Chapter II

Meta-systems & Metaphysical Systematics

I have sought to define an abstract system of specialized and general mathematics as this is shaped within the systems framework. I have posited the central notion of the meta-system as an abstract hypothetical construct that can be used to model alternative systems in theory. Each instance of a hypothetical meta-system can be said to represent a generalized and integrated theory about the system, hence each such theory would have a minimal number of component dimensions of description that would be considered sufficient to that system. These dimensions are derived from the application of alternative mathematical models and theories to the system. The description of the system would be deductively derivative from the theoretic construction of the meta-system. In theory, the correct hypothetical system would yield predictable values as compared to the patterning of the actual systems upon which its description is based or to which it is referred. In this case, it must be seen that two or more hypothetical constructions of the same meta-system might yield correct values for any test case. Competition between alternative constructions should, in time and through testing, yield the correct model, or what we might say, the model that best fits.

This approach serves to integrate various and diverse theoretical aspects of mathematics under a common operational umbrella, in a unified systems framework. It entails also some new and interesting permutations of mathematical theories in a number of areas. The unification of various theoretical constructs within a meta-systems model entails that the meta-systems as a model would be part of a larger theoretical paradigm about such meta-systems. Such a paradigm would in time, through continuous refinement by the inclusion of new meta-system constructs, lead to a universal comprehension of advanced systems theory that would embrace in theory most possible systems that are known, and many that are yet unknown. Such a paradigm would as well come to encompass a growing set of alternative theoretical constructs that would also become improved in their generality and refinement of applicability.

At the same time, the concept of the meta-system provides a theoretical and metaphysical framework for the definition and symbolic description of alternative real systems that is basically non-mathematical or semi-mathematical in character. It allows us to develop a common parlance about which to describe alternative kinds of systems in different frameworks, and by which to coordinate the understanding of different kinds of systems within a common theoretical framework.

In this regard, I propose a form of mathematics that applies to the abstract description and analysis of systems at any level or in any form of expression. Such an approach is also, I believe, to some extent meta-mathematical in the sense that it is a mathematical system of systems, and hence its constructs and concepts embody what is basic about all systems that it seeks to describe, including mathematical systems themselves.

The point of departure for this approach is to posit the existence of an ideal abstract system that has the minimal structural features underlying any and every possible system. I call this a general theoretical model of the meta-system. The study of the possible state permutations that such an abstract mathematical meta-system can undertake I have called "structural systematics."

Underlying this approach is an implicit argument that mathematical systems of systems are in some as yet unspecified way an ideal abstract system of conceptualization that meets all the requirements of pure mathematical systems. This underlying system is not just mathematically abstract, but also metaphysically universal and scientifically general.

It follows from the fact that systems are universally observable to underlie any complex pattern of order in reality, and that all systems are at least hypothetically interconnected in some minimally defining sense, however indirectly. It also follows from this that we can hypothesize that such a meta-mathematical system of systems should provide the basis for the integration of mathematical systems, as well as for the systematic and structural-functional integration of other abstract symbolic systems that are essentially non-mathematical.

Meta-systems science attempts therefore to pick up the theoretical and methodological ball where the conventional sciences have tended to leave off. The main characteristics of meta-systems science and natural systems theory are the following:

1. The holistic emphasis of the contextuality of constructed frames of reference, complemented by analytical reductionism and resolution of particular or specific instances or events.

2. The cross-disciplinary or inter-disciplinary "hybridization" of knowledge systems that follow lines of least resistance in the natural ordering of phenomena in the world, paying respect to the emerging social and historical stratigraphy, landscape and boundaries of knowledge systems.

3. An emphasis upon the theoretical construction of alternative frames of reference derived both deductively from natural and rational reason, and inductively from empirical observation and experimentation.

4. The use of both a "systems" modeling or heuristic approach to learning, design and problem solving, in a framework that is itself meta-logically contextualized by a meta-systems framework that serves to contextualize such approaches within a comprehensive knowledge framework.

5. An emphasis upon the comprehensiveness of objectified knowledge systems, or of a "scientific worldview," that nonetheless does not exclude or preclude or occlude an interest in the particular or the specialized frame of reference and that does not factor out necessarily or methodologically other possible ways or forms of knowing reality.

Whether or not our "total reality" is ultimately disheveled, a cosmological hodge-podge and a fateful crap shoot, or it is quintessential clockwork that Einstein and others dedicated their lives to discovering, becomes from the meta-logically perspective of meta-systems science and natural systems theory a "hen or egg" kind of dilemma. It is a form of paradox that we cannot answer, like Goedel's Theorem or like the Cretan liar, in the terms of its own intrinsic logic, but can only resolve if we are able to step outside of its conundrum and contextualize the complementariness of its relationship. Niels Bohr wrote especially the importance of the recognition of complementariness of structure in reality and its consequence for our scientific worldview and he applied this to the biological and anthropological sciences as well as to his own fields in physics. In this sense, meta-systems science and natural systems theory therefore follows directly in the footsteps of Niels Bohr's observations about the changing ontological and epistemological status of science in human reality.

The theory embraced by this approach is not without its methodological madness. I have sought a combined systems approach that includes information theory and communication theory with nonlinear dynamics, alternative control theory, theory of automata and alternative intelligence. I have sought thereby to define a legitimate role to the understanding of knowledge systems and knowledge systems theory, the role, function, status and structure of knowledge in our reality, and the possibility and probability of non-human forms of knowledge. Such an approach allows us the opportunity to both grapple with the terms of our arguments, however paradoxical they may seem, with one arm, while keeping the other free to stand and work beyond the terms and terminologies implied by an particular argument or problem set. The objective of such an approach ultimately is to integrate any such knowledge into a larger working system of understanding--a system that is ultimately comprehensive in a total, but relative, sense. Knowledge systems science has many interests and many applications, and knowledge theory leads to both experimental methodologies as well as to knowledge engineering applications. There are many pressing issues in our humanly ordered world that are well addressed through these kinds of applications, and particularly when it comes to the problems of the translation and reconstruction of our knowledge systems, and the use of such systems in the inculcation, integration and adaptation of human reality.

Thus we arrive at a final definition of meta-systems science, and that is of a knowledge systems theory and methodology that has the fundamental problem of the integration of reality and the description and explanation of all real phenomena, whether this is natural or humanly constructed.

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We must ask therefore, from a mathematical point of view, what is a system in the abstract sense of the term, and how can we define and describe it using mathematically appropriate formulas?

The mechanical model of a machine is important to this abstract conceptioning of metasystems. A machine by definition is an integrated system of component parts that co-operate to achieve some form of energy exchange or transfer in expectable or predictable ways. Machines generally operate over a period of time, or in an interval duration, during which they exhibit certain state transitions that characterize the system functionally and operationally.

The classical conceptioning of a machine is of course a fairly linear model occurring in some kind of classical Euclidean geometry. Though a classical mechanical model is useful as a starting point to the basic understanding of all machines, it is inherently incomplete when we are dealing with complex second order machine systems that are essentially non-linear in their character.

If we take a simple machine, for instance a screw, we can understand that the thread of a screw imparts special properties to the screw that makes it a machine that is unlike a nail or some other kind of fastener. The screw can be said to have a specially designed characteristic, or trait, like its thread, that imparts a special set of properties to it, like twist. A screw functions in a special and particular way that characterizes it as a typical simple machine. A spring is another similar simple machine. A helical coil spring has certain elastic properties that allow it to be compressed or stretched, and that permit a form of resistance resulting in predictable functions.

In order to get at the nature of a simple machine, we must ask what components or characteristics of this machine impart to it properties that separate it functionally from other types of devices, for instance the minimum features of contrast between a screw and a straight nail, or between a spring and a simple twisted string. We can say that even a rope that has twisted fibers bundled in some complex way about a central axis, or else woven in a sophisticated way, represents a similar kind of complex machine, as might be a nail that has a shaft that's twisted for superior fastening power.

I will go back to Archimede's screw and speculate that all classical machines have at least one axis about which a twist or turning characteristic is defined. This axis may be orthogonally projected as a central pivot point or fulcrum about which a lever or rocker mechanism operates. The turning action, however it is defined, imparts a fundamental non-linear periodicity of a machine by which the machine gains its characteristic properties. We can see that a bow and arrow is not obviously a machine, unless we understand that the arrow is launched from a central fulcrum of a shaft that has springlike qualities.

Generally, we can say that all systems, as some kind of machine, exhibit a defining set of determinants and dimensions that are functionally interdependent, and that are structurally and uniquely characteristic of that system, or kind or type or class of system. These determinants and dimensions in their operational organization, impart structural order, hence "information" to the system. Furthermore, in first order classical systems, these dimensions and determinants tend to be discrete and measurable on some linear scale. In second order non-standard systems, these dimensions tend to be continuous and nonlinear, hence difficult or impossible to measure in some finite and regular interval scale.

I will also claim that any system exhibits an integral design that is characteristic and unique to that system. We can refer to a form of structural relativity that that the function and organization is characteristic to a particular system or kind of system, and hence any system has its own internal frame of reference to which its states and values are relative.

Any system also functions as a kind of device, a device being defined as some kind of machine or mechanism that functions in some particular way. We can refer to functional relativity of any system as being the characteristic patterns of behavior of a system depending upon its internal organizatio as a device.

Finally, all systems maintain what can be called a developmental pattern or cycle that defines the system as a series of state-stages over time. All systems exhibit an inherent dynamic pattern of change or fluctuation of states.

I would say that all systems by definition have some finite set of characteristic values that are part of the initial start state or entrance state into the system. We can call these input values, our what I might coin as "in-go" values. Each system therefore has some predefined initial start state determined by this input set. Systems therefore also have some final stop state, at which point their final "output" values or "outcomes" can be stated. Inputs and outputs can occur periodically, randomly or continuously within a system, and serve to connect the system semi-determinisitically with other systems within a meta-systemic framework. Inputs and outputs, or in-go's and outcomes, can be said to be the value determinants of the system that are independent (initial) or derivative (final) factors that relate the system to a larger meta-systemic context containing other systems.

Defining the positions where inputs and outputs are expected to occur within any given system gives us a picture of the points of articulation of the system within a larger framework of alternative systems. We can say that any other system is an alternative system to the one in question that we are directly observing. We can say that all epi-phenomenal patterning found in nature are basically the outputs of some systemic patterning underlying the structural ordering of this phenomena in some quasi-determined manner. They are frequently the outcomes of the interdependent operation of multiple systems simultaneously. We can say that these same outputs either expire and have no further influence within any system, and hence are truly epiphenomenal, or in some way become subsequent inputs back into the system on some other level or another.

It isclear that how we organize and relate our output-inputs and how we express these as discrete values and how they are changed as a result of their functioning within a system, has great importance to our understanding of systems. For naturally occurring systems, and for all real systems, we have no other way of knowing their structure except through the patterning and organization of relationship between these sets of values and how they change over time relative to one another. The structure can be said to be always implicit to these patterns of phenomena, and our systems of generalization are means by which to render the structural patterning as explicit as possible.

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It is clear that a meta-systemic comprehension of reality attempts to derive an abstract and generally valid conceptualization of the sense of structure that is at least implicit to any and all systems. All systems can be said to be internally ordered and functionally integrated in some minimal sense that serves to define these and set them apart as systems. A meta-systemic system of generalization about all systems must seek to apprehend and concisely explain what is considered to be universal and most basic to any system.

We can say something like the following about general systems:

1. Mathematically, we can identify at least one central function that serves as an internal point of reference about which a system is articulated in a directive manner. In this sense, a system in a minimal sense can be said to be internally relative to some central reference point that defines the main directional property of the system, and which constrains the system such that no other kinds of motions or interactions are permitted. This central "fulcrum" can be referred to as the determining control factor, or the main controlling determinant of the system. Such controlling determinants of any system are effectively scalar determinants.

2. Any system is also, in the classical sense of a machine, a singular entity and therefore has finite properties. All classical systems therefore are finite and bounded in some way that sets the constraining factors of the system, as well as the size of the system. We can call this the limitsor limiting factors of the system.

3. Any conventional system, as a finite machine, can also be said to have some sense of size about it that is in some way measurable or determinable.

4. Any system can also be said to exhibit a static order and shape about it, an internal sense of organization that is unique to that type of system.

5. Systems, as conventional machines, can be ranked as well on the order of their extrinsic scale and their intrinsic complexity.

6. All machines, as a result of their design constraints, perform some kind of action or function in a non-static sense.

7. We know some other characteristics based upon experience at least. We can say that a real machine is one that exists in reality, whereas an ideal machine is one that is only abstract. All real machines approximate imperfectly ideal machines, and approach the ideal machine by diminishing degrees. Thus for any given kind of machine of some kind of design, there is some hypothetical ideal that can be defined for that machine of which each example is but an imperfect approximation. In a metaphysical sense at least, we can speculate upon a hypothetical perfect machine of a given type, however specified.

8. We can specify at least one state or a set of states for any given system, that are unique to that system or type of system, however complex. The states exhibited by a system are unique to that system and functionally defining of that system.

9. All real systems therefore exist in some finite condition that can be said to be instantaneous and in which it exhibits some state-trajectory that defines its characteristic direction of transition or state-change. All ideal systems can be said to exist in some definable condition that is hypothetically instantaneous.

10. The same or similar systems that recur over time or across space simultaneously can be said to form sets of multiple systems. Real sets of systems can be said to be imperfectly equivalent such that they comprise a normal range of variation. Ideal sets of multiple systems can be said to be perfectly equivalent to one another and hence exibihit no normal variation.

If ideal sets of multiple systems are variants of a single system, then they comprise multiple possible sets of alternate systems, and these can be hypothetically said to exhibit an idealized normal range of variation. We can say that such sets are real sets that occur in some relatively non-abstract state. The degree of generalizability of such systems is extendable almost infinitely based upon the relative particularity of any and every included subsystem or member system.

Natural sets of systems can furthermore be defined as real sets of systems that have no non-relative ideal standard and that comprise a range of variation that is both normal and abnormal. In other words, they are underdetermined systems in which some form of nonlinear and random variation normally occurs as part of the system.

For metasystems from an abstract perspective, we can speculate on the preceding pattern of order. We can speculate that in an abstract sense, all systems are generalizable. But systems vary considerably to the extent to which the can be generalized in a relative or non-relative way. Perfectly abstract systems, for instance, mathematics itself is a non-relative system of abstract generalization. Naturally occurring systems are scientifically generalizable systems, but they are essentially relative systems that lack any ideally defining archetypes. We may thus define a continuum of relativity along which any abstract system may be placed. We may also say that in the application of mathematics to the description of naturally occurring system, mathematical descriptions must take increasingly relativistic frames of reference into account.

From this, we can speculate that mathematically, scientifically and metaphysically, a meta-system is a system of sets of system, or generalized hypothetical systems that can be derived from either real or idealized instances of systems. Thus we are capable of moving from an abstract description of a single simple system to a more sophisticated and elegant general description of alternate, complex and multiple systems as they occur either realistically or hypothetically. We can represent hypothetical meta-systems statistically and mathematically in ways that are precise and valid. But we depend at least upon the principle of duration and state alternation or variation of systems, or what might be called the intrinsic multiplicity of systems, in order to derive a meta-systemic understanding.

Naturally occurring systems represent self-organizing machines that are usually quite complex and chaotic and hence never ever approximate to some idealized system. Such natural systems incorporate complex relations and chaos into their design patterns and state transition pathways to such an extent that we cannot discount the chaotic epiphenomena as non-extrinsic to the system. The natural system itself comes to incorporate entropy and disorder as being on some levels intrinsic to its sense of patterning and order. Thus, I believe that in natural systems, we cannot hypothesize some ideal state in exactly the same way that we can for, say, artificial systems built on some idealized design in which we normally try to exclude all kinds of non-deterministic influence.

We cannot say in some nonrelative way what an ideal tiger should look like in the same way we might hypothesize a perfect equilateral triangle or a perfect screw with such and such dimensions. Perhaps if we were to judge tiger breeds, we could arbitarily impose some conventional standards upon tiger-traits. We do this with all kinds of domestic breeds. What we have are only numerous evolutionary instances of various tigers, more-or-less similar and yet all different to varying degrees. By natural standards, the tiger that survives to propagate successfully best approximates some ideal standard, but this is itself a purely stochastic mechanism based mostly upon chance.

We can hypothesize that at any one time, there is an instantaneous if complex range of "tigerness" that is represented by the total range of variation of all extant occurring tigers. This is about the closest we can come to understanding tigerness, unless we are to impose some kind of statistical measures of populational parameters upon our definition of tigerness as an abstract system.

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It appears therefore that in our accounting of metasystems mathematically, scientifically and metaphysically, we must also account for the problem of relativity of knowledge in some systematic way. I identify a kind of "metaphysical relativity" of general and abstract systems as informing out knowledgibility about abstract systems, or our ability to know them in some ideal and perfect way. This forms an inherent horizon of abstraction in our knowledge, and is complementary to the forms of physical and anthropological relativity that I have identified previously. I have already referred to forms of structural and functional relativity of systems that is intrinsic to systems. Systems as they occur in reality tend to be unique, and the defining characteristics of systems tend to be specific to an internal frame of reference within the system. In other words, all systems define to some minimal extent their own independent states, and their states are largely dependent upon its internal conditions.

Ideally abstract systems, as for instance those evident in pure mathematics, are said to be non-relative in the sense that their standards for validation are wholly internal, being an internalized frame of reference that requires not other external reference point. At the other end of the continuum, naturally occurring systems, which are the problematics of science, are said to be completely relevant to the external frame of reference in which they occur. They cannot be validated by internal inference alone. Abstraction in science permits a degree of generalization, but this generalization is always subject to its consistency with its external frame of reference. We can say in another sense, that in purely abstract mathematical systems, validity is intrinsically self-evident, hence always explicit to the generalization itself, while in natural scientific systems of generalization, validation is always implicit to the phenomenal patterning from which it derived and to which it refers.

I believe a related consideration of this aspect of the metaphysical relativity of abstract systems is the degree to which generalized systems can be said to be determined. In general, a non-relative system can be said to be a completely self-determining system, hence a total deterministic one. On the otherhand, natural systems that are said to be relative, can be said to be relatively undetermined systems, their structure being at least partially determined by the contexts of their occurrence.

It is evident above that natural scientific systems of generalization and pure mathematical systems of abstraction are mutually exclusive sets--they can be said only to possibly intersect at their boundary, but they form sets of "truths" that are in a fundamental sense different from one another. This is not to say that mathematics cannot be applied to science, which is regularly is, or that science cannot contribute to pure mathematical knowledge, which it often has done.

I would speculate on a kind of paradigm of metasystems as follows:

The question of metaphysical relativity of metasystems brings up the question of the problem of unification of metasystems, or the possibility of representing all systems in a universally comprehensive sense as a single integrated system. While it is evident and more useful to approach systems from the standpoint of multiple subsystems, it is also necessary to at least consider the challenge of conceptualizing a grandly unified system of all systems.

The problem of metaphysical relativity also brings up a related issue that leads us back to basic aspects of knowledge. Relativity of knowledge always implies an inherent amount of uncertainty about the validity of what we know, and it therefore also implies a sense of unknown. The unknown surrounds what we know with a wall of reflexive uncertainty. We can say that what we know absolutely, like two plus two equals four, we know with sufficient certainty. We cannot say this in a non-relative sense regarding our generalizations about science. We can form universal generalizations that we know with relatively high degress of certainty, but there is always a residuum of critical doubt like a background shadow cast by gigantic cloud over our scientific knowledge.

This is not a bad thing as it drives scientists forward in quest of ever greater certitude about their knowledge. But it does entail that scientific knowledge is always bound by a greater domain of the unknown. The unknown always sets a limit to our knowledge. This same domain of the unknown does not exist in the realm of pure mathematical abstraction. Of course, there are probably many mathematical systems that have not yet been worked out or described, that remain basically unknown to us at this time. But what we do know about mathematics cannot be fundamentally changed or weakened by what we don't know in the same way that the discovery of new evidence in nature or of a new scientific theory might undermine or revise in a revolutionary way what we do know about the natural universe.

Based on what we have said so far, it can be seen that metasystems as a science and as a basis for our advanced systems applications, is itself primarily about abstract generalization and the metaphysical limitations that govern our ability to generalize about what we know. We can say that all generalizations require some frame of reference or inference by which they can be validated as part of some larger system of relations. This frame of reference determines the relativity of the system of generalization.

It is a virtue of systems that they are in some limited sense always, by definition as systems, internally relative to themselves. Another way of saying this is that systems of generalization are never completely relative or nonrelative, but are metaphysically complementary in this regard. What we can say that even strongly relativistic systems exhibit yet some minimal degree of non-relativity about them, from the standpoint at least of their internal structural coherence. What we do generalize and know about them obtains an ideal and absolute condition, however partial this may really be.

Hope for science remains in the relatively non-relative basis for knowledge that can be found in limited truth models. We can be minimally and sufficiently confident that our tiger is representative as a generalizable case of all tigers in some minimal structural sense. We call this inductive empiricism, and our confidence grows on the basis of the law of large numbers. This allows us the possibility of inductive generalization that permits us to take a statstical profile of an instantaneous population as defining of the relatively general ideal type. This is the best we can do with our science. Even our hypothetico-deductive models in science, as for instance the theory of Evolution, rests ultimately upon an inductive and empirical basis. An "average" everyday tiger is minimally sufficient at least from a systems perspective for the understanding of most if not all tigers. In such a system of generalization, we can say that all systems are internally nonrelative to themseles. Therefore they cannot be self-contradictory as non-systems. They are discrete entities in some minimal sense of relative independence.

If we observe 999 swans and they are all white, then we can conclude with reasonable confidence that "all swans are white" even if we discover just beyond the range of our observations that the thousandth swan is in fact black. Actually, to be more accurate, we always say that "most all swans are white" and this kind of statement remains true even if we discover a black swan.

It is in the intermediate range of real systems, which are usually artificially constructed systems, where a sense of non-relative truth-value emerges as independent from the instantiatio of such systems. In this sense, our anthropological relativity becomes turned inside-out, and at the center of our knowledge base is a presupposition of ultimately non-relative absolute knowledge of truth. We use our applied math to real and naturally occurring systems in effect to undo the results of the intrinsic anthropological relativity of our knowlege, to gain a relatively restricted sense of internal coherence. In the intermediate range of real systems, and in the validation of all systems of generalization, it is expected that internal coherence and external consistency become matched up and non-contradictory to one another.

The complementary relativeness of systems of generalization is directly tied to the degree of determination that a hypothetical system exhibits. A fully determined system is a non-relative system. It is also an invariant or constant system. A minimally determined system is one in which random variants are the norm, and not the exception, and hence the system is inherently chaotic in its structural patterning. This idea of relative determinancy sets the "degree" of coherence that a system may manifest. It also sets the complementary degree to which random factors of change that are essentially uncontrollable are inherent to the system. We can make the following kinds of generalizations about systems of generalization:

1. The complementary relativity of any system is measured by the degree of relative determination inherent to the system that is a function of the degree to which random factors control the system in an antithetical manner.

2. Relatively underdetermined systems tend to be metaphysically relative systems which also entails that they are inherently more problematic in their generalizability.

3. Most naturally occurring systems are inherently underdetermined systems.

4. Applied mathematical systems can only be partially sufficient to the description of natural systems.

5. Our certainty values and sense of confidence in our generalizations is directly proportionate to the intrinsic determinancy of any system. If a system demonstrates a high degree of complexity and chaos, then our confidence limits for our generalization must be high because our sense of certainty will always remain low.

6. We can say that fully determined systems are systems that are completely known and knowable, and hence are fully predictable in their functional patterning. Relatively undetermined systems are those that remain in some residual sense unknown and unknowable, hence uncertain, and hence at best are only expectable in their functional outcomes.

7. We can also say that we can only completely know systems that are fully determinable. Fully determinable systems are ones that have a completely internalized frame of inference that defines the system as such.

8. The degree of relative determination of any system will be reflected in the distribution and composition of its input-output variables and values. In general, a determined system will have constant and stable values, while relatively undetermined systems will have values that are dynamic and unstable because they are at least partially random. In a fully determined system, input-output values are completely knowable and hence predictable. In a relatively undetermined system, similar values remain partially unknwn and hence at best expectable.

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So far, we have begged the central problematic of rendering a concise analytical description of a purely abstract meta-system, one that can be said to be internally coherent and hypothetically independent of any real system that represents it. It is evident that the quest of a Grand unified theory of all science that is rooted upon a single set of mathematical formulas is probably misguided and impossible. The differential formulaic application of mathematical equations to the abstract description of naturally occurring phenomena upon all levels of analysis and synthesis determines that problem sets in the sciences have to be approached separately and each on its own merit and particularistic characteristics. A metasystems approach does have a integrating effect in allowing us to see the inherent design of all naturally occurring systems as being in the most general sense possible as "systems" that incorporate both order and disorder into themselves. We can say that all naturally occurring systems are the following:

1. They are complex mechanisms of elements & relations.

2. They are unique to their kind.

3. They are fundamentally nonlinear in their dynamic character.

4. They are stratified and embedded in internal-external frameworks.

5. They express relative complementarity of deterministic/indeterministic elements and relations.

Discussion of the inherent metaphysical relativity of abstract systems of generalization, as this is especially dependent upon the complementary degree of determinancy and indeterminancy any system exhibits, brings us back to a fundamental issue about science in dealing with the nature of order and chaos as this is manifest in the natural phenomenal patterning of reality.

We cannot say that order and chaos areclearly separable on any level, such that extended deterministic functions can rapidly lead to apparently chaotic patterning, and fundamentally random variables can beget ossified structures that appear overly determined. Another way of saying this is the following:

1. There cannot be in naturally occurring systems deterministic relations that are not minimally chaotic.

2. There cannot be in naturally occurring systems absolutely chaotic relations that are not minimally deterministic.

Take an explosion, for instance. We would use an explosion as a classical example of maximum entropy, in which a system of energy is suddenly, in a brief moment, transformed into a non-system. But on another level, even an explosion can be seen to be a minimally ordered process of expectable transformations. Explosions are themselves systemic events, and as such even an explosion is never 100% efficient.

These principles can be seen to be consonant with what we know of naturally occurring thermodynamic systems, and we can conclude that any metasystem is an abstract model of some mechanism that is relatively determined. We can say that chaos and order are both intrinsic and extrinsic to any system, and from this we can propose the following kind of paradigm:

In any system, order and chaos impose a kind of fuzzy relationship to one another, that is its own form of relativity, where we cannot say clearly where order leaves off and chaos begins.

I would propose a minimal differentiation formula characterizing any system A, such that:

A = y(x) = y(x)/(1 - y)(1- x)

x = ƒ (y)

y = ƒ (x)

and the initial value of x = (1/ (initial value of y)²)

Where y would equal extrinsic deterministic inputs impinging upon system (x)

And where (1- y) equals the extrinsic random factors impinging on the same system

And (1 - x) equals the intrinsic random factors existing in the system.

ƒ (y) and ƒ (x) are functional interdependencies of system A within a larger framework, such that the functions of y and of x are unique to the system A or the type of system A and the original values of y and x stand for initial input and state values of system A.

Such a kind of system might describe the minimal differentiation needed to unite any potential metasystem.

Such a metasystemic model can only be understood from the standpoint of its structural reiteration or recursion as a dynamic system, such that we may posite some start state A and some end state A' and any number of intermediate states that unite and characterize the transformation of the system A ↔ A'. This implies a basic formulaic framework for our understanding of systems and dynamics, according perhaps to the following kind of paradigm:

Condition 0: A totally undetermined system is one in which A ≠ A' under any condition and in any sense of relation. This embodies a basic principle for all real systems, and for any ideal system, and that is the principle of non-contradiction. A thing cannot be itself and something else at the same time, in some absolute sense.

Condition 0a: A relatively undetermined system is one in which A ≠ A' in some approximate and imperfect sense.

Condition 1: We can state that any abstract ideal system is abolutely ordered and determined if for any variable relation or transformation occurring, the results are always the same, such that: A = A' under any and every condition, no matter what the intervening processes or variables.

Condition 1a: A relatively determined system is on in which A ± A' in some approximate sense under most conditions in the large. We can call such a system generally determined.

Condition 2: We can say that for any general real system, there is some composite linear equation such that each alternate transformational state A" is the linear equivalent of A → A'.

Condition 2a: A relatively real system is one in which A ≈ A' in some approximately equivalent sense under most conditions.

Condition 3: We can say that any general natural system is generally determined if for any occurring state A there is some composite nonlinear formula such that there is an infinite number of each subsequent A' or any alternate A" in at least a statistically approximate sense upon some normal curve of possibilities, such that A ∞ A'. We can say that A is infinitely representable by A' in some general sense.

Condition 3a: A relatively natural system is one in which A ∞ A' in some normal stochastic sense for most cases.

If this kind of paradigm or order and chaos in metasystems resembles the paradigm of the laws of universal dynamics, it is more than a little bit serendipidous. We can posite a general metaphysical homology between real systems as these are generalistically known and natural systems as these are scientifically known, and this kind of paradigm is the metaphysical equivalent of the laws of universal dynamics in real knowledge systems.

We may state that these conditions governing meta-systems are themselves ordered such that condition 3 can be composed of relative conditions 0, 1, and 2. Condition 2 that describes what I call real systems can be composed of relative conditions 0, and 1, but condition 0 even in a relative sense cannot be composed of condition 3, 2, or 1 and condition 2 or 1 cannot be composed of condition 3. We might put it another way and say that the paradigm of metasystems is stratified in a inclusive/exclusive sense such that lower order conditions can underlie higher order conditions, but not vice-versa. This may be modeled thusly:

We can say that any realization of a lower order condition in a higher order system is always relativized to that order of system.

It is apparent in this kind of metasystemic model that we can say that in a fundamental and absolute sense, disorder underlies all order, and disorder is always more basic to a system than order. We can say as well that order is always derivative or disorder in a relative way. We can say that in any naturally occurring system, there is a universal tendency in the large or in the structure of the long run, to return to a state of relative disorder. Only "non-real" hypothetically absolute systems of condition 1 can be said to not return to some state of relative disorder, because such systems cannot change. They are the minimal differentiation from disorder that is possible. Of course, such systems are in a sense non-existent because they have no direct phenomenal instantiation. We only can know them in an indirect and relative way.

*****

It follows from these considerations of general models of metasystems that the description of the system proceeds from a consideration of its order-to-chaos spectrum, or the manner in which it becomes realized in the continuum of order-to-chaos, as part of a larger system of similar relationships. Another way of seeing this is to say that in meta-systemic models we are attempting to desribe the systematic statics and dynamics of a system, and both statics and dynamics are only comprehensible from within the framework of the order-to-chaos continuum. We may imagine dynamic conditions that lead to fairly stable or "relatively static" states, and we may imagine relatively simple statics that result in fairly complex dynamics.

Static-dynamic descriptions integrate the understanding of order-to-chaos in terms of the functional parameters and limits of any system. We may speculate on some basic sets of relative operational relations, or "transformations" that are definable by a static-dynamic description. I will offer the following alternative possibilities:

Unification: the general realization of any system within the meta-systemic framework of reality. A totally unified system would by definition be a minimally or maximally ordered system.

Integration: the functional consolidation or structural organization of a set of parts into a holistic framework. Integration can be considered to be a relativized instantiation of unification.

Differentiation: the order-to-chaos continuum determines that in the largest unified structure, most systems eventually seek a state of unification in the minimal sense. Differentiation is the result of systems to seek alternative pathways, as a result of the chaos factor in their articulation and reiteration. Differentiation can be considered to be the consequence of integration operating against a background of long-term systemic unification.

Elaboration/Extension: Differentiation proceeds on the basis of continuous-discontinuous elaboration of parts, which can be considered to be the variation of pattern leading to systemic differentiation. These describe I believe basic processes of growth and development of systems by which order-to-chaos may become enlarged.

Alternation: Alternation can be defined as the minimal defining differences between two otherwise similar systems, or two possible states of a generally integrated system. In other words, systems may develop differentially along different pathways, which lead to variation and alternative instantiations of the same system.

Construction/Composition: Systems in their transformation may become constructively unified with other systems in a synthetic and metasystemic sense leading to relative integration/unification of the system. Constructive processes determine the part-whole relationships of static-dynamic systems.

Reiteration/Recursion: Technically, reiteration and recursion describe different programming or control facets of systems, one being relatively continuous and the other by contrast discontinous is its state-trajectories. But both describe a basic transformational characteristic of systems that describes their duration or durability, or systemic durability as a function of the temporal dimension. Transformation implies change, and change isa temporally ordered process. Thus change is coherent, and we cannot imagine a change process that is in a fundamental sense discontinuous and incoherent. Systemic integration implies some degree of deterministic stability that implies a relatively static state. We know these as event intervals defined systematically by the conditions and terms of the system it occurs within. Reiteration describes the set of changes in a gradational or step-wise fasion, and describes a periodicity of fluctuation patterns such that periods of stasis are interrupted by intervening periods of relative disorder. Recursion implies the continuousness of change processes within any system, such that change is alledged to be a constant variable of any system as a function of time. If we imagine a film as a long string or series of frames, then we can imagine reiteration as the stepwise progression from one frame to the next. Realistically speaking, the synergism of a film projection system is only achieved if we run the film in a recursive manner, rather than reiteratively, such that the boundaries of discontinuity of the basic state system is phenomenologically eliminated.

Nihilation/Destruction: A final descriptor of metasystemic transformations is, I believe, the process of nihilation or destruction of any system, which can be defined as the point beyond which any system must be returned to a larger and more fundamental pool of possible systems in a state that, from the standpoint of the system itself, is fundamental disordered or "nonsystemic."

Destruction processes are those in which patterns of chaos appear stronger and statistically more prevalent than patterns of order, and lead to the disintegration of the system as a system. We can say that there occurs a reunification of the elements of the system on another level of relational order.

From the standpoint of metasystemic dialectics, it can be seen that order to chaos are thetic and antithetic elements constraining any pattern of unfolding, and leading to a larger synthetic pattern of relationship in a larger context of relations. At the point of ultimate destruction of the system, we can say that a system has reached a point of no return, beyond which chaotic processes are no longer antithetical, but basically non-thetical to the system. In otherwords, random change process become essentially non-systemic in character, and non-systemic relations intruded to greater and greater degree within a system that is disintegrating.

It is apparent that if we can look for chaos in order, we can also seek order in chaos, as long as we can refer to some kind of metasystemic framework in which to construe such patterning. In a totally chaotic framework, or even in a relatively chaotic framework, we can refer to chaos without apparent metasystemic order.

It is apparent that reiteration and recursion can be put upon a continuum of continuity to relative discontinuity of transition. We might contrapose this with the previous order-to-chaos continuum to imagine a space as follows:

*****

A classical conception of science was implicitly one of linear systems. If we knew the intial start variables for any system, and we understood the exact linear laws that described the dynamics of the system, then we could predict with relative certainty the long term state trajectories of any system. It became apparent in the last thirty years especially, with the convergence of Chaos theory from diverse fields of inquiry into naturally occurring systems, that almost all natural systems are non-linear and therefore in a basic sense do not fulfill the implicit conditions of a conventional scientific worldview that was, by the way, somewhat Euclidean, Aristotelian, Cartesian and Newtonian. Einstein upset the apple cart of science in a fundamental sense, but scientific worldview has been slow to catch up with the implications of nonlinear systems in nature.

Another way of seeing this, is to say that we cannot necessarily predict the outcomes of any natural system in any exact or fundamental sense, especially when we are talking about large structures or structures of the long-run, but we can derive alternative sets of expectations of possible state-transition pathways or trajectories of any such system, given any set of primes. For any given interval period or area, we can even assign probabilistic or stochastic confidence limits to these sets of expectations, such that we can say that, perhaps there is a 99% chance of a major earthquake occurring in Southern California within one hundred years.

We do not call such a statement a prediction in an exact or precise sense. We do not give an exact date or time, and there is always the residual likelihood that our statement may prove wrong. We call such a statement a declaration of expectancy or a definitive expectation within certain confidence limits. We would like to be able to push our confidence limits in our "inexact" natural sciences to be able to make a statement like "In a week there isa 90% chance of sunshine" but most of us know that the weather has not yet been that systemtically modeled.

Behind this, is a theory of confidence or of relative certainty, that affects decision theory. There is also a theory of error that is also important to understand in a basic sense. These will be taken up in the second part on operationalization of systems. I would only say that in a revised synthesis of scientific worldview, we cannot any longer afford to assume a basic predictability of patterning occurring at any level of phenomenological instantiation, even upon those levels of classical mechanics that were considered absolute and inviolable for all cases. It follows also that in the methodological operationalization of our sciences, the goals of falsification, prediction and control are perhaps unrealistic in the larger sense at least. The philosophical implications for science will be taken up in another work.

Control, predictability and falsifiability are in a more realistic view of science only relative conditions that we somewhat arbitarily impose upon our phenomenal observations. Even our observations themselves are somehow "controlled" by definitions of measurement and selection, which in turn are often predetermined by the inherent design of the experiment itself. Error may be introduced at any level in such an operational system. Many purportedly objective statistical studies frequently ignore or forget to declare this in their final statements.

We can say that whatever can be controlled can also be uncontrolled, and what is fundamentally controllable, is also paradoxically fundamentally uncontrollable. This is not apparent in our basic world of molecular interactions, but it is more obvious at the margins of our phenomenological event horizons.

It appears that scientific worldview suffers inherently a basic set of paradoxs, or what can be called a fundamental antinomial uncertainty, about its own ability to know, or knowledgeability about reality. We may choose to ignore this issue and be complacent about its implications for our sense of the world, but we cannot do so without at some level risking a sense of realism about our fundamental relationships with and in reality.

Control is a conceptual construct inherent to systems theory. Our ability to introduce controls systematically in the experimental manipulation of phenomena is the basis for falsification and for our scientific method. But control implies an absolutistic quality of being able to manipulate the variables and outcomes involved in any transition system. We can do this in approximate ways in chemistry. I would replace the term "constraint" for the term control in a nonconventional view of science. Constraint suggests a form of relative control operating in any system. We can see that even our observations themselves may be a form of constraint imposed on the system and thus affecting its outcomes in basic ways. Talking about constraint instead of control leads to a theory based on limits and limiting factors that may in some sense predetermine a system and its consequences in a less than precise fashion.

Repeatability is a basic experimental design concept underlying the notion of control. The ability to replicate experimental conditions to derive the same sets of consequences over repeated independent trials, is held to be the methodological basis of conventional science. It is the foundation of conventional control, which allows us to predict systematically the variation of outcomes as we modify the conditions in a controlled manner. Indeed, scientific progress is usually achieved not through replicability of controls, but by the ability to take into account the apparently random and unpredicted and unexpected exceptions to the rules of our generalization, leading to a revision or modification of our conceptual constructs. In other words, it is in the chance encounter with unexpected outcomes that nevertheless demonstrate an unknown sense of pattern and order that we come to more realistically and more generally revise our scientific systems of generalization.

The experimental system of control that we superimpose upon our observations of phenomena, relating to a theory of measurement, which itself relates to other theories of sets, series and samples, will be dealt with in greater detail in subsequent chapters. It is important to emphasize here that such theory is a conventional construct that is not wholly realistic to actual scientific progress. Its revision leads us to the construction of a systematic frame of reference within which to construe, define and operationalize the concept of metasystems.

*****

Thinking about the relationship between order and chaos in metasystems leads to some interesting conclusions. Systems science provides a heuristic and general framework for understanding the complex relationships between order and chaos in all naturally occurring phenomena, and in elucidating the structural mechanisms underlying such patterning. A system can be seen therefore to embody both chaos and order in its general description and modeling, and a metasystemic approach is, I believe, the appropriate framework for construing advanced systems science in both analysis and synthesis.

To begin with, we can speculate that any system always ranges along a continuum of order-to-chaos, but that there is no real system that is ever completely ordered or disordered:

The idea of a perfectly determined system or a perfectly undetermined system is unrealistic and impossible in the real world, though it can be modeled hypothetically in abstract space. These boundary conditions of our metasystems bring our metasystems into alignment with our theoretical understanding of naturally occurring systems, such that naturally occurring systems always obey the rules of thermodynamics. A perfectly ordered or determined system would be some kind of perpetual motion machine. A perfectly undetermined system would be a total energy reservoir or perfect vacuum that reached absolute zero. It would be the equivalent of saying that there is nothing. I believe these ideas are interdependent to one another, such that our sense of order, whether absolute or relative, is founded implicitly upon some sense of disorder, and vice versa.

Another interesting outcome of thinking about the relationship between order and chaos in metasystems theory is to conclude that there can be no completely closed system, or a system that is finite and totally independent of other systems. Another way of saying this is according to the following paradigm:

1. All systems are interconnected to compose a single heterogeneous & stratified metasytem that constitutes total Reality.

2. Any particular system we can describe is always connected to other systems within the framework of the metasystem, sharing attributes of the larger system.

3. Any particular system in a real sense is always a part-whole description of a set of relationships within a larger metasystemic framework.

4. There can be no such thing as a perfectly isolated system. All naturally occurring systems are interconnected functionally in some minimal sense. We can call this the reality continuum that defines the functional interrelationships of the metasystem.

From this, we can reintroduce the principle of anthropological relativity of our knowledge as underlying the sense of fundamental metaphysical relativity of systems. We can see that even absolutely abstract systems, as these occur in mathematics for instance, are still embedded in human knowledge organization as a system and as part of a larger system of understanding. A derivative of this would be to say that our measurements can never be perfect, and that our understanding of natural phenomena is always somehow minimally conditioned by the frameworks of our understanding and our inherent positionality as ourselves a complex heterogeneous system.

It follows as well that to search for a single "ideal" formula for the ideal or universal metasystem, as some kind of grand unified theory, is perhaps unrealistic and maybe even undesirable. It is perhaps more useful to develop a frame of reference that serves to integrate different problem sets relating to alternative systems with different fields of inquiry and application. The beginning of advanced systems science is about providing such a standard frame of reference for systematically construing our reality.

A meta-system is about a universal frame of reference for reality that serves to comprehend and contextualize all systems, and about the systematic interrelationships that hypothetically must occur in any real or particular system as itself a part-whole example of a meta-system.

Gestalt theory enters into this understanding of metasystemic frames of reference, as it embodies to some extent the basic principles occurring in human pattern recognition, and possible in the abstract organization of knowledge of all kinds. Gestalt theory gives us a handle for getting outside of the internal dynamics and systematics of any particular system, while still maintaining a handle upon such dynamics. It follows from the notion that any "figure" (implicitly, any systems of relations) must always be configured and contextualized within a field (implicitly, any metasystemic framework) by which that figure gains contrast and value.

To go one step further, there in a sense of infinite regress in the contextualization of frames of reference-inference about systems. For any set of relations or specific framework we may specify, it is always itself a figure-frame relationship of a larger system of relations, and we may in turn reiterate the entire construct ad infinitum. We may also see that any figure or part-whole system is itself a framework for an entire plethora of subsystems, and so on to infinitesimal levels. We can see that this sense of reality is corroborated by our understanding of natural phenomena in the physical universe quite well and at many levels.

I believe that the application of Gestalt Theory to metasystems and to their functional operationalization is more than fortuitous in more than one way. Not only does it figure centrally at the basis of human symbolic knowledge, and as the basis for heuristic problem solving techniques, but it also figures theoretically and generalistically in our comprehension of abstract and real systems. Gestalt theory permits both the analytical excoriation of structure underlying phenomenal event patterns, but also the synthetic reconvergence of pattern based upon our structural analysis of underlying systems. Gestalt theory and method provides the operational and functional foundation for the integration of advanced systems sciences in terms of nested metasystemic frameworks of understanding.

If we go back to some basic principles of gestalt theory, we can find some fundamental statements regarding the relationship of order to disorder. We can say that any figure achieves its coherence and unity by the degree of achieved contrast with its background. It becomes a figure of order in a background of disorder, or in a negative sense, a hole of disorder in a field of order. In other words, if a system is to a great degree similar to its background framework, then, as a separable system, it is more problematic than one that has a high degree of dissimilarity with its background.

It follows that no description of a system can be offered without also first describing as well the expected and existing framework in which it is embedded. Any structural description of a system can never be completely internal, but must be both internal and external, relating the structure of its relationship to its naturally occurring context.

We can ultimately say too, that this description must always include as well the point of view of the observer in the final verdict, no matter how remote or indirect. This always introduces a residuum of arbitariness into our observations.

*****

A gestalt framework proceeds from the understanding that in our observations of natural phenomena, we bring to it the conceptual constructs of our sciences, and without such basic conceptual constructs, which are ultimately symbolic constructs, then our observations would not be meaningful. We see rocks in the ground as separate entities because we have some conceptual notion of what a "rock" should be like. This is inherent gestalt in nature, as it allows us to configure a rock from a background of similar and different entities. It can alsobe said to be phenonemological in the sense that each rock is but an instance of a prototypical form of a rock that underlies our symbolic construct. The more instances we have of the more kinds of rocks we encounter in our experience, the better our construct of a rock becomes.

It can be seen that conceptual constructs therefore order our phenomenological experience of reality in meaningful ways, allowing us to selectively focus on some kinds of information as important, and to interpret this information as somehow important to our systems of conceptualization. Thus, gestalt systems permit us to do a continuous reality testing to see if new experiences are congruent with our preconceived notions and expectations of experience, or what we can refer to as the metaphysical constancy of our worldview.

We build constructs from our experience, by means of infering relationships between phenomena that are not otherwise obvious, based on what we can refer to as implicit patterning of the phenomenal points. This is inherently a gestalt pattern-recognition process. A great deal of scientific generalization is indeed built up indirectly from remote inferences based upon properties that can be consistently associated with discontinuous and independent observations.

Consideration of a gestalt framework as the basis for a functional operational methodology to advanced systems science invites a number of fairly radical considerations. Phenomenology as a philosophy has been attacked by both rationalists and empiricists as somehow fundamentally problematic. I believe that gestalt theory implies a theory of the phenomenology of experience. This is not to embrace whole heartedly and without reservation phenomenological philosophy. We must understand that even phenomenological experience can be fundamentally non-Euclidean in structure and pattern.

A phenomenological accounting of reality accords with a metasystemic model in a number of ways. Reality can be said by our definition to constitute an ordered stream of consciousness. As such, it is constrained in certain basic ways--for instance, it always flows forward in time, in one direction. It is through the instantaneous expression of phenomena that we come to know pattern and structure in reality, and it is through the periodic recurrence of such pattern that we come to understanding the sense of structure in a larger framework through extended reference and inference.

A gestalt theoretic approach to metasystems can be understood possibly on the basis of the following levels of systematically ordered description and explanation:

1. Gestalt Phenomenology

2. Gestalt Design

3. Gestalt Analysis

3. Gestalt Theory

To understand gestalt phenomenology, I believe we must invoke a model of the French Art Gallery. Imagine an oil painting of a subject hung on a wall. We, you and I, were invited to attend the premier showing of the painting, in order that we may publish a review of the picture the next morning, and we arrive to find it hanging in a fancy frame on a wall. We stand back at arm's length to view the picture. We study the picture for some minutes to try to get a feeling for its essential design and its meaning. We can say that the theme of the picture is the central part of the system. On the face of the central figure, we notice a curious detail of color and stroke, and so we edge as close as possible to see what the medium and method of execution the artist employed, and there in the corner we find the artist's signature.

But as we study it, we notice the geometrical flow of the pattern of the picture, and the hidden spaces of the background, and the multipoint perspective that is atmospherically reinforced. We realize that the picture is a large picture and we are too close to see the whole thing in a systematic way, so we stand back from our original position several feet. At our new distance, we better see the picture in relation to the frame it is in, and we understand that the person who chose the frame for the painting did a good job, as the frame seems to "fit" with the overall motif and feeling of the picture.

And then we notice that the color of the wall, a neutral sherbert color, also complements well the main values and tonalities of the painting, and we realize that juxtaposed next to it is another very dissimilar painting by the same artist, smaller in size, and on the other side is a similar kind of painting by another artist, also of smaller size. As we take in our view, we can't but help notice the ugly wall socket in the corner of the wall, and we look up to the ceiling to find a filtered skylight with indirect sunlight filtering into the room from above, and giving a nice carmine glow to the room. And then we notice the flow, the molding, the oak boards nicely varnished, and the rug that sits in the middle and is quite fancy.

We then notice a small statue in the corner which also appears to complement the subject of the picture. And while we are noticeing these things, we are interrupted by another spectator who makes some comment about the picture, and this comment redirects our thoughts and brings our attention to a detail of the painting that we hadn't noticed before. And then we grow a little tired and wish to take a break, and we notice a small bench that is strategically place along one wall, from which we can take in a view of the "whole" affair of the museum, and we notice a plain-clothe's guard watching us and we notice a museum staff person going through a door next to the room.

The point of this digression is to emphasize the essential contextuality of our gestalt understanding of the "painting" as a phenomenological event, or even more appropriately, as an encounter. We cannot say that the painting was viewed in isolation from anything surrounding it. We agreed that the colors of the room and other paintings and objects of art complemented the picture well, but that the wall plug stood out in an insulting way from the corner of the room.

When we go to write our review of the event, how much of the context should we include in our recounting of our experiences? Can we say that the sight of the wall plug did not affect our final judgement of the piece, or that the interruption, if it hadn't occurred, might have changed the outcome of how we write our final review? If we focused exclusively on the internal design details of the painting itself, as if it existed in a vacuum of isolation from everything around it, would we be giving our readers a fair sense of what we actually encountered? On theother hand, if we pay too much attention to all the surrounding context, we might as well talk about the war that was happening on the other side of the globe at the time, if we can indirectly tie this to the painting somehow.

It is my estimation that reality always presents us, especially as scientists, with this kind of inherent gestalt problematic of the configuring the central figure to the background context of its actual phenomenal instantiation. We cannot say that the structure of our understanding of the painting was not influenced by the external context of its presentation--that our point of view might have been considerably altered had the museum staff made a different set of choices about its frame, and its placement in the gallery. Perhaps if the sky outside were overcast instead of the sun shinning, the hues of diffuse light cast upon the room might have created a different effect and feeling to the chromaticities of the painting. This kind of effect cannot be discounted completely, especially if a critical part of the painting were its chromatic effects.

We can say that conventional science generally tends to leave out the contextual details in an exclusive focus upon the central subject as if it existed in some kind of hypothetically neutral space or abstract vacuum in reality. A gestalt approach implying a phenomenology of experience would by definition be nonexclusive of the context, but one sense of control to such an approach would be the progressive delimitation of its contexts of phenomenological presentation, on the basis of the degrees of directness/indirectness of its context. We are then construing events containing things, rather than things in and of themselves. And the event, not the thing, tends to be integrative of the entire gestalt experience of the figure and ground.

Gestalt design I take to be a second step in the process of description, and it is the first step towards what we can call a general explanation. Gestalt design can be construed as the holistic experience of the entire structure of the event, with the painting as the central point of reference and articulation about which the event unfolded. Gestalt design can give a treatment of the internal design of the painting itself, or even of the central figure of the painting, exclusive to the receding contexts of its presentation. But the contexts of presentation and the internal design of the central subject of the painting somehow appear to interact with one another. The frame fits and complements the central subject well, and the subject appears to be looking out past the boundary of the frame, even into the center of the room, and points in some other imaginary direction. Gestalt design construes the synthetic and holistic sense of integration that the painting achieves, as an event, or, more precisely, as a thing that is the center of an event.

From Gestalt design, we proceed to a third step in our process of explanation, that of gestalt analysis, at which we seek detailed refinement and resolution to our understanding of the overall design. We may take greater notice of the details. We may search for correspondences with the artist's other paintings, and we may search for clues in the artist's life that relate his experiences in the painting to our own. In gestalt analysis, we seek to understand the structure of the invent, and the holism of the design, in terms of its parts, that are construed as a part of the structure of the whole.

In the fourth and final step of gestalt theoretization, I propose that we attempt a resynthesis of our experience of the event in some manner that allows the event to become cognitively consistent with our other experiences and understandings of the world, particularly of the art world, and particularly the world of the artist and the painting itself. I would call this a symbolic resynthesis of our understanding, as this is what it in fact is, but this seems antithetical to what good science should be about. I would claim though that when we seek scientific generalizations relating to phenomena that we experience, we are doing precisely this, albeit in a manner that may be more constrained in terms of its framework of reference and inference. This last step may come in our actual writing of the review itself, or even subsequently after we read what we've written and that's been published in the paper.

To get at the internal analytical structure of a gestalt event, I would proposing the following lists of attributes or parts of a meta-system.:

1. Prime variables, those elementary factors that are self-constituent to the system.

2. Key variables, or constraining factors that determine the patterning of the event.

3. Relational variables that are incidental or coincidental to the patterning of the event.

4. Phenomenal variables (or points) that are the instantaneous factors that we can observe.

I would go further to suggest that in any gestalt framework of a meta-system, we can ask the following kinds of questions of a system as a whole:

What is the whole value of the system? What does it mean?

What are the dimensions of the system?

What is the centerpoint or central region of the system that defines its most stable center of balance?

What is the negative space or antisystemic variables that surround the system?

What is the size and shape of the system?

What are the apparent principal axii of the system and what is the apparent range of its variation of pattern?

What are the transformational characteristics of the system?

What is its sense of motion, direction and duration?

What is the background and essential context of the system, and how does this appear to affect the pattern evident in the system?

What is the part-whole "thingness" of the system?

This last question ties this approach to gestalt synthesis of the whole in reference to its presentational or phenomenological context, back to the complementary dialectic of gestalt analysis of the whole in terms of the parts and explanation of the parts in terms of the whole.

*****

Before leaving off with this mostly metaphysical discussion of meta-systems, I wish to go back to the minimal differentiation formulas presented midway in this digression. They were presented as follows for any hypothetical metasystem "A":

A = y(x) = y(x)/(1 - y)(1- x)

x = ƒ (y)

y = ƒ (x)

and the initial value of x = (1/ (initial value of y)²)

Where y would equal extrinsic deterministic inputs impinging upon system (x)

And where (1- y) equals the extrinsic random factors impinging on the same system

And (1 - x) equals the intrinsic random factors existing in the system.

ƒ (y) and ƒ (x) are functional interdependencies of system A within a larger framework, such that the functions of y and of x are unique to the system A or the type of system A and the original values of y and x stand for initial input and state values of system A.

In consideration of the conclusions drawn from our understanding of metasystems, we can possibly modify the basic formula to be in keeping with what we know of systems. The funtion of x and y that determines its values at any particular instantaneous state can be said to be fundamentally factors determined by time as a scalar value. Thus:

ƒ (y) = ct/dt (y)/zt

and

ƒ (x) = c't/d't (x)/zt

where c and c' represent change constants for a given period of time t and d and d' represent change dynamics for the same given period of time t and z equals some other unknown set of determinantive scalar values underlying the entire system.

We can also say that for each set of articulations, begining with some initial set of point values, we can derive a transformational relationship between start state A and end state A' such that:

A ≈ [(→ A') or (∞ A")] and until (≠ A)

We can see that z would affect x and y differentially in its instantiation at any particular moment in the system. From this we derive a conclustion that is very basic about the patterning of phenomena in the systems. In general, any differential set of phenomena that shows variation is indicative of some underlying scalar determinant that contrains the system in a basic way.

A meta system is not just a model of any possible system. By itself, however abstractly expressed or mathematically formalized, such a model is rather trivial. In being about all systems or any system, it tells us almost nothing interesting about any system. A metasystem is not just a model, but it is more importantly, a standard frame of reference and inference by which all models and all instances of systems can be organize and compared and contrasted in a systematic way.

In this kind of meta-systemic framework, it is apparent that inference becomes equal in importance to reference. We must be able to infer relationships of constraint and change in the unfolding phenomenal patterning of events. Inference relates what we know and can observe directly to our models and structures of understanding in systematic ways. If we can observe pattern of similar variation, we can infer underlying determination. If we can observe increasing instability within or around a system, we can infer underlying orders of chaos. The issue of inference brings us back to structure or ordered relationship, which implies some form of deterministic variable operating.

In general, we can say that whatever is implicit to the patterning of phenomena, can be inferred, and what can be inferred can be done so in reference to similar and dissimilar sets or points. Reference "points to" things as somehow discontinuous or focal in importance. It is a method of marking out the figure from the background, distinguishing it from its field. Inference implies reference, and reference implies inferability. Any matrix or phenomenal event pattern or set or sample of event intervals can constitute reference points. Indeed, phenomenological experience is itself a vast system that is the first and last frame of reference for our understanding of reality. Not only have we built up conceptual constructs from experience in reality, but we have in turn applied these same conceptual constructs to theordering of our experience of reality. Thus a standard frame of reference should permit us to make systematic inferences relating to the functional structure and structural functioning of a system. I believe that gestalt theory applied to metasystems provides such a standard frame of reference.