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| THE INTEGRITY PAPERS | UIU Group | ceptualinstitute.com |
| Understanding the Integral Universe |
Glossary
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"Understanding the Integral Universe" presents you with more than a few new ideas, also new words with new definitions, and even old words with new definitions. This glossary will help you navigate through the shoals of old mindsets ( lingering relational ideas that form the foundation of prior thoughts and concepts) and guide you toward making new connections, opening up freer unrestricted mental seas to sail upon and explore. It would be good to review and familiarize yourself with the words and ideas in this brief glossary, preparing for the conceptual adventure ahead.
is the mathematical symbol for "function", also known as a "process statement". It can refer to any equation that is relevant to a chosen domain of values, for example: f (x) (voiced: "f of 'x'"). It means "there is a process or function that operates according to variable values that are referenced using the general notation x". Instead of saying "y = x2" (where we look for specific results to help solve specific problems) we can say f (x) = x2 and therefore imply collectively all the possible values y can take when x is allowed to be all possible numbers we can plug into the equation.
I will be using that f notation as an additional natural letter in regular written English word usage throughout this book. I do it as a subtle ever present reminder that relationships which we used to treat as static equations, actually embody the characteristics of real dynamic processes -- and vice versa -- in profound ways, with real applications to our everyday lives. This writing technique will help us remain cognizant that there exists a significant dynamic relationship between things we experience in the physical world and the ways we describe them. I want you to keep these notions in mind as you read words such as f unction. From now on, whether in a mathematical context or in regard to mechanical or biological or economic processes, I want you to appreciate that an activity and a description of that activity are fundamentally....the same thing, because their analogues (their analogies) express scaled equivalences, ever present between them. There exists a correspondence of components and of behavioral descriptions. We create concepts, notations and communication conventions to stand for the events, processes and relationships we perceive. For example, the word apple is not in fact a physical edible fruit. But, by mutual agreement, the word can embody all the characteristics and qualities we are aware of an apple having.
Mathematics is a language that does the very same thing. The relationships we perceive in the world are assigned notations, names and meanings. As we explore and manipulate the relationships of mathematics, seeing what works, what doesn't, what might if we try different configurations and connections, we keep looking back at the real world to see if the new organizations we try really do appear and function in the physical world. (see: Correspondence Principle, below)
In order to make sure that we keep this understanding in the foreground of all that we think and do I have chosen to blend some concepts as they are expressed in the English language. I use the mathematical notation f as another letter of the alphabet for use in our regularly used words. Sometimes you will see the word f function, sometimes f unction (if it is more explicitly "mathematical"), sometimes the word "f luence"(defined below). Whenever you see those word forms you are being asked to recognize an underlying thema: "relevance as a continuous dynamic process"....as opposed to the subtly alternative concept of ....."a process blending otherwise distinct reference states". We will accomplish two things using this f letter form. We will bridge the conceptual world with the physical world and see that they are more functionally unified than they are separate. And we will appreciate the universe as a flow of malleable energy and information. The world is a fascinating coordination of energy, dynamics, forces and things, of real information and potential knowledge. It all coordinates in a very special way that this presentation will make clear.
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is the study of how words -- their written forms and meanings -- a and developed in the history of human cultures and societies. I use the linguistic premise that early human ancestors experienced physical external events and relationships in the world and utilized repeatable gestures or sounds to reference those phenomena when communicating. They in turn used those basic experiential perceptions and behaviors to form the foundation for every word and concept no matter how complex or ethereal, no matter the language, written or spoken. Every intangible notion or idea rests upon the bedrock of a physical phenomea or relationship.
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is a word root of ancient Latin origin. It and its variation "-ceive" correspond to the physical process of taking, gathering, joining. It forms the root of many English language words : accept, concept, percept, except, deception, inception, reception, transceiver, etc. Suffixes and prefixes modify the root notion as to time, place, exclusions, or coordination with other processes. Concept indicates a taking with, a taking together, a combining and incorporating (bringing within our being). The core relation is acquisition. In our universe acquirable things are energy and information. What we do with them depends on how we combine them, coordinate them and have the construction or skills to employ them. But, first and foremost, is the process of taking in. Before we conceive, we experience. Experience is the gathering that leads to the coordination and relevance development we call conception.
I call myself a Ceptualist because I am not alone in the universe. Every part of me whether atom, molecule, organ, body, or soul exists by encounters with the rest of creation. What we are made of and how we are made enables us to incorporate energy and information, which at each moment in our existence makes us more than we were a moment before. Existence, continuity and progression -- relying upon innate abilities and potential abilities. We are part and parcel of an on going process of behavior, a thriving moving interacting dynamic called Universe. We are all Ceptualists because we all interact with and process information.
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is all non-Aristotelian logic systems. Predominantly it includes Boolean Algebra and its most important extension Zadeh (Fuzzy) Logic. Stochastic logic includes all methodologies which have at their core the premise that existence is a mix of probabilities and potential. Boolean Algebra, which rests at the core of modern computer gate functions, straddles the boundary between Aristotelian and Zadeh Logic systems by depending solely upon binary gates. Zadeh Logic improves decision making and feedback control by not following that restriction. Modern physics operates on Stochastic Logic systems such as Quantum Mechanics.
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is the ability of an extant, whether atom, animal or cosmic star, to participate in a range of interactions and still maintain a continuity of form or ffunction or development. Integrity, as we are capable of recognizing it, must be broad enough to embrace such examples as : 1) Primal universal construct: a stable proton existing for the entire life of the universe, 2) Metamorphosis: caterpillar which metamorphosizes into a moth or butterfly (being a singular organic life form which undergoes drastic alterations of its structure in order to deal with different environments, or bio-metabolism, or need-objectives in regards to its survival as a holistic organism), 3) Maturation: as an organism (such as ourselves) matures through several distinct states or forms of maturation while remaining essentially "individual" and uniquely the same, and even, 4) Evolution: (that occurs as organisms interact successfully to a wide variety of encounters on many levels...external environment, random fluctuations in bio-metabolism and genetic sequencing, and so on) where the chain of regenerating-creation can produce wholly different life forms, while relying on an unbroken lineage of reproduction-that-permits-alterations. Integrity is kinetic stability.
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as used by this author, is any distinct and distinguishable quantum. It can be energy, time, space, mass or relationship (either previously experienced or potential). The discourse will explore the current scientific and mathematical notions of "information", the human perceptual notions of "information" and the slightly new way where the author attempts to combine them all. A system and its Integrity can be evaluated in terms of an ability to process information regardless of form or rate.
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is the notion that information can be codified in many different ways yet still be remained intact. This is important in particle/wave analysis and in transferring or transducing information into different forms.
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is the amount of information a system contains. It's minimum value is the amount necessary to maintain on going processes and f functioning. It's maximum value is Information capacity. This is crucial for Integrity maintenance. It is the range where-in kinetic stability can be existentially maintained.
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is the amount of information a system can contain beyond which disruptions and/or dysfunctions occur, or beyond which transformations of construction are effected. This is crucial for Integrity. It relates to maintenance, alteration and adaptation.
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is the range of information flow appropriate to the normal f functioning of a system. Each system has a minimum and a maximum rate at which it can process energy or information and still remain viable. Anything beyond those values will cause a system to cease f functioning or to transform. Its importance is as noted just above.
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is the tendency of a system to dissipate energy until there is no way that energy can be channelled to a higher energy state to accomplish any further work. The notion of energy "dissipation" has been historically and mathematically linked to expanded spacial distribution and enlarged regions of presence. The historical notion of entropy and its opposite, negentropy (see next) have been linked to 20th century Information Theory.
It is the notion of this author that entropy is a more dominant force in the universe than is currently perceived. It may be a broad general rule of f function but more importantly it is a strong and localized factor in systems operations. Entropy can be applied to energy, to spacial configuration separate from energy and to time components separate from the previous two. In mathematical terms, an entropy f unction can be assigned to partial derivatives besides complete systems. Energy dissipation towards a ground state is not restricted to spatial dissipation techniques. A minimum energy condition can also be found when a system comes to rest at a fixed localized region, which is quite distinct from dispersive dissipation.
Most important, the author presents the new notion that interacting entropy regimes can create negentopic behaviors at the next higher order of system f functioning. This is the crux of how the universe establishes complex systems, biological forms and order. Chaos mathematics can track recursive behaviors and stable Prigogine plateaus far from some base starting point, but the operating mechanism is negentropy generated by and derived from interacting entropies.
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is the gauge of a system's complexity, the ability to handle more information and/or energy and otherwise interact with the rest of the universe in more profound and interesting ways. Negentropy is generally associated with accumulations of information, with increasing complexity, and/or with increased concentrations of something into localized regions.
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is the relational organization of several different infinite domains. Georg Cantor in the late 1800's was the first to develop the idea that the universe consists of several different levels of infinity, each with their own distinct capacity or content which does not necessarily have a 1:1 correlation with others. In the sense used in this text the author designates each and every mathematical term as indicative of a distinct infinity, separate from yet relational to the infinities represented by any other terms in a formula. Most distinctly, exponential notations represent a very clear and distinct infinite domain separate from the base domain which generated it.
The base mathematical notation is presented as "kxn". Both "x" and "n" are complex, "n" being its own secondary "kxn" and so forth. This makes "n" fully dimensional for all values, not just positive whole integers. The format allows for zero as a dimensional state that can codify and hold compressed information. The format allows for fractal dimensions. The format creates a progression of exponentially Nested Cantorian Infinities.
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Trõpic Manifolds (defined 1999; pronounced with a long "o" sound)
The notion of Trõpic Manifolds was defined for a paper presented at ISSS 1999 at Asilomar CA. It brings under one thematic term all practical and theoretical notions related to 'entropy', 'negentropy', and "Cantorian Infinities". A Trõpic Manifold is any topological or relational architecture (design model ; enacted matrices) which exhibits internal scalar differences. In phenomenal or physical terms, this relates to density and proximity relations - with the added notion that it is possible to proceed towards lower scalar densities (entropically) as well as toward higher scalar densities (negentropically), yet, always as part of interrelated continuums. Since general and complex systems are plurally architected gradients and extents, Trõpic changes or variances of many different types can be and usually are co-present.
The purpose for establishing this idea is to move away from the limited conventional idea that 'entropy' is in some way only related to 'energy dissipation' and disorder. That is only one facet of it. More broadly, trõpic dynamics must be able to tend in both directions - increase or decrease - based on what factors are present. If only density distributions are present, there still needs to be a way to compare various states or conditions of dynamic systems, no matter what they may be. For example, if you compare the content of a two different line segments, where one can be treated as a 'scaled' up or down version of the other, then in an absolute sense, one will be 'denser' than the other if measured by some common factor or single measuring system. The 'larger' segment could be considered 'less dense' than the shorter/smaller segment - with more 'space' between common marker-points. That kind of comparison isn't just a comparison about 'size' or length variations, but about "trõpic states". One is negentropic relative to the other, and vice versa. If one considers all the possible segments shorter than the shortest, longer than the longest, plus those in between, then you would have a smoooth continuum of variable 'densities', and therefore variations of entropic measure ... a Trõpic Manifold.
The resulting topological architecture is transfinitely and infinitely extended and embedded Cantorspace.
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f luence
is a new word used to replace "dimension". Though conceptually similar to "dimension", a f luence is not a direction in space, or even a "factor". It is more a Cantorian infinity of information that can be molded, stretched, compressed, modified, expanded, or reshaped where the information content is never lost, only altered. It can also be considered a factor in statistical mathematics where there is the notion that a system with 35 variables can be talked about as having 35 "dimensions". It is the author's intention to have future generations appreciate the informational fluidity of the universe. By choosing a new more alliterative word that bears a familial connection with "fluid" the author hopes that we will subconsciously and spontaneously relate to the universe as a place where information and energy flow about incessantly, where all events are interactions and all interactions are inf luences.
Not only is information transferred through and across mathematical dimensions, it is also transcribed through separately distinguishable temporal and spatial dimensions. Some correspond to whole integer values ... such as the historically perceived 3 spatial ones and one temporal one we tend to see ourselves existing in ... but some do not. In order to discuss the panorama of integer and non integer dimensions, the author has chosen to adopt this new word to embrace the larger range of concepts.
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is the full holistic environment of interacting f luences. It is written in its simplest form as "kxn" (see Nested Cantorian Infinities, above). This establishes the notion of iso-present mathematical environments and real environments.
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can be thought of as the ultimate "event horizon". The term "event horizon" was created in conjunction with cosmic "black holes" and is the internal region beyond which we have no information. That is not to say there is no information contained there, merely that we might not have easy access to it. From the earliest Greek geometrists to modern mathematicians a "point" has been almost a conceptual artifact, a "location" we can imagine as being so infinitesimally small that there is nothing smaller or "internal" to it. In this context, the author will blend the two perceptions. When used in current mathematics "point" usually refers to a numerical value that can sometimes be explicitly expressed and sometimes not (even though some can be named, such as Pi , the exact ratio of the length of the perimeter of a circle to its diameter, which has no "exact" numerical ratio). This is one interpretation. An equally valid perception is that a point is the conjugated state of many intersecting numerical domains. Even though it may be undetectably minute, it is possible for it to contain an extraordinary amount of compressed information that correlates to non-compressed phenomena such as waves and particles. This notion will be discussed more fully.
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is a circle that can be geometrically generated by a group of relationships related to two separate points in space. In essence the two points can be the ends of any simple straight line segment which can in turn be understood as the hypotenuse common to many different right triangles. Though related to pythagorean relationships and thus to Trigonometry (on which most all of modern physics relies), the Apollonian Circle shows us an important alternative sequence for constructing a circle. We are not restricted to the pythagorean technique of a circle being all points radially equidistant from a single point in space.
Rather than generating a circle from such an interior symmetric location, we can generate a circle asymmetrically in any direction, and the starting point locations themselves are part of the circle generated. The significance is two fold. First, we can now build important relationships of how curved conic lines relate to straight lines; that is to say, how they "map" one to the other. Second, we now have a more direct way to show how the universe constructs and uses wave forms; how energy and information is transmitted, transcribed and generally interacts. This will enable us to improve our concept of "dimensions". We will see that Heisenberg's Uncertainty Principle is an equation related to information mapping in corresponding but different expressions of "dimensions".
Current mathematics uses the Cartesian assumption that space is primarily describable as collections of straight lines. It is this author's contention that space is a massive coordination of conic spheres. The indication for this is that no energy or information in the universe gets transmitted linearly. It is always and only accomplished by transcription of curvelinear wave forms. Apollonian relationships are more directly applicable to this experience than Pythagorean ones.
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are three variants of existing theorems. The first is a non-symbolic reevaluation of Gödel's Undecidability Theorem. The author challenges Gödel's assumptions and shows that we can have knowledge about and makes very specific statements about things we have yet to experience. The second is a variant of the Apollonian Theorem (above). It applies a simple calculus relationship to the Apollonian Circle and shows us a first order Cantorian relationship of information present in "dimensions" (how information can be retained and constant even though we can express it in several different ways linguisticly and mathematically). This leads to the third theorem which reorganizes Heisenberg's equation as an equation of Information transcription between dimensional expressions.
This leads to the analysis which shows how waves and particles are informationally identical even though internal construction is slightly different. This is relevant to quantum mechanics, tunnelling effects, holography, sonoluminescence, Bell, Bohm, black holes, gravity, chaos mathematics and more.
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is such a fundamental and powerful quality of existence that it produces several monumental consequences. The most important for human consciousness is that every individual can experience and relate to the Integrity dynamic. It is the dynamic process of our lives acted out on many levels at each and every moment from atomic to biologic to social interactions. It requires no knowledge of mathematics or special education. Just being is sufficient. Everyone capable of reading these words has the capacity to find something in this book that they can relate to and understand about Integrity; something applicable to their daily lives, let alone the scientific implications.
The most practical consequence arises from an axiomatic change in human philosophy. We can surmount in whole cloth the old notion that existence is some kind of duality : body~mind, form~ f function, reality~representation. Human conceptualization has the ability to distinguish between an act and its artifact, between events and the names we label them with. In point of fact even an artifact has a role in Integrity maintenance. It must perform in synchonicity with other labels and representative notions. Integrity dynamics, which guide our behavior and organized ideations, are as real a part of the information we process as the metabolic information we process called food.
In order to hold to this high standard of existence means that symbolic notions must mimic the experiential observations they are derived from, and, more importantly, that experiential observations may be and should indeed be organized exactly as our creative symbolic musings indicate. The Ceptualist Perspective holds up for our inspection two very crucial mathematically symbolic notions and asks that we treat them as somehow real in universal structure. To date they have been flippantly disregarded as unrealities which just by chance help us derive specific useful mathematical answers.
I claim that is not so, that our conceptual explorations have disclosed a more correct way of appreciating the universe. One deals with a real mathematical condition which describes one being equal to zero. Since that notation rests at the core of 20th century mathematics, I take the opportunity to explain a possible valid meaning for this and how it arises. The other is the situation where we conceptually model Time as a single dimensional phenomena when to the contrary mathematics treats it plurally. I take the opportunity to explain the reality of multidimensional time and how we physically experience it in our lives. Undoubtedly this will lead to refutation and debate but like Relativity I believe this notion will survive and stand.
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This word is very crucial. I use it infrequently in the written text but, in a sense, it pervades everything. It is a quality of existence easy to recognize -- relied upon, actually -- yet rarely consciously considered. The dictionary defines it a "something existing because of something else". Now that could be anything, any of the Aristotelian Causes, a child born because of two parents conceiving it, for example. But this is different. Heterotelic is an intangible quality of "existence". "Between" is an example. Common sense everyday experience tells us exactly what that means, because we use the experience. But think of it this way in a more subtle, nee mathematical, sense. In one location you have "something". Unless there is "something else" in some other "location", however, you don't have the presense of "between". "Between" comes into existence because there is the existence of two or more non-heterotelic entities in a domain such as space or time or other.
Complexity is a heterotelic phenomena
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finds a new and expanded relationship when considered under Ceptual analysis. Current science and mathematics has limited symmetry to "two part bilateral equality". If you have "something" the only way to get back to a zero-state is to remove an equal quantity. A zero-state is at perfect equilibrium attained by balancing two factors. Ceptual analysis takes a different tack and examines the information relationships and structure of the -Apollonian Circle. The result is a three part symmetry inherent in multidimensional wave forms. Information analysis of the structure (accomplished by topological mapping of wave information) shows that the way to return to a base-state is by moving in units of thirds ("1/3, "2/3). This corresponds very nicely with the discerned architecture of quarks, the basic building blocks of matter.
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can be modeled quote exactly through dimensional progression of the -Apollonian Circle. The RAC geometrically constructs spin dynamics, electromagnetic toruses, and more. The progressions extends from point to string to gravity; from point to string to electromagnetism; and from point to string to strong, weak and spin. Dimensions ( f luences) are multi-temporal as well as multi-spatial, in keeping with phasespace notions.
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is a 20th century geometric discovery. It is related to Newtonian mechanics of orbiting bodies, to parallel lines and fields, and to information transposition via -Apollonian relationships.
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"Controlled motion through a gaseous medium."
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These definitions will give you a strong foundation on which to ceptually relate to the ideas and connections you are about to read. Other terms will be explained.
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