Platonic Solids

God is a visionary artist.  Alex Grey

Hermetic Theory of Creation Series

Part 1: Revealing Secrets of Sumerian Theory of Time
Part 2: Hermetic Theory of Creation: God is an Artist Who Crafted Platonic Solids from the Tapestry of Time
Part 3: Sacred Geometry in Egyptian Myths and the Great Pyramid
Part 4: Messages from the Great Pyramid Builders Conceal Quantum Theory of Space-Time
Part 5: Hermetic Theory of Creation: Understanding Sacred Geometry and the Language of Archetypes
 
 
 

Throughout history, our perceptions of God have been as varied as the lenses through which we view the divine. To the mystic, God stands as an unceasing source of blessings, pouring forth an inexhaustible stream of divine energy that enlivens the spirit. Through the contemplative eyes of philosophers like Hegel, God is perceived as both a logician and philosopher, governing the universe with profound wisdom and order. Meanwhile, to a Master Mason, God emerges as the Master Architect, meticulously designing the grand structures of existence with unparalleled craftsmanship.

Yet, transcending these notions, there lies a profound metaphor awaiting exploration: envisioning God as the ultimate Artist. In this perspective, God isn’t just the creator but the embodiment of creativity itself, crafting the universe with strokes of divinity, imbuing every facet of existence with purpose, beauty, and narrative.

Considering God as the Divine Artist offers a compelling perspective, particularly for practitioners of Hermeticism who rely on the tool of analogy. Just as the human mind progresses through a series of developmental phases – from grasping basic patterns to mastering complex logic and abstract philosophies – so too does the Universal Mind evolve.

Imagine the Universal Mind as akin to a child’s – innocent, ever-expanding, and in the early stages of recognizing patterns and shapes. This fledgling awareness culminates in the creation of archetypal art forms, which serve as the blueprint for the unfolding cosmos, thereby furthering the maturation and intricacy of the Universal Mind itself. Creating art is a common quality, found in young minds and still fascinating to older ones. So, picturing God’s mind like an artist’s makes sense, especially if we follow the Hermetic idea that the core of human thinking comes from God’s nature.

But here arises a beguiling question: where does God, the supreme Artist, derive inspiration from? Embarking on this contemplation propels us into uncharted territories. Artists traditionally seek inspiration from the vibrant world surrounding them, weaving reflections of the external reality into their creations. However, the Universal Mind, the primal artist, exists in solitude, unfettered by external influences, with nothing but itself as a source and canvas of creation. This solitary existence poses a monumental riddle in our quest to understand the divine: deciphering the inspirations and musings of this original Mind before it embarked on the grand voyage of creation. Herein, perhaps, lies the greatest artistic mystery, the genesis of creativity itself, sparked not from external stimuli but from an intrinsic, inexhaustible wellspring of divine inspiration.

In the vast tapestry of existence, if God is the ultimate Artist, then one might wonder what muse could possibly inspire the divine in its act of creation. The answer, paradoxically profound in its simplicity, might be that God draws inspiration from Himself. If God is Time, as some myths and interpretations suggest, then every moment, every instance, and every phase of existence emanates from and returns to Him. Time, often perceived as a linear progression, may in fact be a cyclical dance where the past, present, and future are mere reflections of divine thoughts, evolving and revolving in God’s infinite consciousness.

This cyclical nature suggests that every creation is not an external act but an internal reflection, a reimagining of aspects of the divine self. God, as Time, becomes both the painter and the canvas, the musician and the melody, the writer and the story. The universe then manifests not just God’s artistry but also deeply personal introspection, a perpetual exploration of divine potential and essence. In this boundless loop of creation, God perpetually inspires and is inspired, a timeless artist forever engrossed in the masterpiece of existence, where the distinction between the creator and the created blurs, and all becomes one harmonious symphony of timeless inspiration.

In our upcoming exploration, we will ingeniously interlace two profound models delineated in our previous articles: the model of the artistic mind and the intrinsic structure of time, both perceived as reflections of God’s grandeur. As we venture deeper into this synthesis, we shall seek to unravel the enigma of the cosmos’ first masterpiece, conceived in the mind of the ultimate artist – God. This journey promises to reveal the genesis of the Platonic solids, perhaps the very first tangible expressions of God’s artistic brilliance, forms born from divine meditation within the realms of time itself. Through this integrated lens, we stand on the verge of uncovering a narrative that marries geometry and divinity, shedding new light on the profound artistry encapsulated in the primordial patterns of existence.

 

The Colorful Chronology: Foundational  Model of Time

In this exploration, we will use the Sumerian Theory of Time, reformulating it using the expressive language of colored circles. 

Atoms of Time 

Central to our framework is the “atoms of time”, representing the smallest discernible units of time within the context of comparing two processes. Intriguingly, there are traces that suggest the Greeks once conceived time in a similar atomic fashion, employing the term “atom” as an indicator of the smallest conceivable unit of time

Temporal Palette

How do we juxtapose processes? We operate on the assumption that if a process is N times lengthier than the atomic one, it can be fragmented into N phases. This implies the Mind can uniquely distinguish N distinct stages of the process. The basic atomic process always presents itself as a singular, holistic cycle because the Mind cannot partition it. Subsequent processes, however, can be bisected: the second, being twice as lengthy is represented by two different colored circles, the third by three circles, and so forth.

To mark different phases of processes we will use the language of colors. The idea of the color wheel, pioneered by Sir Isaac Newton, can be harnessed to delineate periodicity through varying hues. Here are color wheels made of 7, 12, and 36 sectors.

Colorwheels

These diverse color wheels offer a vibrant lexicon to demarcate phases of processes spanning different durations. The complete array of our color alphabet, structured in a triangular form, gives rise to the temporal palette. Our experimentation will commence with basic palettes, progressively elaborating them.

Temporal Palettes -Beauty and AI

 

The Temporal Palette furnishes a coherent framework to map distinct phases of periodic processes via colored circles. Nevertheless, the alignment of the temporal palette’s colors can vary. This set of palettes, centered around a specific hue, warrants fine-tuning, reminding us of the potential for diverse tunings. 

Temporal Tapestry & Timewheel 

The temporal palette paves the way for a symphony of concurrent processes, weaving together the temporal tapestry. The foundational architecture of time is essentially a dynamic canvas illustrating concurrent process alterations. Consider processes spanning 1, 2, 3, and 4 atomic periods. Their culmination points are staggered, demanding 1, 2, 3, and 4 atomic periods respectively. To visualize this, we’ll transform the triangle temporal palette into a rectangular graph depicting these processes unfolding concurrently, a concept I’ve dubbed the Temporal Tapestry. This synchronization paints the very fabric of time.

Temporal Tapestry -Beauty and AI

Our focus gravitates towards a cycle where all processes wrap up in harmony; this occurs over 12 atomic periods. Post 12 cycles, this pattern is replicated.  To encapsulate the cyclical nature of these processes accurately, the temporal tapestry can be transposed into a circular format, giving birth to the Timewheel.

Timewheel - Zodiak

For clarity, I’ve removed the atomic layer that does not contain any alterations. Upon closer inspection of the patterns on this timewheel, the Zodiac sign classifications are evident. The inner circle differentiates between positive and negative zodiac signs, the outer circle groups zodiac signs by elements, while the central circle categorizes them as cardinal, mutable, or fixed.

In the realm of Hermetic philosophy, the Zodiac is perceived as a foundational pattern that echoes through the very fabric of the cosmos. This remarkable schema seemingly finds its mathematical echo in a modest yet profound model of time.

By generating a timewheel from the temporal palette of the form (1, 2, 3), we will uncover a hexagonal pattern:

Hexagon Timewheel

Explore the intricate patterns embedded within this time wheel. When you endeavor to connect circles of the same color through linear paths, you unveil three axes and two interconnected triangles. The three axes delineated by the outer circle become the axes of reflection symmetry for the figure within the inner circle. The hexagonal pattern is the germ from which the three-dimensional Euclidean space emerges.

In the intricate world of Hermetic philosophy, a tradition steeped in the recognition of patterns and analogies, this unique structure of the hexagon holds a potential role as a blueprint of life.  The Zodiac pattern too is perceived as a foundational pattern that echoes through the very fabric of the cosmos.

Expanding the temporal palette naturally leads to the evolution of both the temporal tapestry and its corresponding timewheel. For instance, incorporating a process with a duration of five atomic units culminates in a full cycle realized in 60 steps. Subsequent inclusion of a process with a periodicity of 6 maintains the 60-step cycle, unveiling a fascinating correlation.

Temporal Tapestry 60

Herein lies the rationale behind the Sumerians’ adoption of the numbers 12  and 60 as time measurement units. These numbers crystallize naturally from the structured development of a time model built upon a sequence of processes with incrementally increasing periods (1, 2, 3, 4), and its subsequent expansion to incorporate processes with periodicities of 5 and 6.

The concepts of the Temporal Palette and the Temporal Tapestry reveal the key numbers the Sumerians used for dividing time. Here is a concise summary of our discoveries. Each important number stems from a specific form within the temporal palette:

 

Model of the Universal Mind

The principles of an artist’s mind were explored in the article, Science of Art: The Artisan Theory of Mimetic Truth, Meaning, and Beauty. The theory is centered around the concept of pattern, with Harmony defined as a set of patterns inherent in a system. The core proposition of the theory is that an artistic mind aims to create art forms that embed patterns significant to the artist. This theory was articulated using the language of Abstract Geometry

To effectively convey our theory of creation through the lens of colored circles, we must reformulate the principles of an artist’s mind in a simplified manner.  Here, we’ll translate those ideas into an accessible and precise language. The term Form will be used flexibly to depict both abstract geometric shapes and the intricate patterns within these shapes. Let’s adapt the fundamental principles guiding an artist’s cognitive processes to the Universal  Mind drawing inspiration from Temporal Tapestry: 

These creative principles, when distilled and attributed to the Universal Mind, illuminate a model through which the Universal Mind could interact with a temporal tapestry composed of colored circles. For the purposes of this article, these rules have been simplified. In future discussions, we plan to extend this set of rules by adding two more.

The sneak preview of the application of these rules is as follows. Applying the Rule of Pattern to the temporal tapestry reveals patterns like Duade, Triade, Tetrade, and so on. The Rule of Identity breathes life into these patterns, transforming them into standalone entities, laying the foundation for more intricate constructs. For instance, through the Rule of Creation, the Universal Mind envisions a pyramid, symbolizing the Tetrade, crafted from four Triades. We will illustrate how the five Platonic Solids emerge as divine artwork.

 

God’s Artworks: The Building Blocks

Temporal tapestry unveils a rich array of patterns manifesting the inherent symmetries in time. The initial row epitomizes unity, a state of constancy that invariably preserves its essence. Following this, the second row embodies duality, illustrating a rhythmic alternation between two polar opposites and exemplifying pure reflectional symmetry.

Temporal Palette 12

Let’s shift our attention to a distinctive pattern that is apparent in the third row of the temporal tapestry. Initially, we observe a pattern characterized by rotation. The following illustration displays every possible rotation of the rows of colored circles observed in the third row.

triangle rotations

Reversing our reading direction reveals a reflection effect, showcasing another dimension of the triangle’s complexity. We have three reflections displayed in the subsequent illustration.

triangle reflections

Amazingly, the symmetries we observed in the third row correspond to the rotational and reflectional symmetries of an equilateral triangle. The essence and the beauty of an equilateral triangle inherent lies in its symmetries – three reflectional axes and three rotations. 

triangle

 

A triangular form crystallizes as a compact representation of all these intricate symmetries woven into the temporal tapestry.

triangle artwork

 

Thus, the triangle is a Divine Artwork that reflects various patterns and symmetries observed in the third row of the temporal tapestry. The creation of this artwork emerges from the Mind’s desire to express artistic truth, drawing from the Mind’s experience.

triangle

As per the Rule of Identity, this form assumes a distinct identity, characterized by a unique pattern that can be used to dissect the temporal tapestry, facilitating the creation of multiple triangles. The third row of the temporal tapestry, with a length of 12, can be dissected into four distinct triangles. If the tapestry is made out of atoms of time, we can envision these primordial art forms as molecules of time, each composed of three atoms. 

4 triangles

Having observed the creation and extraction of patterns from the rows of the temporal tapestry, our focus now shifts to the fourth row. By applying the same methodology, we see squares materializing as distinct entities.

square

Within the 12-unit segment of the tapestry, we can discern the presence of 3 individual squares.

It’s crucial to understand that the triangle and square shapes arising from the temporal tapestry aren’t the familiar triangles and squares of Euclidean geometry. Instead, they represent molecules of time, proto-forms best captured by Abstract Geometry. The Euclidean space we recognize comes forth at a later stage of creation, a result of the intricate evolution and amalgamation of these foundational primordial forms.

The Tetrahedron: A Manifestation of Divine Artistry

Let’s journey into the realm of artistic creation, focusing particularly on the use of triangles. Imagine fashioning a triangle from three of the triangles we have on hand. By weaving together these three triangles, and drawing inspiration from one, a tetrahedron takes shape. This intricate structure manifests from triangles, each reflecting the overarching theme of the triangle itself. Within the context of Abstract Geometry, we can perceive the tetrahedron – composed of three interconnected triangles – as an embodiment of the abstract triangle.

tetrahedron

The tetrahedron is a remarkable artwork, epitomizing profound harmony. Once we unite the three triangles in the likeness of the third, it becomes evident that each component used for construction is indistinguishable from the inspirational source. This results in the emergence of multiple symmetries.   

tetrahedron

At this point, we have the capability to construct a four-sided pyramid, representing a square formed from triangles. However, the depth and significance of this topic warrant its own dedicated article.

 

Octahedron and Cube: The Embodiment of Duality and Symmetry

Both octahedrons and cube are artistic depictions of hexagonal patterns, the  timewheel obtained from the temporal palette of the form (1, 2, 3). The cube represents the vertices of the hexagon as squares. The octahedron represents vertices of hexagonal form as its own vertices. 

To craft the octahedron and cube, we need a rich canvas – a temporal tapestry boasting a length of 24, from which eight triangles and six squares can be extracted. 

The octahedron can be also visualized as a cube morphed from six triangles, or alternatively, as two pyramids, their bases united to demonstrate polarity. A closer inspection reveals even more pyramidal pairs hidden within, illustrating the principle of triple oppositions through its structure. 

The cube can be considered as four squares connected in an image of a square. The cube can be construed as an octahedron created out of squares. 

Both an octahedron and a cube are divine masterpieces. Not only portrays a splendid array of mappings but stands as a testament to the grandeur of geometric artistry. 

cube and octahedron

 

Dodecahedron and Icosahedron: Cosmic Correspondences

Consider a temporal tapestry generated by a temporal palette in the form of (1, 2, 3, 4, 5), which spans a length of 60 units. The symmetries observed in the tapestry’s fifth row enable us to construct a novel geometric figure: the pentagon.

The temporal tapestry’s precision is truly awe-inspiring. With a length of 24, it furnishes just the right number of triangles and squares to construct both the octahedron and the cube – two inherently dual forms. The marvel deepens when we consider a temporal tapestry of length 60, stemming from a temporal palette shaped as (1, 2, 3, 4, 5). It yields the precise number of triangles and pentagons necessary to assemble two other dual Platonic solids: the dodecahedron and the icosahedron.

Historical discourse often links the dodecahedron with the zodiac. This association posits that the dodecahedron, as conceived in the divine mind of God, serves as an artistic embodiment of the zodiac pattern. Within our framework, the Zodiac is the timewheel generated by the temporal palette (1, 2, 3, 4). Here, each pentagon elegantly symbolizes a zodiac sign. Given the tapestry’s composition of twelve pentagons and twenty triangles, we can seamlessly mold both the dodecahedron and the icosahedron. These two solids, while distinct, serve as artistic reflections of one another through their individual geometric facets, underscoring their duality.

dodecahedron and icosahedron

Geometry is Crystallized Time

Many authors have highlighted the intricate relationship between music and geometry. Among them, polymath Robert Edward Grant stands out for frequently stating in his podcasts that geometry is crystallized music.  However, Time itself can be seen as the ultimate maestro, crafting the most profound music of all: the silent symphony of creation, woven into the tapestry of time. Extending Grant’s assertion, we propose a deeper conjecture: geometry is the crystallized form of Time itself.

Starting from the Sumerian numerical foundations for measuring time -12, 24, and 60 -we find remarkable correlations within the temporal tapestry:

These parallels cannot merely be chalked up to chance. We decipher them by venturing into a theory of creation wherein God functions as the supreme artist. By distilling the intricate model of the artistic mind discussed in  Science of Art: The Artisan Theory of Mimetic Truth, Meaning, and Beauty, we present a streamlined framework, predicated on three foundational rules. This trinity of rules elucidates the genesis of Platonic solids from the temporal tapestry, portraying them as God’s pioneering artistic expressions. 

In this framework, Platonic solids aren’t just forms within Euclidean geometry; they’re better understood as fundamental ‘molecules’ of time when viewed through their vertices and connectivity relations. In essence, geometry is crystallized time.

The abstract mathematical model constructed in this article could potentially serve as a foundation for developing a Quantum Theory of Space-Time. This model is in harmony with the Causal Set Theory approach to Quantum Gravity, which asserts that spacetime is fundamentally discrete. According to this theory, the structure of spacetime is optimally represented as a set of events, interconnected by a causal relationship. Consequently, the relationship between time and space delineated in our abstract model resonates with the principles of the Causal Set Theory approach to Quantum Gravity.

In conclusion, our inquiry has achieved a significant milestone by harmoniously integrating the Sumerian Theory of Time with the metaphor of God as the Supreme Artist. By doing so, we have successfully derived key Hermetic archetypes, particularly those correlated with the numerals 6 and 12, and traced the genesis of the Platonic Solids back to the earliest acts of Divine creativity. This synthesis not only validates and enriches longstanding Hermetic wisdom but also lays the critical groundwork for a comprehensive Hermetic Theory of Creation.

Our investigation has uncovered a mathematical model where spatial forms are constructed from a temporal tapestry – a one-dimensional structure representing time. The concept that continuous spacetime emerged from a discrete structure is not new, allowing us to easily visualize how geometric forms built from temporal tapestries can grow and solidify into forms of Euclidean geometry. This concept permits the envisagement of the creation of 2D, 3D, and 4D worlds built from temporal tapestry.

Could this model inform the construction of a new physical theory?  This perspective theory would include the Mind as a central entity that constructs Space from Time. It will recognize fractal patterns like Platonic Solids occurring at various scales, from temporal molecules to the shape of the Universe. Furthermore, it will incorporate the Hermetic principle of analogy – as above, so below – affirming the consistency between the macrocosm and the microcosm in this structured universe.

Pyramid

 

 

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