Words, ideas and languages follow conventionally accepted descriptive meanings and interconnectably relevant relationships. They may also carry with them tacit perspective biases that are so innately interwoven that we may not readily see how they affect our thought processes. We may be so habituated to this tool called language that we may not easily recognize the subtle ways it restricts or compromises our ability to notice other linkages, other relationships...and therefore the models and paradigms we use. Like walking on the plains of Nazca Peru, we see topological changes in the ground terrain, but do not immediately understand (see) the picture patterns they make until we fly above them, in the third dimension of sky. It is only from the extra-dimensional vantage point that we can appreciate what is happening: something quite extraordinary compared to the merely local surface abberations that we see at low eye level on the nearly two dimensional desert floor.

Similarly, just as any given perspective gives us access to very different specific information sets, not every language on our planet has words or structure that is exactly similar to every other language, having exactly the same meanings and connections of ideas. It is perceptual distance that allows us to see those other patterns...in space and in time (In direct analog, this is just another way of understanding Gödel, Wittgenstein, Cantor, et al...as intimated above, and as I will expound on later).

As detailed by Whorf (1936), Inuit, the language of native Alaskans, has many specialized words to describe "snow". All the various subtle different qualities and aspects snow can take with the slightest combinative differences in temperature, wind, sunlight, structure, etc. English only has one: snow. A "sufficient" set for our level of encounters at the lower global latitudes. But not enough to survive an Arctic way of life.

In English we talk about the "shallows"...land areas just below the waters edge at a shoreline or embankment. French does not have a single-word form that conveys exactly the same meaning. The American native Hopi language is one more suited to predicative dynamics, where-as English is more oriented to material-object specification. Whorf & Sapir (1936) found it easier to discuss Einsteinian relativity with them than with English speaking contemporaries. The Hopi concepts and language are more concerned with "process" than with "datum", "causation"; "time-passage bounded by reference-descriptions" rather than "accumulation of individual events" - which only afterwards is perceived as causality. To the Hopi and many cultures world wide the flow of experience precedes the analysis of it. And this is reflected - and re-enforced - by the languages (images, grammar and symbols/sounds assignments) used. Keep in mind, mathematics too is a language, with specific innate perspectives and biases.

Recently I fancied studying Japanese. Culturally for years I was told that there was an inscrutable, impossible to understand quality, to oriental cultures. I am a North American who is primarily a product of generations of European languages and cultures. In the mid twentieth century the political and economic leaders of my particular society looked to those transpacific cultures and proclaimed them "methodically unified" and "single minded". Spiritual pundits looked to the religions, and social analysts picked apart their mysterious social devotion to an Emperor as the source of this phenomenon. Japan's island existence was seen as a sure factor. But when you get down to it, my friends, the source is simpler clearer and less prone to subsumed "deviousness" in the minds of "foreigners" who, without our having direct personal contact with, we were told to fear as opponents - both in armed war and in peacetime economic competition.

Per this example, I must say, and I can't overstate, that no human on the planet is my "natural" enemy. And moreover, I trust in the ability of my mind to examine and understand things without overburdening myself with negative emotionalism to cloud interpretation.

The first thing a 'westerner' is advised of when learning Japanese (Nippon) is that the language structure makes no distinction between 'singular' and 'plural'. Obviously there is 'counting' that distinguishes 'one' and other countable quantities. But 'book' and 'books' are the same word. A single word embodying two meanings. There is one word for person/people. When a person immersed in that language thinks of things, he or she has a sense of individuality and uniqueness, but, the greater overriding unspoken sense is that "I" am my "human-species", my "family", my "country", or even the company I work in (not 'for'). The "Oneness" of being Japanese - a holistic social organism - is integral to being "me". Nothing mysterious, nothing unnatural, nothing negatively premeditated.

Correspondingly, western languages, and the political organizations we have developed there-on, stress the importance of the individual as distinct from the social order. Individual human rights are integrated through social contracts of mutual agreement. Not by default. And never lost by sublimation. A Japanese citizen, on the other hand, does his best to improve and benefit his social organization because a person simultaneously and automatically improves themself. It is "understood". I am my social unit, versus, I am a member of my social unit. It is all in the language. Our tool of interactive perception and expression.

In many ways, linguisticly mitigated perceptions are the very source of the whole panorama of social organizations, religious beliefs, and philosophical doctrines. Some concepts stress the individual members of a group and their positional hierarchies. Other concepts prioritize ever present dynamics and processes...the developmental relationships. Interestingly, all, within some sort of cohesive story (no matter how intricate or unusually contrived) that binds the individual and cultural "self" images into an on going and workable process of incorporation, growth, continuation and successful responsiveness...for as many parts of the integrated system as possible.

Pursuing this potent mitigator of information processing further, genderizing is another cumbersome artifact, at least in English. As I was writing one of the above paragraphs I wanted to make several references to a single person, either male or female, as "citizen in/of society". But my current language has no easy adjectival pronouns that can deal with that singular concept, without falling back on the few genderized terms available. Very frustrating indeed! I mention it here, as just another example of the random but pervasive quality that inadvertent linguistic structures can place on how we perceive things, relate to things and therefore "think". The same holds true for phonetically sounded or written "rhymes"...and the serendipitous meanings that any of those words may have. This includes even those trivial word combinations that may come into vernacular usage. Vocalize "moon", and the month of "June" comes to mind, not February!

In this very innocent way some sets of concepts become co-linked with others. Moreover, many potential and equally natural connections may be over looked...for generations...if ever! Unless a member of a given society experiences concepts outside the "normal" (usual) set of interconnected perspectives. In such a case, the experiential information set is enlarged and the prior set has an enlarged frame of reference in which to be re-evaluated and reorganized in the mental world view sense. This simple real-world activity has a corollary in the mathematical concepts of Set Theory that people have developed. Gödel found it to be a fundamental reference and  ffunction in his modeling of "sets" and set-types! He concluded by saying that no [formal] set can evaluate itself from the "inside"!

In my way of phrasing it, a system can only be referenced in terms of an "environment" in which it exists and  ffunctions. However, even sentience that is restricted to "internal" existence that is localized within some unspecific but "locatable" boundary can still validly evaluate the nature of phenomenon inside that boundary. It does so by treating any location that is "doing" the observation-information-interaction as being "outside" the rest of its co-existent artifacts.

That is, by subsuming a list of test observations from various different internal perspectives/locations/states (a mental/observational/scientific accumulation of information by "triangulation", if you will, via designating artificial sub-internal boundaries), equally definitive and valid conclusions can resultantly be derived.

This is an appropriate moment to discuss Bertrand Russell's "Paradox of Sets", Gödel's Theorem's (which were a response to the "problems" discussed by Russell and Whitehead), and the premises I enunciated in my 1973 paper which was communicated to staff members of the graduate Biology and Physics departments at SUNY Stonybrook, as well as in communiqués with Elsasser at University of Maryland, and Prigogine who was then in Belgium and at University of Texas. Walter Elsasser was a premier biologist who attempted to discern gross biochemical relationships that might account for the development of biological complexity and diversity from basic chemistry organizations. Ilya Prigogine, the eminent chemist, went on to win a Nobel Prize in 1976 for his late 1960's through 1972 work which mathematically described the appearance of special chemically stable states arising far away from initial equilibrium states. He showed for the first time that stability is not restricted to perfect symmetrically balanced equilibrium conditions. In a sense, his work foreshadowed the qualities later found in Chaos mathematics.

After examining qualities and conditions which many diverse systems display in our energetic universe - looking for those relational dynamics and special conditions that all things seemed to have in common - I concluded the following as some of the denotable arrangements. First and foremost was the tacit assumption that things could be spoken of as "extants" that are distinguishable from the observer. They could be observed and evaluated in very "general" ways, yet always with the muted implication that there was always a definable "something" existing within a specifiable space, or time, or condition, or situation. All things have an "Identity" of some sort, that we utilize to discuss them, and to distinguish their activities by. A coherent innate organization, if you will.

Parenthetically, I am not ignoring the current state of scientific methodology - to rest rigorously and solely upon mathematical formulations as the foundation for quantifying the qualitative aspects of our universe. It is asserted that if it can't be mathematically "modeled", then either the observation is questionable, or the mathematics is incomplete, and not well formulated. It is only in recent times that Chaos formulations seem to give a potential to describe "self-organization" (this thing I label Identity) via symbolic equations. I remind the reader to remember, that we ascribe the conceptual ffunctions to every aspect of a given language, and specifically, to this one we call Mathematics. It can only "do", it can only mirror and represent, the relationships and ffunctions that we first, become conscious of from our interactions with our environment, and only then process into usable relevant forms, of thought and representative language. As "powerful" a language as mathematics is, it is physical reality that precedes mathematics, and not vice versa. There can be as much descriptive exactness in other linguistic forms as there seems to be in mathematics.

At this point, I am speaking about things which are "tangible". Things having place and size and duration.

Within the most general description of space..."universe"...there are locations "internal" to any given system; there are "boundary regions" (whether loosely determinable, or rigid); and there are regions "external" to a Thing itself. In this most general way, there is Self, and by primal distinction, there is "non-self", otherwise termed "environment".

In our Energetic Universe, we have come to realize that there is nothing without Motion. All existing things maintain and ffunction in their self-maintaining, self-organizing ways, through active adjustable conditions and behaviors that are responsive to forces that are operating all the time (over temporal durations). Sometimes this "maintenance" is a response, sometimes it is the forces themselves. The important aspect of this particular discussion, though, is the cognition that Everything ffunctions in a distinguishable "environment".

There is an example I like to use, that speaks to the qualities and conditions that we take for granted. Imagine a fresh edible apple, with all its qualities of delicious taste, seeds stored inside, glossy unbroken skin, a stem curving out of the top. We can muse that there is a "real" apple, or even that there is a general "ideal" apple. It doesn't matter. As long as you ceptualize (bring together the idea/image) the whole true-to-itself form or essence.

We might go so far as to say that nothing else in the universe "makes" an apple what it is, and so, in a sense, an apple is a very distinct and self contained "self-defined" set....complete in and of itself. BUT. I submit a disjuncture. That if an apple were truly "self-defining" it MUST be colorless (!). Moreover, there is no mutual overlap of the set "apples" and the set "colors". Ever.

The external boundary of such an apple, that is, its "skin", can only have "color" if it exists within some environment through which information about a boundary (or any condition-state-event) can be transcribed and registered. An apple only has "color" when it is perceived from outside its primary structural-bound. If there is no environment...logically, there can never be "color"...even if all other qualities remain. An "apple", or anything for that matter, cannot be independently or holistically "complete" by itself alone. A "set" - whether comprised of physical objects, conceptual relationships, or mathematical constructs - cannot be correctly designated unless some co-extant environment is mutually designated and present. An apple has no color if its environment is missing. Similarly, math functions will miss important attributes and relationships if their mathematical environment is not included in our considerations. One of the eventual accomplishments of this presentation will be to examine, understand and then define a mathematical environment - one which will embrace all current math forms and usages, as well as expose important new relationships and potential.

Even Descartes' "Cogito ergo sum" (I think, therefore, I am) falls by the wayside, and body-mind "duality" becomes a frailed limited concept, when held up to the requirement of dynamic information flow. Both require ongoing interactions with an "other" in order to identify and localize a "self". Descartes asserts that Identity recognizes itself without relying on anything external. Kant allows co-extant "non-self", but relies on "material" differences to establish "distinction". Knowledge and information is considered by them as yet some other quality of existence. Not yet appreciated as part and parcel of the process and nature of "being". So. Neither of these systems is complete. They lack the temporal quality of existence, the information interaction quality.

It is this cognition that helps us surpass the formidable logic of Gödel. There are no permanently Formal systems! There may be "coherently closed" systems, but they are always evaluated in reference to some larger and more encompassing environmental system and framework....always.

As I indicated above, and will continue to reiterate, it is our awareness and recognition of things such as this, which once led, and continues to lead, to the mental concepts and paradigms we hold (via processes that are part and parcel of the panorama of diverse phenomena we observe and evaluate and understand), the languages we developed to solidify them in our own consciousnesses (and can therefore use to share with each other...while we utilize our perceptions in maintaining and stabilizing our lives with each other). It is after that, that we developed such things as Mathematics and Set Theory, and even the Russell Paradox.

Admirably though, what Whitehead and Russell attempted, as many before them through the ages tried, was to organize and codify human perceptions of the world, and the relational rules of thought, human experience, and all the conceptual and physical "tools" with which we built many civilizations. One of the fundamental issues they grappled with was "existence" versus "non-existence"...along with a way to describe "things" ...once you fell into agreement that it was "existing" tangible things you were trying to describe.(!) Of course, after you had yourself a "thing", it became important to pluralize the situation...as well as reflect all this back with "non-existence" (whether "never" or "at least not yet" or "not anymore").

From my understanding of Russell's Paradox, it was a 20th Century version of the ancient Greek "Liar's Paradox". When the Liar said, "I am telling a lie.", we evaluated that if he was "lying" that he was really telling the "truth", and that if he was making a true statement, it was "really" a lie. A headache producing conundrum. A paradox.

Russell put it into Formal Set Theory. He defined conditions of a "collection", and of "set". A Set "contains" things. Thus, as an analog of geometric relationships, he attempted to conceptualize and verbalize the experience/observation which I described above. He could talk about "something" that was distinguishable in a universal environment. (For convenience he just happened to constantly leave out cumbersomely persistent references to that co-existing environment (!)).

He then asked the question: Can the Set of all Sets, S, which do not contain themselves as an element, in fact be a member of itself?...or not? He reasoned it to the same conclusion that was done with the Liar's Paradox. That indeed it is another impossible conundrum.

Along came Gödel. He took a step to the side, to gain a different perspective to see what Whitehead and Russell had done. He was a mathematician of the highest order, and so he attacked the problem from a more rigorous and systematic perspective, in order to effectively deal with what is going on in Mathematics (humanity's highest symbol of organization and clarity).

By carefully defining, choosing, using, and developing clear rigorous Axioms...both in scope and application...he denoted 2 kinds of "groupings" : complete "formal" ones, with definable bounds and contents, and open "informal" ones which have qualitative elements, but are without bounds or limits. Again, in another analog of geometric energetics, either "something" exists in an environment, or now, can "be" a ffunctionally open and infinite domain, and thus "be" that something which had been nominally termed "environment".

From this larger more encompassing point of view, he could look into the Russell Paradox (from the "outside", so to speak), and say "Yes, to you inside the boundary of your system, you have a paradox of contradicting conclusions. From my perspective, I just recognize that you will never be able to make a decision! You rely upon Mathematics, which is a Formal and closed system. If we project that the Universe has a finite boundary, we will always be "inside" it, as will our mathematics. And there will be things we can never decide the truth or falseness of. If the Universe is Infinitely open, we will never be able to include all knowledge, and there will be things we will never be able to know the truth or falseness of." This is somehow very comforting to modern mathematicians (!).

Russell understood it as an insoluble contradiction. Gödel understood it as a statement of a qualitative aspect of existence. In a sense, it is sad that the better developed of the two perspectives is ultimately the more limiting one. Gödel expresses that there is a limit to knowledge, and even its "verification". At least the Whitehead-Russell approach harbored the unspoken belief that the attempt to "learn more" might still be worth the effort. (Maybe their differences were borne in the linguisticly founded life-paradigms of their separate cultures (!) Anglican and Germanic.... Russell living on an island, Gödel living on a more expansively connected landmass).

Here, my analysis hopes to gather both of them in under the embracing canopy of an even more important Condition of Existence. Something which they undoubtedly recognized, but did not appreciate the importance of. "Potential" ... the Perpetual Capability for Interaction, that is afforded ALL things in the Universe... through the domains of Time and Space. I will build toward an explanation.

The relationship called "set" has a "real existence" ONLY when there is a "presence" or "presences" that coincidentally establish "relationships" ...one of those "r"s being the aspect that we identify and label "set/s". Such an "existence" is heterotelic...as is exampled by: "between". That is, a heterotelic existence cannot "be" without the presence of prior or simultaneous extants. With that "information" observation (because we can perceive this "relationship" as a distinguishable characteristic of general existence, and, we note that we can ascribe the relationship of "set/s" to many things or situations) "set/s" takes on an existential and independent "presence" of its own. That is the process of inductive generalization. But, "set/s" is a "corollary characteristic" only, even if we can differentiate it and discuss it as a separable component. "Set/s" is not an independent "thing" ... even if it can be conceived of "independently". Therefore, when the attempt is made to re-associate it as being an "original presence" sort of thing the anomaly arises. "Set" is an observation-evaluation-translation-of-information construct. To re-phrase...it is transcendental. Thus their original premises are improper, and any anomaly or paradox is not conditionally a result, rather it is pre-present in the condition of an inaccurate premise. Subtle, but there none the less. To wit, the Paradox is rephrased: "This statement is the expression of an intangible conception, that proposes that there exists a conception that is not a member of the set of conceptions."

            Ergo, the built in dys-solution...the Liar's Paradox :

This is no trivial bit of mental or linguistic gymnastics. It turns out that the symmetry and dys-symmetry of the Universe ... the physics of existence elucidated in recent decades ... relates intimately with this so called "fact" of philosophy!

Russell and Gödel both bump heads when they confuse the two qualities of existence...by the unspoken assumption that there is only one kind of existence ... that something either "exists" or it "doesn't". In fact, this is one of the current given assumptions in the foundation of mathematics...one of the primal references that all else is built on. At the very core though of current math is a related anomalous situation that says that while we would like to have a fundamental Identity definition such as "A=A", always and only, we have to fudge things a little and accept a certain condition where "1 can equal 0"! This unfortunate situation flies in the face of Consistency and Coherence. It is all the more reason to abandon the pure Aristotelian tautology and expand our horizons.

In deference to our ancient forbears, Gödel implies that Socrates' admonition to us all of "Know Thyself" (Gnote' se Auton) is an impossibility and probably a waste of time. Concurrently, the distinction of types of existence recognized in trying to deal with the Liar's Paradox, makes Plato's edifice of Ideal & Real, all the more an impressive attempt to grasp Existence, Life and Being. (the cendent and the transcendent).

We too, however, have a clarity of mind equal to all these great thinkers. And we realize that to draw all these parameters into a coherent cohesive Unity, there is one more essential quality necessary to bring them all together. I call it the BRIDGE-PARADIGM. It is the fundamental relational premise that audaciously connects the known with the unknown. It let's us speak confidently about what we may not have any knowledge of...yet(!). It gets us past the binding boundary that Gödel so rigorously buttressed. It is the premise that while everything is essentially the differentially definable existence of notably infinite domains in which it is noted that Formal systems may have "bounds", those bounds are fundamentally arbitrary, malleable, and not fixed. The pre-eminent dynamic is that once "operations" or "functions" are designatedly fixed and acknowledged, those processes will be applicable in and along any place or time of the domain continuums, whether those locations, times or states have been encountered yet or not.

The Primal A Priori of ffunction, in an energetic Universe, is: Processes have a normality of ffunction beyond any "nominative" boundary limits!!! That is, Perpetual Interaction Capability (also known in some situations as "potential") is fundamentally (even in mathematical descriptions of "force") a "relation to performance on the far-side of any boundary of knowledge, energy event and information".   It is a "guarantee of performance". A fundamental principle...that once a ffunction or activity is recognized (given appropriate conditions and components) the behaviors will be exactly the same, no matter where or when they recur in space or time. In equations of force, the far-side is "the future", where the "bounds" are the moment or instant of perception (presence of the interaction) ... most notably referred to as "the Here and Now"... and the as-yet-to-be-realized locations/times or states-of-being for the active transcription of energy or information. In Spatiality, it is the statistical potentiality of all possible locales, relevant to the specific construction of any Form/System.

In a very real sense, we can now specify a clearer understanding of "objective" and "subjective" phenomena.

A FUNDAMENTAL characteristic of EXISTENCE (or anything relevant to "existence") is...Uniformity, Coherence, Consistency. The PRIMAL ABILITY to INTERACT & FUNCTION. Nothing....absolutely nothing...."exists" in isolation. Consciousness, perception, awareness, identity, innateness, self-ness ...... none of these activities or concepts have any meaning, purpose or relevance without co-extancy through which they are "active-ated" ("motive-ated") ("predicated") .... dynamicly or kineticly referable.

"Subjectivity" is the result of individuation. That is, the presence of separate and distinct extants. "Objectivity" resides prior to that, as a necessarily required foundation from which "subjectivity" arises. Thus, "Objectivity" is NOT extancy, in and of itself. "Objectivity" is a DYNAMIC. It is another way of naming the pre-requisite of FUNCTION. It is the relationship of kinetic activities, of informational correspondence, and not the actual quantae. "Objectivity" resides in the "event-occurrence" process rather than in the participants of the event.

With this being the ceptualized situation, we can arrive at an appreciation of "objectivity" only asymptoticly. The "objectivity" of existence can only be appreciated as we (or any extant) are engaged in its constant "expression" through "subjectively" individual encounters. Constantly engaging in "subjective" and "relativistic" activities is the ONLY window we have for recognizing the totally continuous and persistent OBJECTIVE nature of Existence to {predicate} exhibit those various behaviors....INVARIABLY.

Phenomenological cognitions.....after events....pointing to the "objective" primacy of BEHAVIOR.

In relativity equations, the Bridge connects all pasts and presents to the region outside the time-cone. Even here, any point in space (translated as points in a plane perpendicular to the time continuum-axis), even if out towards orthogonal infinity, can eventually be reached, given sufficient passage of Time. Given an "infinite" universe, there is ostensibly no place or time that cannot be reached ... eventually (using a Turing sequence). Either by direct contact, or by some discernable convoluted indirect network path continuum. That is, this schema is open to all space/time as being linkable either by singular successive sequences of cause and effect, or, by an alternative random maze of links whose only mutuality is that they connect some specifically designatable event temporal-locales. The intervening sequences steps are entirely stochastic until after they occur.

{The above paragraphs have been part of this text since its initial writing in 1991. Just prior to Version14 update in April 1995 I came across a marvelous remark by the creator of Information Theory, Claude Shannon, that deserves inclusion at this point because it connects very directly to the concepts you've been reading. The quote is from Shannon's paper, "Coding Theorems for a Discrete Source with a Fidelity Criterion", which was presented at the 1959 Symposium on Information and Decision Process held at Purdue University. The paper was compiled with several others in the book "Information and Decision Processes" (1960, Robert Machol, Ed.; McGraw-Hill).}

This quote is the final summary sentence of his presentation. I find it exceptionally admirable because it shows how well he truly appreciated and understood the philosophical implications of his intricate mathematics. Before I found his paper I assumed that Shannon was just an extraordinary mathematical technician because that's all that other writers had written about him. I now know that he was a Philosopher of Existence. For that he will be immortal. He summed up 40 pages of extremely technical mathematics with the translation into simple practical English words:

"Thus, we may have knowledge of the past but cannot control it; we may control the future but have no knowledge of it."

Claude Shannon
1959

 

Brilliant! His mathematics wasn't just some technical mumbo jumbo showing us how to eventually build efficient massive computers, telecommunication satellites or the information super highway. It was also about the nature of existence and being.

The past can be evaluated deterministically because our observations track very sequential causes and affects. The future holds the probabilities of all that is possible and will display the results of our participation.

According to my own paradigm, this ultimate co-integration of connectable locales and moments and states of existence, means that information (no matter what the form or relevance) is ultimately linkable with all others ... at least in the Potential. The most complete paradigm is one that embraces all information, past, present and future, and all the ways information is handled where ever and when ever in the flow of existence.

Primal is the understanding, recognition and projection that whatever forces or ffunctions are understood to "be", that they will "be" exactly the same and no different, where ever and whenever they exist. Allwhere and allwhen the conditions and parameters of existence allow. First...there is potential...enabled strictly by the prerequisite of ffunctional compatibility, coherence and consistency. Limits or adjustive qualifications come afterward. Some quality must already exist on the other side of temporary information limits or boundaries to enable us at some later time to meld the specific information we will encounter with what information we already have. We may not yet have the specific knowledge (whatever energy or information it embodies) that exists outside of the information set we have at this moment, but just the fact that such things will be compatible with the world as we experience it gives us information about the characteristics of extancy in total. We can reasonably talk about a quality of extancy which resides "beyond" our reach. It is not an ignominious blackness over there and Gödel is not the "final Word".

In the sense that information retention/processing/utilization is merely a ffunction of energy/information translation/coding, then human perceptions and concepts and models and language are part and parcel of the dynamics of the whole universe...ALL its activities. Most importantly, language and thought are not 'mirrors' of a separate external reality, but an extension of it. The differentiations we were able to make vis a vis an "event - observer" discerned system - the energetics events itself, the spatial & temporal distances between the event and the observation, the participants of the event, the mechanisms of discernment (e.g., our body-brain-mind) that are separate from the structures of the events, the forms and components and definable paths of the energy quantums which constituted the transfer of information from the event to the observer, this over-whelming flood of separate distinguishable "things" made people rivet their attention on the qualities of separateness, apart-ness, distance, "me" distinct from "that out there", "thoughts" separate from brain tissue. What was dramatically overlooked was the "glue" that binds all these things together: the smooth continuum domains of space/time, that permit the fluid flow of energy and information; and which simultaneously are the infinite allowable paths of "environment" that envelop all behaviors and events and phenomenon of existence in the universe.

This is no "pseudo-spiritual" metaphysics, this is no religious genuflecting to a vastness that might cower us because of our self-perceived minuscule form or intellect. No, it is a calm and clear perception of how the universe ffunctions. And who, what and how we are in this place & hour... these places & hours!

The metaphilosophical bind of the Body/Mind "duality" was an artifact of that differentiation ffunction. In some applications, it is a useful tool. But, it is not the true dynamic. This in fact, is what Wittgenstein eventually realized but never got around to clarifying towards the end of his life. That is why he started to pen some changes, and why he was so vehement against all those who analyzed his early work and tried to fortify his original treatments. At the end of his life, he was about to recant everything he had become renowned for!

Obviously, the actual construction of an organism plays a crucial role. It is a combination of the diverse organelles that a creature has - its structural ability and sensitivity to recognize energetics/information events and the capacity to hold the information in useful form - that creates an interdependency on all the sub-structures that operate self-conservingly. All organisms - or ffunctional extants - must have the constructive capacity to absorb and incorporate energy/information, both in rate and in quantity, that does not over stress overall homeostatic ffunctioning. Like wise, there are minimum energy/information requirements necessary for basic maintenance, if not for added growth. Combining these observations, we can apply them in differing yet appropriate proportions, to all systems - living and non-living alike. The quantity of energy/information that is required "from" an environment is one of the distinguishers between living and non-living. But the net result, that of an "extant enduring in an environment", is the crucial observation.

All things can be reduced to a dynamic set of relationships where there is an "internal-ness" a "boundary" and an "environment", that ffunctions with interactive energy across, through and around the boundary - and displaying a resilience to process that energy/information flow, to maintain/enhance form and ffunction. I label this relationship-process dynamic "Integrity", and it works using all the fundamental forces as mechanisms - all under the aegis of general and localizable entropy ffunctions. But the Prime Directive, if you will, the ultimate "motivation" is "Kinetic Stability"... "Integrity". Holism thereby, requires a pervasive and unflagging openness of ffunctioning - the ability to coordinately and smoothly interact in consistent ways (even if energeticly violent). The pre-requisite for holocoherent ffunctioning is perpetual interaction capability of all things in the universe. And the process of Entropy can be discerned and defined as operating in appropriately definable "small-fields", and can account for negentropic building of complexity by establishing domains proper to the range of energetics going on.

By the entropic normalization of forces in an electron cloud for example...the smoothing of energy states to the lowest stable ones possible, larger structures are created ... atoms combine into stable molecular forms. Into forms of increased complexity, that can respond to more environmental energy/information, and process or even hold the input quantae. The ladder of complexity is wonderfully easy to climb once that process gets started and the general environment is hospitable to continuation.

The definition of Entropy...as I see it...is substantially more than the mathematical equivalence of "complete statistical equality of the energy of a system". It is that, but more. I see it as the motive tendency of any system comprised of inter-relational components, to achieve "minimum stress homeostasis". For several of its component parameters, not just energy quantums. One parameter is Spacial Domain: dispersion through an enlarged region of ffunction. An energy quanta which is de-densed (rather than con-densed) , has reduced one of it's entropy components in a very real and ffunctional, yet boundary related, manner. This runs counter to quantum shell models where electrons fall to their lower energy levels (and thus "higher" entropy states) even as they are confined to statistically smaller spatial domains (as a "negentropic" mechanism). The nature of the sub-structures ... those very specifically designatable "interrelated components" ... are crucial for the range and activities of ffunctioning vis a vis Entropy.

In point of fact entropy is not a monolithic ffunction. Not only can it operate in separately concurrent domains separated by determinable boundaries, entropy can also be treated as self-ffunctionally relevant partial differentials!!! That is, several "entropies" (plural) affect and therefore effect the behavior of any given holisticly bound system. Entropy is a ffunction not restricted to "energy" but is applicable to a variety of variables. It may in fact be an assignable quality of each fluencial (dimensional) vector, and therefore, to every separate factor at the tensor/metric levels.

{As I write and re-write this manuscript - which I began after a hiatus of 18 years from my 1973 treatise, "Initial Formulations" - I constantly encounter ideas which must be blended with already written text. This may make for difficult reading for you. It may give you erroneous impressions about the train of development (a situation which I will example for you towards the end of the book). Regardless, here is a moment where I need to refer to something I've just read and learned of. I did not know of it until just these days, but I am encouraged by it because it parallels my ideas that you will read of later on: Nested Cantorian Infinities.

The book is "Beyond Einstein" by Dr Michio Kaku and Jennifer Trainer, (Bantam Books, 1987). Dr Kaku attempts to explain Super-String and higher dimensional theories in layman's terms. In chapter 4 he describes the 1950's work in Japan by Shoichi Sakata at Nagoya University.

"The Sakata school argued on philosophical and mathematical grounds that matter should consist of an infinite set of sub-layers. This is sometimes called the worlds within worlds or onion theory. ... The interaction between the stars creates the galaxies. The interaction between the planets and the sun creates the solar system. The interaction between the atoms creates the molecules. The interaction between the electron and the nucleus creates the atom. And finally, the interaction between the proton and the neutron creates the nucleus."

This basically led Sakata's working group to predict higher dimensional orders and specific balances known as "symmetries" - and the qualities that sub-atomic particles existing at that level would display.

This is exactly what my work has focussed on, only applied to the broader spectrum of complex systems in the universe; The larger intention of this manuscript is to examine the mathematical-ceptual fundamentals and evaluate their presence and application in systems other-than the "atomic" per se. The cosmology of a Grand Unified Theory may be most obvious at those esoteric levels of physics, but they are discernable everywhere else too. It feels good to know that my generalist approach has been in step with more clinically supported perceptions. Hopefully, my re-evaluation of the nature of Calculus will provide a bedrock on which the rest of planetary scientific efforts can relate to and find conceptual significance.}

Again, the clearest example of this are atomic electron shells. The traditional application of entropy has been to the quantum energy states of orbital electrons. External photonic energy, input into an atom and absorbed by the atom, will standardly raise the energy level of an electron there ... an "energetically" negentropic transition. Likewise, as orbital electrons lose energy, they cascade to lower energy states and that is considered an entropic transition.

However, if we distinguish-out the spacial region wherein a state-transitioning electron exists (considering space as a separate partial differential of the equation), then as an electron cascades to a lower energy state, it otherwise becomes more localized and spatially determinable. The entropy of the spatial partial-derivative component decreases, while the energy partial-derivative component decreases its negentropy (its ability to do work decreases). Conversely, as its energy states increase, its spacial-differential also increases .... the electron diffuses and enlarges its statistically potential locations to exist in ... the entropy of the spacial partial-derivative increases.

This runs counter to the historically typical link of spatial occupancy and energy: lower energy in interacting systems ... such as a "gas" ... is associated with larger spatial regions. In certain forms of atomic activity however, we can see that lower energy is associated with smaller (more findable) regions of ffunction. This is the critically important variation of entropy which shows that every partial derivative (space vs energy vs time...compounded) displays its own separate "entropy". There is no one singular "entropy" at work. There is an orchestration of entropies which reinforce and even invert their intrinsic gradients.

When atoms coalesce and combine, several partial-differential components increase their locally bounded "entropies". The conclusion here is that, depending on the component or specific bounded region which might be under evaluation (co-referencing other relevant bounded regions or partial derivatives...as blends comprising a "mutual environment") it is eminently reasonable to have several "entropies" at work simultaneously. They can even ffunction counter to each other, while having an affect on the net behavior of the systems. An entropic change in one component can effect a negentropic change in another component, and vice versa. It is on this foundation that complexity arises in the universe.

Eventually we will be able to apply the notion of interactive separate local entropies to the phenomenon of Time. We already mathematically assign it exponential notations. To remain consistent with the meanings of the rest of our math symbols it becomes equally accurate to say that by the use of these notations we are constantly referring to real multiple time-dimensions. It is even probably correct to ceptually posit separate definable sub-components for "Gravity", and recognize the possibility of an interaction that ffunctions "entropically". Gravity could then truly be accurately described as elastic tensors and metrics (per: Hooke) which follow entropic-gradients in a region! Elsewise, by specifying nested Cantorian Infinities..... each infinite domain continuum can display its own distinct Entropy ffunctions. With the resultant affect of Negentropic ordering of the next outer-nest infinite domain continuum. The sub-components of Gravity being several interacting temporal continuums. Einstein already suggested this by comparing Gravity with acceleration, which is "time x time" and "time x time x time". I propose that the equality might be an identity. Gravity may be the experiential real result of the interaction of distinguishable temporal dimensions.

In separate and simplisticly organized systems (where the "bounds" are highly specific and ordered...such as a gas existing in a rigidly formed container), entropy exists very much the way it has been traditionally conceived. But, when the "bounds" are less "ordered" and are more actively participant in the ffunctional behaviors of what is at hand... that is, are equally and mutually responsive to all the energetics going on and all the transiting partial differential components encountered, in this situational environment, there is an interactivity of several entropies. And the small-field entropy of some components create, drive and determine the negentropic ordering of larger spatio-temporally bounded co-extants .

I was thrilled in October of 1992 when I read that Dr Rudolph Marcus of Caltech was awarded the Nobel Prize in Chemistry for his work describing definable differences in the transfer rates of electrons from one atom to another or from one molecule to another. This covers inorganic and organic reactions. I called and spoke with him briefly in October of 1993, telling him that I felt his work was applicable to chaos and complexity theories. He modestly differed, indicating that he wasn't knowledgeably familiar enough with those efforts, but he would be more than happy enough to forward a copy of his Nobel presentation to me. I will elaborate on his extraordinary achievement later on in this paper. Needless to say, Dr. Marcus's explanation of variable electron dynamics details something which the Integrity Paradigm hints at in its overview and understanding of systems dynamics in general concerning EM fields - interactions and the arising of complex systems through the sheer application of localized entropy. I will be so bold as to say that, even though Dr.Marcus might not yet personally recognize the connections as seen from the perspective of the ideas presented in this work, his understanding and description of electron behavior is the defining explanation of what produces the subtle entropy and negentropy gradients in EM fields around molecules .... and what drives the continual creation of negentropic complexity and life. It is far and away superior to the concepts and methodology being proposed by the current group of Chaos and Complexity theorists, who have to introduce a host of new and subjectively debatable concepts at principle metabolic junctures in order to achieve a pseudo-rational path for the functional complexity of living systems. For example, in a situation where 2 stable energy-minima states exist on either side of a saddle-point transition plateau, Marcus recognizes the bi-directionality of reversible mechanisms and shows that several factors produce a very distinct preference differential (thus giving a gradient when placed within a sequence chain of reactions), yet still noting that on either side of the saddle-point, the reactants will arrange themselves toward the 2 distinct minima. The Chaos theorists, looking at such "behaviors" without linking them to any specific mechanism, say that the molecular configurations are "drawn toward" 2 separate "attractors". It is eminently possible to define, describe and model such behaviors using chaos mathematics. That does not mean that fundamentally simpler traditional ffunctions do not produce them and are a superior way of understanding them.

In short order, I will get to how this translates into mathematical terms, and examine some crucial paradigm shifts that will clarify older accepted formulations, as well as open the door to creating new ones. If you will bear with me though, I want to elaborate more fully on language, symbols and conceptual experiencing. It will be difficult to appreciate or accept the changes I want to make in mathematical symbolism unless you can objectively perceive it as just another language whose symbolic meanings are open to refinement and change.

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