Nature's Fractal Pattern (part II)
JOHN A. GOWAN  Aug., 2010
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This paper has been translated into Ukrainian by Anna Matesh. Many thanks, Anna! See: http://eustudiesweb.com/nature-fractal-pathway/

Table of Contents" Part II
(go to Part I)

(I recommend the reader consult the "preface" or "guide" to this paper, which may be found at "About the Papers: An Introduction" (section III)).

Abstract (from part 1)

(See: The Fractal Organization of Nature (table)) (also at the bottom of this paper)

A General Systems model of the Universe is presented, based on a fractal paradigm. A 4x3 "metric" or fractal algorithm is proposed as the organizing principle of the Microphysical, Biophysical, Astrophysical, and Metaphysical realms. The algorithm is expressed through the conservation laws and forces of physics, symmetry-breaking and the creation of matter during the "Big Bang", the dimensions of spacetime, the quantum rules of atomic order, the families of elementary particles, the structure of baryons, alpha particles, carbon atoms, carbon's molecular and crystal bonds, DNA, the genetic code, the nucleosynthetic pathway of stars, gravitation, etc. The human mind has discovered this order both intuitively and rationally, where it finds expression in the 4x3 (and 4x4) patterns of mythological, occult, religious, philosophical, and scientific "world systems" and cosmologies.

A model of the unified field theory is presented as an example of how the fractal algorithm may be used in system modeling. In its most general form, the 4-part algorithm consists of an input of energy, followed by two complementary conservation modes, then concluding with a restorative force which either returns the system to its actual original state, or elevates it to a "harmonic complexion" or resonant analog of the original state.

The Astrophysical Realm
(gravitation: 4 third-order equations)
Level 9: Stars
(Kepler's 3 laws)

The first cell of level 9 contains the mass particles and aggregates that will eventually condense to form the planets and stars of this first row of the Astrophysical Realm. These mass aggregates range from interstellar gas and dust particles to meteoroids, comets, asteroids, moons, planetismals, and full size planets up to and including "brown dwarfs" ("failed stars" of less than 50 -100 Jupiter masses). This cell recapitulates and carries forward the planetary size range of Gaia in the last biophysical level (row 8). Hence in this first cell we can place all the particles of the primordial solar nebula, including our own planet Earth and similar bodies, provided only that they are not so massive that they become stars.

In cell 2 of level 9 the pairing function is evidenced by gravitational orbits, and the Earth-Moon and Earth-Sun pair are obvious examples. The star-planet pairing is of special significance for the creation of life; this union seems to represent a type of astrophysical male-female bonded pair, with the planet in the female role. In cell three we place the family group of planets of our solar system (or any stellar system), with the 4x3 algorithm function represented by Kepler's 3 laws of planetary motion expressed in 4 dimensional spacetime.

Another expression of the 4x3 or "social" dynamic in the 3rd cell is the gravitational interaction among the planetary members of the system as they form in the primordial solar nebula. These primitive interactions account for many features of the mature planetary system we see today - the various orbital positions and periods of the surviving planets, including their eccentricities, their daily rotation periods and axes of orbital inclination, even the compositions of the planets and the continuing history of their bombardment by asteroids, meteorites, and comets. Our relatively huge moon is a major part of this story (in addition to causing the ocean tides, the Moon stabilizes the seasonal character of Earth's weather), and the role of the giant planets is extremely significant in the evolutionary history of Earth and all the inner planets, and is still being puzzled out. Much of Earth's water, for example, seems to have arrived via comets flung at us by Jupiter. Various important extinction events in Earth's biological history (including the extinction of the dinosaurs) have apparently been caused by the impact of large asteroids, which threaten us still. The belief of almost all ancient cultures in the significance of extraterrestrial phenomena for planet Earth (not just the Sun and Moon, but the influence of other planets and comets), is being born out by modern astronomy, although not in the ways the astrologers had imagined.

In cell 4 we place our Sun, or stars generally, in which the obvious emergent property is the onset of nuclear fusion, the gravitational conversion of bound to free energy and the production of heat and light. The Sun actually represents the first stage of gravitational symmetry conservation - the conversion of asymmetric bound energy (mass) to symmetric free energy (light). Our Sun's radiance is the evidence of a completed symmetry conservation circuit. (See: "The Solar Archetype".)

Level 10: Galaxy
(nucleosynthetic pathway)

Stars are the units of the first cell of level 10; the pairing function is expressed commonly as binary stars. In our case the Sun - Jupiter pair must suffice as an example of a "failed" binary star. In the third cell of level ten I place the 4x3 nucleosynthetic pathway. This is a 4x3 process regulated by the alpha particle (helium nucleus) (4 nucleons each containing 3 quarks), whose extraordinary stability makes it the construction unit of choice, or "brick" of element building and nuclear fusion. Helium 4 and carbon 12 are the first major resonances of the 4x3 nucleosynthetic pathway; oxygen 16 is the next alpha unit above carbon and its unusual abundance (and significance for life) represents the commonly seen 4x4 expression of the fractal (4 alpha particles each of 4 nucleons). The elemental series continues upward in alpha particle units and should reach a third major resonance in chromium 48, four carbons each of three alpha particles. This combination is highly radioactive, however (due to overcrowding of the protons), and the resonance settles at iron 56 with the addition of another alpha particle plus four extra neutrons. Iron is the last element that yields energy in fusion; all heavier elements require energy inputs (as from supernova implosions and explosions). Thus as the 4x3 resonance fails, so too does the exothermic yield of excess nuclear binding energy.

As in the previous Solar System or stellar level, the third cell of the galactic level is rich with structural elements, in addition to the nucleosynthetic pathway. At the galactic level, in a spiral galaxy such as our own Milky Way, we find an extensive disc composed of four arms containing many stellar "nurseries" or star-forming regions, a central bulge surrounded by a "halo" of globular star clusters, giant molecular clouds, nova and supernova remnants, a variety of stellar types, sizes, colors, and stages from brown dwarfs to red giants, collapsed stars including white dwarfs, neutron stars, and black holes, remnants of captured dwarf galaxies, and finally a supermassive black hole dominating the exact galactic center, much as the nucleus of an atom or a biological cell dominate their respective domains. Black holes represent the final step in gravitational symmetry conservation and the conversion of bound to free energy: not only is "proton decay" probably common in their interiors, but over time, the entire mass of a black hole "evaporates" as it is converted to light via Hawking's "quantum radiance". (Current research suggests we should add to this list a huge sphere of "dark matter", much larger and more massive than the visible galaxy.)

In the final cell of level 10 we have the galaxy itself, a gigantic composite structure which can generate within itself all the 92 elements of the periodic table, the first structure of the hierarchy actually large and complex enough to produce its own life forms from the raw material of the "Big Bang" - hydrogen and helium. While humans are children of the Earth-Sun "marriage", all such stellar systems are in turn children of the Milky Way galaxy, our true "island" home in the spacetime "ocean" of the Universe.

Level 11: Universe
(4 third-order equations)

Galaxies are the units of level 11; the pairing function is typified by the Milky Way - Andromeda pair; such pairs are thought necessary to draw out the spiral arms in which new stars and their associated planetary systems are preferentially formed. In the third cell we find great clusters and "walls" of galaxies, surrounding immense "voids", the largest structural elements of the Universe, resembling a "foam" of soap bubbles on an astronomical scale of thousands of galaxies and hundreds of millions of light years. The fractal algorithm of this cell is simply the gravitational force itself, characterized by Einstein as 4 third-order equations - the changing rate of gravitational acceleration in x, y, z, t. Here too, we place the 4x3 form of the Unified Field Theory - the four forces of physics and three energy states - light, matter, charge (in the 4x4 representation we add the term: "force"). In the final cell of level 11 we place the Universe as we know it, a spacetime domain approximately 14 billion years old and also about 14 billion light years in its maximum spacetime dimension. (See: "A Spacetime Map of the Universe".)

As at the planetary level, there is also a "social" function served by the galaxy clusters, involving the gravitational interactions of the galaxies upon each other. Such perturbations, occurring over eons of time, stir the great molecular clouds of gas and dust, keeping the galaxies "young" and active, producing new stars and elemental products for potential new life forms.

The "Big Bang" itself is the mass center (in spacetime) of the Universe, producing the 4 dimensions and 3 particle classes (hadrons, leptons, bosons), and the 3 families of 4 elementary particles which initiates level 1.

The entire Universe is necessary for the creation of Earth life, for only the "Big Bang" can create the elementary particles and dimensions from which atoms and ultimately life is composed, and its vast size is necessary to provide a time dimension of sufficient duration for life's evolution. In turn, galaxies provide the necessary conditions for star and planetary formation and the production and concentration of heavy elements over several stellar generations.

The tendency of the chemical elements to produce complex information systems such as life can ultimately be referred to matter's search for antimatter through the electrical interactions of the chemical bond. This search can also be seen as the attempt of matter to recover its original condition of universal unity, connection, and symmetry, "as it was in the beginning", when all energy existed in the form of light in the first instant of the Big Bang. (See: "Symmetry Principles of the Unified Field Theory"; see also: "Synopsis of the Tetrahedron Model".)

Level 12: Multiverse
"The Tetrahedron Model" (4 conservation laws connected in triplets)

The Universe itself is the unit in the first cell of level 12; in the pairing function of cell two we find the Universe - Antiuniverse pair which nearly annihilated each other during the "Big Bang"; the matter residue of this colossal matter-antimatter explosion forms the material component of the Universe we know today. In the third cell we find a subset of the "Multiverse", the set of all possible electromagnetic Universes, which may be infinite so far as we know. These are all "4x3" universes which convert free energy to bound energy (otherwise they remain simply as light). We take the 4x3 fractal algorithm of our Universe to be a native characteristic of all electromagnetic universes. The 4x3 "metric" of this cell is the metaphysical origin of all the others below it, as found in the 4x3 representations of the Deity in various world religions, mythologies, and systems of mystical, occult, and spiritual principles and laws - and in our metaphysical systems of scientific or natural laws, which are all constructions of the human mind. In this third cell also originates the peculiar characteristics specific to each Universe, the physical constants, which may cause any self-conscious beings evolved in them to wonder at the precise suitability of their particular Universe. But this is like marveling at how nicely your skin happens to fit your body: of course we evolve to fit the special conditions of our Universe - if those conditions allow life forms at all. While we simply do not know what parameters may vary and still remain within the physical limitations of electromagnetically defined universes, one possibility is certainly size, and others may include variations in the value of the weak force asymmetry parameter and the mass of the Higgs boson.

In the final cell of the physical hierarchy, we place First Cause and the full complement of the energy types of the Multiverse, the ultimate representation of the Deity and Natural Law, and the ultimate source of the energy, information, and order of the "Big Bang" and row 1. Here we find all possible universes of all possible energy types, of which our universe is but one "life friendly" member of the electromagnetic subset. Natural law originates here with energy type. (See also: "The Higgs Boson and the Weak Force IVBs".)

Although there is an inevitable circularity about such arguments, the concept of the Multiverse is a "logical" way we have of explaining the values of the physical constants in our Universe which make our life form possible. Constants (for example G and c, among many others) must be adjusted with exquisite precision with respect to each other to produce a Universe in which our particular life form can evolve. One explanation for this accommodation is the Multiverse theory in service of the so-called "Anthropic Principle": we quite naturally find ourselves living in that unique Universe, perhaps one of infinitely many Universes, whose physical constants, just by chance alone, happen to favor the evolution of our particular life form.

Perhaps other life forms inhabit the other Universes - they, too, may think it strange how nicely the physical constants of their various Universes just happen to favor their various life forms - but how could it possibly be otherwise in any evolved system? This view does not deny the existence of "First Cause", but suggests that any notion of a "Divine Being" may be far grander than we had traditionally imagined, or could possibly have imagined. (The Hindus have apparently come closest to this view.)

This scenario also suggests that while in one sense our experience of life is accidental (a chance event in a chance (but suitable) Universe), in another sense it is quite inevitable (because of the large (infinite?) number of Universes, many suitable for life of some form). Our own Universe may even be a cyclic phenomenon on a scale which is far beyond our poor powers of comprehension (see: Scientific American, Oct., 2008, Martin Bojowald, pages 44-51).

In brief, humans need the Solar System to provide our Earth and Sun; we need the Galaxy to provide our heavy elements; we need the Universe to provide elementary particles and sufficient space and time; and we need the Multiverse to provide life-friendly physical constants, and the electromagnetic energy type and laws of our Universe. (See also: "The Fractal Organization of Nature"; and: "The Human Connection".)

We cannot prove or disprove either the scientific or the religious version of the ultimate origin of reality; regarding the question of "First Cause", what one chooses to believe is really a question of personal taste, since all views finally reduce to faith, trust, intuition, or belief of one sort or another. What we really need to comprehend is that we are the Universe in its (locally) conscious, self-aware, self-experiencing, and self-exploring form. This is the universal significance of humanity, beyond the local reproductive schemes of Gaia. Life is what we choose to make it. Choose wisely: choose beauty, symmetry, harmony, symbiosis. (See: "Is There Life After Death?")

The Metaphysical Realm - Overview


The Metaphysical Realm, some would insist, is wholly the creation of the human mind - an abstract realm of ideas and thought, laws and principles, ideals and virtues, which exists only as a product of our brains. Yet others would insist that the metaphysical realm is independently real, but it is only the human brain which is capable of perceiving it - through religion, the arts, mythology, the sciences, mathematics, philosophy: our rational and intuitive faculties. While such a debate probably cannot be definitively resolved, I am personally inclined to believe in the independent reality of the metaphysical realm, at least insofar as the realm of scientific law (including mathematics) is concerned; admitting that much, it is difficult on principle to exclude the rest. For convenience of discussion and modeling, I have defined the metaphysical realm as the arena of human thought - whatever type of reality the reader may wish to grant that domain.
The Metaphysical Realm is both the first and the last stage in the cycle of manifestation, as it provides the template, ideal form, or archetypical principle from which manifestation springs, and toward which it evolves, during the "redemption" or return of matter to a state of perfect symmetry. (Light devolves to matter, which then evolves back to light.)

Concerning the Metaphysical Realm itself, we know little. As it is dimensionless, the Metaphysical Realm may not have levels, but may simply have aspects or attributes instead; the trinities and quadruplicates of various religions and mythologies seem to represent intuitive perceptions of these aspects or characteristics of the Metaphysical Realm.

In the Christian religious tradition, we can identify the Father with Conservation ("strong to save"); the Son with Symmetry (the broken symmetry that produced manifestation representing the birth of Spirit into the World); the Holy Ghost with Entropy, intrinsic motion, or Divine Will and evolutionary direction; and Mary (humanity) with Causality-Information, the Virgin representing the symbolic or spiritual impregnation of humanity with the Divine Gnosis, spirit, or "Word" - humanity's innate awareness of a generalized "spiritual" realm (our awareness of our connection to the Universe). (See: "A Religious Interpretation of the Energy Tetrahedron").

Rationally or "scientifically", the metaphysical realm appears as a level of principle or natural physical law and "given" physical constants which seem to precede and regulate the appearance of the manifest realm of light, spacetime, and the particles of matter. This is very much the Platonic view of the realm of "ideal form" so characteristic of geometry and mathematics, but also sought by the artist in the aesthetic principles of nature, music, architecture, and language, including the "just proportion" and the idealized human form. The principles of symmetry conservation (Noether's Theorem) actually provide a robust bridge between art, religion, science, and ethics.

The "Tetrahedron Model" is a representation of the 4x3 structure (4 triangles) of the metaphysical realm in the mode or aspect of physical law, comprising the generative principles of the manifest universe. Such a representation has only become possible to the human mind in the last century, following upon the great revolution in physics wrought by the theories of Special and General Relativity and Quantum Mechanics.

In terms of General Systems, the cosmic Tetrahedron in its "physics mode" is not a more "correct" interpretation of the metaphysical realm than any of the many intuitive representations offered by religion or mythology; it is simply in a different characterization, a quartet of physically relevant principles, which is useful in its own special way, just as the other models are useful in ways peculiar to themselves. All models of the metaphysical realm are "wrong", in that they must be incomplete, and therefore none can possibly be fully adequate to their task; nevertheless, granting their limitations, some are more useful for specific purposes.

For a scholarly treatment of the spiritual, religious, psychedelic, and occult properties of the Metaphysical Realm, see my father's memorial website, where his books: "Trance, Art, Creativity", and "Operations of Increasing Order" may be found.

The Metaphysical Realm - Intuitive
(4 Elements x 3 Qualities); (the Holy Trinity x the 4 Living Creatures))

For the comparative purposes of a General Systems survey, we are most interested in the intuitive models of the metaphysical realm that exhibit a 4x3 "metric", a trinity or a four-part structure, as these are isomorphic with our physical, natural models. Two ancient, outstanding examples of these, one Eastern and one Western, are the I Ching and Astrology, which have been used for millennia as occult structural models of the Metaphysical Realm. Every religion and mythology attempts to model the metaphysical realm, and to make the fractal or resonant connection "as above, so below". Three- and/or four-part structures are common in intuitive metaphysical and cosmic models. Because this is a reversible equation ("as below, so above"), we can also hope to understand the hidden, invisible, and immaterial structure of the Metaphysical Realm through General Systems models of the physical world "here below" (as provided by science), and extend these to the etheric, nonmaterial, unmanifest, ideal, and "spiritual" planes "above".

The metaphysical realm (human thought) contains two modes, intuitive and rational. The mass center of the metaphysical realm is the human brain, itself divided into two halves, which are apparently related to the two modes of understanding and thought. Only rational and intuitive "World Systems" are considered here. The intuitive category includes religious, mythological, mystical, spiritual, and occult world views, organized conceptually around the general relationship between body vs "spirit", or "manifestation" vs spiritual or religious law; rational systems include philosophy and science, organized conceptually around the general relationship between matter (bound energy) vs light (free energy), or the material Universe vs immaterial natural law.

In its most general application, the metaphysical realm includes all the output of the human mind, rational and intuitive, religions and scientific, for all are the products of abstract thought. A symphony, automobile, religious tract, or scientific text are all examples of ideas made manifest, and in this sense they all represent conservation modes or conserved products of the metaphysical realm. (See also the "Traditional Supernatural" section of the "Fractal Table No. 1".)

Remarkably, a 4x3 "metric" underlies not only the Western religious traditions as found in the Bible, but also occult cosmologies, Western and Eastern. Among other examples, the metric is explicitly expressed in the vision of New Jerusalem, the celestial city of four walls each with 3 gates, and the vision of the four "Living Creatures" surrounding the throne of God, the Trinity. The occult examples, independently derived, are both perfect 4x3 systems, Astrology with 4 Elements and 3 Qualities, the I Ching with 4 sets of male and female "trigrams", exactly isomorphic with the 3 families of 4 elementary particles and their antiparticles.

The Western creation myth (Genesis), is also strikingly similar to our current rational model, the "Big Bang". In both, the Universe begins as light, enjoys a brief period of symmetry (the garden of Eden vs particle-antiparticle symmetry), experiences a disastrous "fall" into "sin" ("symmetry-breaking" - single massive particles in real time and gravity), resulting in expulsion from the symmetric state of the garden. Then follows a long period of "redemption" toward the original condition of "grace" (the forces return the world of matter to light, creating life in the process). Evidently, the human mind has intuited the fractal structure of the Cosmos (and itself), thousands of years before science could produce the physical evidence. "Man created in the image and likeness of God", "as above, so below", "man the measure of the Cosmos", and similar statements are simply intuitive affirmations of Cosmic fractal and resonant structure.

In the "Multiverse" version of cosmic structure, even the "scientific" (astrophysical) hierarchy ends with a hypothetical or metaphysical superstate of absolute symmetry. In the "traditional supernatural" or Christian religious version corresponding to this 4-part hierarchy, we have: God the All-Creator (Multiverse), Christ the Son (our Universe), Archangel (Galaxy), Angel (Sun). Below this celestial and astrophysical hierarchy we find Gaia (Mother Earth - level 8) and humanity (species level 7) (corresponding to Mary) in the Biophysical Realm. (See also: "The Higgs Boson and the Weak Force IVBs" where this hierarchy is represented in five stages because Earth together with humanity are appended to the 4-part astrophysical set as an electromagnetic "ground state".)

The Metaphysical Realm - Rational
(4 Conservation Laws Connected in Triplets)

The Unified Field Theory is the rational equivalent of intuitive "World Systems". Here we find 4 conservation laws connected in triplets - as diagrammed in the "Tetrahedron Model": the 1st law of thermodynamics (energy conservation); the 2nd law of thermodynamics (entropy); "Noether's Theorem" (symmetry conservation), and Causality ("Karma"). A representation of the Unified Field Theory in its full 4x4 Format (which includes the restorative activity of the field vectors) is exhibited in Table 1 and briefly explained below. (See also: "Symmetry Principles of the Unified Field Theory"; and/or "A Short Course on the Unified Field Theory".)

Other than the economy and universality of its fractal format, the feature of particular interest in the rational model is its emphasis on the conservation of certain symmetries associated with free electromagnetic energy (light). Thus when light is converted to matter in the "Big Bang", its raw energy is conserved as mass, momentum, and other time-dependent variables, whereas its various symmetries are conserved as time-independent charges. The charges of matter are the symmetry debts of light. Among light's broken but charge-conserved symmetries I associate electric charge with the jump from the symmetric 2-dimensional wave form of light to the time-asymmetric 4-dimensionality of matter. The gravitational charge is associated with the asymmetric, specific, 4-dimensional "location" of bound energy (Interval > 0), vs the symmetric, undefined, 2-dimensional "non-locality" of light (Interval = 0). The number or "identity" charge of the weak force is associated with the symmetric "anonymity" of photons vs the specifiable "identity" of the leptonic elementary particles, including the leptoquark. (Neutrinos are the explicit form of "identity" charge, which is also carried implicitly by the massive leptons.) Finally, the color charge of the strong force is an internal, quantum mechanical asymmetry of baryons associated with the fractional (sub-elementary) charges of quarks, which must be permanently confined to whole quantum units of charge (units of leptonic elementary charge) to satisfy symmetry and charge conservation.

The conservation parameters of the dimensional domains of free and bound energy are characterized by entropy and symmetry "gauges" or "drives": "velocity c" is the entropy drive and symmetry gauge of the intrinsic motion of light or free energy, creating, expanding, and cooling space, while simultaneously suppressing the time dimension and maintaining metric symmetry. "Velocity T" is the entropy drive or gauge of bound energy's time dimension, creating, expanding, and decaying history, the temporal analog of space. "Velocity G" (gravity) is the conversion gauge or force acting between these primary, primordial, or pure forms of spatial and temporal entropy (the intrinsic motions of light and time), converting either into the other. (See: "Spatial vs Temporal Entropy".)

Inertial forces protect the symmetry of the spacetime metric, charge conservation protects the symmetry of the particle metric. Gravity produces the time dimension of matter via the annihilation of space, thus creating an entropically equilibrated spacetime, the joint dimensional conservation domain of free and bound electromagnetic energy. The dimensions of spacetime are energy conservation domains created by the primordial entropy drives of free and bound energy (the intrinsic motions of light, time, and gravity); the charges of matter are the symmetry debts of light ("Noether's Theorem") (see: "A Description of Gravitation").

The Unified Field Theory has 4 physical forces to account for; in the 4x4 matrix model, these comprise the horizontal axis (see table). Vertically I identify 4 significant electromagnetic energy states and their associated conservation laws and processes: Row 1) Free Energy (light): "symmetry-breaking" and the conversion of light into matter during the "Big Bang"; Row 2) Bound Energy (particles): causality and raw energy conservation; Row 3) Charges (carried by particles): symmetry conservation; Row 4) Forces (field vectors produced by charges): symmetry-restoring forces which pay, or demand payment of, conserved symmetry/entropy debts, reconverting matter to light.

Reading the matrix in the same order as an English paragraph: in the first row, free symmetric energy (light) is the initial input, creating two superimposed conservation domains, one for its wave form (the dimensional metric of spacetime), and another for its material form (the quantized particle spectrum of matter, or the "particle metric" - as visualized in the particle "zoo" or vacuum "sea" of virtual particle-antiparticle pairs). The weak force Higgs boson and Intermediate Vector Bosons (IVBs) produce an asymmetric transformation (decay) of electrically neutral leptoquark-antileptoquark pairs, yielding a single particle of matter (a leptoquark which decays to a proton), breaking the symmetry of the initial free energy state - the first row thus reproduces the creation of matter in the "Big Bang". (See: "The Formation of Matter and the Origin of Information"

The second row represents conservation in the particle domain, in terms of raw energy, time, and causality. Here the energy of light is conserved as the mass and momentum of particles, space is gravitationally converted to time, sub-elementary quarks and gluons produce baryons and mesons; the weak force is represented by the elementary leptonic series, the electron and its heavier kin, the muon and tau. Raw energy debts must be paid immediately (as by inertial forces, or converted to mass, momentum, etc.).

In the third row the various charges of matter are represented as the conserved symmetry debts of light. Unlike raw energy debts, symmetry debts can be paid over time (charge conservation); the time dimension and charge conservation imply and require each other. This is one of several ways that entropy, symmetry, and gravity are connected. One charge is associated with each force and each charge/force represents a specific symmetry debt of light - see above. The forces also have a specific or implied relationship to basic entropy drives, both positive and negative. Gravity pays the "interest" on all these symmetry debts, supplying the energy to create bound energy's time and historical dimension, "negative" spatial entropy-energy subtracted from the "positive" spatial entropy-energy of expanding and cooling spacetime, via gravitational annihilation of space and the consequent deceleration of cosmological spatial expansion.

In the final row, the field vectors of the four forces pay the symmetry/entropy debts held by the conserved charges of row 3, returning the system to free energy and maximum entropy (light is the most entropic and symmetric energy form). The "thumbnail" or summary form is thus: light creates massive particles bearing charges producing forces which act to return the material system to its original symmetric state of light. This program is executed immediately in the annihilations of virtual particle-antiparticle pairs, but occurs much more slowly (but occurs nevertheless) in real time in the absence of antimatter. Gravity pays the "principle" of matter's symmetry debt by the conversion of bound to free energy in stars, black holes, etc. Entropy and symmetry conservation, in their primordial forms as the intrinsic dimensional motions of light ("velocity c"), time ("velocity T"), and gravity ("velocity G"), all in the service of energy conservation and causality, are the ultimate motivating principles or driving forces of the Universe.

For a discussion of the role of Information in the return of the material system to its symmetric origins, see: "The Information Pathway". For a more complete discussion of the gravitational system, see: "Gravity, Entropy, and Thermodynamics".

Conclusion

The material universe can be modeled as a nested hierarchy of increasing size, a treatment which is artificial in terms of its evolution in either time or complexity. Nevertheless, the hierarchy reveals a recurring 4x3 structural and dynamic pattern at every level, including the human conceptual, or "metaphysical realm". This recurring pattern is the essential indicator of a universal General System, the algorithm of a cosmic fractal, apparently latent in free energy, expressing itself in terms of natural law, dimensions, particles, charges, forces, and the elaborated and emergent products of their interaction.

The fractal hierarchy is evidently the "least-energy" pathway to produce the wholly connected physical structure of the Cosmos. The replication of self-similar systems into a nested structural hierarchy has an associated advantage in the transmission and sharing of energy and information via the principle of harmonic resonance. We also note the convergence of this model with the self-feeding iterations, bifurcation patterns, and fractal "basins of attraction" of various "chaotic" models as discussed by James Gleick in his book "Chaos". Our 4x3 "fractal algorithm" would appear to be the analog of some sort of "strange attractor" in the jargon of "Chaos" theory. For more on the 4x3 General System pattern, see: "Synopsis of the Principles of The Energy Tetrahedron".

See: Table No. 1: "Fractal Organization of Nature"

email:
jag8@cornell.edu 
johngowan@earthlink.net

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