The HOLON, the Torus, Energy and Phi (elements of a universal science)

By

Giorgio Piacenza Cabrera

Preamble

What are some of the mathematical forms extraterrestrials might use? What paths does “energy” naturally take to produce changes across dimensions? Let’s attempt to explore!

Introduction

The “holon” is a “whole-part” explored by Arthur Koestler and Ken Wilber trans systemic integral thinkers who are currently generating creative intellectual responses in other trans-systemic thinkers. This “entity” (so to speak) should gradually find its way into discussions on the rise of complexity, self-organization, hidden order, the “information and holographic universe,” and related subjects but we must also recognize that besides Wilber’s model (Wilber, 1995) there are other ways of conceptualizing it or of conceptualizing primary, universal “forms” that complement it. We must, for instance, recognize that holograms, tori and the Vector Equilibrium Matrix found by Buckminster Fuller may all relate with “holons” and with the irrational but economically distributing spiral built on “phi.” This essay is an initial exploration of “holons” and of some related/complementary “forms” as they could apply to an energetic patterning perspective.

The Golden Proportion: As the whole line is to the greater segment, so is the greater segment to the lesser” (Euclid when referring to this proportion as a line cut in extreme and mean ratio). In the “Golden Rectangle” B (the short side) is to A (the long side) as A is to the SUM of A + B.

If B= 1 then A = 1.6180339887…(or “phi” an irrational number that cannot be written as a ratio or as a fraction of whole numbers). The proportion produces no discernible numerical pattern.

It has been duly noted that many natural spiral shapes try to approximate the phi ratio. Should we think of “parts” as hierarchically relating as energy units through the “Golden Proportion”?

Source: http://thinkingmakesitso.wordpress.com/2011/07/17/smear-campaign/

Other Ways to Represent Holons

A bi-torus inscribed within a Golden Rectangle could exemplify the origin of a holon. All the parts of a torus are represented and connected by its (ideally) infinitely small center. It can be a holographic symbol. Also, larger and smaller areas or volumes of the torus can fractally repeat a pattern.

(author’s diagram)

Any rectangle can be divided into two equal sides and this can represent polar opposites but using the Golden Rectangle is more interesting by its fundamentally ordered and pleasing ratio/proportions and because these proportions are irrational (a product and producers of the irrational number “PHI”) they cannot be limited to a structure given by a perfect symmetrical ratio of dividing a figure in two. Phi represents the tendency of extending beyond to complete itself and commune. The bipolar symmetry represents the stable thing or structure. Phi represents the part extending itself and the equidistant bipolar symmetry represents the whole preserving its self- identity.

Main Logics Combine in one Image-Concept

Yin/Yang mirror-like complementary opposites (and idea also used by the Quechua people of the Andes) give rise to a “holon” (which is recognized both as a “thing” and as “not a thing” because it is simultaneously incomplete and complete as a “part-whole”). The relation between the opposites has several ways of being logically interpreted. For example: 1) A mutually exclusive relation, 2) A complementary relation and 3) An indefinable relation. The first logic should promote a society based on the manipulation of exterior objects and emphasizes “parts.” The second logic should promote a society based on the relation of “parts” and emphasize “wholes.” The third logic should promote a mystical and transcending society.

Each relation represents a major “logic” or an intuitively rigorous, self-evident, reasonable way to interpret. Logic “1” is a classical, syllogistic, “either-or” way of finding order by separating distinct “parts.” It applies quite well to a world with mass distinguished by our experience of space and time. In this “sense making” perspective we can determine that the central dividing line divides two equal sides. Nevertheless, in another sense, the sense of “Logic 2” (complementarity) we

cannot determine that the dividing line is exactly on one side or the other or which side it faces. Thus, the dividing line also represents both the identity of opposites and an infinite relation between them. It is real, visual, and understandable but also beyond relational logical reason and thus, indefinable as Nagarjuna seems to have found regarding assertions and negations: Three logics in the holon…all valid.

Tori

Now, let’s imagine the two cone-shaped sides of the bi-torus as spiraling not just out but back into itself and we’ll have a model that may represent how holons express holographically (and fractally) in and out of themselves. The bi polar tori can be visualized inside a Golden Rectangle phi. Their exact symmetry dividing them in two would represent stability and structure, the perfect vectorial equilibrium of forces called “potential” which is the original source of energy. Every higher symmetry in nature is a loss of the polar distinction and a return to a higher, non- visible, potential symmetry.

(Source: http://www.soulsofdistortion.nl/)

Ultimately “Energy” may be perfect symmetry, perfect potentiality, that which is invisible in lower symmetries, but in expression it is specified or “dosed” for different systems. A “quantum” is like a specifically-sized “wagon” carrying energy that interacts with other “quanta” through a pattern. In our known physical universe there’s a specific minimum amount of energy, space, time and information capacity related with Planck’s Constant (6.626068 × 10-34 m2 kg / s). The relating pattern through which any specified amount of energy can relate, expand, fractally multiply and flow back to its origin, may be the so called “Golden Proportion” which is a ratio displayed in the Fibonacci series (0,1,1,2,3,5,8,13,21,34,55,89,144,…) resulting in “phi” (1.618033088…). It is a harmonious progression that possesses an essential relation: the next term simply is the sum of the previous two. I think that the natural, ideal relation among specified energy “quanta” (interiorly connected through this progression) represents and delivers information as Exterior Integral quadrants dimensions.

All fundamental subdivisions in nature (like the “quantum of action” given by Planck’s Constant) would fit into this pattern. If we divide the Golden Rectangle into two equal halves we can represent a perfectly regular symmetry within a logarithmic “phi” proportion not delivering a perfectly regular numerical series. It is the simultaneous completion and incompletion of whole and part and a two-sided, bipolar torus inside the Golden Rectangle which would represent the

original duality (is-is not, Being and negation of Being) that generates the four holon “dimensions” (the Interior, the Exterior, the Indivisible, the Plural) and their combinations as four expression “spaces” or “quadrants.”

In single and double tori energy flows into one pole, flows through the boundary axis, flows out the other pole, twists and returns to the first pole. I think that the double torus circulating inside a Golden Rectangle would be more fundamental. The ellipses represent poles tangential to the two short sides of the Golden Rectangle.

Source: Toroidal-Poloidal Gallery

(author’s diagram)

Source: dailystrength.org

The spiral in phi is a circle (closed cycle) + line (progression, change) + an ideal proportion (ideal phi ratio) between the two. The ratio is so basic to life that it is found in DNA.

Source: http://www.goldennumber.net/dna/

The Vector Equilibrium Matrix found by Buckminster Fuller shows how vectorial forces cancel out with each other in a 3D space and could represent 0-point energy or energy understood as a potential in that space. Any imbalance leads to a force. If the vertices of this figure are placed in the center of tori with the Golden Rectangle proportions we may combine a basic, universal structure with the ideal pattern of movement. I think that “Bucky” Fuller’s “V.E. Matrix” can represent a HOLON’S “whole” aspect as a 3D energetic potential.

The Vector Equilibrium Matrix

(8 tetrahedra, 12 vector lines of force radii, six square faces, six four-sided pyramids, 8 triangular faces)

http://vacuumsingularity.wordpress.com/holofractographic-universe/

The Haramein Model

According to non-orthodox physicist Nassim Haramein, founder of the “Resonance Project” (http://theresonanceproject.org/ ) the basic V.E. Matrix (representing structural and vectorial equilibrium) is a shape that can be naturally surrounded by a torus. Then it can be expanded to form a 64 tetrahedral pyramid grid whose core fits with the structure of the Kabbalah’s “Tree of Life” Is this meaningful coincidence?

Source: http://zero-point.tripod.com/holistic/Holistic.html

According to Dr. Haramein every atom obtains its manifestation energy in exchange with the vacuum. Could it be that every holon, in fact every “thing,” “occasion” or “eventity” also sustains itself energetically through the same process? He proposes that every double torus with energy radially circulating in and out of the center is a manifestation of vector equilibrium as a cube octahedron or tetrahedral array “torqueing” or producing spin while its central part remains still. The tetrahedral array is also according to him coincident with a six-pointed star, like the “Star of David.”

Dr. Haramein finds the related 64-tetrahedron (32 positive and 32 negative) pyramid grid of key universal importance also if tori (here represented as circles) surround each pyramid. He claims that the form which result from removing the V.E. Matrix lines is also found in unique figure in the Temple of Osiris in Abydos, Egypt. It is called the Flower of Life and might relate with the 64 hexagrams of the I-Ching and with the 64 “codons” forming DNA amino acids. This figure (or fractal multiples of it) has been called “The Flower of Life” and has been found in some seemingly genuine (non-human constructed) “crop circles” (go to “Crop Circle Connector” http://www.cropcircleconnector.com/2012/wadenhill/wadenhill2012a.html ) and in Sufi and other mystical paths.

Source: http://vacuumsingularity.files.wordpress.com

Discussion

In Integral Theory Ken Wilber(Wilber, 1995) basically proposes that a Non Dual “Spirit” (which we could also well interpret as an “Intelligence”), a unique entity which is ultimately independent from duality produces it (in a panentheistic sense) and along with it, holons, perspectives, quadrants, holarchies and all the universal patterns that can be associated with holons. It’s not a far cry to affirm that this “Spirit” uses all other related duality-based “integral” forms a (besides those given by holons, quadrants and what quadrants may contain, i.e. “lines”, “stages”, “types” “states” and perhaps more) to manifest its own Life and potential activity as if it were outside of itself. In this brief essay I’m trying to show that there are indeed other such related “forms,” “patterns” or “structures” or “elements” which coincide or overlap with “holons.” These seem to pertain more to a symmetry level higher or prior to the one distinguishing quadrants. In it distinctions like “Interior” Exterior” “Undivided” and “Multiple” are blended as one, for instance in the three dimensional figure of a torus.

It is time to expand the conceptual basis and lexicon of Integral Theory and kindly use other discoveries that can add greater detail to it. These other “forms” also relate with dualities, especially with what we could call “complementary dualities.” For instance, holograms can emerge from phase-conjugate patterns and may relate both with single tori (being able to sustain a circulation between a single point interior and an extended plurality-compatible exterior) and two-sided tori (joined by a single center and the bifurcated volumes representing a polar opposite). Other “forms” (even like the 6-hexagram “I-Ching”) emerge from the basic symmetry and broken symmetry given by complementary dualities (in this case represented by a whole line and a broken line). Like in the “holon,” in the related “forms” I’ve referred to in this essay, there’s always a “whole” aspect and a “part” aspect.

All these other “forms” can be considered complementary to Integral Theory’s own but they may relate more with how energy flows and changes through patterns than with simultaneous correlations and inductively detected and subjectively ascribed “elements” inside quadrants. They can be understood as other aspects of the same “holons.”

I think that the Golden Rectangle, the two-sided torus (bi-torus) and the Vector Equilibrium Matrix (an isometric figure) can be infinitely subdivided in half or infinitely doubled in a rigidly structured way. Thus, they can represent “wholes” as perpetual structures. Able to represent an infinitely small center and their surrounding circumscribed areas, volumes or “bodies” (in relation, interaction and unity with that center) they also represent “wholes”. Nevertheless, all these rigid symmetry “forms” can also fractally extend accommodating the ideal open growth pattern of the Golden Ratio that conveys the irrational number sequence “phi” which can grow as an ideal spiral. Phi derives from a ratio or proportion but no whole numbers can represent it in a fraction or ratio of each other. Even the “Golden Rectangle” can be isometrically divided in a rigid way through its middle (but the most algorithmically elegant relation between the length of its sides doesn’t produce a final whole number). It is a symbol of precisely organized indetermination. It is like a “set of all sets” that cannot be quite determined as a mathematical “object” (or whole unit).Nevertheless, in relation with an actual potential, the set of all sets can be subjectively determined as a whole or unit, just like the unending series of holarchical parts can also be subjectively recognized as whole units.

The rigid structure representing equilibrium, the cancelation of forces, wholeness and potential in a potentially ever-recirculating torus figure or in the “Vector Potential Matrix” figure discovered by Buckminster Fuller can be complemented by a aesthetic logarithm which represents an ever-extending, fractal symmetry of movement, a logarithm of irrational incompletion, perhaps representing the communing nature of “parts.”

I understand “energy from the vacuum” expert physicist T.E. Bearden as saying that “energy” is a tendency to persist which is akin to a potential and to an “identity of opposites” (Bearden 2002). In my interpretation this means ever-implicit “wholeness” and I see it always present in every manifest thing however that wholeness is allowed to express generating the appearance of change or movement. Interestingly, we can say that the essentially self-regenerating toroidal “fields” (which can inscribe a “Vector Potential Matrix”) in exchange with vacuum potential can maintain their identities by being always connected with their infinitely small, potential-seeking center. Nevertheless, the “fields” don’t need to be isolated. They can also relate with other “fields” as “parts” seeking “communion” (horizontally in the same level and vertically across levels). Reflecting an “integral” “second person communing principle” they can be part of larger toroidal “fields” or contain smaller “fields.” If the fields torque with phi proportions they would connect in movement and in harmony generating phi-proportioned “holarchies”

Another way to see how phi toroidal fields hierarchically relate would be through “phi boundary conditions.” The blog “Cosmometry” is a wonderful source to understand this and other important issues. It can be found at: http://cosmometry.net/home. In this blog I learned that when phi

spirals are spun around a central point they naturally generate separate defining levels reminiscent of hierarchical levels structured in a fractal manner. Perhaps if we generate these “boundary conditions” within tori surrounding “V.E. Matrixes” we can detect a higher symmetry way of representing how holonic hierarchical levels distribute energy quanta and information relations.

A Curiosity: Phi is recursive within itself. It almost seems to prove itself (against Gödel’s incompletion theorems). Dividing unity (number 1) by the eleventh numerical term “89” (counting from 1 if we don’t consider “0” a numerical term) in the Fibonacci series produces the….Fibonacci series after a decimal point (the reciprocal of the series). Off course, if we include “0” as a numerical term we would be dividing unity by the twelfth term in the series.

References

Bearden Thomas E. (2002). Energy from the Vacuum: Concepts & Principles.Cheniere Press: Santa Barbara.

Gamble, Foster (2012). Thrive Movement video. Retrieved on July 16, 2012 from www.thrivemovement.com

Klein, Morris. (1980). Mathematics: The Loss of Certainty. Oxford University Press: Oxford.

Haramein, Nassim. (2012). The Resonance Project videos. Retrived on July 16, 2012 from http://theresonanceproject.org/

Lajo, Javier ( 2005). Capaq Ñan: The Inka Path of Wisdom. CENES: Lima.

Laszlo, Ervin y Currivan, Jude. (2008). “Cosmos: A Co-creator’s Guide to the Whole-World. Hay House, Inc: Carlsbad.

Livio, Mario. (2002). The Golden Ratio. Broadway Books: New York.

Wilber, Ken. (1995). “Sex, Ecology, Spirituality: The Spirit of Evolution”. Shambhala: Boston.