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THE FRACTAL ORGANIZATION OF NATURE: PART 1: THE MICROPHYSICAL WORLD
JOHN A. GOWAN
(revised Jan., 2011)

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

(4 Conservation Laws Connected in Triplets)
(Synopsis of the Tetrahedron Model)

Introduction
(See: The Fractal Organization of Nature (Table))

A General System is a recurrent, pervasive pattern found in a multiplicity of phenomena. The General System described in this paper is a 4x3 pattern existing in nature as a fundamental organizing force operating over a vast scale of physical and metaphysical phenomena. General Systems patterns can be used to identify isomorphisms and periodicities within and between disciplines, hence coordinating diverse areas of human knowledge and providing a basis for prediction. General Systems patterns can suggest new ways of looking at existing data, and indicate gaps in an information set. They can be harmful to the extent that they limit, channel, or prejudice our view. Man has always accepted the fact that all tools (including knowledge itself) are potentially dangerous when improperly used, but has nevertheless made himself master of the earth through their judicious application.

Ludwig von Bertalanffy is considered the founder of General Systems theory; for a review of his contributions and other pertinent literature, see Bertalanffy 1968, Laszlo 1972, and Blauberg et al, 1977. (See also several recent books by Ervin Laszlo in this and related fields.)

The rationale supporting General Systems studies is that all systems, whether atomic, biological, or astrophysical, evolve from the same narrow base of natural law, and therefore exhibit similarities representing the persisting trace of their common origin. A set of such systems is proposed in the Hierarchy of Natural Organization, Table 1. Fractal and General Systems models of natural organization are essentially indistinguishable (see Summary section, Part 6).

The Natural Organization Hierarchy

(3 physical realms each of 4 structural levels)

The form, pattern, or General Systems property exhibited by this hierarchy is represented as a 4x3 two-dimensional matrix. The largest expression of this pattern is in the overall construction of the table itself, which is organized into 3 realms: microphysical, biophysical, and astrophysical, each with four levels of complexity. The appended Metaphysical Realm is entirely a product of the human mind, and is a fundamentally different order of reality. It is included to demonstrate the convergence of rational and intuitive thought upon the 4x3 pattern which orders the physical world, including the human brain/mind.

The hierarchy is arranged in order of size, both overall and within realms. Each level is a composite of the preceding level; each level, when complete, becomes the unit from which the next level is accreted. Thus molecules build cells, cells build organisms, organisms comprise species, etc.

Each of the 3 realms is characterized by a force or set of forces, and a 4x3 expression of that force, which is the major ordering feature of the realm. These are identified under the heading of each realm. It is of course a postulate that: A) there are 3 and only 3 physical realms; B) these can each be adequately described by 4 and only 4 levels of organization. While some readers will reject this notion as a procrustean bed, I see it simply as an idea worthy of exploration, for reasons suggested in the introduction. The challenge to reduce the diversity of the natural world to an essential "metric" or characteristic is nothing more nor less than the typical task of science and mathematics.

Four kinds of organization order the matrix horizontally; each is dynamically and structurally distinct. These categories are: Unit, Pair, Group, Compound (or Emergent) New Unit. The Emergent New Unit of one level becomes the founding Unit of the succeeding level. The Unit is the building block of the hierarchy, and is typically identifiable as a distinct entity delimited by some kind of boundary. Thus the quarks of a baryon are confined by gluons, atoms are defined by electron shell boundaries, crystals have definite shapes, surfaces, and expel impurities upon formation, DNA binds only to a complimentary copy, cells have membranes, organisms have skins, the genome of a species is closed or exclusive, etc.

The Pair category recognizes the universal significance of the interactive dyad, or apposition of polarities, be it proton-electron, female-male, Earth-Sun, or matter-antimatter. The Group category is the site of the regulatory or organizing field of force for each level of the hierarchy. It is specifically in this category that the 4x3 General Systems force, pattern, or property is found. The fourth category, Emergent New Unit, is seen as the product of the operation of the organizing field of the third column.

The horizontal dynamic of the hierarchy may therefore be generalized as follows: a system begins as a bounded, distinct entity (the Unit), interacts in a significant way with another similar unit (the Pair or Dyad), is operated upon by some type of 4x3 organizing force acting through a large number of units and dyads (Group category), finally developing (in consequence of the organizing force) an emergent and defining new property which becomes the next unit in the hierarchy (Compound/Emergent New Unit). (See also the "Land-Jaccaci" dynamic associated with this structural series as described in the Introduction to the Summary, Section 6.)

The following discussion is a reader's guide to the Hierarchy of Natural Organization, Table 1.

Part I. The Microphysical Realm

(3 Families each of 4 elementary particles)

General Discussion

Although I designate the first level (row) as consisting of particles, in modern physics this level is hardly distinguishable from that of pure force, since every force is believed to originate with the exchange of a particle, known as a "boson". Because there are four known physical forces, there are presumed to exist four kinds of boson: the graviton (gravitation), photon (electromagnetism), weakon, or Intermediate Vector Boson (IVB) (weak force), and the gluon (strong force). Bosons are one of only three classes of particles from which all matter is made; the other two are known as leptons and hadrons. The photon, or quantum of light, is the most familiar boson, and the electron and proton are familiar examples of leptons and hadrons, respectively. Hadrons are any particles composed of quarks (protons, neutrons, mesons, and their heavier relatives); quarks carry the strong force "color" charge. Leptons, being elementary particles with no internal parts, contain no quarks but carry "lepton number" or weak force "identity" charge (electrons, electron neutrinos, and their high-energy counterparts). Although the energy of gravitation creates (in stars) the elements of the periodic table, due to its inherent weakness and the small atomic scale, gravitation plays no other part in the ordering of the atomic world (at least in the modern universe). The microphysical realm can be described as 3 particle types (bosons, leptons, hadrons) in 4 dimensions, but several equally relevant 4x3 characterizations of this realm are possible.

Another fundamental expression of the 4x3 pattern at the particle level, commonly cited in the literature of physics, is that of the "fermion families" (the leptons and hadrons taken together), which form three distinct groups in terms of energy, each composed of four particles. Each fermion "family" consists of a quark pair and a lepton pair, designated as follows:
(1) up and down quarks, electron and electron neutrino;
(2) strange and charm quarks, muon and muon neutrino;
(3) top and bottom quarks, tau and tau neutrino.
(Ordinary matter (including stars) is composed exclusively of the first (lowest energy) family of fermions.)

We can characterize this realm as 3 fermion families each consisting of 4 particles. There are in fact a large number of combinations of particles, charges, dimensions, forces, and quantum numbers which might be used to characterize the microphysical realm, because the arithmetic or metric of 3 and 4 is extremely common at this fundamental level of natural phenomena. One which includes characteristics of both the atomic nucleus and electron shell is: 3 particles (electron, proton, neutron) x 4 quantum numbers (n, l, m, s).

Level 1: Particles; Baryons

(3 quarks each of 4 charges)

The first line of the hierarchy has largely been explained in the introduction. It concerns the genesis of the material universe, light, spacetime, and matter. Like the other lines of the hierarchy, it must begin with a Unit which develops in complexity through the stages of its line to finally produce an Emergent New Unit as its evolutionary product. But we clearly have a problem with the first unit - unlike the remainder of the hierarchy, the "genesis" unit cannot itself have a predecessor, since we would essentially be asking what precedes the Big Bang, the origin of the Universe? We cannot know, we can only speculate: this is the question of First Cause.

It is possible, of course, to treat the hierarchy as circular, in which case the last cell of line 12 is the predecessor of the "genesis" Unit of line 1. The Cosmic Snake bites its tail, Alpha follows Omega, and a new Universe is born from the old, in an eternal cycle. While this may very well be true, I think it is better to simply confess our ignorance on this point. The standard scientific theory is that the Universe began as a single, non-dimensional point of infinitely high energy density, which is the scientific way of saying that nothing can be known about the initial condition. This qualifies as a unitary state, nevertheless, since all charges, forces, dimensions, and energies of whatsoever kind are assumed to be unified and in equilibrium with each other in this initial condition. This is equivalent to the intuitive or religious presumption that the unity state of "God" or the "Word" preceded the creation of the physical universe, so it would seem that all parties to this question might be satisfied if we simply identified the genesis unity condition as First Cause. I might also identify the final unity state of line 12 as First Cause, since the end is as unknowable as the beginning, and equally all-encompassing. The implied circularity in this designation is the inevitable consequence of our fundamental inability to know anything beyond the limits of our own Universe.

The compromise I will adopt is to follow the Bible's Genesis and begin the hierarchy (row 1) with light, the simplest and most symmetric form of energy (and the only energy form which can create its own conservation domain (space) from its own intrinsic motion), and end it (row 12) with First Cause. The second column is always the pairing function, which in the Genesis stories of religion and the intuitive realm is occupied by a primordial dichotomy, whether light and dark, Yin and Yang, or Adam and Eve. Typically, this second stage of the "Cosmic Egg" is almost universally conceived as a male-female dichotomy, or division into some type of opposite or complementary polarity. In the physical hierarchy, I identify this second stage of genesis as the symmetric era of the Universe following the Big Bang, when the cosmos consisted of only two components, spacetime and light. In this case spacetime plays the conserving feminine role, giving form to the male energy, light. Even though the interaction of light and spacetime is producing particle-antiparticle pairs at this time, the particle pairs are in complete equilibrium with the photons that create them, simply anchoring one end of the particle-wave continuum of light, instantaneously annihilating and reforming. Our candidates for the primordial pairing function are actually numerous, including space and time, matter and antimatter particle pairs, positive and negative electromagnetic charge, electric vs magnetic forces, particle vs wave, etc.

The third cell is where the 4x3 pattern of particles, charges, and forces makes its appearance. Here we have particle-antiparticle pairs of all types of particles, including leptoquarks, the ancestor particles of both leptons and baryons. Leptoquarks are a sort of "fractured" elementary particle, whose internal components will later form the quarks. The complexity of the leptoquarks is necessary to allow the formation of electrically neutral particles (neutrons and their kin). The quarks function as mass carriers, and so long as there are equal numbers of particles and antiparticles, this leptoquark era of complex and compound particles remains symmetric. The function of mass at this early point of Cosmic development is apparently to provide a compact carrier for energy, since at early times the Universe has lots of energy but very little space. It is in this third cell that we place the 3 families of four elementary particles. This is the primordial "quark alphabet soup" (Gamow's "Ylem") of the early micro-moments of the Big Bang.

In the fourth column, the symmetry of the early Universe is broken as an imbalance in the weak force with respect to its interactions with matter vs antimatter produces a residue of matter particles. Lacking antimatter annihilation partners, the matter particles become permanently "trapped" in expanding and cooling spacetime. The four forces lose their unity or implicit state and become explicit conservation responses to the broken symmetry of both light's particle and wave form (particles are asymmetric light; time is asymmetric space; gravity is asymmetric spacetime).

While this is, scientifically, one of the least understood lines of the hierarchy (because the asymmetric particle-producing mechanism of the weak force remains obscure), we nevertheless can see, if only in a piecemeal fashion, the generative ingredients of the 4x3 pattern which will later become such a dominant feature of physical evolution. First, we have the 4-dimensional structure of spacetime. Second, there is the electromagnetic field, which Maxwell described with his four famous equations. Third, there is the gravitational field, which Einstein described as four third-order equations. Fourth, we have the 4 physical forces acting upon and through three classes of particles: bosons, leptons, and hadrons. Fifth, we have the production of 3 particle families each of 4 particles (the quark and lepton families and their three energy levels).

The compound baryon (a hadron composed of 3 quarks, the familiar proton or neutron) is the final product of the operation of this asymmetric and complex field law, 3 quarks each carrying 4 charges: electric, color, flavor, and spin. The confinement of quarks by the colored gluon field to the internal triplets of baryons defines the boundary condition of this primordial particle. Leptons and baryons are further defined by an implicit or hidden "identity" charge, carried in "bare" or explicit form by neutrinos. Only elementary particles are distinguished by identity charges (quarks have no associated neutrinos). It is likely that the baryon's identity charge is carried by an (as yet undiscovered) leptoquark neutrino.

The baryon, with its 3 quarks, 4 charges, and 8 interacting gluons (each gluon is composed of a color-anticolor charge), all quarks exchanging color charges at the speed of light, is a particle of incredible internal complexity. Within its beating heart of "colored light" lies the mystery of manifestation, and upon its stability rests every higher structure of the manifest Universe.

The complex and enigmatic proton, the ground state of the baryon, forged in the Big Bang from a mixture of light and the metric of spacetime, is a particle so stable that in terms of human time scales it is essentially eternal. The proton is the foundation stone of the material hierarchy, the ground state product, the resolution of the first Microphysical level. The creation of matter is the "work done" by the incredible energy density of the early Universe, work which, due to the operation of entropy, will never be repeated (unless the Cosmos collapses in a "Big Crunch"). When the plasma cleared at "recombination" (300,000 years after the "Creation Event"), the proton with its mass, charge, spin, gravitational field and time dimension, was revealed as the adamantine masterwork of an almighty cosmic Smith.

(See: "The Higgs Boson and the Weak Force IVBs", an expansion of row 1 into a 4x4 General Systems model of the "Big Bang".) (See also: "The Origin of Matter and Information".) (See also: "The Particle Table".)

Level 2: Atoms; Alpha Particles; Elements

(4 nucleons each of 3 quarks)
The nucleosynthetic pathway is of course technically complex and I can only touch upon a few of its major way stations - helium, carbon, and iron - and the "brick" or common unit of its construction, the alpha particle (helium nucleus). In the 1930's Hans Bethe worked out the fusion pathway for the conversion of hydrogen to helium that allows our Sun and similar stars to shine for billion of years. The creation of helium from hydrogen in the Big Bang was worked out by George Gamow and his group in the 1940's; the creation of the remaining elements in the interior of stars (from "Big Bang" hydrogen and helium) was worked out by Fred Hoyle and his colleagues in the 1950's. For a discussion of the exciting history of these epical discoveries, see the books by Singh, Silk, and Weinberg listed below in the references.
Cell 1) The atomic level begins with the baryon unit, a non-elementary particle composed of 3 quarks and 4 charges, held together by a field of 8 gluons exchanging three strong force "color" charges. The "ground state" baryon is the proton, the nucleus of the hydrogen atom, the first, simplest, and most abundant element of the periodic table. (The "Big Bang" produced all of the hydrogen and most of the helium in the Universe in an approximate ratio of 90% hydrogen and 10% helium; stellar nucleosynthesis has added considerable helium since.)

Cell 2) Several examples of the pairing function can be found at the level of atoms, of which the most familiar is the electron-proton electric charge couple. Here we see the important example of the lepton-hadron pair, in which the lepton (rather than an antiproton) functions as an alternative charge carrier balancing the proton's electric charge (since the modern universe lacks antimatter). Other examples include the proton-neutron "nucleon" couple and magnetic couplings between electrons (spin pairs) in the atomic shell. The nuclear pairing is most significant for nuclear physics and the production of the 92 natural elements in stars; the electron pairings are most significant for chemistry and the formation of molecules. Another pairing at this level is that between the electron and its neutrino; finally, we note that the common form of hydrogen is the diatomic molecule, H2.

Cell 3) The field or group dynamic at the atomic level is typically played out in the interior of stars, where hydrogen atoms are stripped of their electrons and their nuclei are fused to build all the elements of the periodic table. As in the production of baryons in the Big Bang, the micro- and astrophysical realms are inseparably intertwined.

The first stage in the nucleosynthetic pathway is the creation (from hydrogen) of helium nuclei, or alpha particles, perfect 4x3 systems consisting of 4 nucleons (2 protons and 2 neutrons), each composed of three quarks. The alpha particle is an extremely stable nuclear configuration, so inert that it, rather than the more reactive proton, becomes the unit of element building in stars. For this reason elements with even atomic numbers (numbers of protons) are considerably more abundant in the Universe than those with odd atomic numbers. (See: "The Strong Force: Two Expressions".)

After helium, the next major step in the nucleosynthetic pathway passes through beryllium (2 alpha particles) to the formation of carbon, another perfect 4x3 nucleus, composed of 3 alpha particles each of 4 nucleons, actually a nuclear "triple resonance" of the 4x3 system (since baryons themselves are 4x3 systems). The plateaus of nuclear stability represented by helium and carbon suggest that some 4x3 organizing field controls their formation. It will probably be found in the interaction between the three quarks and four quantum numbers regulating the color, flavor, electric, and spin relations between nucleons in compound atomic nuclei. The simple efficiency of the tetrahedral bonding pattern in the helium nucleus is also a significant geometric factor contributing to its stability.

Adding a 4th alpha particle to carbon produces oxygen; hydrogen, helium, oxygen and carbon are the most abundant elements in the Cosmos, in that order. The relative abundance of oxygen is suggestive of the evolution of the 4x3 carbon system to a 4x4 system, the same tendency we see in our General Systems models. Such similarities are not considered trivial or coincidental in the context of General Systems. Carl Jung noted the same phenomenon in his metaphysical "archetypes": a "trinity" typically evolves into a 4th component (for example, Mary in the Christian Trinity, and the evolution of matter from the "trinity" of light's conservation laws).

The next perfect resonance after carbon in the element fusion sequence would be an element of 48 nucleons, (4 carbon nuclei each of 3 alpha particles). With 24 protons this nucleus would correspond to the element chromium. Chromium 48, however, is highly radioactive and unstable. The resonance fails at this level simply because the electrical charges of the 24 protons repel each other so strongly that 4 extra neutrons must be added to dilute their influence, producing the stable chromium 52. However, the most stable nuclear configuration near chromium 48 is iron 56, an alpha particle plus four neutrons above the actual numerical resonance (48). Iron 56 is the endpoint of exothermic fusion reactions (reactions which yield net energy); all elements heavier than iron require endothermic fusion reactions (net energy input is necessary to fuse them). Hence the failure of the resonant 4x3 nuclear form signals the end of energetically favorable nuclear configurations, as we should expect.

Cell 4) The orbits of electrons in 3-dimensional space are controlled by just 4 quantum numbers, designated n,l,m,s (shell number, angular momentum, orbital magnetic moment, and spin). It is probable that four analogous quantum numbers control the configuration of the nucleons (protons and neutrons) in the compound atomic nuclei of the heavier elements. We find that atoms are thoroughly a product of the operation of a 4x3 General System, which controls the creation of their constituent parts (3 families of 4 elementary particles), the ground state quantum unit, the baryon (3 quarks each carrying 4 charges), their relative abundance and nuclear composition (through the alpha particle and nucleosynthetic pathway in stars); and their nuclear and chemical properties through the four quantum numbers and charges of both the nuclear and electron shells. The 92 natural elements of the periodic table are the final product of the atomic level. The completed or filled electron shells of the inert or non-reactive "noble gases" exemplify the closed boundary condition of this second level.

Here we must make a special note of the curious division of the atomic system into two vastly different energy domains, the nucleus and the electron shell. The "Hierarchy of Natural Organization" would bifurcate at this point - if we were presenting it in a more natural evolutionary sequence rather than simply ordering it by size - into: 1) the astrophysical realm ruled by the information and high energy of the nucleus; 2) the chemical and biological realm ruled by the information and much lower energy level of the electron shell. The high-energy astrophysical realm is concerned with repaying the symmetry debts of light via fission, fusion, and the gravitational conversion of bound electromagnetic energy (mass) to free electromagnetic energy (light), while the low-energy biological realm is the information pathway by which the universe becomes self-aware and experiences itself. The two domains join not only in the atomic structure of matter but in such astrophysical associations as stars and their life-bearing planets. The information content of atomic structure, both nuclear and electronic, as exhibited by the periodic table of the elements, is the rich material basis for all higher information systems in the chemical and biological realms, and much of the detail of the astrophysical realm. We owe our existence to the remarkable dual nuclear/electronic structure of the atom and especially to the most amazing atomic species of them all, carbon, with its multiple examples of 4x3 resonance levels in its nucleus, electron shell, and molecular bonding patterns. It is of course only another instance of the "grand economy of Nature" that it is precisely in the paying of symmetry debts by the nucleosynthetic pathway of stars that the information content of the periodic table in generated, producing thereby the necessary information base for biology and the evolution of cosmic self-awareness through living systems.

Level 3: Molecules and Crystals; Carbon

(3 alpha particles each of 4 nucleons)

Atoms are the units from which the molecular level of physical organization is constructed. The pairing function at the molecular level is the ability of atoms to form several types of stable bonds with each other through the interaction of their electron shells, including the sharing of electrons between shells (covalent bonding). Chemical bonding depends not only on the mutual electrical attraction of the proton-electron pair between and within atoms, but upon the magnetic attraction between the north and south poles of spinning electron pairs. Simple inorganic crystals can be produced at this level of organization, such as quartz (SIO2) or table salt (NACL). Water (H20) and molecular gases such as H2, N2, O2, and CO2 are further examples of this simple level of atomic pairing.

The expression of the group property at the molecular level depends upon a more complex type of covalent bonding that produces the chains, rings, branches, and intertwined 3-dimensional configurations of organic chemistry. Covalent bonds involve a "sharing of differences", which is characteristic of the "Group" position, or Cell 3. An empty position in the electron shell of one atom is filled by the electron of another atom, forming the so-called "covalent" bond. Organic chemistry is carbon chemistry and carbon is a perfect example of the 4x3 General Systems pattern. The carbon nucleus consists of 3 alpha particles each of 4 nucleons; in turn the 4 nucleons of the alpha particles each contain 3 quarks; finally, the 3 quarks each carry 4 charges. As explained above, the carbon nucleus is a triple resonance of the 4x3 system. Furthermore, carbon's electron shell has 4 valence electrons (bonding sites) in the 3rd shell (1S2, 2S2, 2P2). Carbon is the only element which has the 4x3 pattern in both its nucleus and electron shell. Finally, carbon has an amazing 5th 4x3 resonance in its tetrahedral (4 triangles) bonding pattern with other carbon atoms, producing in its most perfect form the diamond crystal. (Significantly for the development of life, water also forms tetrahedral bonds.) Fred Hoyle's famously predicted nuclear resonance energy level of C12, permitting the formation of carbon from beryllium in the nucleosynthetic pathway of stars, is yet another remarkable property of the 4x3 fractal algorithm leading to the evolution of life.

Organic chemistry, and therefore its emergent development life, is fundamentally produced from a 4x3 General Systems physical base. Inorganic molecules and crystals and simple organic molecules and crystals such as benzene are typical products of this level. This is essentially the level of inorganic and abiotic organic chemistry, including simple crystals, such as the carbon diamond. The expulsion of impurities from a growing crystal lattice, the exclusive bonding pattern between atoms of their own kind, and the specific shapes and regular surfaces, angles, and geometry of crystals are all boundary effects of the crystal level. It is through crystals that the regularities and order of the atomic realm first make themselves known to humans. Crystals have always been prized not only for their beauty and rarity, but (somewhat like meteorites) as messengers from an unknown realm.

Level 4: Functional and Cyclic Chemical Systems; RNA/DNA

(3 chemical groups x 4 nucleotides)

Level 4 is the level of typical biological molecules, large organic crystals, prebiotic but functioning, cyclic molecular systems, and especially, RNA/DNA, molecules that copy and replicate themselves, standing upon the threshed of life, but lacking the organizational complexity and completeness of life itself - there is no "self" or personal identity at the fourth level. Organic molecules, including the nucleic and amino acids, proteins, lipids, and carbohydrates, are typical of this level. Cyclic and functional chemical systems, producing "work" of some sort, including replication and simple energy capture, are typical activities of this level, lacking only an integrated system function to assume the mantle of "life". At this level, we also visualize the cyclic activity of the Sun and Moon (light/dark; hot/cold; wet/dry) as "priming the pump" of life, much as the application of "artificial respiration" can revive a drowning victim, or start a newborn baby breathing.

The pairing function at level 4 we identify as the special type of molecular bonding (hydrogen bonding) which allows organic molecules like amino and nucleic acids to cohere firmly but not violently. It is this type of gentle bonding that makes complex biological molecules possible. The direct electron shell bonding of the previous crystalline level is too energetic for biological systems (producing energies typical of your fireplace rather than your metabolism). The pairing function is further expressed in the DNA molecule itself by hydrogen bonding between pairs of purine (guanine and adenine) and pyrimidine (cytosine and thymine) amino acid bases, which in turn are elaborated in long chains forming the famous double helix. (Uracil replaces thymine in RNA.)

The group property which forms the DNA molecule is again a 4x3 dynamic, evident in its 12-part chemical constitution: DNA consists of 4 nitrogenous bases (guanine, adenine, cytosine, and thymine), each connected to a sugar group and a phosphate group. The three-member groups are called nucleotides. The phosphates form the backbone of the long chains, holding the sugars together; the sugars in turn hold the nitrogenous bases, which bond with each other across chains. DNA consists of four nucleotides, each composed of 3 chemical groups (phosphate, sugar, nitrogenous base).

With the formation of the DNA (or RNA) molecule, we come to the boundary between the inanimate and animate realms. Indeed, many viruses and virus-like particles (viroids, retroviruses, micoplasms, prions) exist which are less complex than a typical DNA molecule. In level 4, linked and replicating organic chemical systems acquire and exchange energy, evolved perhaps in response to diurnal/tidal cyclic energy inputs. The organizing center of level 4 is RNA/DNA. RNA also links and catalyzes chemical systems which acquire, store, and degrade energy. The emergent property of RNA/DNA is molecular replication.

Replication vs Metabolism

Of course level 4, the critical molecular precursor to the life of level 5, is still very poorly understood. Level three we understand as the level of molecular structures and crystals. Level five we understand as the level of the cell and its constituent functioning biochemical subsystems. In between crystals and cells we have a crucial molecular level lost in evolutionary time, with a pairing and a 4x3 group stage. These latter two are both supplied by RNA/DNA. These molecules also produce the emergent property of this level, replication, which appears as a complex recapitulation of the 4x3 crystal growth of carbon in the level before, and is necessary to the still more complex reproductive mechanism of the level above. A crucial difference between crystal growth and RNA/DNA replication is flexibility, scope, and qualitative domain: while the former accretes a single specific molecule (such as silicon dioxide, for one example), the latter replicates molecular information - any information. The fact that RNA also catalyzes reactions which capture and transfer energy helps us understand how a replicating molecule could arise and prosper in the first place, combining metabolic (energy capture and processing) and replicating roles. Replication, in this view, is the serendipitous, emergent property of a molecule (RNA) whose original function was metabolic - energy capture, processing, catalysis, utilization, storage, etc.

Finally, with replication comes competition for limiting resources, and evolution at the molecular level. Competition and evolution are further emergent properties of level 4, consequent upon the replicating capabilities of RNA/DNA, whose importance for the rapid development of life from chemical precursors (as occurred upon the early Earth) cannot be overemphasized.

The crucial fact that DNA is both a 4x3 fractal resonance and a replicating molecule has a very powerful implication for the origin and abundance of carbon life in the Universe (see: "Newton and Darwin: the Origin and Abundance of Life in the Cosmos").

Crystal Accretion vs DNA Replication

DNA is a replicating, molecular information code. Once molecules begin replicating information (level 4) rather than simply accreting ever-more copies of themselves (crystal growth - level 3), the pathway (through competition and evolution) to complex, independent living systems is well and truly set. The fractal character of the life system is thoroughgoing. Information begets more information - information systems are naturally suited to create fractal, nested hierarchies of themselves, a characteristic we see everywhere in biology. The crystal cannot create from its environment the raw materials it needs to grow, but DNA can, including creating-capturing the energy necessary to acquire and utilize these materials. Eventually, DNA is able to modify and create its own environment; the culmination is reached in humans where information assumes its most powerful form in terms of the abstractions of language, mathematics, and science, whose material output or expression is technology. With humans, an entirely new "artificial-synthetic" fractal iteration of the evolutionary and information system of DNA is evolving - through biotechnology and the computer revolution.

The jump from crystal growth to information replication is a qualitative, dimensional shift, a discontinuity which is so profound that it must proceed through a molecular, material code (DNA) to retain a necessary contact between parent and child, between the physical world of atoms and the abstract world of information. As Chardin notes: "We must eat to think. But what a lot of ideas are in a slice of bread!" It is this great discontinuity between the realm of chemistry and the realm of information which is at the heart of the mystery of the origin of life. And yet with hindsight we see how the information realm is encoded by the molecular realm of DNA. The pathway from one to the other is made more comprehensible by the fractal 4x3 nature of DNA, which carries the atomic and molecular tetrahedral crystal bonding pattern of carbon (and water) into the information coding system of DNA.

The origin of living information systems is not an accident; it is the natural chemical consequence of the atomic-molecular character of carbon and water. The abiotic 4x3 fractal algorithm of organic chemistry evolves naturally into a 4x3 information replication system. The serendipitous intersection of the 4x3 abiotic fractal resonance hierarchy with a replicating molecular configuration (RNA - DNA) - which can also code for information in molecular form - is the key transformation from simple crystal growth to complex living systems.

Recapitulation and Further Thoughts Concerning The Origin of Life

The crux of the problem or mystery surrounding the development of life is confronted in level 4 of the Microphysical Realm. This is the transition level between the abiotic crystal level (3), with its emergent property of crystal growth and replication, and the first life level (5), where we already find a functioning and reproducing cell with that special emergent property uniquely characteristic of life, the selfish "Self", the self-interested "Identity" which actively pursues and defends its own survival, reproduction, territory, and food supply, including aggressively attacking others cells to further its own interests.

We actually can see in the abiotic phenomenon of level 3 crystal growth - self-similar replication, and selective bonding to atoms/molecules of its own kind - a prefiguring of the biological phenomenon of the reproducing, living self or cell. Life is a sort of highly organized, extremely complex, eating and reproducing carbon liquid crystal with an "attitude" - that is, a self-interest. What characterizes the transition between these two levels, the crystal (3) and the cell (5)?

Often in General Systems we don't know the details, we just know the pattern. Level 4 is one of those places; nevertheless, the pattern itself is very helpful in sorting out what details are or will be important. We will nevertheless write down as much as we can.

The pairing cell of level 4 is the double helix RNA/DNA molecule; the 4x3 fractal expression in the group cell is the molecular composition of RNA/DNA: 4 nucleotides each composed of 3 chemical groups, a phosphate, a sugar, and a nitrogenous base. In the final cell of level 4 we have, in a variation on the crystal level below, an exclusive bonding pattern which is not strictly self-similar as in the crystal, but restricted nevertheless to complimentary base pairs. This transition level 4 is also characterized by three related emergent properties: 1) molecular replication; 2) the molecular encoding of information; 3) molecular competition for limited resources, leading to evolution at the molecular level.

We must also conceive of level 4 not only as a stage, but as a chemical and thermodynamic process taking place in an environment which is "friendly" to the development of life. We know from the Miller-Urey experiment and subsequent observations that the abiotic environment of Earth was replete with the amino acids and precursors of RNA/DNA. These molecules are common even in the molecular clouds of gas and dust in interstellar space. The primitive oceans of Earth were simply full of these molecules, and the 4x3 structure of RNA/DNA is a least-energy chemical configuration. This is the central point about the 4x3 fractal resonance: it is the "least energy" solution to many structural forms, probably because spacetime is 3 and 4 dimensional. But in the case of amino acids and RNA/DNA, we have a special convergence of 2 abiotic phenomena, the least energy (and therefore preferred) 4x3 fractal solution of chemical combination and permutation, and the self-similar replication or bonding pattern of crystal growth, resulting in the epiphenomenon of molecular replication. The realized fractal pattern of RNA/DNA happens to be capable of growing and reproducing itself, recapitulating the emergent crystal property of level 3 below it, and prefiguring the reproductive property of level 5 above it. The convergence of the 4x3 fractal pattern with a replicating molecule has enormous implications for the development and abundance of life in the Universe. The emergence of life from chemistry can no longer be thought of as an unlikely, random, or chance event; on the contrary, it is a favored event because of the fractal 4x3 form of RNA/DNA. (See: "Newton, Darwin, and the Origin and Abundance of Life in the Cosmos".)

While we can be sure that at first the development of RNA/DNA was a very imperfect and fragmentary process, we are dealing with a "friendly" environment consisting of oceans of molecules, millions of years of time, constant inputs of heat and light from the Sun and geothermal activity, the stirring and mixing of the wind, waves, and tides, cycles of temperature, cycles of wet and dry, etc.

Once DNA/RNA is formed it begins replicating mindlessly like any other crystal, essentially "eating" its environment, the amino acid primordial "soup" in which it is born. RNA/DNA makes copies of itself which will compete with each other for the limited number of amino acids in the primordial oceans. This is the second emergent property of RNA/DNA and replication: it makes its own competition, leading immediately to the "original sin" of Abel/Cain and sibling rivalry. RNA/DNA molecules, being copies of one another, all require exactly the same "food" or environmental inputs. Competition with members of one's own kind for identical, limited resources produces the most ferocious of all types of competitions ("no war like a civil war"), and will rapidly lead to both extinction and evolution. Of utmost importance is the fact that unlike crystals, RNA/DNA encodes molecular information, and therefore can "learn" through competition and reproduction, and hence evolve.

The transition from the replicating crystal to the reproducing cell is the transition from passive acquisition of suitable materials from a friendly environment to the active seeking for and/or creation of those materials. Life is an organic crystal that has "learned", or otherwise become competent (through evolution, and because RNA/DNA encodes information), to make its own way in an environment that may be less than completely friendly and benign. Life can seek out and/or manufacture its own food (the materials it needs for replication and maintenance, etc.), defend itself, maintain and repair itself, reproduce itself. It is an organic crystal that has "grown up" and can take care of itself, seeking its own fortune in the world. Its characteristic "self-interest" is a consequence of competition for limited resources; this makes life appear "greedy" and even "nasty", but competition is the root cause of evolution and the development of a self-interested identity, or causal, active "agent".

We should emphasize also that RNA/DNA "eats" to reproduce, that is, the metabolic and reproductive activities at the molecular level are one and the same (food and sex are not distinguished at this level; perhaps this is the beginning of our problems with obesity). This is a helpful concept when trying to understand the thermodynamic origins of reproduction: it is a metabolic, energy driven process first, and the reproductive profit or gain is realized later. It remains so even in us.

Significantly in this context, RNA, which is thought to be the more "primitive" of the two molecules, is not involved primarily in reproduction, but in catalyzing metabolic processes and constructing amino acids. Furthermore, both mitochondria and chloroplasts, two early "metabolic" organelles (in that both are concerned with energy production), incorporated wholesale into cells as symbionts, both have retained their own DNA and reproductive mechanism, demonstrating again the primitive and strong connection between reproduction and metabolism, food, and energy processing. The point is that energy inputs (as by the diurnal solar cycle) can lead to replication as well as simple energy intake in a system in which eating and replicating are the same process, or in which metabolic and replicative systems are contained in and performed by the same information-encoding molecule, as seems to still be the case for RNA.

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