Metacosm

"Metacosm”

Oil on canvas, 70” x 40”

2015—2022

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The word "metacosm," is defined as a system that encompasses cosmos systems, both the macrocosm and microcosm, as a transcendent field of forces that is beyond the created world. I didn't know this word at the time of first thinking about this painting and idea but it really fits with what I am trying to show with this piece. Especially how it relates to the torus geometry, and how it is a type of meta-archetype or pattern in sacred geometry, that shows up in the way the universe organizes itself at all scales, from atoms to cells to planets to stars to galaxies. 

Metacosm is about imagining the cosmos as an infinite fractally nested self-generating and self-creating bifurcating multiverse, which if bifurcating inside of itself infinitely at every plank length instance of difference/expansion, could represent a branching parallel torus universe structure (or metaverse) within the metacosm, that would be a way of thinking about a 5th dimensional view of 4th dimensional emergent bifurcating timelines or universes, or a 2-D slice of 4-D branchings within a 5-D concept.

"This is a creating universe not a created one." 

— Walter Russell

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The drawings for this initially where rough sketches of torus forms trying to find a shape and order that could nest within itself, which then lead to being laid out within an inverse square grid, with the torus as an expanding field/universe within a circle shape.

Initial drawings for Metacosm

It wasn't until recently when I discovered George Leoniak's geometric construction for the mathematics of the golden ratio that I realized how the Metacosm torus geometry and nested torus pattern, though not directly in phi circle proportion, can formatively interrelate with the phi ratio circles, the vesica piscis circles, and the circles created from the inverse harmonic square grid pattern. 

George Leoniak's geometrical construction from the mathematical equation of the golden 

ratio (√5+1 divided by 2 = Phi (1.618…)) created from the vesica piscis. 

√3 circle geometry relationships overlayed onto Metacosm

Metacosm circle geometry studies.

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The torus archetype, which is closely connected to the circle and vesica piscis, is both an archetypal field-form that is transcendent, beyond all creation, like the circle, and connected to the notion of the whole as a sphere, but then also is an archetype very present in natures way of organizing energy and matter into flows, vortexes, and cycles, into self-reinforcing self-organizing patterns or fractals, in matter and life and mind. 

As an archetype it seems specially preordinate, a-priori, and nondual, because it is both a formative transcendent background and static unchanging constant, but also an archetype of dynamic self-organizing fields, and emergent complex systems. It is an archetype transcendent of form but while also being emergent with dynamic form; both an archetypal blueprint-form, and an archetypal formation pattern of self-organizing fields. 

In short the torus is both a transcendent meta-structure and emergent meta-pattern, both macrocosm and microcosm; both above, and below; a Metacosm.

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"The indication is of the notion of a plane of being that's behind the visible plane, and which is somehow supportive of the visible one to which we have to relate. I would say that's the basic theme of all mythology, that there is an invisible plane supporting the visible one." — Joseph Campbell

"Spiritual science seeks to connect the human being with the great laws of the universe, the great laws of the cosmos. The deepest impulses of spiritual science will be understood in the true sense of the word only when people realize how extensively we are actually searching for the connection between human beings and the great transcendental laws of the universe.” — Rudolf Steiner

"I believe that scientific knowledge has fractal properties, that no matter how much we learn, whatever is left, however small it may seem, is just as infinitely complex as the whole was to start with. That, I think, is the secret of the Universe."— Isaac Asimov 

“Every moment is of infinite value, for it is the representation of a whole eternity.” - Goethe 

“The Universe designs itself … every particle, every molecule, every organism, every celestial body in the Cosmos, exists and develops in the context of every other.” – Paul Harrison

"The whole universe is based on rhythms. Everything happens in circles, in spirals." – John Hartford

"That which is now called natural philosophy, embracing the whole circle of science, is the study of the works of God and is the true theology. As to the theology that is now studied in its place, it is the study of human opinions and of human fancies concerning God." –Thomas Paine 

"The cosmological picture that emerges--a map in time as well as in space--is not what most of us expected. It offers a new perspective on how a single "genesis event" created billions of galaxies, black holes, stars, and planets, and how atoms have been assembled--here on Earth, and perhaps other worlds--into living beings intricate enough to ponder their origins. There are deep connections between stars and atoms, between the cosmos and the microworld. . . . Our emergence and survival depend on very special "tuning" of the cosmos--a cosmos that may be even vaster than the universe that we can actual see." —  Martin Rees 

"To the eyes of a human of imagination, nature is imagination itself" —  William Blake 

“What makes every real work of art of interest is that it reproduces the mystery of Creation which operates in the Microcosm as in the Macrocosm, in Man as in the Universe.” — Edouard Schure 

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The Integratron Root Square

 

 “The Integratron Root Square”

6” x 6”, acrylic on canvas, 2022
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“Geometry is knowledge that appears to be produced by human beings, yet whose meaning is totally independent of them." 

— Rudolf Steiner

In the process of geometrically exploring the relationships between the first three root ratios (2, 3, 5) and finding a way to integrate them visually in a meaningful way into a kind of symbol, or put them in a relationship that could be simplified or contained within a square, I discovered this overall way of integrating the three roots, what I am calling the "Integratron Root Square."

What I'm interested in are how these fundamental root relationships with the 2, 3 & 5, and their shapes (the square, triangle, and pentagon), are interconnected and inter-generating universal constants. It's hard to imagine them as separate functions or laws, especially when the certain extended geometrical properties of lines of different ratios or grid patterns or circles overlap almost magically to create just the exact different ratios, points, and angles needed, and integrated in perfect alignment. 

“The dynamics generated within the three primary shapes are illustrative of the self-organizing forces of nature.” - Jonathan Quintin

These three roots, the square root (2), cube root (3) and phi (5) encompass both even & odd numbers, with 5 being an integration of both, altogether form a trinity of generative principles or roots (Jonathan Quintin). Phi or 5 has the quality of something extra it seems, it has the uneven/indeterminate generative/emergent element or creative and self-balancing dynamic seen by living systems, a self-referencing feedback property, or a "dynamic fracticality", in relation to the Fibonacci sequence, seen in both animate and inanimate pattern formations in nature.

“You will know, as far as it is allowed to a mortal, that nature is from all points of view similar to itself.” - Pythagorus 

The Pythagorean Trinity, Fibonacci Sequence, and Creation Geometry

To me this trinity of generative root ratios seems to be connected to what is called the Pythagorean Trinity (Ken Wheeler), and the relationships between the first five numbers in the Fibonacci sequence, (1, 1, 2, 3, 5). In the metaphysics of the Pythagorean Trinity, the One is considered ultimately transcendent and absolute, beyond any representation, but is represented as an indefinite dyad (1,1), as an inseparable transcendent principle and manifest attribute of the One, that makes up the first two numbers of the Fibonacci sequence and the first part of the Pythagorean Trinity. The first 1 represents the intrinsic transcendent in principle, and the second 1 its inseparable extrinsic attribute.  Thinking about this, the two initial overlapping circles of the vesica piscis come to mind as a kind of visual, with both representing a "one."

The golden ratio emerges from the two systems of geometry generated out of the vesica pisces, the ad triangulum and the ad quadratum (root 3 and root 2), and these two geometries were generated from two perfect spheres or circles or infinities or "ones" overlapping at their midpoints. So two circles (pi/infinities) overlap to create root 2 & root 3, which then those geometries overlap to create root 5 (phi/golden ratio). This relationship between the square and cube,  (2, 3), is the second part of the Pythagorean Trinity, and represents the emergence of the principle of duality and its relationship with the One, which links back and creates a trinity, representing the manifest universe and all things in 3 dimensions.

The third part of the Pythagorean Trinity are the relationships between 3 and 5, the cube and golden ratio/phi, the trinity and life (being/ontology), and is the final integration or "consubstantiation" of the first two parts of the trinity (Spirit-Matter/One-Many/Transcendent-Immanent).

The feedback of the Fibonacci sequence seen in this way is the feedback of life or phi with the continuum of the present moment, the One, or the "irreducible One" as R. A. Schwaller de Lubicz phrased it; the self-balancing and self-organizing and spiraling of polarities and dualities back into the constant creation of the present moment, the infinite one-continuum of the eternal ever-present, with its many uncertain and emergent outcomes, bifurcations, and growths. 

In this way, geometry is an interactive and deductive metaphysical tool we can use for understanding and discovering the inner "mechanics" of the universe, its generative archetypal constants, and the ultimate source of the transcendent and its connection to all things.

This is the metaphysics of the origin of process, the origin of order, and the origin of origin; the fact that all logic, order, and rationality in the universe originates from numbers and shapes with irrational roots and principles is quite the curious mathematical mystery.

“The compass is the most important scientific instrument that humanity ever invented.” — Keith Critchlow

"The study of geometry is a meditation on the harmony of the cosmic order." — Pythagoras

“Details make perfection, and perfection is not a detail.” ― Leonardo Da Vinci

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Initial study for Integratron, compass & pencil

Extended circles & lines

Fractally embedded root ratios

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"I have a distinct feeling that number is a key to the mystery, since it is just as much discovered as it is invented. It is quantity as well as meaning." —Carl Jung

"Number thereby throws a bridge across the gap between the physically knowable and the imaginary. In this manner it operates as a still largely unexplored mid-point between myth (the psychic) and reality (the physical), at the same time both quantitative and qualitative, representational and irrepresentational." —Marie-Louise von Franz

"It may well be the most primitive element of order in the human mind... thus we define number psychologically as an archetype of order which has become conscious." — Carl Jung 

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Alternative study with root ratios and 

pentagonal geometry (Albrecht Dürer method)

The three roots overlaid and aligned with Leonardo da Vinci's Vitruvian Man geometry

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"Unity is plural and, at minimum, is two." — Buckminster Fuller

“One becomes two, two becomes three, and out of the third comes the one as the fourth.” — Maria Prophetissa

"The one engenders engenders the two, the two engenders the three and the three engenders all things." — Tao te Ching 

"All the effects of nature are only the mathematical consequences of a small number of immutable laws." — Pierre Simon de Laplace

"Where there is matter, there is geometry." — Johannes Kepler

"The harmony of the world is made manifest in Form and Number." — Sir D'Arcy Wentworth Thompson

"Geometry purifies the eye of the soul, since it is by it alone that we contemplate the truth." — Plato

“There are fractal codes containing the laws of creation and the more we understand these laws the more we can apply the harmony that is apparent in nature as a more powerful force in our own lives. There is truth and purity in natural things and our contact with them nourishes the soul and illumines the mind.” - Jonathan Quintin 

"Music is the arithmetic of sounds, as optics is the geometry of light." — Claude Debussy 

“With light poise and counterpoise, Nature oscillates within her prescribed limits, yet thus arise all the varieties and conditions of the phenomena which are presented to us in space and time.” — Goethe 

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Psymatic Self: Geometries of Consciousness

 

"Psymatic Self: Geometries of Consciousness" 

28" x 14" 

Oil on canvas, 2012

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“The individual is an aperture through which the universe becomes aware of itself.” - Alan Watts

“The world is full of vibrations originating in the manifold dynamics of dissipative self organization.” - Erich Jantsch

 "Thermodynamics shows us that we have the same entropy-producing function as other naturally occurring matter-cycling systems that grow in regions of available energy. Although life has been identified as, and reduced to, its genetic architecture, its capacity to chemically copy itself, this ability is ultimately secondary to its energetic function." - Dorion Sagan

“The surface of the Earth is the shore of the cosmic ocean. On this shore, we've learned most of what we know. Recently, we've waded a little way out, maybe ankle-deep, and the water seems inviting. Some part of our being knows this is where we came from. We long to return, and we can, because the cosmos is also within us. We're made of star stuff. We are a way for the cosmos to know itself.” - Carl Sagan

"If you have the idea that you are something with form, that you are limited by this body, and that being within this body you have to see through these eyes, God and the world also will appear to you as form. If you realize you are without form, that you are unlimited, that you alone exist, that you are the eye, the infinite eye, what is there to be seen apart from the infinite eye? Apart from the eye, there is nothing to be seen. There must be a seer for an object to be seen, and there must be space, time, etc. But if the Self alone exists, it is both seer and seen, and above seeing or being seen." - Ramana Maharshi

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This piece is connected to a long interest in exploring the notion of "What is the Self?", mainly in relation to the issue of the mind-brain or subject-object dichotomy, and the intrinsic unity. The Self seems to be a complex unity of both organism and environment, individual and collective, of the transcendent/mystical and immanent/scientific-material, the infinite and the finite, and of energy and matter. In this I wanted to visualize how this apparent duality could be seen or explored symbolically through geometric relationships. 

With the piece on the right I'm trying to show how the brain is a processor for energy, matter, and information coming in from an environment outside but inherently and dynamically connected to it, and from four directions, or in four dimensions expanding outward. In a way the brains bio-interactive cyclic feedback loops of various sorts. its various brain wave states, or cymatic-like frequencies of consciousness, create the emergent sense of the central Self, that can also open into expanded states, and to a kind of cosmic identity that reaches out into larger and larger horizons of Self knowledge and awareness of extended environment, and with the universe as a whole.

The piece on the left is kind of like the view from the inside of this process, or the intangible interior subjective dimension of an individuals mind, or the "I" in the eye of the beholder. 

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Macrodynamic Morphogenesis Series

"What lies beyond the visible world is always imaginary, as a play of images. There is no other way to talk about the invisible in nature, art, and science." Jacob Bronowski

While providing a chance to interact in real time with abstract ideas, Cymatics experiments help show the ways that forms and patterns emerge from fluid and symbiotic interactions, and the ways that transformations of forms or patterns can happen in the natural world. 

Working with this visually I want to express a symbolic quality to the fractal and self-similar field-like and vibrational processes that can relate to dual micro-macro and whole/part aspects of morphogenesis, evolution, self-ogranization and development. My intent with the Macrodynamic Morphogenesis series is to show the fractal multi-level embededness and interconnectedness of pattern and form in nature throughout the history of matter/energy complexity; the unifying gestalt or whole/part unity that emerges out of the field interaction of open and natural and living systems. Traditionally this nested order and unity of nature, man, and cosmos was known as the Great Chain of Being, but often with the bad flavor of anthropocentric hierarchical dominance and religious piety at the top, and a misunderstanding of emergent and developmental whole/part hierarchies in nature. More contemporary thinkers like Arthur Koestler along with, Ken Wilber, Rupert Sheldrake, Ralph Abraham, Mark Edwards, and others have used the word "holon", termed by Koestler, to describe something that is both whole and part simultaneously, and mutually embedded in larger and smaller sub-systems or contexts or fields of intricate interaction, or 'holarchies'. This organic stratified stability or nested holonic order is the way nature emerges and builds upon itself through self-organization within various types of environments or fields, or morphic fields.

Nonliving and living systems can both express this holonic nature coupled with the properties of emergent self-organization in phenomena all throughout the universe. It can be seen in 'physical' atomic organization, in molecular domains of nonlinear inorganic chemical oscillations(Belousov-Zhabotinsky reaction), and in the living biological and cellular and ecological domains(Turing-Lorenz), extending into the chaos of the neural and mental domains of cultural information exchange and interior psychological developmental complexity (SpiralDynamics/memes). All open and dynamically evolving systems in both interior and exterior domains have the self-transcendent and fractal like qualities of emergent self-organization and whole/part irreducibility/indeterminacy. In another way, the dynamical systems view of fractal chaos can be said to put bifurcating cracks in the imagined subjective/objective walls that stand between science, nature, and art.

(EROS: Emergence)

"Origin Ocsillation-Transformation", 2010, oil on canvas, 61 x 61

"Self-Similar Cellular Resonance", 2009, oil on canvas, 61 x 61

"Nonlinear Neural-Net Macro-Intricacy", 2010, oil on canvas, 61 x 61

With the notion of a unified macro-sequence or continuum or stream to evolution, in each painting in the Eros: Emergence triptych I am trying to express a relational resonance or field dynamic of the whole/parts coming together into a higher or more expansive whole. This is what the philosopher Alfred North Whitehead, along with the philosophical-psychedelic ethnobotanist Terence Mckenna, have talked about as being a "concrescence point," or a shared density of self-organized complexity, throughout and with the emergence of each domain.

"Creativity is the universal of universals characterizing ultimate matter of fact. It is that ultimate principle by which the many, which are the universe disjunctively, become the one actual occasion, which is the universe conjunctively. It lies in the nature of things that the many enter into complex unity." Alfred North Whitehead

With Mckenna's creative, prolific, and visionary writings and dialogs about this overall macro-process, and in finding some overall unifying nature to evolutionary dynamics, he came to use the Greek words "Eros" and "Logos". Similar to the way both Carl Jung and Ken Wilber used the terms, they express a relatedness between the feminine and masculine principles. In many ways, aspects of these old notions of the Eros and Logos resonate strongly with the new sciences of emergent complexity and the strange attractors of fractal mathematics. With Eros emerging and embracing wider and more connected wholes, and with Logos being a type of multi-dimensional logic or transcendent multi-dimensional attractor space.

A way of thinking about attractors could be that they are really geometrically higher dimensional spaces in the universe. Even the basic dimensionality of the overall universe and the space-time continuum suggests an over all fractal process. Fractal geometry is often referred to as the geometry of the fourth dimension, and unlike the other dimensions, the first, second and third dimensions correlating with the line, plane and solid, the fourth dimension adds the element of time and change, which creates the world we experience. So the cosmos can be seen on the whole as an open system of systems where everything else is related and connected to everything else in a constant change and evolutionary feedback.

This to me visually suggests that a higher dimensional attractor or archetype can be imagined or hinted at through the integrating and complexification of perspective through time. This has been one of the main inspirations for the second triptych series Logos: Attractor, and for me is about the line and the integration of perspectives creating the circle, which leads to the source. 

(LOGOS: Attractor)

"∞" 2010, oil on canvas, 61 x 61

"∞" 2010, oil on canvas, 61 x 61

"∞" 2010, oil on canvas, 61 x 61

Inspired by the mandala, sacred geometry, and the many mystic visionary artists throughout history going back to the first cave paintings I want to use these paintings as a way of sharing visions and interconnections that go beyond words. I have long admired and respected the work of amazing contemporary visionaries like Alex Grey, Paul Laffoley, M.C. Escher, Mati Klarwein, (and many many others considered as "outsider artists" to the art world, which has become too isolated). In particular, like many of these artists, I want to focus consciousness towards a meditative and scientific state of awareness and reflection, aiming to connect with a contemplative space that suggests that both scientific rationality and intuitive spirituality are trying to understand and feel connected to the same primordial Mystery. Albert Einstein's quote about the experience of the mysterious seems most fitting when thinking about this.

"The most beautiful and most profound emotion we can experience is the sensation of the mystical. It is the source of all true science. He to whom this emotion is a stranger, who can no longer wonder and stand rapt in awe, is as good as dead. To know that what is impenetrable to us really exists, manifesting itself as the highest wisdom and the most radiant beauty which our dull faculties can comprehend only in their most primitive forms - this knowledge, this feeling, is at the center of true religiousness." (Albert Einstein)

His understanding of this was a transformation of his personal consciousness that I think helped him understand what can be called a type of ‘rational mysticism’ or 'trans-rational experience'(including rationality). Again, another one of Einsteins quotes on consciousness and the validity of the mystical experience from a scientific perspective.

"A human being is part of a whole, called by us the Universe, a part limited in time and space. He experiences himself, his thoughts and feelings, as something separated from the rest--a kind of optical delusion of his consciousness. This delusion is a kind of prison for us, restricting us to our personal desires and to affection for a few persons nearest us. Our task must be to free ourselves from this prison by widening our circles of compassion to embrace all living creatures and the whole of nature in its beauty." (Albert Einstein)