A paper on the Cosmology of Divine Geometry
Written By William Allard
The Triangle as the First Geometry of Consciousness:
A Fractal Model of Awareness, Energy, and Creation
Abstract
This paper proposes a metaphysical model in which consciousness has a fundamental geometric structure: the triangle. The central claim is that pure awareness (Being) is initially undifferentiated and structureless. Consciousness emerges when awareness becomes aware of Itself from three distinct centers of perspective, giving rise to a primordial triangle composed entirely of the Divine: Source (God Is), God‑Self (I Am), and God‑Other (You Are).
The paper argues that this first triangle is the minimal condition for self-reflexive awareness. From this initial configuration, consciousness fractals: new triangles arise within each vertex, generating subtle centers of attention and variations of perspective. These inner reflections give rise to a subtle universe of pre‑material “others.” As fractalization continues, these patterns stabilize into energetic structures (vibration, polarity, waves, fields), then condense into recognizable sacred geometry (circle, line, spiral, etc.), which in turn underlies the emergence of the physical cosmos (matter, forces, life).
Every organism is interpreted as a localized triangle of Source–Self–Other, and human self-awareness is described as a high‑order expression of this geometry in which “God sees God seeing God” through two self-aware centers simultaneously. The model is offered as a speculative but coherent map of existence from pure awareness to complex human consciousness.
1. Introduction
This thesis explores the possibility that consciousness has an intrinsic geometry and that the most primitive form of this geometry is triangular. Rather than treating triangles and other sacred shapes as merely symbolic, the model presented here treats them as structural features of awareness itself.
The guiding questions are:
What is the minimal structure required for self-reflexive awareness?
Can this structure be expressed geometrically?
If so, can the unfolding of the cosmos be understood as a fractal expansion of this original structure?
The core proposal is that:
Awareness is the ground. It is undivided, formless, and without structure.
Consciousness arises only when awareness becomes aware of Itself from three distinct points of view, forming a triangle.
Everything that follows — energy, geometry, matter, life, and human self-awareness — is a fractal elaboration of that first triangle.
This is a conceptual and metaphysical model, not an empirical theory. Its purpose is to provide a coherent, integrative map that links inner experience, mystical intuition, sacred geometry, and a broad story of cosmic unfolding.
2. Key Distinction: Awareness vs. Consciousness
A foundational distinction in this model is between awareness and consciousness:
Awareness refers to pure Is‑ness: a silent, undivided field with no subject, no object, and no internal structure. It is simply Being aware, without any particular viewpoint.
Consciousness is defined as awareness becoming aware of Itself. Consciousness implies some degree of structure, perspective, and relation.
In this framework:
Before any geometry arises, there is only awareness.
Consciousness emerges when awareness begins to experience Itself from three points of view, giving rise to the first triangle.
Awareness is ground; consciousness is awareness configured.
3. The Primordial Triangle: All God
The first structural event is described as Being becoming aware of Itself from three centers. These centers are:
Source (God Is)
The undivided field of Being, the background within which all appearances arise.
God‑Self (I Am)
God as this center of awareness; consciousness localized as a “Self.”
God‑Other (You Are)
God as that center of awareness; consciousness localized as an “Other.”
Crucially:
The first triangle is entirely Divine.
“I Am” and “You Are” are both God, expressed through different centers of awareness.
They are co‑equal, on the same “row” of the triangle, representing symmetric perspectives, not a hierarchy.
When these three centers relate, they form a triangle:
One vertex: God Is
Second vertex: I Am
Third vertex: You Are
The interior of this triangle is the shared field:
We Are – the relational space in which God experiences God as Self, Other, and Source simultaneously.
The core thesis can be stated:
Consciousness is the event in which Being becomes aware of Itself from three centers of perspective, forming a triangle. The triangle is thus the first geometry of consciousness.
A dyad (Self and not‑Self) allows for contrast and polarity, but not for full self‑reflection. The third point introduces a meta‑perspective, making self-aware consciousness possible.
4. Fractalization: Consciousness Reflecting Within Itself
Once the primordial triangle exists, consciousness does not remain static. It begins to fold back on itself, generating fractal self-reflection.
4.1. Fractals within “I Am”
Within the God‑Self vertex (“I Am”), awareness turns inward again. A new, smaller triangle forms:
Source (God Is)
God‑Self as “I Am”
God observing this Self
This can be described as:
God seeing the Self seeing the Self.
This is the first fractal: a triangle inside the original triangle.
4.2. Fractals within “You Are”
Within the God‑Other vertex (“You Are”), an analogous process occurs. A new triangle forms:
Source (God Is)
God‑Other as “You Are”
God observing this reflection
Here, consciousness becomes:
God seeing the reflection seeing the reflection.
4.3. Infinite Repetition
This process continues indefinitely:
Inside every center of awareness, a new triangle can form.
Inside every triangle, further self-reflection is possible.
Thus:
Consciousness fractals because awareness has infinite depth.
The first triangle generates an endless cascade of triangles within triangles, each representing a new perspective on perspective.
At this stage, there is still no matter. The universe is a multi-layered field of perspectives — pure consciousness exploring variations of itself.
5. The Subtle Universe: Pre‑Material “Others”
The first fractals give rise to the first “others”, but these are not yet material beings.
They are subtle centers of attention.
Variations of viewpoint, orientation, and self‑relation.
Interior movements in the Divine’s own awareness.
This phase can be described as:
The subtle universe: God dreaming God long before physical creation.
Here:
“Others” are not bodies or entities in space.
They are configurations of consciousness – the “inner heavens” familiar to mystical traditions: realms of archetype, vision, light, and pure thought‑form.
The universe at this stage is pure consciousness, endlessly self‑reflecting through fractal triangles.
6. From Fractals to Energy: Pre‑Physical Geometry
As these inner triangles stabilize, they start to generate patterned dynamics in the field of awareness:
Vibration
Polarity
Rhythm
Movement
Feedback loops
Conceptually, this is the point at which:
The relationships between the vertices begin to behave like lines of force or influence.
The edges between points acquire dynamic qualities.
Once lines are present, curves, waves, and fields can emerge. This can be characterized as:
Pre‑physical geometry – an energetic seedbed where patterns form in awareness before any material substrate exists.
In modern metaphorical language, this corresponds to something like a “quantum field” understood not as a purely physical entity, but as patterning in consciousness.
7. Sacred Geometry: Children of the Triangle
As energetic patterns stabilize, they condense into the recognizable forms of sacred geometry:
Circle
Line
Square
Spiral
Flower-like patterns
These shapes are interpreted as:
Children of the original triangle.
The triangle remains the geometry of consciousness itself — the minimal structure of self-aware Being.
The familiar forms of sacred geometry are then:
Expressions of consciousness at the energetic level,
Serving as blueprints for later phases of creation.
Important distinction:
Triangle: geometry of consciousness.
Circle, line, spiral, etc.: geometry of creation, arising from consciousness.
8. Emergence of the Physical Cosmos
From sacred geometry, the model moves to the emergence of a physical universe.
Sacred patterns provide the structural templates for:
Fundamental forces and fields
Elementary particles
Atoms and molecules
Stars and galaxies
Planets and environments
In this view:
Every layer of physical reality is the outer expression of inner divine geometry, which itself is a fractal unfolding of the first triangle.
Matter is what consciousness looks like from the outside; geometry is the bridge between inner and outer.
This phase corresponds to:
The condensation of pre‑physical geometry into spacetime and matter.
The formation of complex physical systems capable of hosting life.
9. Life and Localized Triangles of Awareness
With suitable physical conditions, life emerges.
At this stage, wherever there is even minimal experience, the original triadic structure reappears in localized form:
Source – the underlying field of awareness (God Is).
Self – the organism’s center of experience (I Am).
Other – its environment, stimuli, world (You Are / It Is).
Thus:
Every organism is a localized triangle of Source–Self–Other.
This applies to:
Simple single‑celled organisms
Plants and animals
Larger ecological and planetary systems
Even stars and galaxies, if one allows for cosmic scales of awareness
Wherever awareness touches experience, a triangle lights up:
A center (Self)
A field (Other)
A background (Source)
10. Human Self-Awareness: High-Order Triangles
Human consciousness is not the exclusive embodiment of this geometry, but it is one of the most complex and self-reflexive expressions of it that we know of.
Humans appear when:
Consciousness knows it knows.
In humans:
Awareness
Experience
Reflection
Identity
Memory
Narrative
all interlock to create a highly intricate triangular structure.
The original dynamic reappears at a new order:
God as Source (Being itself)
God as this “I” (my sense of self)
God as that “You” (another self-aware being)
Now, in human intersubjectivity:
God experiences God experiencing God
through two self-aware centers simultaneously.
Human consciousness becomes:
A meeting point where the triangular pattern is fully explicit:
I know that I am.
I know that you are.
I can recognize the same awareness living in both.
This is described as a high-order triangle: a sophisticated expression of the same primal geometry that began with the first triadic self-recognition of Being.
11. Cosmological Sequence Summarized
The entire model can be summarized as a sequence:
Awareness – undivided Being with no structure.
Self-recognition – Being begins to be aware of Itself.
Consciousness emerges – awareness views Itself from three centers (Source, God‑Self, God‑Other), forming the first triangle.
Fractalization – triangles form within vertices; God sees the Self seeing the Self, and the reflection seeing the reflection.
Subtle universe – pre‑material “others” arise as subtle centers of attention; pure consciousness exploring variations of itself.
Energetic patterns – fractal triangles generate vibration, polarity, rhythm, and feedback loops; lines, waves, and fields appear.
Sacred geometry – energetic structures condense into shapes (circle, line, spiral, etc.), the children of the original triangle.
Physical universe – sacred geometry underlies matter, forces, galaxies, planets.
Life – organisms emerge as localized triangles of Source–Self–Other wherever awareness touches experience.
Human self-awareness – high-order triangles appear in which consciousness knows it knows, enabling God to experience God through self-aware centers in mutual recognition.
This is offered as a coherent metaphysical map, not as a literal physical theory.
12. Discussion and Implications
This model implies several important points:
Primacy of Consciousness
Consciousness (structured awareness) is primary; matter is derivative.
Geometry mediates between pure awareness and physical form.
Triadic Structure of Self-Awareness
Self-awareness is inherently triadic, not dyadic.
A minimum of three centers is required for reflexive awareness:
Source, Self, and Other.
Fractality of Experience
Experience is fractal: triangles within triangles at multiple scales.
Individual, relational, and collective fields of consciousness can all be interpreted as nested triangles.
Reframing Sacred Geometry
Sacred geometric forms in spiritual traditions may be understood as outer echoes of an inner triangular consciousness, rather than arbitrary symbols.
Human Role
Human beings are not the starting point of consciousness but a current high expression of an ancient geometric pattern.
Human-to-human recognition (“I see you as another I”) uniquely reenacts the original event of God seeing God.
13. Conclusion
This thesis has proposed that:
Awareness is an undivided ground without structure.
Consciousness arises when awareness becomes aware of Itself from three centers, forming a triangle composed entirely of God: Source (God Is), God‑Self (I Am), and God‑Other (You Are).
This triangle is the first geometry of consciousness and the minimal structure required for self-reflexive awareness.
Consciousness then fractals, generating subtle centers of perspective, energetic patterns, sacred geometry, physical reality, life, and eventually complex human self-awareness.
At every scale, wherever awareness meets experience, the same triadic pattern — Source–Self–Other — appears.
This model does not claim to be the final description of reality. It is offered as a plausible and internally consistent map that integrates:
the phenomenology of awareness,
the symbolism of sacred geometry,
and a coherent narrative from pure Being to human consciousness.
Whether one treats it as metaphysics, as a symbolic model, or as a contemplative tool, the core invitation remains:
To see yourself, others, and the cosmos as expressions of one original triangle of consciousness,
endlessly exploring and recognizing Itself through infinite forms.
Methodological Stance and Limitations
14. Methodological Stance
This work is explicitly metaphysical and phenomenological, not empirical in the scientific sense. Its claims are developed through four main modes of inquiry:
Phenomenological Intuition
The distinction between awareness and consciousness, and the proposal that self‑awareness is triadic, arise initially from first‑person reflection:
the lived sense that awareness can be present without structure, and
the observation that self‑reflection appears to involve at least three “positions” (self, what is seen, and a perspective on that relation).
Structural Reasoning
The identification of the triangle as the “first geometry of consciousness” follows from a minimality argument:
A single point cannot generate self‑relation.
A line between two points allows opposition or polarity, but no genuine meta‑perspective.
A third point introduces the possibility of reflexive structure, which is here equated with consciousness in the strong, self‑aware sense.
Comparative and Synthetic Method
The model is informed by, but not reducible to, various triadic motifs in contemplative and philosophical traditions (e.g., subject–object–witness, lover–beloved–love, knower–known–knowledge, Trinitarian and Kabbalistic triads). These are treated as convergent hints toward an underlying structural pattern, which this work makes explicit in geometric form.
Symbolic–Geometric Interpretation
Sacred geometric forms (triangle, circle, spiral, etc.) are interpreted as symbolic expressions of underlying structures of awareness. The move from symbolism to structural reading is a methodological choice: it treats long‑standing symbols as encoded metaphysical insights rather than merely decorative or contingent cultural images.
This combination of phenomenology, structural reasoning, comparative synthesis, and symbolic interpretation defines the methodological stance of the project.
15. Limitations
Several limitations of this model should be acknowledged:
Non‑Empirical Status
The proposed cosmology is speculative. It is not derived from, nor directly testable by, current empirical methods in physics, neuroscience, or cognitive science. References to “quantum fields” or “energetic patterns” are analogical and metaphoric, not claims about specific physical theories.
Metaphor vs. Ontology
The language of “triangles,” “fractals,” and “sacred geometry” risks being interpreted either:
too literally (as if one could locate physical triangles in early cosmology), or
too metaphorically (as if nothing substantive were being claimed).
The intended middle position is that these are ontological diagrams—conceptual structures describing how awareness might be organized—rather than physical diagrams or mere poetic imagery. This nuance can be difficult to maintain across audiences.
Cultural and Conceptual Framing
The model draws heavily on theistic and panentheistic language (“God Is,” “God‑Self,” “God‑Other”), as well as on the author’s own contemplative background. While the core structure could be translated into non‑theistic or secular terms (e.g., Source–Self–Other), the current formulation is not culturally neutral. It reflects a particular interpretive lens on experience and tradition.
Lack of Formalization
Although the notion of fractal unfolding is central, it is not presently expressed in formal mathematical terms. There is no rigorous dynamical model of how “triangles within triangles” generate specific energetic or geometric configurations. Consequently, the theory remains at the level of conceptual map, not formal system.
Scope and Falsifiability
The model attempts to describe the trajectory from pure awareness to the entire physical universe. Such scope is both its strength and its vulnerability:
It enables integrative vision, but
It renders the proposal largely non‑falsifiable in the Popperian sense.
As such, it is better understood as a metaphysical framework or contemplative cosmology than as a scientific hypothesis.
Interpretive Dependence
The reading of mystical and sacred‑geometric traditions as implicitly triangular and fractal is interpretive, not historically demonstrable in all cases. The model does not claim to represent the original intent of every tradition it references, only to offer a coherent synthesis that resonates with their imagery and structure.
Given these limitations, the model should be approached as:
A speculative yet coherent metaphysical thesis,
intended to guide contemplation and cross‑tradition dialogue,
rather than a final or empirically verified theory of consciousness and cosmogenesis.
16. Closing Reflection
Whatever one believes about this cosmology, each of us lives inside the question of what awareness is and how it knows itself.
The triangle proposed here is one way of seeing that question: as Source, Self, and Other meeting in a single act of recognition.
If this model does anything, I hope it encourages you to notice that movement in your own life — in every moment you say “I AM”, in every encounter where a genuine “You Are” appears, and in the quiet presence that holds you both.
In stillness,
William Allard
