Chapter VII

Meta-systems Science

Metascience is the philosophy of science framed metalogically from a scientific point of view, in terms that can be said to be denotatively scientific. Science as a human knowledge system has its own history and sense of development. Metasystems science is a formal and systematic approach to scientific knowledge systems of various kinds, achieved through independent verification and logical non-contradiction. It can be said in general that any ideological system, to achieve symbolic unity and closure in reality, will encompass and embody certain kinds of logical contradictions that are the result of certain kinds of pragmatic fallacies in the application of scientific knowledge. For a science to claim the metaphysical status of being truly non-ideological, it must pass certain tests of empirical or observational realism, communicative efficacy and logical non-contradiction. This is most often easier said than done, because symbolic ideological implications enter into even the basic terms and terminologies that we use to define a scientific worldview, at any level. This forms the ultimate limit to science, the limitation of the anthropological relativity of our scientific knowledge. This limit underlies other kinds of critical limitations in science, for instance certain physical relativities in the observation limits of our knowledge. Though we may not be able to ultimately transcend these kinds of basic constraints in scientific knowledge, we can develop devices or means for achieving indirect observational and ideological parallax for the objectification of these limits as such, and for ascertaining in some probabilistic manner the possible realities beyond.

The point of departure for natural systems theory and metasystems science is the observation, first made by Heraclitus, that all naturally occurring systems must change, and change is a continuous and intrinsic aspect of all such systems. The problem of change creates a dilemma in terms of theoretical description, and especially in terms of systems science, as in a conventional way systems are seen as being synchronous and structurally unchanging. Most of our terminology and vocabulary to describe systems carries with it the connotation of static and unchanging realities. When we seek the scientific essence of most systems, the immutable laws governing systems, we seek the eternal verities, the absolute noumenal truths that are held to be perfect and unchangeable. As far as we now, most, if not all naturally occurring systems that we deal with obey the basic laws of thermodynamics, and remain relatively imperfect processes that are forever modulating in some chaotic manner. We run into an even greater sense of dilemma when we come to the realization, for instance, that even our basic laws of science may be somehow changing in ways we scarcely understand.

It seems a basic presupposition, that gains some support in physical systems theory, that all naturally occurring systems, upon all levels, are subject to continuous change at some rate. This casts a relativistic shadow of ultimate uncertainty over all our knowledge and science, but the classical quest for classical and immutable laws governing the order of natural relations does not seem to hold forever and for all things that science must consider. We end up instead of grand and comprehensive theories, with partial "covering law" models that hold exceptionlessly for a certain range or level of phenomena, but which must be replace on other levels by other theories or models.

We are led in such a manner to ask some ultimate kinds of questions about physical reality--such as whether the universe is infinite or not, and whether there is some ultimate beginning or end to this reality, and how did it all come into being anyway. And we are faced only with the understanding that we will not be able to ultimately answer these kinds of questions, but also with the imperative that we must answer them to try to make sense of our world. And it follows therefore that the kinds of answers we provide to such fundamental questions, end up having tremendous implications in terms of our scientific worldview and our operational approaches in science, upon very basic levels.

Metasystems science does not throw up its hands to concede that it cannot be bothered by such questions, as their answers creep into our formulations and view of the world however implicitly, however indirectly. We invariably end up trying to answer these kinds of questions in terms of our theoretical constructions whether we intend to or not. The point of departure for metasystems science is to make explicit what otherwise would remain implicit and surrepetitious in this regard--by explicitly evoking the terms of the basic arguments and dialectics, we gain control over the theory construction processes that we otherwise relinquish in the name of disinterested inquiry and neutral scientific method.

Metasystems science proceeds from several interrelated presuppositions regarding the natural ontological status of knowledge in reality. In general, it can be said that the structure and pattern of our formal and functional scientific knowledge comes to reflect the patterning of the empirical phenomena it represents in certain critical ways. This is a first metalogical precept of metasystems theory.

1. All natural systems are a priori to our understanding or knowledge of them, but such systems are only made known through our knowledge. Without our ability to observe and record and remember such event patterning in nature, we would have no coherent knowledge of them, and they would therefore exist in reality as implicit only to the phenomenal structures that underlie such understanding.

2. Natural systems are in essence possible abstract and general structures that remain implicit to the informational patterning of natural phenomena at all levels--the role and goal of scientific theoretization is the excoriation and empirical substantiation of these underlying patterns of order in nature, at whatever level they are found to occur. Such systems are in essence knowledge structures that are a product of our own reasoning, experience and imagination--they are not the actual patterning in and of itself, though the illusion of symbolic reification may make them substitutable for such patterning. In general, such patterns are demonstrated through relational similarities and event anomalies that can be defined in terms of formal or heuristic rules and their exceptions.

3. All natural systems are:

Therefore, all naturally based knowledge systems are also:

Interconnected upon multiple levels,

Complexly underdetermined

And non-isolatable.

There is no empirical pattern in the universe that is completely isolatable from the natural context of its occurrence. Similarly, there is no possible theory about any such pattern that is also completely independent or isolatable from its primary source of reference, or from other forms of knowledge about other patterns that are interconnected.

There occurs a single set of exceptions to the above stated generalization, and this reflects the status of a certain class of abstract knowledge that is logically coherent and which has no primary reference to naturally occurring systems. This class of knowledge primarily constitutes the language of science, mathematics, in its various forms. It is because mathematical knowledge in its logical coherence and abstraction stands completely apart from the things it is used to represent, that it can function effectively as an objective basis for the communication and articulation of scientific knowledge. Related to this kind of knowledge are forms of possible knowledge that relates to questions of the ultimate and the ideal. Because some kinds of logical relations are abstractly necessary and unavoidable, this same system sets up the paradox of being able to imagine other kinds of logically correct and ideal systems that are in a strict sense non-mathematical in form.This provides the motivational basis and inquisitive force to scientific research--because we can imagine ideal systems.

Metasystems science allows us to step objectively outside of the normal dialectics of science, between holism and analytical reductionism, and to see in a metalogical way a system that is both superorganic and synergistic and also individualized, particularistic and unique in its instantaneous event structures. There is no sense of giving preference to one way of looking at a problem over the other, opposed viewpoint. Instead, it seeks a comprehension that allows such contraposed points of view to be reconciled and put together as facets of the same system. The possibility of metasystems is realized when we come to understand that such dichotomies reflect the limitations of our knowledge and not of the systems we seek to understand in nature--in other words there is no necessary basis for a false dialectic between contrapuntal perspectives if both perspectives are simultaneously true at the same time. Then it becomes important to reconcile these perspectives and to try to understand the system for what it is, beyond the limits of our knowledge.

The point of departure for metasystems science is in the objectification of Goedel's Theorem, which states ultimately that there is no escape from the kind of paradox represented by such a statement "This is false." This kind of statement introduces us to the liar's dilemma, that the man from Crete said all Cretans are liars, and it points up a very basic and specific design feature inherent to human communication and language--that is the duality of patterning that results in the possibility for prevarication. When we consider that a conventional, or standard, Popperian view of science rests upon presuppositions of falsifiablity and falsification, we recognize the critical importance of Goedel's Theorem. We may never be able to absolutely prove the truth of any relation drawn empirically from observation, though any such statement can be easily disproven by the demonstration of exceptions. A science to be empirically based must be fundamentally inductive in the derivation of such generalizations as "All swans are white." The basis for all relativity, scientific and anthropological, is in the introduction of the exception and exceptability for any rule that we may formulate derived ultimately from external reference points in reality. Again, the only form of knowledge not subject to such prevarication is abstract logical knowledge that is internally referential--but that is the ultimate difference between artifical intelligence and natural intelligence as we know it. The former can only refer back to itself in a closed system, while the latter must always refer beyond itself to the larger field of relations from which it is derived.

In a sense, scientific theory and truth only emerges as rules are gradually developed to which no counter exceptions have arisen--so far few such theories have proven to be completely or totally unexceptionable. There is in this sense an operative heuristic principle that the larger the subset successfully subsumed by the theory or generalization, the more mileage it gets, the "truer" and more valid it is. We have really no choice but to proceed in such a manner.

The only other way out of such a conundrum of our knowledge is to see that any referential system that has as its locus a range of phenomenal patterning beyond itself is ultimately a language system that has certain inherent limits and features of its own design that constrain it in certain ways. Scientific relativity becomes as much a linguistic and anthropological constraint of our knowledge systems, or rather in our ability to know in any objective sense, as it is intrinsic to the physical phenomena itself. Objectivity is in this sense ultimately a question of communicability of knowledge as it is a question of the realistic representation of external pattern or the truthful abstraction of any sense of underlying order.

When we recognize that Goedel's theorem is ultimately a language problem upon which any external or natural logical system is based, then we can see that only by strict external reference of such a system can we determine its truth or sense of non-contradiction. "This" as a simple subject-noun is of an indeterminate reference, and can refer to more than one thing--if we specify in more certain terms exactly what "this" refers to, especially as something that is available to independent observation, then we are in a better position to assess and resolve its sense of paradox.

It remains the case that if our knowledge is forever imperfect to the task of understanding the underlying sense of order to the patterning of natural phenomena, then it is even more true that our language employed for the representation of such knowledge is even less adequate. It does not serve our purposes to so restrict our terminological framework to precise denotative terms that we can describe nothing that is real or complex--the strength of human language is its inherent weakness, and this is a part of its paradoxical relativity as well. The symbolic power of language to describe, imagine and intuitively fill in the gaps of understanding is as much a fundamental instrumentality of science as it is of worldview. The critical linguistic difference between science and worldview is, I believe, that in science language should at least in theory always have some empirical point of departure and return--a common reference framework that is rooted in basic ways to phenomenal experience. Ideological language ultimately must point only inwardly to its own sense of truth, and to its own intralinguistic reference points. Any external reference to such a closed system is ultimately secondary and peripheral to its main sense of legitimization or validation.

Another way of looking at the metascientific solution to the problem posed by Goedel's theorem, is to understand that the primary reference of any such statement is and must always be some form of empirically or observationally verifiable experience--preferably that can be verified through some non-arbitrary system of standard measurement and reference. The alternative solution can only be ideological and hence non-scientific because unfalsifiable. In this latter case, primary reference extends to the internal logic of a system of rationalization used to justify a determination of the statement in the first place.

The point of departure for metasystems science can be seen therefore to extend from a certain kind of methodological solution to the class of dilemma inherent to the linguistic and symbolic structure of knowledge, as is represented by the paradoxicality or antinomiality of a statement that can be inherent contradictory--that can be either or both true and false simultaneously. It is to be found that only by the superimposition of some arbitrary but standard system of conventional measurement, can we hope to overcome such a dilemma in a manner that is sufficient for a scientific worldview. Measurement theory remains largely neglected and taken for granted--but its influence in the procedures of scientific verification are as important for the social and psychological sciences as they are for the biological and physical sciences. It is beyond the purview of this outline to elaborate more fully a metascientific theory of measurement, except to note its central relevance to the operational definition of metasystems science.

Measurement involves the superimposition of some arbitrary standard of reference that has certain characteristics:

A zero reference point

A standard or set scale of incremental measure

Scalability

A substitutability of scales or standards by conversion.

Associated dimensionless or dimensional properties that exist independently of the exact measure or value of the scale.

Predefined units of analysis readily exist in the physical sciences but are not very obvious in the social sciences. Atoms have fairly discrete properties that make them predefinable as units of analysis, as do molecules, cells and organisms. The closest proximations to units of analysis in social sciences are individuals in a gross sense, within a populational dynamic framework. Beyond this, we can designate various forms of social units, or alternatively, "cultures" as discrete historical entities that have some kind of relative or areal boundary separating them from other groupings at various levels. But beyond a superficial definitional sense, the agreement usually ends. In spite of a century of cultural anthropology, there remains as yet no pat or standard definition of its principle object of inquiry, culture. Self is also something that can be defined in a multi-faceted manner and for which there remains little if any agreement.

This kind of measurement refers mostly to a parametric standard, and does not necessarily include a non-parametric standard, though it is possible to extend measurement theory and practice to non-parametric systems if certain kinds of assumptions are made and certain limits acknowledged. Non-parametric values have no precise or equal scale to determine the value of the thing being measured, but it implies that all things so measured are of an equal or more or less equivalent value, even though such value is not determinable in any precise way. Equivalence of scale remains implicit only in non-parametic measures, and there is no necessary zero-reference point by which to arrange such values relative to one another.

There is another related set of dimensions important to measurement theory, and this involves the question of the human dimension of measurement, and the possibility especially for error of measurement and for inexact estimation. Sources of possibile error in any measurement system are multiple and overlapping, and this invites the dilemma of Zeno's arrow to the problem of measuring static what is in fact dynamic, and measuring as finite and discrete what is ultimately, or on some other level, infinite and indiscrete. This does not even broach issues of error in recording or translating such measurement, or theoretical issues of its interpretation and framing in a larger system of reference and knowledge. An arbitrary system of measurement is just that--it is arbitrary to an agreed point reference point or shared point of departure. Such a system is a true system only in as much as they are derivatives of mathematical systems in an abstract sense, and are constructions of such systems in an applied sense. Nevertheless, the statement can be made that all such scales or measurements are ultimately relative to the person doing the measurement and to the implicit social contract of agreement that makes a metric system legitimate, for instance, over a pound system, etc.

Sources of error in measurement systems are perhaps more obvious in human sciences or observational biological systems when there exist few if any non-arbitrary points of departure for such systems, nor any standard means for ascertaining discrete values in complex behavioral patterns, etc. In general, nonparametric measures are more applicable and useful in the human sciences than they are in the physical sciences, when even what is being observed may be so complex that it is subject to multiple interpretations without any standard frames of reference.

Measurement theory brings us directly to the issues in metasystems science of the paradigmatic complexity of sciences as these articulate as informational patterns upon different scales and levels of analysis. Progress in scientific theory depends upon the ability to create a common ground of uncontestable agreement in our knowledge structures based upon objective measurement. Scientists far removed in time and place can return with the same instruments and derive the same accuracy and reliability of measurement of a discrete event structure as their predecessors. Paradigmatic agreement may be easier to achieve or at least more obvious in the physical sciences, where entire paradigmatic systems emerge with a great deal of predictive efficacy, than in the social sciences where there can be said to be very little paradigmatic agreement, even upon a definitional scale.

Measurement theory brings us to the question of statistics, number and set theory and the use of these in the description of complex natural based systems. It goes almost without saying that there are different kinds of statistics--statistics are really nothing more than a systematic means of description of relational patterns of complex phenomena, and depend upon fundamental units of analysis and appropriate measures for these units. Descriptive statistics is readily elaborated to predictive statistics and to even a form of prescriptive statistics that rests upon game theory and probability theory. Statistics also implies a complementary system of knowledge, what can be referred to as "dynamics" and it is at least implicit that most statistical description has as its goal generalization of dynamic patterns underlying statistically defined relationships. Dynamics involves change in stable systems; statistics involves the description of such systems as stable structures. We may also speculate on the role of synergistics of systems, which incorporates both an understanding of the organiismic patterns of structure represented by systems, and by the emergent patterns and properties of such systems that are a function of their operation and that are approached holistically as if the systems were themselves somehow discrete entities. In general, I would claim that these relationships involve one form or other of operational and general systematics, and the patterns of relationship that are predictive and that can be said to be mechanical. Mechanical systems can be said to be systems that exist naturally or artificially (human made) in reality, and that exhibit certain types of intrinsic/extrinsic properties--primarily of energy exchange and informational capacity. No organized system of energy exchange is without informational capacity, and no informational system that has external reference can not be about some form of energy exchange. Such energy exchanges, upon one level or another, are always reduceable to scalable measures. It is the case that there are informational systems that have no direct representation in terms of energetics, unless we consider the bioenergetics of the functioning of the human brain that produces such systems in the first place.

The operational basis of metasystems science rests upon the operational elaboration of advanced set theory, or what I refer to as the description of set theory, via means of the articulation of alternative possibilistic statistics. A metaset can be said to be a simple collection of complex entities.

All sets are subsets of some larger hypothetical set, and all sets are composed of some collection of subsets. It appears that in reality, there is no end to the infinite regress of sets. In general, the level of set that we work upon depends upon the units of analysis and frames of reference we impose upon our data. We may look at the same set of events, say a couple kissing.-a phsysicst might see a collection and demonstration of subatomic forces, a chemist the articulation of a bunch of molecules, a biologist.

All sets have a complex multi-level identity--they are or can be complex representations of simple things composing it. All sets are simultaneously subsets of some larger metaset, paragimatically alternative sets of some class simultaneous sets, and a metaset of some system of composite subsets.

From an operational point of view we must adopt a more restrictive definition of sets in general. We can say that they are a collection of "things" that share some sense of affinity, or what is known as "cardinality" making those things common members of a shared set. Sets are composite entities. The type of set can be designated by the nature of the cardinality principle or relations governing the shared identity of its constituents. A set may be a 'grouping' that is intrinsically organized in a more or less complex manner, or that are relatively independent of one another except in some indirect way. All sets have a certain size in the sense that they are bounded entities.

In general, the cardinality of a set is defined by the determinants that characterize the members of a set--in this sense any set is a collection or sample of related objects or points that may be said to be relatively determined or undetermined. Most sets in nature can be said to be partially determined, and the determinants that define the cardinality of the set can be said to consist of implicit rules of ordering defining the identity of the members and the possible relations occurring between members.

A metaset can be said to be a superset of one or more sets, either defined through time or across space or both, in which the cardinality defining the membership and relational order of the parts of the set is either variable or alternate. A metaset is inherently dynamic, changing in its order and composition, and this sene of dynamic change in the constitution and behavior of a set can be topographically mapped in hypervolumetric or complex multidimensional space.

Sets can be combined and related to one another, and set theory largely involves the possible logical relations between sets and leads into other forms of mathematical theory. In a sense, statistical samples and derivative datapoints represent virtual sets that can be superimposed upon different forms of data, rendering this data in terms of sample points manipulable to various statistical techniques of description and analysis.

A matrix can be said to be a special kind of metaset that is defined in a reiterative or recursive manner, and that has a fixed set of constraints defining the breadth and size of the set, and also the nature of the relations between the members of the set. In general, a matrix can be said to be a fully determined set of a special type, and I believe matrices are actually rare in nature with a few noteworthy exceptions, and are demonstrated more through the reiterative or cyclical articulation of natural systems over time than by distribution of systems in space. An exception to this might be said to be the reiterative structure of DNA in genetic encoding. Crystallytic structures of atoms and molecules are said to have matrix type structures, but these matrices constitute gross geomatric descriptions of the distribution of molecules within a lattice framework, rather than a fully determined matrix that functions as a system.

It is beyond the scope of this introduction to elaborate in more detail the mathematical aspects and permutations of set theory as this may apply to metasystems analysis. It is important to state though that statistical systems consitute the principle means of expression of metasystems analysis in terms of set theory, and the main aspect of general statistical description and analysis are in terms of what can be called "possibilistic statistics." All statistics constitute a form of heuristic representation, analysis and modeling that describe what can best be described as hypothetical metasets that are purported representative of natural systems and that exhibit patterns that are relatively non-random in distribution or reiteration. We do not need to invoke more exotic forms of statistics, as for instance Einstein-Bose Statistics, to explain the possibilistic aspects of statistical analysis and description of metasets.

It is true that statistical measures can generate profiles and descriptive variables of metasets that only indirectly represent reality, or that do have any direct representation in reality. Such systems are nontheless considered to be relatively valid within a certain range of statistical probability, and to the extent that they can be said to be valid, they exist as a metasystem independent of the actual sample points from which they were derived.

Set theory is important to metasystems in that it provides an operational and methodological handle to the description of complex systems, and it provides a means for framing and analyzing possible relationships occurring at different levels of complex system. In general, it comes as a paradox that as long as systems can be accurately and reliably represented, the larger and more complex the system, the better and more realistic the possible representation that may be forthcoming for it.

Another point of departure in the elaboration of metasystems analysis is in the definition and conception of what I refer to as alternative number theory as complex variables. A particular data point is a set may represent a particular range of values, or, even a number of different ranges of alternative values. The identity of any particular number within such a system is therefore inherently multidimensional and complex. Furthermore, any point may be a variable that is defined by both dimensional and dimensionless parameters, and may in fact constitute a subset of possible points, each of which in turn is represented by another complex alternative variable. Each alternative variable can therefore be said to be completely relative to the variables that in turn define it within a relational complex. Discrete values may be associated with such variables at different points and times.

In general, a metasystem can be said to be an integral of a metaset that is articulated within a larger superset framework or context, and which determine or govern the relations occuring in the state-path behavior of a metaset. A metasystem is primarily concerned with the problem of integration of sets or metasets over time and space, in a manner that there arises emergent or synergistic properties of the system as a whole that cannot necessarily be predicted by the analysis of its parts or constitutent subsets. A metasystem comes to have a particular dynamic state-path behavior that usually fluctuates over time. A metasystem can be thought of to be composed therefore of one or more metasets in interrelation that are changing through time or across space in significant ways.

Consideration of metasystems analysis invariable brings up the issue of contextual analysis of the superset or the framework for the articulation of the metaset. The question of context is largely a question of identifying the significant figure ground relations that serve to define the identity of a metaset in contrast to and identity with a shared background of other relations. In general, the question of appropriateness or relevance of contextual information is important to an understanding of a metaset in its natural context. In a world in which everything is at least indirectly connected to everything else, it is easy to see how too much of everything else can serve as so much noise in the understanding of background relations affecting the dynamics and behavior of a metasystem.

There is also a critical sense that inherently underdetermined metasystems can form a complex set of alternative pathways, or alternative event spaces, in the unfolding of their possible state path behavior--these alternative pathways are nowhere ever fully predictable, though we can expect certain probabilistic pathways forthcoming from them. Such systems in their unfolding are said to be chaotic.

The relationship of matrix theory to set theory comes when we understand that much of this apparent chaos in complex systems can be organized within a framework of possibilistic event spaces that may be defined statistically as a discrimination table through which all possible pathways of a state-path trajectory of a system may be defined and identified.

It is possible to construct such matrix discrimination structures by means of intercorrelational analysis of sample sets in which at least some indirect relation can be hypothesized, even if no direct causal relation can be demonstrated. Intercorrelational analysis provides a means for mapping complex sets in multidimensional space, in a manner that the relationships become sample points in a relational structure. The sense of the reality of the original data point is lost completely in such representation, and only relational structures are represented in hypervolumetric space. Such intercorrelational analysis is based upon a principle of cardinal numbers as alternative data points, derivative as partial determinants of complex systems. Such a method allows us a means of comparing complex relational systems in a shared or common metaspace.

From discrimination tables and intercorrelational representations and matrices of partially determined alternative variables, it is possible to apply a set of arbitrary decision rules, or what are more formally defined as heuristics for the selection of alternative pathways and for the determination of relational rules that can be said to be implicit to and underlie the complex organization of a system.

From this, rule-based systems may be devised that provide a more formal description of the complex state-path behavior of metasystems, and from these systems we may test for the accuracy of simulated models to our observational measures of real systems.

Governing these kinds of systems can be said to be a form of hypothesis generalization that isolates key operational rules or relationships that govern the articulation of a system and that regulate and partially determine its outcomes and dynamics. Paradigmatics can be said to be a form of dialectical counterpoint and argumentation of alternative competing rule sets or systems, often defined conceptually or symbolically by key operating metaphors, that govern metasystems in a general if not in a universal way. Paradigmatics lead to a competition of competing ideas and theories, and eventually to a sense of progressive understanding of the structural nature of systems in a parsimonious manner.

Heuristics, in modeling, in learning and in exploration of alternative possibilities, can be said to play an important role in this process overall. Heuristics has rarely been formally defined--it consists of modeling and modeling theory, and the representation of real systems in abstract terms. It can involve game theory and simulation, as well as in scenario forecasting.

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It is important to reiterate the important and unique role that mathematics plays in metasystems science. Mathematics is the language of science, and science cannot achieve the degree of objectivity or logical noncontradiction necessary except by means of the strict adherence to and application of rather formal mathematical rules and relations. Pure mathematics has no external reference beyond the rules of its own logical relations and identity. As a language it is a sign system that, unlike natural human language, permits no internal contradiction. It is beyond the purview to speculate about the a priori nature of abstract mathematical systems, except to remark that they exist as ideal possibilities that appear to be structurally immanent in all naturally occurring systems. Another way of saying this is that they are the consequence of the fact of the systematic ordering of nature in the first place--without such ordering science as we know it would not be possible. The first rule of a natural science is therefore to state that abstract order preexists in the natural patterning and chaos, before our observation or understanding of it. By virtue of our own intelligence and capacity for knowledge and understanding, we bring to reality the possibility of abstractly representing these ordered relationship underlying all classes of natural phenomena in a way that is mathematically correct and accurate--we bring with our models the possibility, indeed the realization, of alternative ideal systems, mathematically defined and represented, that have no clear manifestation or reference in physical reality.

I believe it to be a source of infinite sublime wonder and awe that this is repeatedly demonstrated in nature--that we should have evolved a unique ability to imagine such possibilities, and by their imagination, to make them a part of our reality. Once we have defined the rules of science, they become as much a part of our world as if they were set in concrete or stone. Whether we wish it or not, we can realistically see the world in no other way than that defined by science--science permanently alters our view of the world. It then becomes our choice how we make use of this understanding.

What is sought is a characterization of naturally occurring systems that has general applicability to a broad range of such systems and yet which might retain some efficacy as a theory that can lead to operationalization and experimental results confirming or disconfirming the theory. A systems theory of natural phenomena is not the same thing as a scientific theory or explanation underlying the reasons for such phenomena. It is a frame of reference for the connecting of such theory to other theories and other kinds of evidence, and it provides theory with a framework for interpretation of evidence. All naturally occurring systems obey certain fundamental physical principles and principles of design or order that cannot under all circumstances be violated. These principles serve as fundamental constraints guiding the behavior and patterns of natural phenomena that we can then classify as one kind of system or another. A system, to be categorized broadly as such, must exhibit conformity to those kinds of constraints that serve to characterize and distinguish different kinds of systems from one another. We can thus come up with a larger system of classification for naturally occurring phenomena, to which would be added as well some other kinds of systems that are not directly "natural" but that relate somehow to naturally occurring systems upon different levels of integration. There occur rules or principles that can be said to be universal at least to the largest class of systems that are known so far to us. This is not to say that there might not be even some larger class or framework that remains unknown about which little is known or observably obvious to our muddled heads. Discovery of new kinds of systems must await the acquisition of new forms of information and/or the reframing of old information in new ways. Past experience in such discovery processes and a broader history of knowledge entails that these future discoveries will almost certainly occur. Science lives with the illusion, very deep-seated I believe, that it had somehow exhausted itself or rather its central subject or object of knowledge, and that it has therefore little new to learn about reality. Nothing in fact could be further from the truth.

Efficiency in ecological and evolutionary frameworks is relative to the system and the surroundings being described. A mechanical definition of efficiency is a relatively high ratio of output to input in a working system. A maximally efficient system accomplishes a set of effects (an end state) with the minimum of waste or effort. We can contrapose efficiency of a working system to the complementary state of entropy we can assign to a system, which for a closed thermodynamic system becomes the measure of the amount of total energy unavailable for work, or the relative measure of disorder or randomness in a system (in any given state). All naturally occurring systems, including human systems, must obey the laws of thermodynamics, which means that we can have no perfectly efficient or perfectly non-entropic system.

Work is defined as the informational (nonrandom) organization of energy to achieve some desired effect or product or to maintain some systemic state of order within a given amount of time. Work in its most fundamental sense can be defined as the systematic transfer of energy from one form or state to another, or state transformation. Work induces a kind of change therefore, and results a form of change. This form of change is the opposite of natural entropic tendencies towards increasing randomization. I will therefore call "positive change" any state transformation that results in an increasingly non-entropic state, and a negative change as any state transformation resulting in an increasingly entropic state.

All naturally occurring systems change.

No system that exists cannot change--there are no static systems.

There are no perfectly entropic or random states in reality.

There are no perfectly ordered or non-random states in reality.

All systems are changing either towards increasing order or increasing disorder.

All other things being equal, all systems will tend towards increasing disorder if no work is done to increase order.

Since work is always be definition imperfect, and because all systems tend in the long run toawards increasing disorder, all working systems must eventually become dysfunctional as systems.

Naturally occuring systems can therefore be called informationally stochastic or "self-organizing" systems because there occurs no well-defined, external causal agency that determines the organizational structure of the patterning of a system.

An organized system is one that is intelligently ordered, or "informationally coherent," to perform some minimal form of work. Intelligent ordering of any system is a measure of that system's integration and relative state complexity.

1. All systems are part of a larger, more entropic environment that constitutes the surroundings of a system.

2. All systems are thermodynamically open to their surrounding environment.

3. All systems are composed of multiple components and thus are multi-factorially determined.

4. The determination of any system, according to the laws of thermodynamics and of informational dynamics, is always incomplete--systems are thus complexly underdetermined.

5. Systems are therefore subject to continuous state change that is both exogenous and exogenous.

6. The complex under-determination of partially open thermodynamic systems entails that all such systems can perform only a limited amount of work for a given duration of time.

7. Eventually, all naturally occurring systems must disintegrate and cease to function (to do work) as informationally coherent systems.

It is important to distinguish between total entropy of a complex system and the net entropy of such a system.

1. Naturally occurring systems are self-organizational working systems that achieve some sense of complex equilibrium within its environment.

2. Equilibrium is an entropy dependent and temporally dependent relationship of a system, such that the higher the equilibrium of a system, the lower its total entropy, and the longer lasting the system will be.

3. This equilibrium can be understood in terms of the ratio of net efficiency of the ratio of energy input into a system (E_I) over the energy output from the system (E_O) plus the energy lost from the system, or the instantaneous disorder of the system (S) equals 1.

K = E_O / E_I - S = 1

4. All natural systems will tend towards some optimum value of equilibrium that will be a function of the time and size of the system. Equilibrium of a system is a time dependent function, such that a system will increase in order towards equilibrium, achieve a stable state-path trajectory, and eventually then decrease in order back towards total disequilibrium.

5. The measure of the efficiency of a system is positively correlated with the measure of the integration and informational value of a system.

6. A totally disordered system is a one that exists at the lowest potential energy state and has the least amount of informational value, whereas a hypothetically and totally ordered system is one that exists at the highest potential energy shate and that has the greatest amont of informational value.

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Advanced systems science concerns the theoretical and operational modeling of complex processes and patterns that occur in nature or that are the product of human endeavor. In general, it concerns systems that are large and very complex, in which there occur many different interconnections between multiple components upon multiple levels. The basis of natural systems theory and advanced systems science is the construction of mathematical models allowing for analysis and application to the original system. In essence, this is what, I contend, experimental science accomplishes, in one field after another, via what is conventionally understood as the scientific method. The key in understanding advanced systems science is the management and operational modeling of superlarge and supercomplex systems.

What is sought from such modeling is performance optimization of a system that stems from a correct understanding of its interfunctioning parts. The challenge in developing this kind of understanding is to realize that within any system there are always numerous tradeoffs. Achieving a sense of working equilibrium does not define the function of an ideal or perfect system.

All natural systems are constrained by the principles of entropy and thermodynamics. No natural system can function in an ideal manner as can be represented by an abstract mathematical model of such a system. The inherent constraints predetermining the functional limitations of any system become multiplied exponentially as the number of components of a system grows with tremendous complexity. It can be expected therefore that, while reasonably high efficiencies can be obtained from relatively simple systems, it is very difficult to achieve even low levels of efficiency in very complex and large systems.

Most larger systems can be said to be incompletely, or only partially integrated.

The applications of mathematical procedures for the analysis, construction of models and optimization of systems is based upon information and experience, and does not extend from a consideration of pure mathematics.

Choice of mathematical model to apply to a particular problem set in systems analysis depends upon many factors, and often alternatives exist for the same problem set that are theoretically driven. The application of different mathematical models can be found to depend centrally upon the conceptual framework in which the problem set is defined within.

The determination of particular or general performance criteria for the operation of a given system, or for its state behavior, is ultimately based upon what we select as the appropriate or desirable state-variables governing the system, and predetermining our analysis of the system. These criteria drive our mathematical formulations and functions toward the setting of arbitrary performance criteria expected from a given system. Performance criteria are normally arrived at in pure and theoretical science through experimental investigation and careful, measured observation of the behavior of systems. It is when naturally occurring systems do not perform as expected or predicted by our models and theories, that we are led to conduct new experiments and to devise new theoretical frameworks for the explanation of the discrepancy of behavior that we encounter. What is discrepant are not the systems that occur naturally, unless we have an undue influence in their behavioral outcomes, but the models that we apply to such systems.

For scientific knowledge to be complete and effective, it must proceed from conceptual frameworks of understanding to the formulation and testing of applied mathematical models, and even the experimental simulation of systems, in order to systematically demonstrate the correctness, or "goodness" of fit, of the model. The performance values we seek therefore in natural systems science is not the performance of naturally occurring systems themselves, but of our models and simulations of such systems. Mathematics, as a language of science, is not a pure or abstract language of mathematical theory and philosophy. It is rather the applied language of mathematical engineering and description in which dimensional structures and values can be readily quantified. Various mathematical methods have been elaborated for this purpose. We speak of stochastic, deterministic, adaptive and optimal models. We speak of various forms of control theory, and linear and non-linear dynamics characteristic of such systems.

The scientific description of complex natural systems is never complete nor perfectly accurate. Most descriptions of very complex systems are crude and oversimplified compared to the actual informational content present in such systems.

In natural systems theory, if everything can be said to be connected to everything else, then by logical deduction we may conclude that we can deliver eventually a kind of model of a total system that serves to define the operation of all interconnected systems. Furthermore, we assume that these connections have some kind of logical value. In other words, they can be defined by conditional rule sets.

Science serves two purposes--the understanding of the rules and principles regulating the natural patterning of reality, and the construction of alternative realities that serves to extend biological survival on earth. While the first objective may seem apparent to most people, the second object may appear to have ideological implications.

Metasystems science as a form of metaphysics that is involved in heuristic problem solving through the use of hypothetical models concerning reality.

Issue of the vision of science being limited if science serves, as purely disinterested inquiry, narrow ideological interests.