ROSEentropy.htm

"I greet you, respected ancestors, dear companions, and cherished future." . . . We were all present in the furnace of the Beginning, called the Shinn-yu Event, from the Nippon ideogram for "motion", when all time and space "became". We swirled and intermingled as potential, and then as realized forms, in sequences of titanic stars and then in histories of atoms and molecules and metabolisms, which assembled and reassembled, in explorations of process. No matter our individual lineages, we are literally made of all the ancestors of our existence, and we will contribute to the shapes and comprehensions of all the progeny who will succeed us. Sensations and thoughts.

Last year at ISSS98 in Atlanta I was fortunate to be very critically challenged for presenting an unconventional interpretation of entropy. Where as I had thought it to be an obvious extension and generalization of the conventional uses of the word, apparently that wasn’t the case. It’s my intention with this paper to fix that oversight. The best way to begin is by discussing the word ‘flying’. By historical experience and observation, ‘flying’ was done by creatures having wings. Even Icarus tried to re-shape his body to gain that ability, as ‘to fly like the birds’ was the metaphor that captured sentient imagination. The modern era has seen the invention of flight using mechanical devices, and in fact we’ve gone through a major re-definition of the verb ‘to fly’, though you will not find it updated in any dictionary yet. At best, you’ll find that the original ‘definition’ (more properly, ‘observation’): 1. To soar through air like birds, which has merely been addended with: 2. To soar through air like airplanes. 1,2. ..with wings.

But the concept of ‘to fly’ was substantially changed, not simply added to. What once meant: "a life form moving through the air by its own volition and ability", has now become "controlled motion through a gaseous, fluid or morphable space regardless of technique or process"(Rose,1992). We went from a highly specific example, criteria and use, to a general process, which is quite unrestricted in how it gets implemented. Manta rays fly through water, aerialists fly among trapeze bars, and planes, airfoils, balloons and off-planet craft fly through the densest to the sparsest particle distributions. Even humans fly - through corresponding concept spaces - with equal ease. This has been a major paradigm shift, even if not clearly specified before now.

What I am attempting with ‘entropy’ is a similar shift in comprehensive meaning. Immediately, I must refer you to the excellent 2 part article done by Peter Corning and Stephen Kline (1998) this past year in Systems Research & Behavioral Sciences, detailing the dozens of uses, misuses and diverse applications or meanings of ‘entropy’, which science and systems research is saddled with.

The ideologic standard of General Systems is our guidepost here. It is the notion of ‘invariance’ ... that which can be transposed into any situation or context and still remain - notable, unique, and pertinent - unchanged regardless of application or context. Examples include the power laws, which can be found in physics, chemistry, biology, and economics. The question is, is there such an invariant that is apropos for entropy, the second law of thermodynamics, the seemingly irresistible time-arrow of enacted behaviors?

The framing notion for that thesis is the atypical axiom: that which we assume to be ‘models’ of how existence might be organized, may not simply be models but may isomorphicly correspond to substantive agents which have the capacity to produce real forces simply by being gradiently organized.

Any architectures - termed, ‘trõpic [long-o] manifolds’ - produce impetus momentums where ever a scalarity within the architecture varies. Form gives rise to real function. Dimension space templates the relationships of impetus momentums - action tendencies and potential - before any forces actually arise, or are at least collateral with their arising. So in essence, ‘entropy’ is the primal a priori intrinsic in topological architecture and is the precedent trackway which produced forces follow as they arise. Since dimensional unfolding produces many scalar-different relationships, there are many trõpic pathways. Trõpic gradients (lumped historically under the single label ‘entropy’) are not corollaries to the 4 fundamental forces, but come before them. Priori architecture produces the enactments we actually observe, allows for dynamics in specific and general, and suggests a continuity of performance that is everywhere and everytime accessible to other performances. The universe in all its diversity is a self-sensitive self-sentient entity. It is even possible to show that local entropic gradients, such as within the pure architecture, can produce negentropic activity - the tendency towards more order and or complexity. This model, in fact, has a natural fit with Odum’s concept of ‘emergy’ (1982/1998) - which shows an invariant of 2 special and paired wave functions, cascading out of the solar pump and acted out in ever increasingly complex systems which can store and process emergic energy in coordination with one another.

Notions of entropy - including its corollaries ‘negentropy’, uncertainty, information, work potential, etc. - have been stretched far beyond the initial notions developed during the birth of the industrial age. Using volume, temperature, and pressure variables, "entropy" - defined as the lack of a system’s ability to do work, being an ever increasing exhaustion of the ability to effect change - helped model the dynamics of heat relative to water, in its solid, liquid and all important gaseous state. Steam, or any gas under pressure localized in a container, could be released and made to accomplish mechanical work. The wild swirls of chaotic molecules could be harnessed to do things for people. The more heat, the more tightly compressed, or, the denser in free movement, the more work could be done. By releasing and dispersing the pent up localized energy, work could be accomplished. In the main, the physical relationships were well characterized. Energy depletion was empirically seen as a diffusion and dissipation of particles, and as a reduction of over-localized energy, being distributable among more particles and places. The energy was literally ‘spread out’ and smoothed, as it were, becoming unlocalized.

Spatial localization - as by gas compression - was a fundamental attribute, associated with any ability to knowledgeably specify where things are in a system, re space or time. Container boundaries give an easy and direct model of the concept. Confinement infers definite location and being findable; findable infers knowing; knowing infers ‘orderliness’; order is pattern; pattern is continuity; continuity is memory; memory is information. In rigid close-quartered solids there are designatable relations relative to specifiable locations. Oppositely, diffusion/dispersion (being too scattered to account for details) goes with low gas pressure, low ability to do work, and was designated as higher entropy by Clausius (1865). Greater entropy is: more diffusion, chaos, randomness, indeterminacy, mentally ungraspable, un-knowledged, and as Shannon pronounced it, a lack of usable information, measured by probability partitions.

Boolean applications focused on the ability to specify that a locus is either 1 or 0. Information and un-information - order vs disorder - were designated as probabilities required to specify states or data. Krippendorf (1999) cautions however that uncertainty has both precise and loose natural meanings which often get conflated, and adds, ‘entropy should not be confused with uncertainty’. But the tendency is natural and concept homeophors are indeed present. In regard to ‘negentropy’, he states the only reason for assigning it a negative sign is ‘that it yields positive information quantities’ since the log of a probability is always negative. I would suggest an alternative and non-arbitrary explanation, having to do with non-commutative functions, topology, and normal symmetry breaking. It is possible to show (Rose, 1992) that any 3 variable loci which can be linearly correlated have referencing relationships which cannot avoid including at least one negative component when relations are measured or enacted among them. The same holds for 2-loci, but is arbitrary and irrelevant. For example, it would have been equally reasonable to stipulate that electrons have a positive charge and that anti-matter electrons are negative. The assignment makes no difference if applied consistently throughout..

Continuing in the original vein, it is crucial to note that if current common sense ideas about entropy seem, or are, problematic then some other invariant quality, besides the casual if not wrongly accepted ones, should still exist for all these uses.

To find it, I start with some new definitions. All physical and modeled systems have to happen somewhere. Within larger domains, members and energy can be in all sorts of localized or dispersed locations and relations. So, I start with designating a name for any potential behavior spaces where these changes and variations can occur, Trõpic Manifolds; "trõpic", to embrace entropic and negentropic behaviors, with priority on increase/decrease changes rather than on fixed values from single states to single states; "manifold", to make clear that this is all part of topological continuums of n-dimensional expressions. As an aside, behavior spaces - and real relations within them - may be quantized, but they are first and foremost, present in smoothly continuous domains. First we have to specify spaces where variants, differences and gradients can occur, then we can talk about the interactive processes among gradients and the attributes that transcend context.

For simplicity and brevity sake, I ask you to keep in mind Bateson’s remark about information and bit as "the difference that makes a difference" (Bateson,1972). Also, envision the Einsteinian (1916) relativistic universe as the basic model for a Trõpic Manifold. Spacetime (a behavior space) is uniform in all directions, except where it is smoothly ‘dimpled’ by the presence of mass or energy. A ‘dimpling’ is a continuous distortion that is ‘away from undifferentiated uniformity’; it is a local continuous gradient of accumulated ‘differences’. Zero distortions, null or minimum dimplings then, are the highest entropy states for specific systems, with minimum presence of ‘differences’ and highest uniformity of ‘smoothness’ - possible in both any local region and in any definable extent of the open manifold. Take note of the highlight on ‘minimum’. It allows a system to have some minimal disportioning yet also be in a no-work-possible condition.

Consider a black-hole or singularity in an otherwise empty Trõpic Manifold. It produces the most even set of distortions of behavior space possible. We can conjecture then that there should be a singular "process rule" for trõpic gradients that can produce not only diffusions of energy/mass through space and time, but, can also induce and account for accumulations and accretions in spatial localizations. One possibility is to ascribe to trõpic manifolds natural scalar distortions which differences in their dimensional architectures are entrõpically poised to undo themselves, i.e., have a tendency to ‘smooth’ back towards minimum differentiations and most unstressed states, even though differential stresses are a natural imposition of dimension-unfolding. Like a stretched rubber band with the propensity to return to its unstretched state. The suggestion is being made here that spacetime is more like phasespace and that interacting orthogonal or precessional dimensions (Fuller) can induce the arising of real felt forces. In one schematic thread, the attractive force, gravity, is seen as the product of orthogonal temporal vectors moving energy/matter along an entropic gradient into a configuration that will eventually bring the trõpic manifold of spacetime to a state of minimal asymmetrical distortions. Entropy potentia of a trõpic manifold itself can induce and cause negentropic spatial localization of real energy/mass. The structure of existence must harbor its own "abilities", not just display some "form".

‘Smoothing’ - understood as a process toward coarser graining, fewer systemic variances, and as the essential quality of the physical process of entropic progression - is an intrinsic process, even applicable to the seemingly ‘inert’ architecture of dimensional topology. Smoothing becomes the enactment of going towards least deformity, differentiation and fewest differences within a Trõpic Manifold, by any means or mechanisms. Entropy, as the invariant process, evens out whatever local variances are present.

In physical systems for example, the average times and distances for particles to get to next-interaction loci in place or time are more evenly distributed through the total behavior space. So here again we have relationships that are correlated to spatial location concerns not just informational ‘differences’. The same can be applied to the graining of electromagnetic and gravitational variances, which ‘smooth’ throughout distribution space, as the gradients, divergences and curls for any given length across a conic surface become less curved the further away from the focus to a distant radius of curvature. The angular turning - directional change, angular distorsion, stress, or ‘intrinsic variance’ and amount of conic vector displacement - from a straight line ‘zero turning’ basis, is more severe the closer to the center of radius than further away. Field distortions minimize both when all the mass or energy that can distort spacetime are localized in one place, as well as when they are maximally diffused and spread throughout that space. Only the most general invariant trõpic process mechanism must account for both possibilities with equal ease.

My message is simple and 180 degrees in apposition to all of modern science. The tendency towards energy exhaustion, maximum diffusion and so on - high entropy - was once seen only as an artifact separate from the 4 fundamental forces. In the proposed model a generic entropy supercedes the fundamental forces. It is a potentia to enact process which comes before the mechanisms that do enact process, and this intrinsic in the architecture of dimensional topology. Since the measured forces are enactions, they all follow rules that are preemptively established by innate gradients of dimensional architectures. One way or another, the behaviors of quantum mechanics and thermodynamics and the fundamental forces are products of the rules applicable to both the topological architecture of dimensions as well as energy/mass entities that exist embedded within behavior space. Our main concern is a particular thread of these notions, that speaks to what it takes for systems to endure and to retain integral processing capacities. In a universe thriving with energy, mass and individual performances, the concern is defining how integral entities interact with one another - supporting co-existence and mutual endurance.

There are only two techniques possible. Either be so isolated and independently self contained that negative influences are avoided or nullified, or, be capable of improving behavior potentials in order to cope with new or different energy and information and still be resilient enough to encounter, survive, and even improve future behavior space potentials by adaptation and morphing. This last notion is the new and most general rendering of what ‘fitness’ actually means in regard to evolution. It embodies the observation that evolution produces organisms which tend to be more competent and capable in dealing with alternative encounters ... whether focused toward specific local econiches or open to more flexible behaviors in larger environments. Energy capacity or control isn’t maximized, neither is entropy specifically maximized ... especially since coordinating systems typically have their own gradient strengths and directions.

What becomes most important is the latitude to engage in future processes and encounters. Systems with the most resilience or range of behavior options tend to be the ones that endure. The one important caveat here being that these will always remain tendencies and propensities, there are no ‘absolute guarantees’ as far as some final performance. Specific encounters will skew successes, with these situations being typically viewed as being the result of ‘real environmental pressures’. Specific outcomes will indeed be ‘attractor basins’ - loose gaussian clouds of process - whole, identifiable, but with nebulosity and processional freedoms at any moment.

Each system can be said to have its own range of behavior options, and also have alternative options, as contexts and environments and coordinations with other systems produce meta-level frames of performance.

The enactment of increasing complexity in living systems has been characterized by Odum (1982) as the ever increasing storage of energy stemming from the singular pump constantly flooding the earth’s environments with energy .. the sun. He has not only deduced the presence of a pair of invariant wave functions that are applicable to all levels of organic assemblies, which together produce cyclic patterns of growth, sustenance and dissipation typifying all organic systems, but he has also theorized a common exchange unit - ‘emergy’ - that is applicable to and usable by various complexities of assembly, including metabolisms, whole organisms, communities, economies and polities.

In a tour de force Odum can model the behaviors of diverse processes that have typically been reserved to the venue of fractal modeled attractor basins and catastrophe theories. But, there is a part missing from his work however, and I’m happy to say that I think it’s something I can contribute to, so to support and fortify his achievements.

The solar pump is not the ‘originating’ empirical a priori source of energy that drives living systems into existence. The sun itself is a product of other dynamics streams and trõpic gradients... the mechanism of Robust Non-fractal Complexity ... which implements the first energy source, the fundamental forces, which are the momentums and fields of subatomic wave/particles.

The first "source" of energy rests in the structure, dynamics, organization and behaviors of atomic particles architecture. Once enacted, the primal energy/mass entities of existence endure and continue without any additional motive input required. Their existences are not thermodynamically or dissipatively compromised, since they essentially act as insulated perpetually perpetuating solitons. They are the ‘inexhaustible’ first-source.

Complex living adaptive replicative systems only exist when the essential forces of nature and architecture of existence channel through two Trõpic pathways. One path (Rose) contributes the essential mechanism by which complex assembly is achieved, and the other path (Odum) contributes the added energy that induces the emergence and production of significantly higher Complexities, organisms, associations, and Life.

Complexity in its broadest definition is synonymous with pandemic universal dynamics of any sort. Robust non-fractal complexity - the general form/process - is perceived and defined this way:

Trõpic Manifolds are understood as <1,2,3> combined, being the essential ‘self-defined sets’. Energy/matter within such trõpic manifolds which recursively display or enact coordinated activities summarily constitute ‘complex behaviors’, amounting to interactively linked activities in a shared behavior space.

This is the fundamental mechanism of complexity production. It is accomplished through a variety of processes by can be essentially described as the convergence of separate but interact-able local trõpic manifolds which can intersect over mutual operating parameters.

The simplest examples are two atoms which share electrons and form molecules; or, persons who can have a game of catch; or, people or entities who can commercially exchange commodities; and even the continual sharing of ideas. Sharing and exchange of any sort constitute the de-localization of sub-system members into a broader relative-environment. This is an increase of its ‘local entropy’ and an enlargement of possible behavior/distribution space. Such exchanges effectively limit the behavior space options of the agents which constitute the next hierarchic level, among which the exchanges are occurring. Reduction, narrowing and focusing of their relative behavior spaces, causes the agents to coordinate and bind their behaviors, in a negentropic phenomenon. When mutually shared attributes permit these kinds of interactions, the entropy of sub-systems can cause/induce/create negentropy at the next larger level of assembly.

This last notion is critical. The behavior ranges of the members on both levels of organization must be compatible and share at least partially, some common behavior space. The systems can function independently and are not required to coordinate, especially if several factors come into place, such as specific proximity vis a vis the strength of generated fields to affect other systems. When sufficient parameters do fall within mutual ranges - typically towards the lower range of momentum space - then the systems bind and their respective Trõpic gradients synchronize. [In the original formulations of this paradigm, the nested assemblies were appreciated as having fully opposite and reciprocally directed trõpic gradients, except where they intersected and became behaviorally bound. The model was a letter Aleph .. overlapped mirrored s-curves. The more accurate schematic is of these curves displaced diagonally in behavior space, a skewed aleph graph.] This holds for as long as field interactions or energy/particles are exchanged with a denotable measure of regularity, where communications can be measured as both potential probabilities and actual probabilities greater than zero, for individual directed exchange. One-way transfers are sufficient for cause and effect evaluations. Recursive recurrent and sufficiently sequential transfers (two way or more) are required to accomplish Complexity.

Figure 6. Nested processes ~ which are independent and competent gaussian
assemblies ~ share process rules, and function concurrently. (Leiker Graphics)

As complexities are enacted and established, the coordinated manifolds synergistically enrich, service and support each other, enabling meta-level behaviors that were unavailable or inaccessible before. This is ‘emergence’ - but as comprehensible process, not mystery - and is an alternative to autopoietic and autocatalytics interpretations. Regarding the organic world, what I have described is the fundamental, ever present, and primary mechanism of chemical molecular complexity building - which does not require stellar furnaces in order to take place. Nicely, though, the innate energy/matter architecture and forces and compatible field manifolds split along two paths. When they eventually re-combine, the companion streams of trõpic processes work to enact greater complexity. One path provides the underlying mechanism, while the other provides the pump towards improved and bigger option-spaces.

The previously described venue is essentially an electro-magnetic one, but Gravity is also at work. Gravity is the product of temporal entropy (Rose,1973) and becomes the process by which scalar asymmetries and dimples in the basic trõpic manifold of spacetime itself motivates or moves energy/matter to accumulate in relatively minimum locations and so minimize distortions of the dimensional manifold. Simply put, masses attract and combine - forming stars in some cases - because, as indicated, a manifold in which matter exists can be most uniform and minimally distressed when everything is localized together.

What happens electro-magnetically in large mass cases is the creation of havoc. Wave/particles impinge on one another with such proximity that the EM fields are pushed to hyper-activity for all the possible atomic particles and mass weights and field fluxes present. The result are titanic furnaces - stars - which both produce new nuclear organizations and generate intense releases of massive amounts of energy. It becomes the emergy pump which drives energy into the already molecularly complex systems sitting primed, ready and waiting with its process mechanisms in place, to produce higher levels of complex organization, behavior spaces and behaviors.

Systems become hyper-integrated all the way up through within and among each other. Qualities and behaviors arise that were not present in the ‘simpler’ levels of complexity, but they all unquestionably share and enact the one invariant design/process of complexity concordance, displaying it in all the marvelous diversities of mechanisms, interactions and experiences. Local capacities to hold and pass along energy means that every system displays one if not several abilities to recursively absorb energy as a heat sink and radiate off energy as a local negentropic source, all the while contributing to the entropic spreading and re-distribution of the energy through the entire and increasingly larger function space, re the energy componente themselves. The eigenspaces where wave/particles can be found increases as the number of transfer agents increases. The distribution space where valence electrons can be found, for example, increases with the number of atoms binding. The entropy of the binding-space is higher than if fewer atoms participated, over a potential domain. In such cases, there is greater diffusion and ‘disorder’. There is improved systemic stability, per Shannon, as a result of the increased number of ‘communication’ connections. It is a situation of diffusion on one level, with connection resulting on the other - together producing bound and complex behaviors involving both levels of process structure.

‘Evolution", being sensitive to real physical extents, qualities and activity options enacted - or potentially available - in environments and coordinations of living systems, is the tendency - as apropos conditions are present - to improve the abilities of Life to encounter and to endure and to reach higher plateaus of existential competence. I’ll repeat that. Evolution is the tendency to improve the abilities of Life to encounter, to endure and to reach improved existential competence. Evolution is existence’s commitment to explore and expand into all the option spaces of behavior that may ever be available in this universe. Life is composed of all the ancestors of its existence, and will contribute to the shapes and comprehensions of all the progeny that will follow and emerge.

Entropy is characterized as the pervasive templated tendency towards smooth undifferentiated uniformity. It is the differences (verb) caused by differences (form). It is the process that templates the production of impetus momentums before any forces actually arise; it is formatively intrinsic first within topological architecture and so therefore is the precedent trackway which produced and enacted forces follow as they arise. Since dimensional unfolding produces many scalar-different relationships, there are many trõpic pathways. Trõpic gradients are not corollaries to the 4 fundamental forces, but come before them. This architecture produces the enactments we actually observe. It allows for dynamics in specific and in general, and suggests a continuity of performance that is everywhere and everytime accessible to other performances. In this way, the universe in all its holistic diversity is a fully self-sensitive self-sentient entity.

In closing, it is difficult to categorize what these trõpic manifold ‘tendencies’ are. The Integrity Paradigm proposes them as being a bit different from the conventional notions about "Laws of Nature". Broad ideas/applications of such concepts as "entropy is the smoothing of behavior space" and "systems improve when their option spaces are enlarged and accessible" are real, pragmatic, plurally applied and as vague as the open systemics they have to address. I see them more as "policy statements" about how systems perform, even as "process rules" you might say .. with all extants and events being "process rule examples" (PRE’s for short). The only saving grace to me - as well as potential justification for this stance - is that even the bedrock concept of current Physics, "inertia", is well understood but is totally undefined formula-wise. Such behaviors are observable, definable and real on all levels and in all applications ... nascent and expressed. They reflect the nature of ‘infinite’ where ‘being’ is a motivator for process not a snapshot out of Time. Both are at once effible and ineffible. It is just that with entropy, we have a better chance at mathematical modeling, even though conceptually we’d probably be better off leaving it nebulous, transcendent and vaporous - an attractive space

I'll end by sharing with you with two literary snippets, a comment by Buckminster Fuller from "Critical Path"(1981), and a poem of my own.

Ode to a Vanishing Point

The Point of these discussions is oh so frail indeed
Just when you think you "see" it
It "vanishes" complete.

Or rather, should I say we start with .. "double" takes
      (the things that norm' come last);
Reverse the order ... START with   two co-linear ... "parallel" paths!
     For then, out at ..........INFINITY ...... the "point" appears at last !!!
And out beyond our vision ... we see !                                                                                          (beyond our grasp).

But fear not, gentle warriors, in the Battle for Clear Minds,
     These convoluted caperings just help us pass The Time.
And like the Jabber-Wock who strolled
     Along the beachy-sea,
Twas "infinity" beneath his feet
                                   (where ever he did see).

Uncountable grains jibed tender soles
As poddingly he went
   As his brain did valiant wrastlings
   To understand this .... God's foul fowl jest.
   And .... the reason why ... there is this or that
   And, of course, of : "was" "will be".
And oh my dear, a quaff of beer
   Might help us more plainly see!!!!

So, into the soup ( or fray ) my dears
Whatever be your pleasure
Except as musings (wandering here)
Some things are beyond our measure.

Twas briley in Deo's design
              that we be "less than" her/him
And save for some twinkly twist of Being (hidden in his/her grin)
                            We might just never know it all! . . . .
                                                . . . . just where "the point" begins!

Or: where it ends or where it goes or has it
          Umpteen umpteen toes
Oh round the Universe we goes
          Spinning ever ever so
                       A tizzy wizzy whirly twirl
                                   until the light goes on :

A crucial skill we all must master
       In this worldly place of lathe and plaster:
Wheeling .... ("tooling" as Sapiens do
                                        to even get 'round to market)
We won't get a License to travel Space and Time
                                             Until we can parallel park it !!!!!

Bateson, Gregory (1972). Steps to an Ecology of the Mind, Ballentine, New York.
Burkhardt, Helmut (1998). "Ecological Sustainability through Alternative Energy" , ISSS 98 Atlanta.
Corning, P.A. and Kline, S. (1998). Thermodynamics, Information and Life Revisited. I,II. Systems
              Research and Behavioral Sciences Vol 15,4 pp273-296 & 6, pp 453-482. Wiley, West Sussex.
Einstein, Albert (1916). "The Foundation of the General Theory of Relativity", Annalen der Physik.
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Hebb, Donald. (1949). The Organization of Behavior. Wiley, New York.
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            http://pespmc1.vub.ac.be/ASC/NEGENTROPY.html
            http://pespmc1.vub.ac.be/ASC/uncertainty.html
            http://pespmc1.vub.ac.be/ASC/inertia.html
Odum, Howard. (1982; 1998). "Emergy". ISSS 98 Atlanta.
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            University of Illinois Press.
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            http://www.ceptualinstitute.com/uiu_plus/1973.htm
Rose, James. ('1972,1992). Understanding the Integral Universe, Ceptual Institute, Miami; Minden.
            http://www.ceptualinstitute.com/uiu_plus/UIUcomplete11-99.htm
Rose, James. (1995). "Getting Past Godel."
            http://www.ceptualinstitute.com/uiu_plus/godel.htm
Rose, James. (1996). "The Conscious Continuum"
            http://www.ceptualinstitute.com/uiu_plus/evolcons.htm
Rose, James. (1992) "Ode to a Vanishing Point". Ceptual Institute, Poetics. Internet.
Tsang, I.J. and Tsang, I.R. (1997). "Tuning Complexity on Randomly Occupied Lattices", Proc.Inter. Conf. on Complex Systems,
            (NECSI) Nashua, NH.
            http://wcc.ruca.ua.ac.be/~inden/iccs/front.html
Tsang, Ing Ren & Tsang, Ing Jyh (1998). "Ing Ren Tsang & Ing Jyh Tsang", Ceptual Institute (internet).
            http://www.ceptualinstitute.com/genre/tsang1.htm