

Anthropological relativity of knowledge does not spell disaster for our scientific understanding. In fact, it spells greater realism and objectivity for it, because it allows us self-reflexive recognition of the limitations of our own knowledge. Surely, we will never achieve absolute knowledge of reality, but we can push the relativistic limits of what we know infinitely towards the goal of an absolute model. The paradox of this is that the natural phenomenal event patterning of the universe itself is fundamentally relativisitic itself, what I will call universal physical relativity. Hence, even if we could develop a sense of objective parallax about our shared reality, especially in relation to some alternate alien form of intelligence, then we would still have the physical event horizon of our observable universe to impede our awareness of the whole of reality.

I will hypothesize therefore two sets of event horizons that operate in the theoretical-phenomenal construction of our sciences:

I would hypothesize as well an intermediate event horizon that is constituted by the biological foundation of our human intelligence. But that is an issue that I do not believe to be central to this argument except to point out that non-human biological forms of phenomenal experience and intelligence may broaden the range of possible observation and inference possible, if we can seek to comprehend these.

Universality: All delimited systems are subsets of a larger infinite system, hence they are embedded and contextually defined within larger systems. The total system is what I will call "Total Reality" and it subsumes as its objective foundation in physical reality the total physical universe.

The presumption of the principle universality is extremely important to our understanding of advanced systems sciences for several reasons. First, it governs what can be called the "Reality Principle" upon which advanced systems sciences is based. This Reality Principle is a first principle of advanced systems science and will be further elaborated in the next section.

Several points about the principle of universality are important to explicate here:

First, whatever the basis and limits of our knowledge about any given system or possible system, there is always some larger realm of possible knowledge relating to that system that remains unknown but not unknowable. This defines the basis for the extra-physical relativity of our knowledge and our sciences.

Second, all systems are at least indirectly interconnected in a multiplex network of relationships that is infinitely complex. The ultimate aim of our advanced systems sciences is ultimately the objective understanding of the total reality.

Third, to the extent that we have objective understanding of physical reality in terms of systems, this objective knowledge is congruent in at least some minimal way with the overall patterning of Reality.

In other words, objective, scientific understanding of reality is universally congruent, such that the same principles governing the function of the system under a specific set of circumstances can be predicted to be the same for any other systems of identical characteristics in some other time or place.

Structure: All systems exhibit some minimal sense of order that is defined by deterministic relations within and between systems that have predictable or expectable consequences. Structure of a system is defined and measurable by its degree of achieved integration.

Structure is, systemically speaking, the minimal deterministic ordering of relationships necessary to the self-definition of any system. Our sciences attempt to get at this minimal definition of structure governing any particular system or set of systems. It describes the central problematic of our systems sciences.

As part of the Reality Principle mentioned above, we can state that all of reality is minimally ordered or structured in some complex way that we probably do not yet fully understand, nor can ever completely comprehend.

Dynamics: All systems change or are subject to change. Systemic change is dynamic in the sense that it can follow alternative transition pathways, such that the system may enter alternative states in its historical development.

In general, it can be said, that change is the basis for both order and disorder in reality, such that systemic variation of phenomenal pattern leads to increasing differentiation and relational complexity of reality, which in turn results in increasing degrees of chaos.

It can be clearly stated, that, except for change, we could not comprehend reality fully or even partially, and, in deed, we could not have reality as we know it. All systems are in fact temporally organized systems that are defined by change processes through time. The diachronic patterning of systems is the basis of their phenomenal event-structures.

The explanation of change is paradigmatically vital to the objective imperative of advanced systems sciences in understanding the minimal structural patterning of reality at all and any level of its phenomenal expression. In deed, paradigms in the larger sense are defined by the ability to explain and predict changes in event systems.

We can state clearly that in any system, there is always some minimal sense of order that is evinced through expectable events occurring over time. Observation and systematic measure of these events constitutes the empirical basis for our science.

Entropy: Entropy is extremely important to the understanding of systems, because it guarantees that all systems, being part of larger systems, are noisy and imperfect in their function. They exhibit in the patterning of the long run the tendency towards decay and total annihilation or dissolution or disintegration as systems.

We can say that entropy is the consequence of change in reality, and the basis for the fundamental relativities underlying our limits of understanding reality at any and all levels. It guarantees that no systems in reality are perfect or absolute, and that therefore neither can our scientific comprehension of systems be perfect or absolute as well.

We can say that entropy is the ultimate expression of constraint in Reality, such that, in the structure of the long run and in the large, all systems are "absolutely" entropic in some ultimate and final sense. We can use it to explain death of biological organisms and extinction of species. We can use it to explain the fundamental dynamics of the universe itself.

We can say also that in change process, entropy is always contraposed to some minimal sense of order within systems. It constitutes therefore an indirect measure of structural order within any system.

Whatever systems we encounter in our explorations, they will at whatever level they happen upon exhibit these basic characteristics. There are three other operating constraints in our understanding of systems:

1. We may say that our systems science, whatever its form or subject area, is always based upon a limited fund of knowledge, from which we must infer the larger system as it occurs in reality. We ever only understand a part of the larger system, and we must use the patterning that we find in the observable area, to infer the patterning in the areas of the system that we cannot directly observe. To go one step further, we normally would impose some degree of statistical measure of non-random occurrence of pattern in our determinations. Statistical description and determination of probability plays an important role in our systematic knowledge of reality.

2. We can therefore hypothesize a kind of pie chart of our systems understanding as follows:

This pie-chart of our advanced systems sciences is derivative of the previous diagram of the relativities of our event horizons.

3. For any given system, a similar kind of pie of knowledge distribution chart can be developed, that can stand for the larger, generalized system, or for any particular instance of a generalizable system or for the total system at the same time.

It can be seen that when we begin defining the discrete values and discontinous boundaries of a particular or general system, we begin to isolate and distinguish that system from all other possible systems. The chart would come to take on distinguishing characteristics that would represent its development as a separate and unique system occurring in reality. All systems, or any possible system, or some generalizable "hypersystem" can be similarly represented in this way by modifications to the same basic knowledge pie.

Systems science is concerned both with the analytical differentiation of systems within systems, and with the synthetic unification of all systems within a single abstracted total system that can be represented by the same chart. Thus each time we achieve the relative comprehension of some subsystem, we improve our understanding, however slightly, of the total possible system.

I will call this the principle of holothetic unification of systems that underlies their identification as such, or as "systems" in the larger sense, and that underlies our comprehension of systems science as a purposive and ordered kind of inquiry.

Each system in its design and function therefore contains partial information that is relevant to all other systems, as well as to the total system of which all are a subset. It follows that if we can understand any particular subsystem well enough, we may be able to infer in a sufficient manner the total system, without having to comprehend other or most other systems.

There would be a caveat to this, and that is that our understanding of the total would be critically limited by the particularistic constraints upon which we based our comprehension. Thus it is in the systematic inclusion and extension of our understanding to multiply occurring systems, especially upon different levels of integration, that we achieve a more comprehensive, and hence more realistic, comprehension of reality.

With improved abstracted understanding of the total system, we can increasingly apply this knowledge to other systems in order to facilitate our understanding of these subsystems as well. Hence information contained in each subsystem provides information about all other subsystems also.

Our systems science is therefore "meta-systemic" in the sense that it comprises a system of systems, in a form that resembles the structural patterning and design principles of all systems. We can hypothesize therefore a kind of second-order feedback cycle operating in our advanced systems sciences that permits us to alter our understanding and even our observability and applicability of our knowledge, based upon what we learn about alternative systems.

In other words, the more we learn about some systems, the more we understand about all systems, and the easier it is to discover information not previously known. Furthermore, this feedback cycle describes a cyclical growth process that defines a node that is asymptoptically stable in the large and in the structure of the long run. Our systems science is therefore intrinsically progressive in the development of its knowledge, and, because the total system is regarded as infinite and unlimited, there is no intrinsic or apparent extrinsic limit to this pattern of knowledge development in advanced systems sciences beyond the phenomenal event horizons themselves.

Discovery and exploration of systems, whether these are naturally occurring or artificially constructed, does not have to be based on blind serendipidity in our quest of new knowledge and understanding. Advanced systems science is based on the presupposition that, because all systems share similar design features and are interrelated on some level or in some way, no matter how indirectly or remotely, a metasystemic system of all systems can itself be discovered that facilitates and systematizes to some extent the processes of exploration and scientific discovery.

The heuristic and functional operationalization of advanced systems science is therefore justified on the basis of its ability to be applied to all areas of knowledge and understanding in an equivalent and productive way. There is one important caveat in this claim. It is that in any particular area of application, advanced systems science and the models derivative from its operation must be consonant and consistent with the informational patternings of the phenomena that it seeks to describe or replicate. These particularistic systems, at whatever level, will tend to be isolating, particularizing and unique to the system they occur within, and thus our systems science in its application will always tend to be incomplete and imperfect.

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In the previous section I mentioned in passing what I call the Reality Principle and I consider this reality principle to be extremely important to the comprehension of advanced systems sciences. It therefore needs to be more thoroughly elaborated before we can begin to construct science more comprehensively and systematically. The Reality Principle can be called the first and most basic positive principle underlying advanced systems sciences. It goes something like this:

1. There is a single, minimally integrated reality that encompasses all things possible, known or knowable.

a. In an objective sense, it is a shared or intersubjective reality, such that we, as its principal subject knowers, are a part of its reality. The limits of our shared reality is the physical relativity of the phenomenal event horizon.

b. It embraces all aspects of reality, even subjective realities, such that ultimately our subjective experience is at the center of reality. The limits of our subjective reality is the anthropological relativity of the phenomenal event horizon.

The subjective and objective are fundamentally two sides of the same coin of reality. Reality is the entire coin of our experience. We cannot escape reality, even in our flights of unrealistic fancy or in our ideological falsehoods.

2. Reality is infinite and unbounded except in relativistic ways. Therefore all finite systems are partial and incomplete parts of the whole system of reality.

a. There can be no absolutely closed or complete system.

b. All systems are made up of other systems and are part of other systems.

3. Reality is ultimately chaotic and entropic in the structure of the long run and in the largest sense possible, because it is always subject to the law of universal change.

a. Systems are always imperfect.

b. Our knowledge of systems is always imperfect.

4. There cannot be no reality, or anything that is not a part of reality somehow. Hence,

a. All things are somehow explanable in terms of reality, even noise and entropy.

b. There are no non-relativistic absolutes.

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At the outset, I will state that all systems by definition are several things:

1. The total system is infinite, and composed of an infinite number of subsystems of infinite dimensions.

a. Any observable or knowable system is a subsystem of the total.

b. Any observable or knowable system is a partial instance of a general class of similar kinds of systems within a larger framework of systemic determination.

2. All systems are working systems--that is, they perform some kind of function that is based upon energy and information exchange.

a. Working systems can be defined as systems that maintain order in either one or both of two ways:

3. All systems are finite and limited in some intrinsic and extrinsic way.

a. A system may be both finite and infinite at the same time.

b. Limits in a system describe boundary conditions or constraints that serve to maintain the internal stasis of the system as a self-consistent and self-defining entity.

c. Limits in all systems are always manifest both spatially and temporally.

4. All systems are imperfectly bound. Hence, they are always minimally "open" systems which openness is a measure of their relative entropy, among other possible things.

a. Limits that bound and demarcate systems generally fluctuate and change over time, leading to the developmental state-alteration of the system in the structure of the long run.

5. All systems are bound within larger systemic contexts and in turn come to encompass sub-systems. Hence,

a. No system can be completely construed independent of its normal context.

b. Each distinct instance of a system has its own relatively unique context, hence all systems tend to be historically particularistic in their phenomenal event patterns.

c. A system as a theoretical and descriptive construct can represent a general class of independently instantiated systems as a unified or differentiated set of systems in the large.

6. Ultimately, in the total system, all systems are interconnected as subsystems to all other systems however indirectly and remotely.

a. Contexts are all encompassing in a non-exclusive sense. For any given system, we may define a contextual hierarchy of relations that are pertinent to that particular system such that relations can be construed on the following levels:

b. Contexts define both exogenous and endogenous sources of change that are both stabilizing and chaotic, such that we can describe the following quadratic paradigm for all changes:

7. Systems define cyclical patterns of deterministic relations, or control or regulatory structures, occurring within and without the systemic context upon multiple levels, and these patterns of interrelationship generally preclude the possibility of defining ultimate causes or strictly prime mover or unicausal arguments.

a. There is a regularity and periodicity of recurrent interactions that define relationships in all systems and that provide a sense of long-term asymptoptic stability to such systems.

b. There is an inherent source of uncertainty and undetermined variation of pattern of relation in all systems that provide a sense of instability to systems leading to alternative state-transition pathways. No system is perfectly determined.

8. Our understanding of systems, whether these are pure or applied, natural or artificial, is always imperfect and incomplete.

a. Generally, systematic approaches to understanding systems are both analytic and synthetic at the same time. We may seek to analyze a system in terms of its parts and their functional interrelationships, or we may seek to synthetically comprehend the synergistic functioning of the system as an integral whole.

b. Our understanding of all systems is always fundamentally anthropologically relative to our own anthropocentric and subjective horizon of knowledge.

c. Criteria of scientific objectivity are based upon inter-subjective trans-substantiation of knowledge, and upon presumed relative independence of the event phenomena to our phenomenal experience as determined by their measurability upon some objective scale or set of scales.

9. All systems demonstrate a minimal coherence that is describable in terms of mathematical equations and symbolic definitions.

a. All systems have a minimal and discrete set of core values or variables that define and govern the behavior of the system.

b. These core values and variables are intrinsically continuous and non-discontinuous, but they are unique to the system and hence are definable in mathematical or symbolic terms.

10. All systems can be said to manifest some developmental pattern as self-definitional systems, such that they exhibit some kind of developmental life-cycle that can be described in concise general terms.

a. The developmental cycles of systems are complex and tend toward chaos, such that in the long run they lead to asymptoptic instability and systemic disintegration.

b. Systemic cycles frequently recur with some expectable or predictable measure of periodicity.

Other features serve to distinguish systems as such self-definitional entities. Our definitions of systems are of course tautological to the need to define a system as such. All things are systems and are simultaneously part of other systems, and systems abound and interpenetrate one another in complex and multiplex ways. All things, at whatever level, therefore share the basic design aspects common to any and every system. We have not exhausted the list in this regard. It is important to understand how such explication of systems design features permits us some operational handle upon our scientific and theoretical constructs pertaining to systems in general and in particular instances.

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Advanced systems sciences face a common set of structural challenges. These can be seen as the challenges of complexity, contextuality, comprehensivity, causality and chaos:

1. Complexity: The challenge of complexity in systems approaches is the difficulty of resolving the information explosion when analysis is carried progressively and gradationally to lower and lower levels, or to encompass broader and broader systems.

2. Contextuality: The challenge of contextuality is to recognize that all systems are embedded at whatever level within other larger systems, and in turn encompass other sub-systems. At each point in each system, there are a larger set or framework of relationships that structure and give systemic significance to that particularistic set. In the problem of contextuality, we must ask, how much context is sufficient theoretically and operationally.

3. Comprehensivity: The challenge of comprehensivity resides in the issue that all systems are interconnected with every other system. We cannot conceive of a perfectly isolated system. Systems are also embedded at multiple levels within other systems, giving rise to the problem of multiplexity and the interpenetration or multiple integration of different systems. Our approachs on some level must embrace and resolve the challenge of comprehensivity.

4. Causality: Causality is inherently a challenge to systems approaches because the classical conception of causality implies, among other things, linear relationships between variables, and logical relationships between variables and undirectional relationships between variables. Such relationships are rarely found in systems analysis. Causality becomes multiply deterministic and underdeterministic in many systems and usually yields to complex descriptions of systemic feedback cycles and developmental state-trajectories or pathways.

5. Chaos: The problem of chaos stems from the issue of inherent randomness of under-determined relations, and from variation of patterning found within systems, and from indirect causal chains that impact upon systems at many points.

We can resolve many of these basic challenges in several related ways:

1. The assumption of total systems: All systems are a part of a total system, which can be comprehended scientifically as such, and its subsystems thus contextualized within its framework.

2. The assumption of critical feedback cycles: Sub-systems gain identity in the larger system by means of feedback mechanisms that are inherent to the functional integration of the system as somehow separate.

3. The assumption of solutions: We can develop what constitute simplifying solutions to complex systems, by identifying the main or key variables involved in the feedback relationships established within any system.

4. The assumptions of models: We can develop on the basis of our simplifying solutions alternative models of the system that allow us to manipulate the variables of the system in a controlled manner.

5. The assumptons of dynamics: All systems exist in the long run in some form of asymptoptic stability or instability. External relations and internal variations that affect the system result in state changes within the system that can lead to its structural modification, its disintegration or its development. Systems thus follow alternative state trajectories, and possible pathways such a system might follow is the basis for defining the paradigm of the system as a hypothetical and theoretical construct.

What I propose is a meta-systemic science of systems, that in itself comes to comprise a system of all systems. It is based on the study of all systems in a systematic and controlled fashion, and leads to the experimental application of artificial systems, as models, to a variety of specific problem sets.

The key design characteristics of all systems seem to me to be the following:

1. All systems are working systems.

a. They are imperfect systems.

b. They can be measured by their relative efficiencies.

2. All systems therefore have some form of functional integration.

a. All systems can be mechanically described in terms of their functional interrelationships.

a-1. The functional relationships between parts condition the descriptive analysis of the parts.

b. All systems exhibit some measure of supersystemic synergism.

b-1. This synergism is conditioned by and is part of some larger system or set of systems.

c. Each part forms its own synergistic unity that is conditioned by and subsumes some other sets of systems.

d. All systems define some complex form of functional equilibrium or stability of integration.

e. This equilibrium as a system is always fluctuating.

f. This pattern of fluctuation in the long term leads to state-transition changes that affect the parts and the system as a whole.

g. The patterns of fluctuation of any system obey some theoretical set of limits that define the range of normal function, within which equilibrium can be maintained, and beyond which equilibrium must yield to entropy.

3. All systems communicate information at multiple levels.

a. Information is either boundary-maintenance, endogenous or exogenous.

b. Information can be defined as the functional parameters of relationship between the parts of a system.

c. We can distinguish a continuum between deterministic information and noise.

d. Systemic information is always describable in two interrelated forms:

1. mathematically

2. symbolically

4. All systems can be understood and described in terms of their information, in a manner that is scientifically useful such that:

a. We can build working models of systems.

b. We can use the models to test propositions regarding the nature of the system.

c. This testing is experimentally controllable.

d. We can apply the models to the construction of new systems.

e. We can use validated models for our theoretical construction and dialectical revision of alternative paradigms.

Natural systems theory is organized upon three strata of natural information function. At all three levels there appears to be a core of related systems theoretical principles that are applied in fundamentally different but similar ways. The same core appears to me to underlie and account for almost all levels of programming in artificial intelligence research. I have come to the conclusion that in all working systems, there is a core set of theoretical principles that operate in the determination of such systems. As working systems, these are systems that are amenable to mathematically based analysis and modeling whatever the level of our understanding. It entails that we may reduce our units of analysis to discrete or continuous variables that enter into structural relationships. This can be applied with equal effect to human systems as to physical systems. I believe this describes a systems paradigm. My hypothesis is to delineate and explicate this core working system, that underlies all systems, and then to functionally extend it to alternative systems development.

*****

The problem of theoretical integration of our advanced systems science underlies the requirement that our solutions are in some sense sufficiently simplifying, or at least, reductionistic of the complexity. We cannot afford to account for all phenomena in a particularistic and detailed sense, hence our models and paradigms must get a lot of mileage before they can be accepted as such. A single theoretical construct must be at least potentially capable of construing a great deal of information, however indirectly.

Mathematical and symbolic explanation serves the purpose of theoretical integration of systems sciences in a number of important ways. They operate hypothetically at all levels of advanced systems theory, and serve the purpose of model building in systematic terms that allows us to heuristically extend and test the models.

Because systems are about the relations between things, relations can be described as variables themselves that relate the things to the system. Thus the identity of the component parts is critically defined by their relational identity within the "structural" relations of the system they function within. Mathematical explanation is important to the definition of the relational values and variables of such systems, such that they describe the nature of the system that is to some extent independent of the intrinsic values of the component parts as isolatable entities. In theory at least, the same forms of mathematical description can be applied to relational values across of broad range of different kinds of systems.

Mathematical description/explanation is a form of symbolic definition of variables and values, but symbolic definitions of terms and their relations encompasses a broader range of semantic and theoretic values than can be accounted for by mathematical formula alone. Thus, in many areas of more complex systems that are derivative of more basic systems, especially in human and social systems, the language of description is frequently insufficient to the task of simplification that is required in these areas. Symbolic language itself, as a broader base than the more constraining mathematical description, often falls short of the task of sufficient explanatory power in these super-complex derivative systems.

Mathematical integration depends upon our capability to express our primes as symbolic variables to which a range or alternative series of values may be attached. These values are held to be numerically definable upon some scale of measurement, hence they are inherently quantifiable in at least some parametric or non-parametric form. We can presuppose a broader class of qualitative nonparametic or discontinuous values that can be described in a kind of quasi-mathematical or abstracted form of equations. This is sometimes found in highly systematized social science applications and descriptions, but their explanatory power or generalizability is frequently left wanting.

I have proposed to develop a body of mathematical models as heuristic devices that can serve in model building and theoretical construction work in all areas. These can be used as tools in advanced forms of analysis and constructive synthesis in systems science, and serve as its foundation.

These models can be used in the construction of various programming functions that serve the purpose of hypothetical modeling of systems in various state-transition trajectories. These synthetic functions can be used in the analysis and heuristic testing of applied systems to various contextual frameworks, with limiting contextual conditions being built-in or defined within the framework of the function itself as systematic inputs.

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"Science," as it is published in textbooks and journals, can be distinguished by several defining features. First, there tends to be the use of mathematical formulas for the concise, non-rhetorical description of basic laws or principles. Second, such literature appears to be logically coherent and empirically as consistent as possible, as permitted by the explanatory model of the thematic point of view of the paper itself. Third, and not least importantly, is the use of diagrams and illustrations of central points or complex realities. In this last sense, often a single picture can be worth ten thousand scientific words. Fourth, generally speaking, most scientific texts are defined and codifed in terms of some specialized jargon that is shared by a community of like-minded scholars and that embodies a set of shared exemplars that informs that particular paradigm.

And so it must become with advanced systems science that we must develop a language, both mathematically and jargonistically, as well as a logical system of reference and inference, and a system of shared exemplars appropriate to its constructs and operationalization. We must also liberally but carefully employ diagrams, tables and illustrations as an intrinsic part of our dialectic. I believe this trend in scientific literature reflects also the folk notion that "seeing is believing." Legitimacy and credence appears to be much stronger based if and when we can reinforce our arguments with at least two dimensional visuals constructs.

I propose that there is a special mathematical system, jargon, logical-symbolic system, system of shared exemplars and working models, and pattern of illustration that in particular informs and helps to define advanced systems science in its basic core areas as well as in its derivative and applied regions. The mathematical system I have proposed to develop I have termed symbolic mathematics. The logical system I developed I propose to call relational symbolic logic. Shared exemplars and working models in a comprehensive sense describe a natural set of models that exemplify important theoretical design features of systems. Diagrammatic illustration of advanced systems science and its related and applied areas have already been developed and will continue to be so developed.

It can be said in general that advanced systems science involves a distinctive style of mathematical modeling, computational programming design, alternative design analysis and the unconventional use of knowledge and heuristic designs or devices in the contruction , operationalization and functional integration of its fields.

*****

The symbolic mathematical language I propose for the development of these working heuristic models is based upon an understanding of a looser conception of math as symbolic language in the possibilistic and probabilistic description of reality. Math is based upon rigorous, faultless numerical and relational logic. It is a restricted variety of symbolic language in terms of string theory that occurs more naturally and more loosely in human language. A strong and perhaps irrefutable case can be made for noumenal archetypes of a priori concepts like 0 and the triangle, that inform mathematical theory in basic ways.

The mathematical language I propose must therefore range upon a continuum that embraces both a more restricted and rigorous set of constraints on one extreme, and one that embraces on the other extreme a minimally ordered set of constraints necessary to the symbolic reasoning on the other extreme. In general, the distinction between predictability and expectability of results is the kind of differential that this continuum expresses.

In general, I would state that the goal is the development of a single, cohesive, middle range system of terminology and constructs that embraces both dialectical extremes in an effective manner. Therefore, the operational terminological system I propose as being appropriate for advanced systems science is consists of an intermediate range of mixed and hybrid forms.

The kind of symbolic math I am concerned with is a form of math that is applied to real world problem sets at all levels, and that therefore requires additional criteria of external consistency and in turn looser criteria of strict internal coherence. Hence, this math must be capable of introducing and dealing with uncertainty variables and values at all levels of its articulation as uncertainty is manifest in the naturally occurring world at all levels.

Furthermore, this math must be capable of dealing with the inherent complexity represented in all systems, as well as with the contextual interconnectedness of all systems upon multiple levels. This means that while we may strive for elegant and simple equations to understand complex realities, these elegant equations cannot be straight-forwardly derived from direct experience. They tend to subsume enormous complex formulations that define and lead to the values expressed in such formulas.

My artificial intelligence teacher taught me in my struggle to compete with young computer wizards, that complex problems have to be approached by breaking them down into simpler units, then followed by subsequent synthetic recomposition into larger functions. I would say, in addition, based on further experience, that the initial analytical attack to any complex problem or problem set must be based on some implicit theory or meta-logical conception or definition of the problem set as a hypothetical possibility or set of possibilities in imaginary hyperspace.

Such possibilistic hyperspace is in essence an unknown landscape, or what can be called a search-solution space, that has astronomical, almost infinite size or magnitude when it is seen in a random and chaotic way. It is an "exploded" space in its minimally ordered form. The unknown space represented by an unsolved problem set can be said to be in its original form minimally ordered, and thus maximally entropic and chaotic. It becomes the functional goal of our systematic understanding, best exemplified in terms of our mathematical languages, to be capable of resolving this problem by the reduction of systematic complexity to manageable proportions. Ideally, the most parsimonious solution is the best, most optimal and most correct solution to any delimited problem set, though we can never ultimately know if there might not be some better solution available.

We can make the following kinds of statements regarding such uncertainty and randomness in our problem-solving capacities:

1. Systemic integration produces information and yields energy for directed purposes, hence solutions to systemic problems result in working models.

2. Disordered and chaotic anti-systems consume energy without purpose and yield energy entropically. Informationally such systems are noisy and also inflexible and maladaptive.

3. The anti-entropic maintenance of inefficient systems consumes energy in an entropic way.

4. Optimizing solutions tend to minimize the inefficiency of systems and maximize their integrated functioning in realistic ways.

5. No system can be absolutely ordered or disordered, but remain relativistically both ordered and disordered on some level.

6. All systems tend to fluctuate about some stable state-trajectory, which will itself fluctuate. (i.e., all systems change in time)

Computers and computer programs generally cut through such vast spaces in a very systematic and extremely rapid way--they can do this kind of linear processing far faster than can people, who remain relatively slow to calculate all the variables if left to their own neural devices. But human beings have a certain advantages and an innate facility for thinking divergently that computers lack. This allows people to occassionally jump to higher orders of organization in such space, and hence to solve problems that computers are fundamentally incapable of solving, at least not without a tremendous volume of linear processing beforehand.

Math allows us to systematically do the following:

a. Define ideal states and min-max limits within any delimited system.

d. Define optimal solutions and progressive integration of definitions leading to a

more exact ideal end-state.

I believe that it is the last function that is of greatest importance in understanding the significance of relying upon mathematical description for advanced systems sciences. It should at least in theory provide a common objective language by which to achieve the necessary comprehensivity, unification and integration of systems sciences in all areas and at all levels.

I also believe clearly that for mathematical description to be capable of achieving this primary function, it must be adapted and demonstrate adaptability to a universal range of alternative phenomena. It must, in other words, be transformed and rendered applicable in a flexible way that preserves both its internal coherence and maximizes its external consistency with the world. This is of course a systemic challenge to mathematical language, as there will always be some sense of trade-off between rational coherence and empirical consistency.

Two sets of things come to our rescue in overcoming this dilemma in the development of a suitable language of description. First, progressively integrated and complex mathematical functions can be handled efficiently by means of computational devices through systematic and exhaustive analytical parsing and processing. Secondly, human intellect, which always remains at the center of our understanding, is capable of synthetically jumping to final solution states that encompass entire orders of magnitude of complexity.

Thus, in the first pass of the delineation of our mathematical language, we must embrace the central dialectic between these two alternative analytic and synthetic procedures.

In the first pass, we must be capable of delimiting and clearly identifying the problem set in the first place, in terms of its key components and synergistic functioning as a system. Problem identification is itself problematic, and has its own dilemmas. We may say something like the following:

a. Any hypothetical problem set is itself part of a larger problem set and there is some infinite or total problem set of which all others are some subset. In a sense, the entire issue of human comprehension of reality is a total problem set, of which all else is some derivative subset. I will call this the total reality problem.

b. The ultimate goal of advanced systems science is optimal comprehension of the

total reality problem.

c. Specific solutions to particular problem sets tend to be relative and unique to that problem set.

d. General solutions to non-particular or encompassing problem sets tend to be generally applicable to some larger hypothetical range of problem sets.

e. General solutions are derived from the correlation of specific solutions (empirical inductionism), and in turn deduce to alternative particular solutions (hypothetical deductivism).

This ultimately defines the central goal and purpose of advanced systems science, and that is the progressive global identification and resolution of the total reality problem.

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The mathematical language of description I propose for advanced systems science I will call applied symbolic mathematics and inferable mathematical symbolism upon which it is based. As an applied form, it resembles engineering on many levels, and we can call the form of engineering forthcoming from it as heuristic and experimental systems engineering. Intrinsic to this language are several built-in capabilities:

1. Symbolic mathematical definition of all significant terms and relations minimally applicable to a delimited problem set.

2. Matrix organization and systemic linearization of possible problem-sets.

3. Systematic stratification of problem sets in possibilistic hyperspace.

4. Progressive integral refinement of linear to nonlinear problem sets through programmable functional procedures at all stratified levels.

5. Distributed-Object Symbolic oriented programming framework.

6. Statistical-intercorrelational sampling & measurement procedures, including heuristic uncertainty procedures.

7. Rule-based decision structures & search-solution engines.

8. Alternative model construction & application.

9. Paradigmatic definition, refinement & application.

10. Differential & rank-ordered feedback between the last and all the other levels.

****

In the construction of our symbolic mathematical language certain pressuppositions appear to me to be in order. These are something like the following:

1. Total Unification: Unity may be represented by the integer 1 or by the variable U, which implies a perfect state for a delimited finite, or total infinite system. We can say that in an ideal sense, 1 or U may represent either a particularistic, finitely delimited instance of a system, or it may represent the total possible system that encompasses all systems. We can subscript 1 depending on its implicit representational value. We can substitute 1 by some hypothetical variable that stands for some value or system that is a part of the total system.

In all instances and in all forms, 1 describes and encompasses both the initial hypothetical start-state and the final end-state. 1 therefore represents some inherent variable of unification, and it will be represented alternatively as 1_U or U₁

2. Perfect Equation: In any total or delimited finite system, the actual system is represented by a composite set of variables that occur on the left-hand side in the initial start-state and final end-state or stop-state, and always equals unity on the right hand side.

2a. The corollary of reversible identity. If equatability exists on both sides, then they are interchangeble and of isomorphic identity.

2b. The corollary of boundary identification of finite sets.

Only the largest sense, with perfect unification, can we achieve perfect equations.

3. Systematic Realization : imperfect Actualization or actual Imperfection: Whatever the hypothetically ideal equation, there will be some imperfect imbalance in the equation between left and right side, which will require resolution in some systematic manner. Realized expression on the left-hand side is always somehow unequal to the idealized state unity on the right hand side. The relational expression between them becomes in a sense an implicit ratio.

3a. The corollary of irreversible Non-identity.

3b. The corollary of intrinsic-extrinsic variability.

3c. The corollary of continous alteration.

4. Abstract Representation or transcendant abstraction: Variables may be infered from and represent real values. Central to the success of advanced systems science is the presupposition that our language of description is sufficient and accurate to the problem of representing the reality in a minimally consistent way.

4a. The corollary of discontinuous stability.

4b. The corollary of state alternation.

5. Improper Integration: The final end-state on the right-side of the equation of unity is always unbounded and infinite, and thus cannot be properly represented in its equal form by the expansion and development of terms on the left-side of the equation.

5a. The principle of assumable equivalence-correspondence.

5b. The principle of progressive approximation.

5c. The principle of measurability

5. Stochastic Differentiation or Chaotic Transformation: Left-sided values are transformable in an infinite number of ways that are partially random.

6. Relative Uncertainty: There is always some measure of relative uncertainty that is expressed on the left-side of the equation and that is itself always a complex and inherently undetermined set.

6a. The principle of contextual indeterminancy. Contextual relations between systems tend to be underdetermined to the degree that they are indirectly removed or remote from the central system in question.

7. Absolute Limitation: Certain absolute limits exist for any system which define constants that can be approached by elements or instantaneous states of a system, but which can never be obtained in an absolute way.

8. Stratified Determination: Systems stratify based upon deterministic relationships that are more basic or derivative. Basic systems underlie derivative systems such that derivative systems are synergistically greater than the basic systems that compose them. Stratified determinations allow derivation of more complex formulas from simpler sets, and, differentiation of basic general formulas into more complex sets that they represent.

9. Stadial Substitution: One set of formulas may take the place of another set of formulas at each state-stage of the development of a mathematical description. This is accomplished through systematic substitution of equivalent terms within strings.

10. Gradational Alternation: Formulas may be fundamentally changed or transformed on a structural level based on several alternative principles, such that the resulting sets are not equivalent to the preceding sets.

10. Dialectical Correlation: Alternative sets or matrix structures may be contrasted or contraposed or compared within one another in systematic ways to render some measure of difference operating or occuring between them.

11. Programmable Distribution: Functional operations and complex sets may be distributed through programming structures.

12. Infinite Chaining: Open-ended and infinite strings may be produced on one or the other side of an equation. Also, an infinite number of permutations may be developed on either side of an equation.

13. Control Regulation: Key defining or regulating variables are factored into formulas that express limiting or boundary maintaining factors associated with the variables.

13 a. variable recursion

13 b. state-reiteration

14. Nonlinear Exchangeability: Values may be exchanged between left and right sides of relational sets to create non-linear patterns of state-alternation.

14 a. The principle of energy transfer

14 b. The principle of information exchange

14 c. The principle of communication

*****

Advanced Systems Science accomplishes functional integration of its areas of involvement by means of progressive application and refinement of general problem models to integrated problem sets in reality. Thus, through functional integration that is inherently problem oriented, advanced systems science naturally crosses conventional disciplinary boundaries, and provides the framework for a truly cross-disciplinary approach to real world and hypothetical problem solving.

At the heart of the core system is a working model of advanced systems analysis. In doing the work on natural systems theory, I have come to the understanding of the similarity of principle and design underlying all naturally occurring systems, and I expect, to be found in most artificial systems as well. I believe this core system constitutes a theoretical paradigm governing all systems, hence its explication should be useful in the application of systems sciences at all levels.

The basis of advanced systems science is its comprehensivity of approach and its functional integration as a working system. Underlying the comprehensivity is what appears to be a basic set of universal patterns of structural relations that can be mathematically modeled in approximate and general form. The basis of this is, I believe, that a systems approach is about systematic interrelations between things however we must define these things. On some level or another, these things involve some level of energy exchange or tranfer. Often these energy transfer systems are "multiplex."

The identity and character of the things involved in these relational systems is to some extent determined by these systems. This allows us to map things at different levels as variables with continuous and even dissimilar values.

In general, systemic pattern or order has certain design characteristics about it. First, it is generally a working system of relationships, or the result of some kind of working system. Therefore, it follows patterns that are fundamentally thermodynamic. We expect several things from thermodynamic systems. First, they rely upon some form of energy entrapment or control mechanisms. Secondly, they tend to be variable in patterning, and tend towards entropy or decay. Always, there is some kind of similarity or correspondence of pattern, both spatially and temporally occuring to relative degrees, and recurring over time, either on a continuous (recursive) or discontinuous (reiterative) basis. As a system, also, we would expect that it would be by definition bounded in some way, and that it has a finite number of discrete variables or values that compose and account for the patterning we observe. Also, to go a step further, we would expect systems to be historically developmental or evolutionary in the structure of the long run, so we should expect that the system will advance through a series of patterned state-alterations.

Natural systems sciences are complementary to the traditional disciplines, and therefore should be considered to be a form of lateral integration within the framework of the formal fields of knowledge. It suggests a kind of secondary program that cross-cuts disciplinary specializations and invites part-time involvement of a variety of scholars as well as minor programs by students. Such a program should be able to reinforce any particular scholar's involvement in whatever fields they may be specialists within, while simultaneously providing a broad range of scholars the platform for interdisciplinary communication and for heuristic exploration of ideas that may be beneficial within their own respective frameworks.

The table below sets up a kind of programmatic paradigm that covers all possible areas, and describes a kind of organizational framework for such a paradigm that would be appropriate to the organization and application of comprehensively integrated knowledge:

We may specify a functional integration of human knowledge that is defined not by the natural stratification of information in reality, as it is by the organizational and operational distribution and purposes to which such knowledge is inevitably applied or applicable in the world. This informs the structural-functional organization of knowledge systems such that this teleological chain of functional integration is consistent across different kinds of information. We can thus speak of the functional coordination and integration of various areas of knowledge application within such a framework, and the interrelationship between these areas.

We can further consider in the table below the cross-disciplinary dimensions within each of the fields, as depicted in the table below:

The possible interrelationships between levels and orders of information pattern may be obvious or not. We might infer a two-way structure, such that basic relational patterns are not to be accounted for by more elaborated and derivative systems. In this context, we cannot say that human systems predetermine and account for physical or biological systems. But we might also say that human systems can have an influence upon such systems, in multiple ways.

We would also want to set up a similar table of values for any one area or cross-section of levels and interrelate the functional categories of the systems, or compare functional interrelationships between different systems.

We might want to ask about the theoretical aspects in each of the functional areas, or rather the humanistic aspects, etc.

Combining the three sets of tables together creates a kind of automated database system, as long as we define clearly the relational values between the different systems. If we alter the values in one area of a matrix, we might be able to determine the kind of impact such a change might have throughout the matrix. Thus, we might want to define two sets of values for any bit of information or subsystem occuring, both in its relational dimensions characteristic and unique to that instance or subsystem, and its relative values in terms of all other possible occuring systems within the framework. In such matrices, we may also muliple matrices together in different ways.

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Such a program may have a number of interesting possibilities for creative organization, development and application of knowledge outside convention bound frameworks. We can speak of a functional methodology for the operationalization of advanced systems sciences in an integrated way. Methodology encompasses both the methods used for analysis and synthesis, or the procedures for research and experimental design, as well as the methodological rationalization that accompanies and justifies the use of a particular set of tools, procedures or methods for a particular problem set.

Operationalization allows us to construct, use and revise models in testing environments that can be regulated and controlled. Below is an outline of potential application procedures within this system:

1. Theoretical-Methodological Dialectics: The dialectics of Analysis/Synthesis arise from the multi-level interrelatedness and interconnectedness of all naturally occurring systems such that the y are everywhere and always, at the same time, systems within systems. Once we specify a certain level we must recognize that there are both synergistic patterns and analytical part-whole patterns related to that level simultaneously.

2. Correlational Pattern Analysis/Synthesis: Consideration of this kind of analysis proceeds from the observation that strict causality is historically chaotic, but only epiphenomenal to systemic organization of patterning in the universe. In other words, things are caused to happen, like hens laying eggs and eggs hatching young hens, because they are part of a larger framework of deterministic relationships. To get at the deterministic structure of this larger framework, one must step beyond the logic of direct causal explanation as inherent insufficient language.

3. Transformational Analysis/Synthesis is the complement of correlational pattern analysis, in that it entails a study of the effects and causes of pattern changes within a system, which can be called state alternation.

4. Contextual Analysis/Synthesis: Any thing that happens, or any inferrable system of relations, always occurs and is configured against a background field of contextual relationships, and of contexts within contexts, that requires some degree of specification and delimitation in our definition. The challenge and dilemma of contextual analysis is the specification of how much context is enough, necessary and sufficient, for an explanation of a particular pattern, process or phenomenal event.

5. Relational Structure Analysis/Synthesis: This suggests the operational establishment of experimental control structures & artificial research conditions & environments for the testing of theories in various levels, as well as the use of various forms of heuristic designs for modeling & prototyping of alternative design configurations.

Advanced systems theory is metalogical in that it provides general knowledge structures about theory itself, in patterns homologous to the structure of theory at any level of natural information patterning. We can say that basic theoretical designs found at all levels of natural informational pattern are homologous in design principles.

This is so not only because they arise one from another in a larger "hiearchy of correlations," because natural information patterning in reality appears everywhere to follow certain basic principles of non-linear self-organizational design.

This suggests a noumenal design science that is independent of any given instantiation of its patterning, as well as possibilities for its elaboration and application to artificial and alternative systems of informational construction.

Blanket Copyright, Hugh M. Lewis, © 2005. Use of this text governed by fair use policy--permission to make copies of this text is granted for purposes of research and non-profit instruction only.

Last Updated: 04/19/05