THE INTEGRITY
PAPERS (LINKS TO CEPTUAL READINGS)
GENRE WORKS (OTHER WRITERS)
POETICS
MINDWAYS (LINKS TO GLOBAL THINKERS)
"NON-FRACTAL COMPLEXITY" (Order the Videotape)
| THE INTEGRITY PAPERS | UIU Group | ceptualinstitute.com |
Integrity: The Proper Philosophy for Complexity, Consciousness and Creation |
[1,2,3]
We are as much creatures of style as we are of reason. We have a sense of the Beauty and Harmony of our universe even in the midst of exploring the most intricate functions and mathematical connections - elegant being the word most easily and often applied to the equations which best mirror the physical events we experience and strive to understand. In fact, in the same sense that the highest praise we bestow on p is that it reads like poetry and on poetry that it reads like p, art approaches science even as science approaches art. And, the way that we holistically embrace these diverse appreciations is to organize as many aspects of experience as possible into consistent singular paradigms.
Our modern science is firmly based on the language of mathematics and the conceptual relationships found within it, spanning from the dawn of human thought, through the ancient cultures, arriving at the extraordinary and formidable construct it is today. Some of our cognitions are quite new where as others were there at the beginning. As George Gamow points out in "One, two, three . . . infinity" [4] it's quite probable that even our earliest ancestors at the dawn of human consciousness had an appreciation and sense of immensity and vastness that we now associate with sophisticated concepts of infinity. Most obviously humanity coped with counting the uncountable in at least two ways. The first led to spiritual speculations, while the other attempted to wrestle it into manageability and real world application. Religion was spawned in the first instance and in the second came computation, geometry and mathematics: never ending divisibility, and, never ending inclusion - the immensely minute and the immensely great.
But, uncountable content was not the only quality associated with infinity; human perceptual relationship to set group content also became a factor. Out of this appreciation came all the mathematical philosophies of Leibnitz, Newton, Descartes, Cantor, Russell, Whitehead, Gödel and others. At this point in mathematical history Gödel in particular has the strongest conceptual hold on how we perceive what we experience. Prefaced by Descartes, then Russell and Whitehead, knowledge or strictly-experienced-information became the first criteria for designating Set construction and content (including Null-set). Russell and Whitehead exampled the experiential boundary idea as a wall. Beyond an observed surface boundary limit there could be anything. Without experience there is only inference as to what is beyond or behind. There is only speculation not fact, probability not proof. Even our most stochastic science - quantum mechanics - displays a familial type of wall: Planck's Constant. Though our mathematics can delve into regions far smaller, physical reality seems to cordon us off from a significant portion of experience-able existence. Heisenberg too imposed an information restriction on us: interactions enable some information transfers and preclude others. Gödel added a final twist to this and firmly seated humanity - any physical consciousness really - on the side of the boundary that is limited and finite. He effectively shackled human intellect by building a logical fortress which eternally precludes us from omniscience (not that lack of it really plays any particular importance in our strivings however). Finity never will be Infinity.
Taken as a whole these formidable reasonings go a long way to support our condition of information sequestration. It seems natural then, as we continue to strive to bring order out of disarray to make better sense of our world through the application of mathematical models and relationships that mirror and recreate our experiences, that even here some of us are cowered by Gödel's culminating pronouncement (more a subjective inference really) that because we will never know it all we will never understand it all, especially the underlying dynamics. I'm sorry, but that reasoning just doesn't follow. And most definitely, it is not an appropriate mathematical conjecture in light of Cantor's work and Chaos/Complexity in general. Most definitely it is out of synch with all probability functions, even if information incompleteness is an undeniable characteristic to be reckoned with. There is a light that transcends the limitations.
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Environmental Set Theory: Correcting Gödel
Gödel thoroughly overlooked what is by far the more important quality of existence: its uniformity and consistency. This quality is indicated by the mere discovered presence of some few singular mathematical relationships which model systems behaviors, not so much because of what those few precious correlations are as it is the ability of those correlations to be applicable anywhere and everywhere. The uniformity of existence resides in perpetual compatibility and per force that must be the first foundation of all probability functions. Even Andre Linde's studies of possible inflationary domain universes having different structural constants [5] are founded on holistic compatibility as first a priori. Universes with different structural constants either work or do not because consistent application of those constants produce functioning viable organizations or they don't. Very simple, very cut and dried. Interactions can only occur where and when there is mutual compatibility to interact in existentially supportive ways.
As we continue to look for specific formulae to mirror our world, we note that it is not the singularness of the formulae which is important but their pervasive applicability which is the superior quality. We can deduce something very important from this. Our knowledge grows more expansive with each passing moment. What was unknown a moment ago transforms into known via additional encounters. That is because it had the stochastic potential to do so. Relying now on this simple recognition we can surmount Gödel's culminating and binding strictures. We can say something very definitive about things we have yet to experience. We can assert that we know something about the unknown. It is compatible with us. Perfectly. Besides Linde's tacit a priori, it is an assertion easy to demonstrate in another way.
Imagine a closed chain of intersecting sets. Each has information which is confined to within its boundary even as the boundary includes portions of two or more other bounded regions. Any sentience within each exists within a Gödel Limit, yet the overlaps and looped connection of them all is founded on information compatibility first and foremost, regardless of the information content of any of them. Existence therefore is a mutuality of potential, not a conglomeration of bounded separations. We exist in extended environments and are simultaneously part of the environment for all else even as all else is environment for us. This holds true even when the bounded sets are different mathematical systems. Even Linde's mutually inhospitable domains still have the ability to interact with each other.
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Consider for a moment the apex concept of Complexity Theory: complex adaptive systems. We aver by this the existence of holistically independent systems which interact with environments and successfully endure and prevail. And, even though we tend to define such systems as denotable apart from all else, we instinctively know that all exterior boundaries are amenable to encounters, if not to adjustive interactions. A glass sphere adrift in a volume of methane will have a different experience than if the gas were hydrofluoric acid. An amoeba will have a differing range of experiences in a volume of water depending on whether there are nutrients present or if the pH is acidic, alkaline or neutral. A recursive metabolic loop will persist based not solely on its own sequential structures but on the presence or absence of appropriate molecules and energy conditions at each stage. Some conditions enhance survival, some enable it, some put stress on it, some preclude it.
For all things in the universe their physical or behavioral "edge of the envelope" is more opportunity than limitation, threshold level not strict preclusion. And, no closely definable system is truly complete without an extended environment. Consider this important relationship if you will. Imagine apples. One, many, none, ideal or real, past, present or future it doesn't matter. Organize a set called "apple". Ascribe to it all the qualities you find appropriate: 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 a general "ideal" apple. It doesn't matter. As long as you conceive or bring together the idea/image of 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. If an apple were truly "self-defining" it must be colorless! Moreover, there is no mutual overlap of the set "apple" and the set "colors". Ever. The external limit 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, can never be independently or holistically "complete" by itself alone. A "set" - whether comprised of physical objects, conceptual relationships, or mathematical constructs - cannot be accurately designated as complete 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 extended mathematical environment or matrix is not included in considerations (even if they can be conditionally ignored). One of the eventual accomplishments of a true post-Gödel holistic theory - one more appropriate for Complexity - will be the examination, understanding and definition of wholecloth mathematical environments - which will embrace all current math forms and usages, as well as expose important new relationships and potential, such as providing for the simultaneous presence of Abelian and non-Abelian functions in a single schemata.
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Linking Levels of Complexity: New Relationships
Such a system will enable us to easily reach across all levels of complexity, and, even if we find similar formulae applicable to quite different levels of being, we won't require the constructions of each level to be identical. Fractal imagery implies repetitive presence at any order of magnitude. But Complexity is not restricted to that. The two are more profoundly linked, not by form, but by information relationships applicable to the levels of construction. For example, a 6-carbon atom benzene ring has a highly stable dynamic structure. It retains its principle structure while capable of a wide range of interactions, environmental transactions and alternative amended forms. In the late 1960's and early 1970's a number of social demographic studies [8] were done by some Japanese research groups. They noted that (taking into account the restraints of terrain and rivers) human habitation clusters showed a significant 6-loci cluster structuring. Some of this was ascribed to socio-political territorialism, some to optimum economics flow. The fascinating thing is that with all the variability of human intercourse for what ever reasons we can postulate there are certain stable relational configurations which shine through even so. Energy or information flow dynamics seem to favor certain 6-body structures (noting that preclusion of others was nowise inferred), and indeed, the reasoning may be as simple as optimum planar packing of core energy sites.
The point of this example is that organizational requirements will permit the same mathematical formulations to show up again in different situations as conditions warrant. Unlike the laws of gravity and electromagnetism, the mathematics of complex systems are not always applicable in all situations. They arise conditionally, can fall into non-applicability, then arise again later. And, several different formulations might need to be applied simultaneously, not sequentially (otherwise precluding one when another is in effect). Under one approach to evaluating molecular stereo-configurations for example we might evaluate two equally probable states of a single molecule only statistically. Yet a more complete and accurate perception would include the awareness that the two such configurations also present to an environment two distinctly different electromagnetic profiles and that one molecule by itself can function as a Boolean gate which permits or denies the furthering of some metabolic cycle because of how its alternative EM fields mesh with others present.
In this sense, the software is in the hardware. Traditional approaches have treated data as something stored in a holding matrix, which has its own information aspects. That is the classical Turing structure. But Complexity demands something more, something more than "storage" and "form translation". Complexity really rests on any system having the energy/information to maintain its own coherent structure while having yet again the capacity - using the same sub-constructs as it uses for itself - to encounter, retain and remit extraneous energy/information, and therefore be part of a larger value-added information process.
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Calculus: The First "Information Theory"
Cognizance of this leads us toward reevaluating information in general, and also to considering just how neg-entropic Complexity can result from or co-exist with general entropy. The first striking realization to be gained here is that Calculus was already an information-processing function when Shannon came along. The whole information edifice of our world today is actually built on a procedural and relational tautology. Shannon used an implicit information function - Calculus - to define an explicit one - Information Theory. Presumptive information was used to organize discrete information. This notion doesn't invalidate his work, rather, it reasonably goes towards confirming the "software in the hardware" thesis. Given organizations not only have the capacity to "store" information, their internal states and potential states correspond to program coding. Optional configurations and concentrations will enable or preclude secondary reactions. Linear nucleic acid coding is not the only form of information storage.
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Entropy Redefined: the Complexity Builder
Keeping in mind the prior discussions about systems persisting in extended environments, this thesis is crucial as it enables us to build new evaluations concerning entropy. Entropy holds dominion but complexity is the offspring of negentropy. We must therefore designate a paradigm that allows for the simultaneous presence of separate entropy and negentropy configurations. We can accomplish this by distinguishing each and every source of "information" in any equation and permit each source it's own entropy, distinct from that of any combinative function. In particular, we must more carefully redefine exactly what the various characteristics of entropy are. The traditional concepts may not be enough.
Entropy originated with the notion that a system varies in its ability to do work. The Industrial Age equipment through which it was analyzed showed very specific dynamic relationships, and a mathematics was devised to mimic those behaviors, specifically gas compression. Work, however, is a subjective perception because "usefulness" varies with other conditions. Even so, mathematically we could affix the quality of "disorder" as a quantity regardless of other conditions, and this quantity became the fundamentally definable aspect of Entropy. Disorder quickly became associated with randomness (Shannon's "noise") and in particular spatial dispersion and diffusion. The less confined and more locationally random a given amount of energy is the less able it is to "do work". I assert that this is not the only factor affecting relative entropy, nor its singular criteria. Electron cloud entropy shows a notable exception as do results of friction in large scale systems.
In both instances a lower work state is arrived at that is associated with spatial localization and relative confinement. A body at rest relative to its environmental companions is in its highest action entropy state. Any non-zero relative momentum has a greater potential to do work even though on the larger scale of examination ignorance of exact locale reduces the determinism of the system to do such work. Shell electrons likewise move to slightly reduced loci when there is photonic energy reduction. Reduced energy obviously reduces the relative ability to "do work" too but is here associated with a gradient cascading spatially in toward a nuclear center-of-mass location. So spatially, entropy can be associated with dispersion or confinement as the result of several distinct mechanisms.
What this enables us to discern is that local entropies (derivative of several mechanisms) are a potential source of complexity arranging interactions. The primary thing to look for is relative reduction in the ability to do work, or more properly, the work accomplished when an entropy increase occurs. That can come from spatial changes, momentum changes, configuration changes, or energy content changes. Valence electrons interact with the available valence shells of other atoms. When atomic proximity and momentum conditions are appropriate valence bonds enable given electrons to spatially disperse around two or more atoms rather than one. In the traditional thermodynamic sense their presence is slightly more chaotically arranged, more spatially diffused and therefore in a slightly higher entropy condition. The atoms though have simultaneously done something quite opposite. Within a larger context their entropy has decreased. Molecules are more complex than separate atoms, they are more spatially linked. Their combined momentum has more work potential. The atoms are behaviorally linked yet that resulted from a separate entropy matrix. Electron cloud entropy co-created atomic molecular negentropy.
Awareness of these relationships will permit us to escape some of the perplexing anomalies of current Complexity. In order to get the right answers we must recognize the proper parameters. In Complexity explorations we must have a clear understanding of the underpinnings of behavioral dynamics. Having the numbers is not enough. Understanding environmental conditions is key. Understanding that several entropy gradients interact simultaneously is key. Understanding that innate construction is intermingled with potential information relationships of and with other constructions is key. This means that frame-of-reference relativity is crucial in Complexity considerations. Complexity needs to deal with several different frames of reference at the same time in order to make sense of things. That cannot be done if we pre-assume Gödel limitations. It may well be that we have to employ multiple forms of identical functions in larger formulaic matrices where the functions use different size information bits because they refer to interacting but distinctly different scale domains.
Information capacity is dependent on all possible energy configurations and all possible interarrangements with environmental components. The functions are most likely compounded exponentially (in a diagonally infinite series)[1,2] with some entropy gradients being directionally reversed at each exponential level, where information content expands factorially as well in some cases and in others as distinct Cantorian Aleph sets. Each level of behavior generally has its own information bit-size requirements and its own functional Integrity (dynamic stability) [1,2,3] so even though smaller scale or larger scale information is present, other-level information is buffered. It is not absent, merely above or below registration or significance thresholds. This would indicate that L. Zadeh's Fuzzy Logic [6] techniques need to be employed in addition to Boolean/Turing ones. That is, linear sequential mechanisms have been used with the implication that once a decision gate has been reached and a choice made, the non-choice is precluded from present participation. That is not the only case. Looped feedback will keep all prior information possibilities present with the weight of that potential being dependent upon residual content and the spatio-temporal arrangement of the loop (back connected information channels). The way such information remains present but not active is to require simultaneity mitigated by weighting functions . . . Zadeh Logic.
To understand Complexity we must mimic the total information openness of existence. This is a strict non-Gödel condition/requirement. For a while that will be frustrating for us because models and artificial constructs will always lack the functional completeness, efficiency and Integrity of natural systems. Our challenge therefore will be to come to grips with the appreciation that formal algorithms are closed even as we expect them to mirror systems that are totally open to a spectrum of energy/information encounters that we cannot perfectly predict or deny the presence of. How much information is required to initiate a computer command? How many photons were required at that Boston church steeple to reach the visual threshold of Paul Revere's eyes to satisfy the binary Boolean gate message that the British were coming or not? Which level of existence defines the "information bit"? Obviously, Relativity reigns in Complexity too. There are many relationally connected forms of information. There are many entropies, many negentropies.
Existence is a nesting of energy/information systems. Each is inter-related with all others while having their own independent behavioral Integrities. The important quality of complex dynamic systems is more than what energy or information states they are in at any given moment. The important quality is what states they have the potential to be in. That is the stochastic condition. That is a condition that breaks the Gödel Limit wall. It rests on a pre-requisite quality that we know must reside on the far side of temporal/temporary information boundaries: compatibility for future interaction.
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For Complexity to be a guiding weltanschauung for the years to come it must put forth the most expansive and embracing concepts that humanity is capable of. Truth is not restricted to closed analytical perfection and most definitely not to so called "complete" descriptions of singular events. There is validity in variance, in imperfection and most important in multiplicity too. They all provide information. The Complexity worldview must account for them all . . . acknowledging the full spectrum of conditional events . . . including the variances as well as the exactitudes, the present and the non-present; the determinant and the optional, all events - the significant and the small. Nodal regularities and equilibria are not the sole signature qualities of dynamically stable systems. The signature quality of integrally stable systems is the potential to encounter other energies and information and endure the event - which enables further intercourse - where the new combinations establish new dynamic equilibria. The vitality of Complex systems is enhanced by options where new connections and energy/information channels mean new opportunities. Complexity depends upon behavioral opportunities not just insular stability. With an embracing paradigm like that Complexity can and will be the conceptual standard bearer for future generations.
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[1] : Discussion of the Four Plane Universe Conundrum; Initial Formulations for a Unified Field Theory. Working paper.
[2] : Understanding the Integral Universe.
[3] : Integrity. Forthcoming, 1995.
[4] G.Gamow: One, Two,Three... Infinity. Viking Press, 1961.
[5] A.Linde: Scientific American p.48(8), November 1994.
[6] L.Zadeh : Fuzzy Sets and Applications. John Wiley & Sons, 1987.
[7] L.Zadeh : Fuzzy Sets and Their Applications to Cognitive and Decision Processes. Academic Press, 1975.
[8] Ekistics: Reviews on the problems and science of human settlements.| return to top |
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