The Dyad is asleep in the Monad. Awakened, it unfolds into the Triad so that the Tetrad is completed in the Decad. All things come from this and return to it again.
Coherent systems are present wherever life is: wherever atoms bond together and wherever light propagates. Without coherence, entropy would overtake order, and no life would be possible. There would be no periodic orbit or rotation of celestial bodies, no metabolism, no DNA, no hydrogen fusion, no electricity, and no mental conception of anything without the persistence of certain fundamental rules establishing their necessary preconditions.
Triangles, or rather trinity-ness as a kind of underlying pattern at the formative level of things, is a precondition for the presence of order.
We can find the 3ness balancing, organizing, and integrating everywhere we look. In music, triads make up the basic structure of chords. These fundamental harmonies are built by stacking three thirds together. It is because of the harmonic structure of music, (2:1 ratio) that these thirds are the most consonant of acoustic forms. But the harmony of triangles is not just about music. It is in the very movement of life, thought, and evolution itself.
The Hegelian dialectics show how the power of triangles is in operation on the level of thought. Dialectics refers to the process of making a philosophical argument involving two opposite and contradictory positions. Hegel points out that the opposites of two competing positions are reconciled through a third that includes and transcends the finer points of both. The process begins with a thesis. The thesis is countered with an antithesis or contrasting view, but then after some negotiation, the two are integrated into a synthesis view. This process is one of sorting out the strengths and weaknesses of each view and combining them in a view that includes both its earlier truisms but also transcends them in a view that’s more comprehensive and more whole than either of its earlier parts. Thesis > Antithesis > Synthesis
This 1 2 3 approach to gaining philosophical understanding is also represented in the growth of evolutionary complexity itself. From basic parts, more complex things and definitions emerge. From understanding simple things, more advanced things proceed. By stacking consonant notes, more rich and complex tonal structures are created. This ever-present three-ness is at work wherever there are individual parts coming together in groups to make bigger, more complex wholes. It is said that the creative advance into novelty, whether we are talking about biological organisms or evolving values spheres, follows this formula. Body, mind, and spirit, past, present, and future, and myriad other examples illustrate the harmonizing presence of three-ness throughout existence.
The Neoplatonists also had a conception of the universe that brought to life the essential trinity of existence through the concepts of plenitude, continuity and linear gradation:
1. Plenitude is the idea that the universe is full of life and variety exhibiting maximal diversity.
2. Continuity is the idea that the universe with its infinite series of forms, shares some attributes with its neighbors. i.e all creatures have to eat and reproduce.
3. Linear Gradation is the idea that this infinite series is arranged in hierarchical order from the smallest and simplest things (microcosm) to the largest and most complex (macrocosm) in a nested chain of being. This nested chain is called the Great Chain of Being or holarchy.
Holarchy ~ A system composed of interacting holons.
Holon ~ An autonomous, self-reliant unit.
The great chain of being then self organizes the primordial life force’s creative push into novelty, complexity, and higher order integrations. Its pattern of self-organization from smaller individual things to larger individual things is called a holarchy. Holons are whole parts. When they come together, they make bigger whole parts. Atoms cohere into the higher order complexities of molecules, which organize into cells, cells organize into organisms and organisms organize into ecosystems and societies. Letters form into words, words into sentences, sentences into paragraphs, and paragraphs into whole ideas.
Where does this order come from? Is there a will, a kind of pre-existing intelligence, a primordial agenda or motive force leading to an evolutionary apex? Whatever it is, it is clear that there is a habit of self-organization that has been built into the blueprint of the universe. This blueprint, we will come to see, has some basic rules. When we track them to their irreducible components, we find what we might call universal axioms. Among these axioms are the activities of recursion, symmetry, and harmony. This holy trinity is the basis for all the activities of mind and matter. And though triangles are themselves discrete mathematical objects that live in the domain of geometry, we can also imagine the essence of triangle-ness extends beyond them, living as a type of what Whitehead would call “eternal object”, reproducing themselves wherever things come into being.
A classical way to discover the universal axioms is through arithmetic and geometry.
Through the ages, the project of Hermeticism, Qabalah, and Pythagorean philosophy is to locate the irreducible and ubiquitous principles of mind and matter or axioms and develop practical means for their application toward the betterment of human life. Hermetic texts like the Kybalion, the Corpus Hermeticum, and Qabalistic books like the Sepher Yetzirah and the Zohar, offer what seem to be just that – detailed accounts of the fundamental laws of nature and a process we must undergo to merit an understanding of them.
In these books, these axioms or cosmic principles are often described in allegorical terms, telling stories about people or describing alchemical recipes that present but also conceal their full meaning. Readers must look deeper into the meaning of the texts, considering them sometimes for years before they reveal their secrets. The Torah, for example, which means the Book of Law is a scripture that describes the blueprint of creation. In it is not only the psycho-spiritual implications for creation coming into being for us personally but through the encoded wisdom of the Hebrew language it also provides the basis for the geometry of space-time and the physical structure of the cosmos.
Contrasting the mythopoetic narratives of spiritual scriptures, esoteric number theory, arithmetic, and geometry are doing the storytelling, and the implications of its propositions are perhaps more thinly veiled – if that is, one understands that the equations, formula, and forms are articulating the numinous dimensions of being and becoming. In esoteric number theory, the maths are the stories, the cosmology is written in the integers directly. How they come into being and how they behave tells many things about the esoteric nature of creation that is otherwise inconceivable.
But this approach to the big questions has its advantages and its weaknesses. On the one hand, this method might lend itself more readily toward the development of reason and logic since it deals with math and number theory. But it might not be obvious that numbers are not merely describing abstract concepts, they’re describing the qualities of being – our being, the relationship of self and other, the nature of perception, love, life, creativity, death, and divinity. Numbers are describing what is possible, how something comes from nothing, and how it could be that as far from the origin of creation we get (zero), we are still embedded within it, reducing and summing to it eternally. The essential nature of divinity is preserved and incarnated in all the myriad forms it brings about.
To peek into the cosmic habits revealed by numbers and geometry and have a look around is no small thing. But when we do, we find astonishing features, nested symmetries, infinite variety coming from basic activities, and something like a subsistent universal and ubiquitous design weaving beauty, harmony, and coherence throughout existence.
One of these cosmic habits is the principle of vibration.
Everything moves, everything vibrates, says the Kybalion.
The law of vibration has a preference for harmony which is a kind of coherence governed by three-ness. Harmonics is a term used in various disciplines including music, physics, acoustics, electronic power transmission, and radio technology. In each of these fields, harmonics is important because it determines the behavior of wave propagation. This means the difference between whether or not the power stays on. Harmonics, put simply, is the law of doubling or halving or two-ness, we could call it. But like a waveform oscillating between two poles, a central axis is there to orient balance and integrate the two poles.As the dualisms of polarity, vibration and gender come into being, its centralizing or synthesis agency comes into being along with it.
Cosmic habits are elegant and ever-present – even beautiful. In a kind of self-similar iteration of inexplicable order, these patterns can be seen everywhere. Or rather, they can be seen at the formative level of everything. From a larger picture, everything is moving toward greater harmony and complexity, and it does so harmonically. Yes, randomness and entropy have their hands in all of it too, but thanks to harmonics, balance is always tilting toward equilibrium and integration.
So why is there so much harmony and symmetry in nature?
How is it that there could be so much order when chaos and randomness seem to be more likely? What is it about the unseen quality of nature that allows it to give rise to coherent complexity which culminates in things like language, music, and art? Ultimately, the principles of arithmetic and geometry are able to point to a meta-narrative because they are themselves an expression of it in the abstract realm of reason.
Our meta-narrative or grand narrative, our story about the universe, what we are, and what IT is, largely defines the nature and quality of perceptions and experience. Our grand narrative decides how we organize our hierarchy of values and meaning, determining what is worth doing and what interpretations of events seem the most reasonable. If we hold an atomistic or materialist’s view of reality exclusively, assigning meaning to existence and even our own lives is pointless. Alternatively, if we see reality as a living organism giving birth to emergent self-organization that aims toward an omega point of super-unity, everything that is and all that happens is interpreted in that broader meta-context and life is ornately and inherently rich with meaning. Most of all, we matter.
Idealism VS. Materialism
We can think of the dualism of idealism and materialism as the thesis and antithesis of the Hegelian dialectical. Idealism is the idea that the fundamental substance of the universe is mental in origin. Materialism conversely is the idea that the fundamental substance of the universe is made of atoms. In idealism, matter comes from a primitive form of consciousness, while for materialists, consciousness comes from atoms. What then is the synthesis view that reconciles these opposite and contradictory views? What type of understanding might reveal a solution to this seemingly irreconcilable paradox? The project of Hermeticism and spirituality or higher development as a whole helps to bring about is a quality of consciousness that includes and transcends the finer points of each of these views.
The synthesis view of reality transcends and includes idealism and materialism in a meta-narrative that can be illustrated in and through the language of esoteric number theory.
From the perspective of a unitive cosmology or coherent meta-narrative, purposefulness and order for the entire universe become so evident that life and love, truth, beauty, and goodness are recognized as the most precious things to value. So precious that everything else is subordinated to it, and all meaning is made in relation to and in service of it. Everything else becomes secondary. This is the meaning of the old Hermetic axiom “Love is the Law, Love under One Will”. This is exactly right for reasons we could spend our entire lives demonstrating. And we will, but along the way, we’ll enrich our perception of the fundamental laws of the universe and correct any of our false notions so that our lens is cleared and something of practical value can be brought to bear on the world’s challenges.
The difficulty is, veiling our view of a fundamental unity is a fundamental duality. Duality gives rise to a near infinite array of paradoxes that are seemingly irreconcilable. Before these paradoxes are transcended, integrated, or healed, the universe and the self appear as fragmentary, divided, or disconnected from a coherent set of patterns and principles that orient us to a larger reality and its inherent order. Duality creates a limit on the mind’s ability to see reality clearly. The project of spiritual development is a process of increasing the depth, complexity, and integration of our awareness to such a degree, a kind of harmonic coherence phase locks, and all the seeming paradoxes are reorganized into a new higher-order symmetry.
“[…] provability is a weaker notion than truth”
― Douglas R. Hofstadter, Gödel, Escher, Bach: An Eternal Golden Braid
Our fragmentary, chaotic, and divisive mode of perception and interpretation give our meaning-making processes a major dose of incoherence. Our science, epistemology, and ontology are confused and conflicted. Material science is separate from the social sciences, general relativity and quantum mechanics don’t match, and no one knows how to integrate them. Panpsychism, the synthesis view that solves these problems, isn’t very popular and still seems to most people like a new form of anthropomorphism or more sophisticated and equally delusional perspective as idealism. So as its stands for most of us, the scales don’t line up, the domains don’t correlate, the equations don’t match, and theories contradict. The upper and the lower, the inner and the outer are seemingly divided and never the twain shall meet. But this perspective can be overcome. The inherent paradoxes and impossibilities can be transcended. And esoteric number theory offers elegant proofs to bring the mind to the threshold of the synthesis view.
Such a project was the concern of Pythagoras who used number theory, natural philosophy, geometry, and gematria to try to understand the underlying structures of creation as a means of authenticating the mythopoetic narratives of mysticism through reason. Because numbers and shapes are a part of the inherent codices of creation, and since they provide a means of investigation that can be objective and rational, esoteric mathematics is exceptional in its ability to illuminate the mind and circumscribe the underlying formative patterns at the root of reality.
In part three, we will further explore the Pythagorean method, investigating three-ness more deeply, and also how three-ness extends into four-ness, building up the complexity of the Great Chain of Being. Click to read part 3
1 + 2 = 3