<Book Index>


Chapter 1

Process Compartments as a Foundation for Ecological Control Theory

(last edited: May 23, 2006)



Theory of process compartments

The new thesis

The three transforms work like this

System image

Bi-level emergence, mathematical and physical models

On the question of symmetry

Process Compartment Hypothesis (PCH)

Stability, the hidden illusion

The new mathematics, and the new science






In Prueitt (1995), a theory of process organization was proposed as foundation to a computationally grounded class of generic mechanisms, algorithms, and data encoding. This theory attempted to take into account the creation and annihilation of natural processes localized into coherent phenomena by the cooperative behavior of complex systems.  Its formal foundation lies in pure mathematics and in thermodynamics of “weakly” coupled oscillatory systems having strong internal regulation and relatively weak intersystem influences.  The initial application of this foundation was in quantum neurodynamics and in cognitive neuroscience (following the conferences hosted by Pribram 1992, 1993, 1995, 1995 and Pribram’s books 1971 and 1991.) 

A simplification of the foundation will occur as we introduce structural ontology (Adi and Prueitt 2004).  This simplification is linked to data encoding, using the key-less hash table [1], and to the real time formation of structured information about the process being modeled.  The simplification is motivated by a complex theory of natural process.  The new information science retains the simplicity of data encoding and algorithms; while being consistent with the familiar, but truly complex, private experience with one’s own awareness. The techniques and assertions of fields like artificial intelligence do not have this simplicity nor naturalness. 

The core assumption made, in the theory grounding structural ontology, is that regularity of natural patterns are caused in part by tendencies to ignore small differences.  Systems, perhaps even non-living systems, are involved in the emergence of function from substructure.  Function imposes certain equivalences during the formation of natural category.  It is the phenomenon that natural category emerges that motivates all of the theory and observations that follow.  We ask “how” natural category arises and we use our answers to encode, into data structure, structural information about emerging categories.  The encoding is localized as “n”-aries, as discussed in Appendix B. 


In a familiar instance, we observe the tendency to remember only part of experience and as we do this we often treat the particular as if a thing seen before.  The experience and previous experience are categorized together and seen as being the “same thing”.   An example would be a discriminatory behavior or preference for one type of food as opposed to another. 

A relationship between human mental imaging and action-perception cycles is implicated as being part of the mechanisms that create experiential category.  Some scholarship about this relationship is presented in order to help define intellectual background.  This background is needed to ground a human-centric use of machine ontology, sometimes called web-ontology [2].  The “n”-ary encoding is the first step in developing an alternative to W3C standards.  The core insight is that action in a reacting world leads to an observation about the consequences of changes made to a responding system and thus informs the responding system about itself via changes made and perceived in the system's environment.  Web-ontology has been ushered in by the Semantic Web movement and by the related academic field of artificial intelligence.  However, the origin of information design sets with a few self appointed “knowledge engineers” and not within normal everyday usage.  The “n”-ary alternative is used within action perception cycles, where part of the cycle is embedded in normal everyday usage. 

In the last part of the twentieth century and the first part of the twenty-first century government extensive and persistent funding of so called software agents lead to mistakes in the design of web ontology.  The mistake revolves around the notion that computer programs can be the same as natural intelligence.  The situation remains difficult to clarify. 

The theory and technology for “structural” machine ontology was developed in the years 2001 – 2004 and is presented in later chapters.  Between 2004 and 2006 we developed a working understanding of the semantic web information technology standards.  These standards are developed using collaborative processes by the W3C and OASIS organizations.  The standardization process itself is an example of the formation of natural category, and thus the causes of the specific standards lend insight into the formation of natural category.  In this case, the observation is made that W3C standards developed to help the information technology sector achieve business objectives, whereas the OASIS standards were more oriented to shifting the origin of control, in new information design, from the software vendor to social process.  [3]

How can the scientific literatures curb this business oriented conformational process by exposing when in nature one finds truly non-deterministic processes? 

In Prueitt’s 1995 – 1996 work, an analogy to human self image is used to communicate how natural compartmentalized processes act in a natural setting.  The analogy is broad enough to cover any natural system, ie a complex system in Rosen’s use of language [4].  Mathematics is a simple system when seen in isolation from its role as a communicative language of science.  An outline of some mathematical concepts was developed and expressed.  This outline is given below.  The formal concepts are related to the study of emergence and stratification of physical processes.  Over the past two decades, the outline was not filled out to the degree that it should have been.  However, the 1995-1996 work seems as valid in 2006 as it was in 1995.  To finish this work would seem to require changes in support structure so that the mistakes persisting in artificial intelligence and semantic web communities can be directly challenged.  Recent trends are hopeful and can depend on well established formalism and extensive scholarship. 

Mathematics, in Hilbert spaces [5], gives description to how compartments might be studied in the context of temporally registered energy distribution in separated spectral strata.  Mathematics in Hilbert spaces can be mapped to descriptions expressed as discrete formalism [6], giving us a rigorous transfer of correlation analysis to data encoding in the form of “n”-ary web ontology. 

We found others working on technology and descriptions that depend on an encoding of structural ontology into spectral strata.  By structural ontology we mean actual reality, not the abstraction that one finds in web ontology language (W3C standards).  We mean the structure of natural category observable via direct perception or even instrumental measurement such as with electromagnetic or optic devices. 

An analogy between spectra processing in the brain and computational process within structural ontology is to be established in later chapters to ground a text retrieval and knowledge management paradigm for distributed collaboration in web environments.  Chapter 10 is developed, in 2004, in collaboration with several colleagues to reveal the nature of the Adi structural ontology for natural language understanding, and the corresponding generalization of his development experience.  This generalization is a “generative methodology for creating structural ontology.” 

Appendix B expresses a notational system consistent with the above remarks. 

Theory of process compartments

Prueitt’s 1995 theory of process compartments described what might be necessary to the organization of experience.  First, it may be necessary that natural phenomenon self organize into strata, and that the phenomenon in each strata emerges through an aggregation of substrate phenomenon.  Natural category forms through a reification of functional invariances imposed during periods of emergence.  Human memory systems may be responsive to managing the aggregation process.  The real situation cannot be expected to be simple.  Complexity is defined as a property of real situations, particularly during the emergence of function [7]. Complexity as defined by Robert Rosen seems necessary.  A non-deterministic aspect to the emergence of function may be necessary if the exercise of choice occurs.  For us this is not a religious concept, but one developed from direct experience not only with our private observations about human choices by with underlying physical, and non-living, properties.  Non-deterministic phenomenon may always be present anytime an emergence of something is occurring.  We are reminded that many of the real mechanisms on which human choice depends are observed in non-living systems.  Living systems may be expected to take advantage of underlying physical phenomenon.  Part of the mechanisms involved is what we call “awareness”. 

A specific number of mechanisms are involved in the expression of attentional behavior, such as awareness.  In stratified theory, we represent these mechanisms as acting with elements of substructural memory resource.  The aggregations of substructural resources are also thought to be by environmental constraints.  The mutual entailments, the full set of causes, are thought to create meta-stable compartments experienced as mental events. 

These compartments are physical phenomenon and should be observable if one looks in a proper way.  However, scientific reductionism asserted that logical coherence must be used to express the full set of causes, and this just seems to not be the way the natural world is organized.  Again, the notion of coherence can be understood as something that is build up from phase coherence seen in electromagnetic fields.  To expect that all “fields” must be forced into a single coherence may be logically satisfying to some, but the impact that such an imposition would have, if this were possible, would be an annihilation of everything.  We do not see this annihilation phenomenon in astrophysics.  What we see is both coherence and shifts between complex systems while coherence is challenged and systems undergo change. 

The contents of experience, however, may not be directly observable except by the person him or her self who is “experiencing” awareness.  In stratified theory, the compartment is seen as a physical phenomenon with stability far from thermodynamic equilibrium.  The compartment’s stability depends on the substrate as well as the environment.  Simply stated, the compartment emerges from a substructure and is constrained in its form and function by a set of laws imposed as environmental influences. These environmental influences include constraints imposed by neurophysiology. Underlying the stability is phase coherence [8]

Using notational language about the structural ontology of process compartments, the relationship between mental imaging and action-perception cycles is modeled as including a set of generic mechanisms.  We then use analogy to develop the stratified web ontology first proposed by Prueitt in 1999 [9]. 

One conjectures, that in biological systems, these mechanisms are available to an intentional system behaving within ecology.  Based on an extension of Soviet-era cybernetic, we developed the specific set of structure-to-function relationships, involved in a specific phenomenon.  We will see in later chapters the development of a “generative methodology” designed to create a model of the cross scale mechanisms that are involved in the emergence of compartments of various types.  The generative methodology uses formalism that describes these generic mechanisms.  Again, the key concept is that during emergence the needs of the environment shape the potential that develops due to the aggregation of substrate.  One sees this phenomenon in physical chemistry, when molecules form and expression functional properties.  In organic chemistry, the cross scale expression is often far most complex.  An example is gene and cell signal pathways expression [10].

We conjecture that the emergence of any type of physical phenomenon can be modeled in complex situations, specifically in the situations involved in the formation of mental event.  We argue, philosophically, that the regularity of any of these naturally occurring mechanisms is reinforced due to minimal energy and effort constraints that must apply to any living system competing for survival. We mean by this that the living system develops a perceptual system that relies on as much regularity in response requirements as possible.  From this argument we have developed an approach towards deploying computer based ontology with three layers of abstraction.  The result is structural ontology having a simple data encoding.  The data encoding is so much simpler that W3C web ontology language standards that the eventual adoption of these encoding methods is seen problematic to the current information technology industries.  Adoption barriers exist for this reason.

To understand structural ontology we need description and motivation for generative methodology.  A generative methodology is used to develop structural ontology through an iterative process.  The motivation for generative methodology comes from a number of origins.  Most of the material in this book is designed to reveal these origins.  In 2006 an OASIS standard [11] was adopted that specifies examples of computer mediated development of web ontology templates, and the necessity for periodically involving human decision-making.  The primary concept being introduced into information technology standards by the OASIS organization is that choice points must be identified through a process of human decision making, and that resulting computer based web ontology is then usable as part of an automated production of multiple possible outcomes.  The natural emergence of category is finding an expression using information production standards.   The OASIS standards places community based resources in the hands of those who seek to shift the origin of the design of social information from the few to the many. 

Starting in 1991, on obtaining a research position at Georgetown University [12], we reached into several disciplines in order to ground the generative methodology.  Ecological psychology, founded through the work by J. J. Gibson in the 1950s and 1960, was a good place to start.  Ecological control theory emerges from an understanding of the generic principles involved in the relationship between action and perception.  To be sure, the concept of Darwinian evolution is modified to include mechanisms that produce replication of functional responses to perception and provide regularity in the acting and behaving of living systems.  It is these replicated functional responses that we look for in applying the generative methodology.   Prueitt’s efforts, 1985 – 1988, on theoretical immunology and on formal models of biological neural networks were also instrumental in the formulation of generative methodology. 

According to theory developed within the ecological psychology academic community, action-perception cycles generate compartments out of a system image in the presence of external stimuli.  For Prueitt, compartments always meant organizational stratification.  Stratified theory defines "system image" as a reflection of temporal non-locality realized in a field manifold and having meta-stable potential localities (attractor regions), and ecological affordance (Kugler et al, 1990).   The system image is thought to encode into some part of its mechanisms information about these attractor regions.  How this is done was one of the open questions. 

The notion of a substructure, from which material is aggregated, is essential to how we formulate the theory behind the generative methodology.  It is the entanglement of the consequences of those elements of substructure that are present locally that forms a key part of what types of systems develop based on the disposition and natures of the basins of attraction that come to exist in the field manifold.  And, to carry this model a bit further, the basins of attraction become the center of attraction for specific phenomenon, each having a complex nature.  By complex we mean a system having a hidden endophysical reality and existing within an interacting ecosystem.  The production of a formal theory has to address complexity carefully, for reasons that are explored in detail in Chapter 2.

In 1995, Prueitt’s notion of system image was in reality little more than a metaphor, but one that was essential to what followed next. He realized then that naturally occurring compartments form from these mechanisms due to affordance (e.g.: ecological need) over periods of specific duration.  A great deal of Prueitt’s (1985- 1995) work is based on a study of the extensive work by Pribram.  Pribram’s work should be consulted for a more in depth review of the scientific literature about human brain function.  If the reader is lost in reading about Prueitt’s concept’s, it is best that the appropriate background in Pribram’s work be mastered.  Pribram indicated that the affordances in mental images of plans and behavior are as much a product of a "perceptional" affordance as of the environmental affordance.  Thus the issue of anticipation and memory is opened to examination.  The long discussions, in the years 1987 – 1995, between Pribram and Prueitt lead Prueitt to understand not only the nuances of Pribram’s philosophy of life and science, which was for Pribram the same thing, but also to have a sense of the physical grounding of human perception, awareness and cognition in physical reality.  Pribram called this “scientific realism”. 

Prueitt examined the role that memory and anticipation has in the expression of human intelligence during the years 1987 - 2004. Human memory research and cognitive neuroscience was studied as well as the completion of a study on the mathematical models of neural and immune system function. 

It is perhaps expected that the limits of classical logic and physical science were found to be a restriction on his investigations.  These limitations were understood by an examination of the works of bio-mathematician and category theorist, Robert Rosen.  Progress in synthesis was made during an extended discussion with Peter Kugler, 1991-1994, on anticipatory mechanisms and limitations to formalism.  Kugler had made a study of Rosen’s work during his studies at the Beckman Institute (1986-1992).  (need detail). 

For example, his examination identified extensive evidence that learning occurs sometimes without awareness, i.e., the clinically investigated phenomenon of blind sight.  A technical discussion on blind sight research literature is deferred.  The point to this chapter is that many layers of scientific evidence indicates that the internal image of self creates mechanisms that do in fact conserve the conservation laws known by physical science, but impose additional constraints in the exercise of awareness.  

The mechanisms operate during the emergence of forms.  Substructural constraints are conformed to specific regularly existing forms, or patterns.  The patterns are recognized by the system of systems as a function needed in accordance with affordances.  These affordances are not merely defined by the conservation laws, but are also defined by constraints imposed from the top down, i. e., from the collection of system images acting together as part of the system of systems. The top down constrains shape the formation into one of the patterns that fits within the anticipatory constraints imposed by the system of systems. 

The notion of ecological affordance was coined by J.J. Gibson (1979) to refer to structural invariance as perceived within the regular flow of information, organized energy fluctuations in the retina layer and interior structures through the optic system. Initially this concept was oriented, by Gibson's behavioral training, towards the external world. In Prueitt’s theory of process compartments Gibson’s affordance notion is extended into a theory of systems within systems, or a system of systems.  System emergence is controlled under a non-local coupling expressed by the two complementary notions of "external affordance" and "internal affordance." A proper discussion can be made regarding this internal/external difference by using the endophysics and exophysics language introduced by Rossler.  An extended discussion on this was made with Pribram over the period 1987 - 1995. 

Affordance is a more generalized notion that the notion of entailment.  A specific affordance allows other entailments to become realized is a way that also fulfills the affordance.  The door way affords walking through.  The physical conversation laws are fulfilled by not walking through the door, or walking through the door.  However, the affordance allowed by the door is fulfilled when intentionality, choice, leads one to walk through the door.

The complementary notions, of internal and external affordance, are not separable in real existence.  They are notions that are abstract in nature.  In formal modeling the representation of affordance and entailment often become separated and lifeless.  The induction of the formalism leaves a great deal of information behind.  The formalism is an abstraction, and in this case only roughly captures the essence of the real world phenomenon.  This is to be compensated for as we try to understand how middle world event are supported by the endo-physics of those real things, complex systems with internal and external realities, as they are manipulated by the common exo-physics.  These considerations led Prueitt to hypothesize about how machine encoding of invariant data patterns might follow the “architecture” of the human brain in a way that is not expected from the neural network literature.  He thought, that the memory mechanisms and the anticipatory mechanisms might be developed separately as data structures encoded as n-aries, i.e., in the form

< r, a(1), a(2) , . . . , a(n).

Beginning in 1994, he began to believe that formalisms for the endo-physics and the exo-physics might be separately developed and then combined properly.  As the combination occurs in the present moment, as in the entanglement of memory and anticipation, a just-in-time differential formalism might give a good estimate about the characteristics of self-expression that we know as “intelligence”.  Such formalism was found in 2003.  The description of differential and formative ontology (Prueitt, 2003) will be addressed in later chapters. 

The analytic position is not easy.  For example, we can think of the system image as the collection of all affordances, and yet the notion of collection is somehow not correct. We deal with the paradox not only of the set of all sets, but we bring to the discussion almost all classical paradoxes. 

The system image should be formally represented as the interface between an endophysics of the internal causes of the compartment (its atoms) and the exophysics of the environmental demands.  But an analytic treatment has been difficult to find.  Very few academics have thought out the issue of stratification and entanglement in this way, although many have agreed with Prueitt that the differential and formative ontology has interesting applications in information science.  The academy has not been accepting of the changes that are required to mathematics and to science.   The interface relationship was treated in V. Finn's work on quasi axiomatic theory (see Chapter 2, section 2), but the viewpoint is so deeply grounded in systems theory and complexity that the relationship, as expressed in his work, has not yet been received within the American scientific community.

It is important for historical reasons to view system orientation towards temporal invariance as an intertwined relationship between observations and observed. In fact, this temporal relationship is seen as a fundamental one in the development of the perception of objects. 

(Author’s note: In a final draft we will add references here and some discussion of memory and perception research.)

One can imagine that adjusting the relative phase between energy spectral patterns in the optic flow delineates temporal invariance in representational mechanisms [13]. Levine and Prueitt (1989, 1993) described, using Hilbert mathematics, non-specific arousal as an attentional reset mechanism.  How else could one explain visual perception?  Visual perception is in the now, without recent past images in the perceptual field, and yet how we seen is subject to what we have seen in the past.   Furthermore, one can assume that the delineation of temporal invariance makes it possible for memory stores to encode patterns separately from a continuous recording of the full experience of events. This set of invariance, the elements of which we call memory artifacts, has an average duration and thus must be the consequence of some type of temporal compression.  Pribram returns to the discussion of Gabor functions at this point in order to create a convolution over some extent of space and matter (Bruce McLennon, 1993). As one can see form material in Appendix B, the convolution plays the essential role in processing data structure encoded in the key-less hash table. 

The convolution acts to combine elements that are similar or that have some binding that requires elements be placed together. Similarity is a function of many things, all or most of which is developed as categorical abstraction and expressed in the “n”-ary data structure.  Even with convolution operators, this technology is far simpler than the W3C type web ontology, using ontology web language and ontology inference layer standards. 

If the combining process is not cross scale then we have an instance of categorical abstraction (cA).  If the combining is an aggregation into a whole that has functional properties at a higher level of organization, then this is an instance of event chemistry (eC).  The difference between cA and eC is in the perspective one takes.  Categorical abstraction has no notion of coherence, only localized facts.  Event chemistry, on the other hand must express strong coherence even if the field’s basins of attractions, and environmental affordance, are not a single coherent whole.  Abstraction involves the reduction of information.  Events add information about functional properties and consequences arising from the pragmatics of a specific situation. 

The compression of aspects of events into natural category makes use of what mathematicians call the law of large numbers. The artifacts are thus statistical in nature since multiple occurrences must be part of experiences before these artifacts can be encoded as a memory substrate. Many open questions are revealed within this discussion.  The formation of natural category is bound together with a dual process.  The emergence of events imposes on category formation the situational reality, the distribution of substance and the “other” processes surrounding that specific event.  Like the mechanisms involved in natural language formation and use, natural categories are shaped by the reality into which categories are expressed.  As natural category forms, the nature of the category is tested and tests the re-expression at future time.  The emergence of a specific event; however, is far from a purely statistical phenomenon.  In 2002, Prueitt developed categorical abstraction and event chemistry based on the above remarks.  

The new thesis

In our revision of the author's original conference publication (Prueitt, 1995), we advance an argument, originally given in Prueitt (1997; see also Chapter 3). The argument is that the human memory store is built up in a metabolic substrate that is composed of protein conformational states and metabolic reaction circuits.  This argument creates an alternative to the conjecture that the human memory store is in the connectivity of neurons, as is commonly asserted.

Our viewpoint follows from the scholarship of Pribram (1971; 1991), and others in the fields of neuropsychology and systems theory. In this viewpoint, the memory store is composed of radiant energy guided conformational circuits at several levels of process organization; metabolic, protein conformation, and quantum. We will also see in the author's interpretation of Russian quasi-axiomatic theory that a tri-level computational architecture more completely models the relationship between experience, memory and behavior, than does models of all or none neural computation in neural networks.  This interpretation suggests how one might eventually produce machine intelligence that interacts with the natural world in ways not accommodated by the silicon processors of the early part of the twenty first century.

According to the work presented in this volume, it is to be believed that, in all natural intelligence a primitive measurement, without memory, of the environment occurs through a generic mechanism. The mechanism must be available to metabolic repair cycles expressed in living processes.  Cell signal pathway expression is one example of science that must acknowledge the interplay between non-locality and locality.  A review of this literature is encouraged, but we will not take the time to do this review now. 

We conjecture that, as a generic fact, a measurement mechanism is derived from "opponency induced symmetry".  There is evidence from many sources that opponency mechanisms are responsible for many of the processes that induces mental imaging.  In particular, following Penrose, we suggest that there is a process that cannot be modeled as an algorithm involved in the emergence.  This process is called “self orchestrated collapse”.  Again, the literature here is extensive and diffused, so we will not go into this as fully as might be undertaken. 

During the induction of a mental state, additional constraints are imposed by the nature of metabolic processes that are occurring as one part of the casual substrate for the images that form. The image is thus the natural emergent compartment through which specific function needed by the biological system is achieved.  The contents of the image is "informed" through memory and the sensory experience and enfolded into a mental event. Through a delay in symmetry induction the system becomes capable of introspection and awareness (Pribram, personal communication).

In stratified theory, there are always at least two perspectives. From the one perspective, the total energy of a system is concentrated at a point in time space, and from the other perspective the system is responding to the distribution of energy over a longer period of time, as encoded in a frequency spectrum.  Locality and non-locality co-exists as a principle of nature, not only in particle physics. 

Because of the time scale, one can assume that the coupling of substructural processes occurs at the micro-process level resulting in discordant interaction and a reshaping of the energy manifold at the macro level. The difference in frequency expression, between micro and macro processes is, we assume, what is measured by the orienting nature of human awareness. Of course this has been a very difficult problem. 

The measurement process is not yet awareness, but rather an attentional phenomenon that is more than the mere reaction rates of metabolic process (as Grossberg's embedding field theory assumes[14]). Understanding the differences between awareness and measurement occupied the author’s time over the past fifteen years, particularly in my many wonderful conversations with Peter Kugler. Over this period of years, Kugler's focus on the measurement problem changed. His initial focus was on developing mechanical systems that one might hope would simulate the measurement of the environment by a biological system (Kugler, 1987). Starting in the mid 1990s he began to focus more and more on a deep analysis about what perceptual measurement IS NOT, and then to an analysis of the nature of science, logic and art (unpublished class notes). The nature of his book is deeply enriched by Dr. Kugler's friendship. However our reflections about the nature of perceptual measurement remains unfinished.

Although theoretical issues are often discussed in the chapters of this book, we will be most concerned about the proper scientific and formal grounding of computational Knowledge Management (KM) technology, or what we now call knowledge technology. This grounding is made in the framework of a tri-level architecture, in early chapters, and then extended to the generative methodology for producing structural ontology.  So we will return to this theme often. 

We will say at the outset that the tri-level architecture is a convenient myth that Prueitt created.  He did this on his own.  He used this myth to create the basis for a new information technology. As myths go, this is certainly more credible than the theories of artificial intelligence.  Knowing that the tri-level architecture is a convenient myth is important.  The tri-level architecture only assumes that the measurement problem, and the consequences of measurement - e.g. representation, is sufficiently managed so that some new economic value from knowledge management using the tri-level architecture can be demonstrated.  Perhaps one rational for discussion of the measurement problem is to remind the reader that a proper solution to the problem of representation is not often easy.  The scientific basis is not listened to, due to the power of scientific reductionism.  However, if a technology were to be finished based on the tri-level architecture, it might be that the scientific re-vision might follow. 

Natural science knows a great deal about measurement and representation in a perceptional system; for example as indicated in the books by Pribram and his colleagues. We look at neuropsychology through the eyes of his work, because Pribram is the only neuroscientist who is able to claim a theory of the whole brain, except perhaps Changeux, Freeman or Edelman or Grossberg. From our interpretation of Pribram's work we feel able to ground the tri-level architecture in experimental neuroscience and in what Pribram, and many of his colleagues, refers to as quantum neuropsychology. Pribram's work suggests to us that "perceptional measurement" results in a cross level transformation of energy that is subject to some class of patterns that depend on co-occurrence of energy distributions.

During a course taught by Pribram at Georgetown University (Spring, 1999), he described a series of three sets of Fourier - Inverse Fourier transforms of the optic flow.

The three transforms work like this

The process starts with an inverse Fourier at the retina lens. Here the scattered light of the environment is focused into a retinal process that builds an energy manifold through the action of what is modeled with a forward Fourier transform. The physical processes in the brain are not as simple as the Fourier transform that is involved in the development of a hologram with glass lens.  The retinal process is a metabolic process that has complex protein conformational reaction circuits. Note that quantum mechanical processes are involved in the absorption of protons by redopsin molecules, in the retina, and that this single class of events must be the gateway events in the metabolic circuits that produce a single distributed manifold and coherent awareness.  The redopsin molecules have two metastable states, a high-energy and low-energy state.  The high-energy state contributes to a field potential and when sufficient molecules have been pushed into this field potential then the field itself can be taken up by innervating dendrites projecting from the Lateral Geniculate Nucleus.

The resulting energy manifold is sampled by the axonal dendrites of the Lateral Geniculate Nucleus (LGN).  The LGN is half way between the eyes and the visual cortex.  The neurons of the LGN provide a sequence of non-linear processing in rout to a re-spreading of energy/information into the layers of the cortex. This spread is the second Fourier transform and becomes linear as the information, including timing information, is encoded in the frequency spectrum. The reason why it is a Fourier is due to the underlying physics of lens and the species (Darwinian) need for effortless data fusion.  In the linear spectral domain data fusion is merely concurrence of energy fields. The process control mechanisms merely need to push the two energy fields together. Nature finds an exceedingly simply solution to the difficult problem of data fusion.

The third linear transform produces object consistencies that we perceive as objects in the world. This third transform occurs over a period of time and involves movement in space-time. The author interprets the neuropsychology to mean that the third transform acquires code from metabolic processes occurring in the limbic system and in the association cortex and spreads this code across many brain regions.

Code selection involves the induction of a set of basis elements for the Fourier, or Fourier like, spectrum (as channels or dimensions in phase space) and a phase value from the underlying metabolic circuits. The physical processes that we model as a forward transform distributes the results of visual processing and integrates context and pragmatics into the field. The field then must be sampled by one more inverse transforms from the spectral domain to produce a specific recognition of object invariance.  The nature of the pragmatic axis is perhaps the most difficult to model, but for our purposes we say that the pragmatic axis is that which exists only in the present moment. 

It is important to note that the model having linear transforms may actually be refined and made better by a model having a non-communitive composition of many non-linear transforms. Each of these transforms is "cross scale", and involves the measurement of "beable" (term taken from David Bell's work on non-locality in quantum mechanics) like phenomena, from substructure.  Modeling these processes really takes us beyond the “normal” mathematics, what the mathematician calls Hilbert mathematics.  The question that the author has been concerned with is about how to extend or modify Hilbert mathematics.  The stratified theory has been only a partial an answer to this question.

The reader will see a stratified architecture expressed in the logic that is presented in later chapters of this book, in particular in the chapter on Mill’s logic. The stratified viewpoint is not a mainstream viewpoint.  In fact, mathematics could be applied quite differently than it is if other viewpoints were common.  For example, most mathematicians are trained that linear transforms are merely approximations to the more important non-linear transforms. Our analysis of the neuroscience suggests that linear is desirable, in a Darwinian sense, because of the efficiencies of linear processing in the spectral domain. Thus the conjecture on the linear process being the aggregated result of many non-linear processes, if true, would be counter to the standard viewpoint.  There are many other issues that neuroscience have with classical mathematicians.

The reader may wish to reflect on the earlier discussion about coherence, and non-locality.  Coherence and linearity are made from the same cloth.  Non-linearity may be suggesting that “other” systems are close by and are interfering with the coherence locally.   Linearity and non-linearity may both be a function of localization, whereas non-locality may not be describable in terms of ordering.  This fact, or observation, may be the key to convolutional processing of Ontology referential bases (see Appendix B.)  Clearly these issues reveal important open questions. 

A case can be made that the physical mechanisms that allow human induction delays the other wise regular propagation of radiant energy (see Eccles, 1993).  Perhaps it is also true, that in highly intentional systems, the duration of emergence is extended to allow self-image to interact more strongly during the formation of a symmetric barrier to action.  Eccles claimed that induced symmetry is globally linked via some holistic mechanism to produce a mind-body interface and to thus establish the means for spiritual awareness by biological systems. He argued that the human synaptic structures have unique, to human, characteristics that intensify this possible spiritual awareness [15]. The mechanisms also produce cognitive ability far in excess of non-human animal through a multiple level transformation of energy distribution. In this way, plans and goals are incorporated into the substance of the resulting mental compartment. This delay should be empirically observed as irregularities in processing of regular metabolic activities occurring in the neurons and associated gilia. So the case being made can be tested in a rigorous fashion.

Perhaps it is important to note that the framing of the issue of dynamics in terms of linear and non-linear might be less relevant, than the main stream supposes, to the ultimate cause of understanding what we do not now understand about perceptual processes in complex systems. The cross scale process is neither linear nor nonlinear because the definition of the linear or the non-linear systems requires that a set of observables have been nominated before a formal mathematical problem is set up.  The cross scale processes have no known formal representation. 

System image

Measurement and representation are not the only two classes of difficult investigations.  In the previous section we have outlined an interpretation of part of the vast neuroscience and mathematics literatures.  In this interpretation we find evidence that the physical stratification of processes that we do in fact find in physics is inherited in the process that occur in the brain.  The stratification suggests that an understanding of emergence is essential to understanding the nature of perception and cognition. 

We also need to talk about and have some appreciation of the notion of system image.  Our study of cognitive processes is undertaken in a quest for new information technology that is different from what we know today.  In this study of cognitive processes, we see the system image as an assembly of coherent associations, made from the spectral domain of energy frequencies. into those metabolic processes that are available at the moment the awareness occurs. We conjectured that the association induces a non-localized action during an initial period of energy compartment formation. This non-localized action is treated in our theory as from a “system image”.  An autonomous core is the origin of a periodic expression on several levels of organization. The expression of this core is the system image.  The system image shapes the process of emergence through synchronization of sub-processes. Of course, a correlation between induction and the introspection of awareness, as well as intentional control, might also be found in the core. These mechanisms are cross scale in nature and thus highly speculative, but nevertheless are reflected in the tri-level architecture.

In 1995, Prueitt conjectured that the nature of the self-image is not fully understood by anyone, but one can easily see its role in the formation of very different perceptions of the same world by different people. One might conjecture that compartmental emergence takes place concurrent with perceptual measurement and results in the formation, or movement, of initial conditions for actual metabolic processes in the brain system. The metabolic processes would be composed of available reactants that are called on, by process gradients, to fulfill the image of self. In this picture of self, we again see the three levels; substructure, the compartment and other compartments that interact with each other, and the intervening set of environmental affordances that reflects how compartments behave in its environment.

The self-image "sits over at the side" and represents the knowledge of the world as well as autonomous intentionality and whole system continuity. We can observe evidence that living systems have knowledge and intentionality, he argued. And even non-living systems, if such a term makes sense, have continuity. However, this image may or may not be observable. Likely it is not observable, except to the system that it is the core of. Nor is self-image a statistical artifact. Each image is unique and the uniqueness is also likely to be the partial cause of its influence on other processes. Its expression is mixed with the assembly of substructural elements and the constraints of ultrastructure, but it seems to have an "other-than" status. A language of self-image expression might be developed through the study of cell morphology and physical ontology, but the methodology for the discovery of the full nature of cross scale phenomena is likely to quite different that discovery methodologies that can be successfully employed regarding the substructure or the ultrastructure. Self-image is neither the aggregation of elements from substructure nor the constraint of ultrastructure, nor is it proper to identify it as the autonomous whole that we observe as an element of the middle world.  Each is unique.  We understand self image only informally and only with a great deal of knowledge and wisdom.  

As we consider the essence of object recognition, we can assume that the problem of object representation has been solved in some way, or in some partial sense. Using the tri-level architecture, recognition of things can refer to things in anyone of the three levels. In each case a different part of the representation problem has to be solved. The architecture is based on metaphor between these things and the neuropsychology cited. Naive recognition, the recognition of things in the world by a perceptional process, occurs when memory subfeatures combinatorically express to produce features, invariant sets, of the compartment that supports the mental awareness.

This expression results in the initialization of boundary conditions (initial conditions) within the compartment, and the compartment supports an energy-spectrum phase-coherent mental event. This naive recognition does not always require a symbol, and in fact the use of a symbol may reduce the awareness artificially to recognition of some aspect of ultrastructure or some element of substructure.

It is likely that two different symbol systems are necessary to produce a separate awareness of substructure, and make a clear distinction to what is ultrastructure and what is substructure.  Would such formalism be regarded as “mathematics” and the observations made using this formalism as “science”?

It is certainly the case that science works through a process of "encoding" empirical observations into notation. Symbols systems and a common interpretation of the meaning of the symbols is the basis for the development of science. But Prigogine [16] and others question the possibility of having a formal system revealing a complete description of the processes that support emergence and the emergent consequences.

The tri-level architecture suggests that separate symbol systems can be developed, one for substructure and the other for ultrastructure. One would think, after reviewing the architecture, that two separate sciences, each based on quite different principles, might evolve in the near future. The two objects of investigation are quite different, in that the substructure is statistical in nature and the ultrastructure is categorical in nature. It is perhaps an accident of history that statistical artifacts have been more developed than have categorical artifacts. We say this because category science should be as useful as statistics, but for reasons of cultural expression statistical science seems to have been developed first. As a result of this maturity, statistical systems give us the best possibility for verification of some aspects of the tri-level architecture. For example, the effect of cross scale movement of initial conditions should be observed as discontinuous jumps in the predicted path of metabolic reactions.

These jumps in measure of metabolic expression should, in theory, produce sequences of discrete middle world events, modeled by event chains in which the notion that one event causes the consequent event is incomplete. The effect might be seen during the characteristic reaction of ATP energy conversion resulting in metastable state alterations in protein. Again conjectures of this type can be tested in a rigorous fashion. Discontinuity in neural processing of a stimulus signal is discussed in Chapter 4.

Representation of substructure can be via statistical artifacts, but can never be perfect because, in classical statistics, categories are formed based on similarities and not dissimilarities. The Russian work in quasi-axiomatic theory does make use of "negative knowledge" but this use of negative knowledge leads to complications that are not resolved by anyone. If both similarity and dissimilarity is completely accounted for then each event might be mapped to exactly one category and there would be too many categories to make sense of the world. Practical consideration leads us away from David Hume's enigma regarding the know ability to know the world. The world has not been made sense of in this way.

The notion of an emergent energy landscape, or manifold, is central to understanding Prueitt’s notion of a process compartment. In the next section we will use simplistic mathematical models as a means to illustrate this notion. The model does not have a counter-part to the notion of self, or system, image, and is thus bi-level in nature. The mathematical model is briefly introduced here and then extended in the later part of Chapter 2.

Bi-level emergence, mathematical and physical models

This section considers a simple mathematical framework for studying emergence.

Consider a small or large set of coupled oscillators:

dj/dt = w + SUM( c G(j)),

(with j the oscillation phase, w the intrinsic (constant) oscillation, c the coupling and G any non-linear function), having various types of network connections (architectures) and initial conditions. The architecture would be expressed in coupling that may be positive or negative. The coupling may also be variable and reflect certain regular features of the circuit dynamics of metabolic reactions.

These systems are observed to partially or fully synchronize the relative phase of individual oscillations. We assume that the system develops systemic and regular behavior that acts as a partial control over the values that the coupling takes on. This control is from the higher level (of organization), of the two levels, to the lower lever.

In some cases the resulting phase locking between oscillators is easily seen to be trajectories in the very simple dissipative system

H(j,dj/dt) = 1/2 m dj/dt 2+ 1/2 k j 2

where k and m are constants, and j is phase (of internal to external expression), and t is time.

In this simple case, the intrinsic oscillation of each trajectory can be mapped to closed loops (circles) on the surface of the manifold described by the above equation as a n + 1 dimensional parabola. These loops then form the basis for the oscillators as seen from one additional level of organization. The formalism would appear to imply the possibility of an infinity of numbers of levels, each created only from the entanglement from a single substructure.

When n = 1 this is the unforced, undamped pendulum. When n > 1, and there is a coupling term between the oscillators, then the oscillators are merely coupled harmonic pendulums.

The harmonic case is simple. Consider a system of rotators that is fully connected, the connection strengths constant, and the initial phase conditions evenly distributed around a circle. The oscillators will phase lock into their initial intrinsic oscillations since connectivity averages out over the entire architecture. Some computer simulations are sufficient to bear this out.

Harmonious interaction occurs when the intrinsic oscillations and the coupling walk in tandem. Discordant interaction between subsystems is correlative to opponency based symmetry induction and consequent formation of a new compartment, in the form of a basin of attraction in the energy manifold. In either case, the interaction occurs through excitation, inhibition and indirect, or allosteric, causes from a substrate consisting of internal to external expressing phase systems. The excitatory or inhibitory causes are often expressed as a field effect; whereas allosteric effects are propagated in a cascade of micro-events that are part of well-established metabolic circuits. This is particularly well illustrated in cell membrane.

On the question of symmetry

Many of the open problems in fields related to situational analysis, control theory and medical/psychological/ecological therapy are related to a systemic response to discordant interaction. Thus, it is important to have the class of formal systems, described above, produce logical (formal) compartments that reflect natural mechanism. A computing environment appropriate to the simulation of cross scale phase locking allows us to create conditions whereby the emerging manifold has strange attractors as discussed by Kowalski et al (1989; 1991) [17] and others. As important to semiotics, the creation of such a manifold can be observed directly in the presence of symmetry breaking "seeds" derived jointly from system subfeatural competence, i.e., the ability of subfeatures when combined, and system image. The phenomenon of symmetry collapse is where interpretation can be placed, and where a second order cybernetic system (a system image controlling induction) is needed (Chapter 3, Section 5).

The induction of symmetry is indicated by several schools of scholarship as a mechanism arising from specific molecular structure and neuro anatomical features.  Symmetry induction is explicit in the Adi structural ontology (Adi and Prueitt, 2004) as well as in the principle of Human-centric Information Production (HIP) developed by Prueitt (2001 – 2004).  Adi’s observations regarding an ontological substructure to language were quite independently developed and expressed in a 1086 patent.  The design principles of HIP are discussed further in later chapters. 

For the purposes of computational analysis, symmetry in these systems can be broken in several ways: (1) un-evening the distribution of initial conditions for the phases j, (2) un-evening the connection strengths w, and (3) time varying the intrinsic rotation of individual oscillators. These three conditioning factors of the suggested class of simulations enable a theory of programming for the tri-level architecture. This theory of programming has yet to be capitalized on. We conjecture that a derived theory of programming can be incorporated as a new computing technology based on optical computing and Knowledge Management. The key to this new information technology is the new OASIS standards on service blueprints and human choice points [18].

In the physical theory, energy symmetry is broken while opponent based induction measures informational invariance in an incoming data stream. The opponent processing is bottom up, from memory stores, and top down from category policies. In the tri-level architecture, a voting procedure manages this process in a way that seems to be grounded in the interpretations about human memory given in Chapter 3. Within the frame of neuropsychology change in memory access and category policy might correspond to a shift attentional focus. The resulting process compartment has a manifold with invariant sets that reflect both input data invariance and subfeatural combinatorics that results because there is a specific memory store being composed within a specific category policy.

Initial conditions are created that complete patterns intrinsic to both the data stream and subfeatural memory, and produce an internal representation to be read by a system downstream. The interpretation occurs in a context supplied within the physical processes occurring in the process stream and is related to both the available category policies and the measurement of pressure on the policies to change in accommodation to environmental non-stationarity.

There are two focuses to this book, the technology that leads to structural ontology and anticipatory technology, and the science that we must ground this new technical within. The author already suspected this architecture in 1995 when the first draft of this chapter was written. Now we know that the architecture has a realization in a specific type of tri-level machine intelligence that we will see developed and demonstrated in the final chapters of this book.  The architecture provides structured, and stratified, ontology and anticipatory mechanisms.  In the near future, we believe that many different computational system architectures will be modeled after complex cross scale phase locking that occurs and has stable symmetric induction. A mutual induction will connect the computer’s data mining capabilities with the human centric information production that structural ontologies support.  Pribram's theory of human perception, presented two sections above is illustrative of the natural science that suggests this future.

Process Compartment Hypothesis (PCH)

PCH (statement): Temporal coherence is produced by systems that are stratified into numerous levels and produce compartmentalized energy manifolds.

Connectionist models assume that a neural system builds internal representations with geometrical and algebraic isomorphism to temporal spatial invariance in the world. The PCH provides a common foundation for investigations of internal representations of this type. It also provides a means to study the linear and non-linear transforms that serve as formal models of these representations.  Models are useful in our attempts to understand the interaction between independent systems supporting these representations. The PCH assumes a stratified organization; with compartments emerging from substrata and globally acting images providing top down constraints in the form of rules and laws. In all cases, compartments exist as embedded and transient complex subsystems of other compartments. The PCH assumes an embedded and stratified organization whose stability comes from substructure and whose plasticity comes from adaptive categorization.

In theoretical constructs that model the PCH, compartmentalized processes, or process compartments, are linked processes that are localized in space and time. Their definition, in this way, shifts the ambiguity from the term "process compartment" to the two terms "process" and "localization," separating the description of a compartment to a localization process and to autonomous evolution in time from initial conditions. This autonomous evolution is within an integrated whole. The evolutionary control of micro-process is entailed by a non-local (holonomic) influence. This control by a non-local constraint is what makes the tri-level architecture quite different from connectionist neural networks. The tri-level architecture is more like what is now being referred to as "evolutionary programming".

A natural characteristic generic to all process compartments is that compartments have a formation phase, a stability phase, and a dissolution phase. The localization phases are reflected in an assembly and disassembly phase in the tri-level architecture. The process phase is reflected in the stability produced by the system image.  While stable, the control is more likely to have an internal origin. During aggregation and dissolution, the origin of control is external and internal.

The formation and dissolution phases have not been fully described in the research literature, except as a singularity in the classical formulation of its thermodynamics. Like our view of our own finite life, we have a tendency to assume that the stable phase of a compartment is existent from a distant past to a distant future. We can examine this assumption by reflection on the Minkowski time cone.

The classical time cone, called the Minkowski time cone, is formed by intersecting two symmetric cones in such a way as to overlap only on a non-empty set of dimension zero and aligning both cones to a single axis of symmetry. Choose a direction for the flow of time and associate each line, that is fully contained in the union of the cones and that contains the single point of intersection, with the trajectory in state space of a set of observables for a particular system. This geometric exercise produces a linear model of the sequential nature of present moments, with a unique relationship between the past and the future. This time cone assumes a Laplacian world.  The Laplacian worldview assumes that future event structure is fully predicable from one set of initial conditions.  The world would be fully deterministic.   It does not account for non-locality in space or time. There are no singularities within this notion, except at points of infinity.

When a compartment is stable, and its rules of evaluation constant then we should expect an illusion within the compartment endophysics that looks like the Minkowski time cone, and yet the exophysics shows a birth or death event. Under special circumstances, compartments develop an ability to perceive outside of self and thus to interact in a meaningful fashion with other compartments.

Stability, the hidden illusion

A compartment's stability phase is better understood than the formation phase or the dissolution phase. Why is this, in spite of the clear evidence for life or death events? The answer might already be suggested in the last several paragraphs.

Stability itself enforces a single set of laws and these laws act, more or less, in a classical fashion. The rules are not changing, or at least they can be made sense of in a consistent fashion. Coherence establishes context. The notion of consistency is here essential, and is related to coherence in energy distributions - something that we will learn more about later on in this book. We have already discussed, very briefly, holonomic theory depends on phase coherence. The stability of the compartment comes from phase coherence similar to that which produces light wave phase coherence in lasers.

Conditions on the total energy, and the interchange between potential and kinetic energy, are clearly the primary constraints that are placed on all compartments during its stability phase. Beyond this energy conservation rule, we know many general principles also applies to compartments. For example, the intrinsic observables of a compartment embedded within a biological system will reflect an "internal" representation of its degrees of freedom. In living systems, this representation is not as simple as that of a system of coupled pendulums, which are closed to interactions with the affordances of the environment. As a general property, the sum of energy transfer in and out of a compartment boundary remains almost constant, at least when measured over the natural frequency of the compartment. So the complexity of a stable autonomous system provides a barrier to understanding conditions and principles that lie outside the autonomous system.

We feel that the issue of what stability is, in a specific case, can be traced to the first causes that were present during the creation of the compartment. We can conceive that the compartment itself has formed from an election of degrees of freedom, or observables from some larger set of potential nominations. Once formed, the observables become that which we can see.  We may think that only energy and matter are involved in the formation of life, and know nothing about anything else. We cannot see these other things, and we know that many mistakes where made by primitive science regarding the unseen.

It is easy to adopt the notion that what we can directly see is all that there is. However, what can be seen does not explain the world we live in. Steward Kaufman’s model of the autocatalytic sets demonstrates the emergence of specific patterns of activity that establish themselves when a parameter of average connectivity crosses a threshold (Kaufman, 1997). This work, on emergent computing and evolutionary programming, establishes the potential for a science of complex systems that accounts for the unseen.

We may hope the logic of common reasoning and the dynamical entailment of initial conditions in a mechanical system are established by the same formative mechanisms. From the combinatorial span of the consequences of these mechanisms a process compartment defines a stable state space where all chains of events must lie, or the compartment itself must die.

We may hope that the forces that shape emergence are consistent with the processes that form some valid viewpoint within the mind of humans. Thus, if our theory is deep enough and our power to observe clear enough, then mankind may hope to develop situational logics and logical entities that allow us to really get a grasp on the dynamics of any particular complex system, and to represent this dynamic in a way that is consistent with human reasoning. 

In the tri-level knowledge management architecture the stability in question has to do with the stability of interpretation of sign systems and information. This interpretation involves the aggregation of exemplars into memory elements as a means to relate sign systems to past examples of interpretations of similar information (see Chapter 12). This is managed via voting procedures (Appendix A) and Mill's logic (Chapter 6).

The new mathematics, and the new science

A mathematical model of dissipative system, within a stratified relationship, is advanced in the next chapters. The author believes that this model is categorically invariant to Russian quasi-axiomatic theory and thus has implications to the text understanding and knowledge management portion of the later chapters of this book. The computer implementations has some surprises, both because of the simplicity of the key innovation, the key-less hash table, that the dependencies between a new discrete formalism and continuum models of dynamical representations of human knowledge, as expressed in patterns of co-occurrence of terms.  The new discrete formalism is called Ontology referential bases, or “Orbs”.  Differential and formative ontology is demonstrated and illustrations are given as to how these theories and technologies will reshape information science. 

What we get, in differential ontology, is a categorical invariance between two formal systems, one discrete and computer implemented and the other continuous and represented by Hilbert space mathematics.  This works builds on one half of the author’s 1988 PhD thesis, “Mathematical Models of Intelligence in Biological Systems”.  The claim is that work in one system will transfer to the other system. Whereas this transfer back and forth between formal analysis can be taxing to someone not aware of the basis for the transfer, it never the less may produce a computational implementation, as a background process, useful to distributed knowledge management.  The homology between discrete and continuum models allows a direct path to encoding data based into electromagnetic spectrum. 

Will this approach lead to a unified theory for complex systems?  We think so.  Much of the work in complex system is incomplete.

One way to a complete the theory of process compartments is to combine the work on coupled oscillators (Hoppensteadt, 1986; Kowalski et al., 1989; 1993), and neural networks (Grossberg, 1985), with quantum neurodynamics (Pribram, 1973; 1991; 1993; 1994). Moreover, the notion of categorical invariance between Russian quasi-axiomatic theory and stratified dissipative system can be worked out quickly. This gives us a direct path to refine the data mining processing in the tri-level architecture in such a way as to ground Knowledge Management and Complexity Science in both mathematics and experimental life sciences.

However, some central problems remain.

Compartments are embedded. When created, a compartment separates phenomena that once had a direct interface. When a compartment has been annihilated, two levels of phenomena that were separated now interact. Once created, input to a compartment conforms to the new compartment's degrees of freedom.

The result of transformations in energy distributions is modeled as the action of a transformation on a vector. The computation of transform coefficients are presumed to be accomplished by fast adaptation of structural constraints, like dendrite spine shape, protein conformation, or neurochemical agents reflecting neurotransmitter concentration. This must be done with the flexibility required to select from multiple (optional) responses in ambiguous situations (see Pribram 1991, pp 264-265).

The ubiquitous phenomenon of response degeneracy  demonstrates a deeper problem.  At a conference hosted by Daniel Levine in 1991 on optimality, the author discussed the rationale for regarding response degeneracy (see Edelman, 1987) as complementary to optimality (Prueitt, 1997). We expressed the view that the creation of viable options would be complementary to optimality if all but a few selective response potentials are somehow held ineligible for deterministic evolution toward a local basin of attraction. This viewpoint provides the critical introduction of non-computational processes into the theory of process compartments.   The challenge here is to extend and modify who science defines mathematics and how mathematics defines science.

The viewpoint expressed is properly complex, but not overly complicated. By this, we claim a new viewpoint that accounts for the ontology of physical processes in a minimal way. We find the optimal solutions to old problems by by-passing the very means in which these problems were defined. 

Consider the mind-body problem.  As suggested by Sir John Eccles (1993), intentionality could be expressed during brief non-linear restructural transitions of process compartments. Eccles points out that the geometrical arrangement of synaptic boutons supports a femto-second process controlling the release of the transmitter vesicle mediated by Ca+ influxes. A process selected through evolution to conserve neurotransmitter provides the control. The process, that Eccles describes, has the effect of creating a homogeneous probability distribution measuring the likelihood that any one of six boutons will carry the gradient field interchanges between the presynaptic and post-synaptic events. Eccles sees this mechanism as the interface in which his notion of the mind couples to his notion of brain by changing the probability and timing of synaptic events.

Pribram and Eccles agree that synaptic events play a role in the formation of network connections at a higher level of organization.  At critical locations, even distribution ratios are maintained while a distributed energy gradient increases to a high level. Symmetry and increased gradients result in a barrier and thus in the formation of a trigger. The trigger is released at the point where self-organization can be effectively influenced (Eccles, 1993) by other integrated process compartments. The trigger then closes the process that Pribram identifies as a "temporal lens" and results in awareness.

Hameroff has identified similar symmetry generating mechanisms in the geometric structures of the microtubulin assembly as well as in the temporal dynamics of microtubulin formation. Microtubulin play an important role in cell mitosis and may control some aspect of the connectivity of neuronal ensembles through the fine alteration of dendrite arboration as well as influence second messenger cascades guiding long term potentiation (Hameroff, 1987).

Pribram has investigated other mechanisms that might be shown to be the active mechanism of extending non-locality effects, seen in Bell's inequalities, to macro events involving ordered water and superconductivity in conformational propagation of structure along the surface of neuron membrane.  Since slower processes are required to conform to the oscillation frequency of the emergent process manifold, the initial biases created during symmetry induction are structurally reflected in a system image. The longer the symmetry is maintained the more completely the system competence is sampled.

We have some work to do to bring the viewpoint together.  For examples, the notion of human self-image, although not well defined within a scientific literature (Bandura, 1978), can be used as metaphor for an higher order "agent" that mediates the formation of compartments and shapes the compartments' evolution. The metaphor suggests that compartments involved in the transformation of stimulus traces are shaped by cross scale interaction like that modeled mathematically, as temporally stratified coupled dissipative systems in section one of this chapter.

Transformational realism interprets neuro-psychological evidence in the context of the process compartment hypotheses. This form of realism can be stated in the following fashion. Simple combinatorics of system competence express elements of a behavioral repertoire. The longer the symmetry the more completely the consequences of action in the external world is sampled. The result is a convolution of two scales of observation resulting in a new set of observables. The convolution, however, can have a kernel that biases outcome and thus differentially delineates the creation and initial conditions of emergent compartments. This kernel is the system image.

Thus, the human self-image itself needs not be a non-material mind/body interface as perceived by Eccles (1993). The image merely occupies a band of energy distribution. The bands are separated by gaps in the distribution. Event exchanges between energy levels could alter probabilities during phase transitions of compartments whose existence is brief when compared to the agent and thus have many of the same properties as envisioned by Eccles. Of course, this type of interface may be more complex than the simple cross scale interactions indicated by computer simulations of dissipative systems.

Perhaps we could say that the primary distinction between a coupled dissipative system without system-images and a system with self-images is that self-image is a phenomenon that interacts intentionally in a probability space. This intentionality could be in opposition to the local laws of dynamics. The induction of a symmetric barrier to the expression of lawful processes would be evidence that space/time non-locality is involved in the expression of human self-image.


We have suggested that compartments form through the lens of a temporal coherence. These systems stratified into numerous levels and produce compartmentalized energy manifolds (PCH). Process compartments, and not merely networks of neurons, are the prime candidates for the proximal causal mechanisms producing behavior. This view is consistent with those expressed in Changeux and Dehaene (1989):

"A given function (including a cognitive one) may be assigned to a given level of organization and, in our view, can in no way be considered to be autonomous. Functions obviously obey the laws of the underlying level but also display, importantly, clear-cut dependence on the higher levels. At any level of the nervous system, multiple feedback loops are known to create reentrant mechanisms and to make possible higher-order regulations between the levels" (pgs. 71-72).

At all levels, in anatomical regions and across time scales, generic mechanisms appear to operate. Complex models of prefrontal cortex interaction (Levine & Prueitt, 1989; Levine et al., 1991) with other cortical systems and with limbic systems, require a formal model of intentional processes (Rosen, 1985; Kugler et al., 1990) that rely on these mechanisms.

The theory of process compartments provides a framework to integrate models of processes operating at different time scales, as well as clarify the natural role for structural constraints in signal production and interpretation within and between levels of organization (Pattee, 1972). Stratified processing within and between transient compartments can then be seen in ecological terms.

From this theory we may ground the foundation of machine mediated knowledge management in a science integrated from open complex systems theory, neuropsychology and computational science.

[1] The key-less hash table is derived from the Gruenwald patent where by alpha numeric “letters” are treated as base 64 digits, and the ordering native to the integers is used as a means to eliminate the hash function.  See Appendix B.

[2] Web Ontology Language (acronym “OWL”) is a standard produced by the organization W3C.  URL: www.w3c.org. 

[3] The key to understanding the differences between W3C and OASIS standards is an understanding of the phenomenon of coherence.  As in the development of personal knowledge, the coherence of a viewpoint need not be rational when viewed from a different viewpoint.  W3C establishes an extreme assertion that there is only one coherent viewpoint, and that is the one it creates by asserting a unique meaning for individual terms or phrases.  In addition to this assertion of unique meaning, the W3C standards are directed to impose first order logics, description logics and determinism on any model of social or business processes.  This assertion is consistent with scientific reductionism, but is inconsistent with the multi-cultural foundation to the American culture.  The current struggle, in mid 2006, is to conform OASIS to the W3C view of natural process.  This conformation is partially being achieved via web service modeling language standards proposed to OASIS by a number of industrial powers, including DERI in Germany.  Web service modeling language makes a number of useful contributions, but it does not acknowledge the limitations of formalism, nor of the de facto control over information design being conveyed to knowledge engineers by these standards. 

[4] Robert Rosen:  URL:  http://en.wikipedia.org/wiki/Robert_Rosen

[5]  Hilbert spaces forms a branch of modern mathematics:  URL: http://en.wikipedia.org/wiki/Hilbert_space

[6] Prueitt, Paul S. : PhD (University of Texas at Arlington, 1988)  Thesis on homology mappings modeling biological systems exhibiting learning, in particular plant and animal immune systems  The thesis had two parts, the other part was on neural models of selective attention, following the experimental work by Karl Pribram and using the embedding field theory produced by Steven Grossberg. 

[7] This definition of complexity following the work on category theory and bio-mathematics developed by Robert Rosen.  In this sense of the work, “complexity” cannot be “computational”. 

[8] Pribram, Karl.  See Appendix  “Brain and Perception” 1991 ERA

[9] See also Appendix B.

[10] See the work on gene and cell expression web ontology at www.biopax.org

[11] OASIS BCM URL: www.busineecentricmethodology.com

[12] Prueitt was appointed Research Professor in the Physics Department at Georgetown University from September 1991 to May 1993.

[13] Levine, D. & Prueitt, P.S. (1989.) Modeling Some Effects of Frontal Lobe Damage - Novelty and Preservation, Neural Networks, 2, 103-116.

Levine D; Parks, R.; & Prueitt, P. S. (1993.) Methodological and Theoretical Issues in Neural Network Models of Frontal Cognitive Functions. International Journal of Neuroscience 72 209-233.

[14] Grossberg, Stephen. (1972a). A neural theory of punishment and avoidance. II. Qualitative theory. Mathematical Biosciences, 15, pp. 39-67.

Grossberg, Stephen. (1972b). A neural theory of punishment and avoidance. II. Quantitative theory. Mathematical Biosciences, 15, pp. 253-285


[15] The author meet John Eccles at a conference hosted by Karl Pribram in 1994. 

[16] Prigogine, I. (1996?) “End of Certainty”

[17] Kowalski, J. ; Ansari, A. ; Prueitt, P. ; Dawes, R. and Gross, G. (1988.) On Synchronization and Phase Locking in Strongly Coupled Systems of Planar Rotators. Complex Systems 2, 441-462.

Kowalski, J., Labert, G., Rhoades, B, & Gross, G. (1992). Neuronal Networks With Spontaneous, Correlated Bursting Activity: Theory and Simulations. Neural Networks, 5, 5, 805 - 822.

[18] The URL is: www.businesscentricmethodology.com