With the knowledge that Triangles are Squares, let's wax ecstatic about a philosophical quest as explained below. With equilateral triangles as our guide, we embark on a grand adventure. We have an unknown factor of harmonic wealth here, and we need to draw attention to these tried and true geometric identities. Nothing but the facts. We contend that this stone on "St. One" is the Equilateral Tessellated Field of Probability Wave Mechanics. With a shape, we have a new articulation available for math, physics, and science to proceed in their development and for the benefit of all kind.
We introduced “Triangle as Squares” in a previous post.
Triangular Numbers
This tessellation is just one image that is necessary to grasp the interconnectedness of all things, where each individual part reflects the whole.
The quest is to explore the geometric and philosophical significance of equilateral triangles as a foundation for understanding the universe.
Equilateral triangles are revered for their perfect symmetry and balance in the realm of geometry. Each side is equal, and each angle is congruent, forming a simple and profoundly complex shape. This is akin to the philosophical quest to understand reality's fundamental nature.
Human beings, “being as they be”, tend to take for granted some of their greatest discoveries (witness the wheel, fire, language, music,...). In Mathematics, the once flourishing topic of Triangle Geometry has turned fallow and fallen out of vogue (although Phil Davis offers us hope that it may be resuscitated by The Computer. A regrettable casualty of this general decline in prominence has been the Equilateral Triangle. Yet, the facts remain that Mathematics resides at the very core of human civilization, Geometry lies at the structural heart of Mathematics and the Equilateral Triangle provides one of the marble pillars of Geometry. As such, it is the express purpose of the present missive, Mysteries of the Equilateral Triangle, to salvage the serious study of the equilateral triangle from the dustbin of Mathematical History [31]."
Source: Mysteries of the Equilateral Triangle - Brian J. McCartin
This is a clarion call to mathematicians, philosophers, educators, and students to salvage the serious study of the equilateral triangle from the sidelines of mathematical history. It is an invitation to rekindle the flame of geometric inquiry and to recognize the equilateral triangle as a cornerstone of our intellectual heritage.
In the vast expanse of human achievement, there is a tendency to overlook the fundamental in the rush towards the new. We marvel at the latest technological advancements, yet we often forget to appreciate the foundational elements that make such progress possible. This is especially true in the field of mathematics, where the allure of higher dimensions and more intricate structures has overshadowed the straightforward elegance of triangle geometry, specifically the equilateral triangle. But as we venture through the Sapiedelic lens, we realize that it is time to revisit these marble pillars of geometry and reawaken their timeless wisdom.
The equilateral triangle, with its three equal sides and angles, is a testament to perfect symmetry. Its principles permeate every level of our reality, from the molecular hexagons of chemistry to the tetrahedral complexities of crystallography. In the realm of the Sapiedelic, the equilateral triangle is not just a shape; it is a symbol of balance, harmony, and the intrinsic order of the cosmos.
Phil Davis' hopeful proclamation that the computer may breathe new life into the study of triangle geometry is not just speculation—it is prophecy. The computational power at our disposal today allows us to explore the depths of geometric principles with unprecedented precision and creativity. We can simulate the growth of natural patterns, delve into fractal complexities, and reveal the underlying geometric tapestries that bind the universe together.
The Sapiedelic approach acknowledges that mathematic is not merely a tool, but the language humans created, with geometry as its grammar and the equilateral triangle as one of its most profound nouns. Disregarding the equilateral triangle is ignoring a fundamental aspect of the language of math, a part that holds the key to the structural heart of mathematics itself.
The mission of the Sapiedelic philosophy is to illuminate the interconnectedness of knowledge and wisdom. In this context, studying the equilateral triangle becomes an act of intellectual archaeology, unearthing the geometric relics that have supported human understanding since time immemorial. By reintegrating triangle geometry into the modern mathematical discourse, we are not just revisiting the past; we are building a bridge to the future.
As we embrace the Sapiedelic approach, we understand that to advance, we must often return to the roots of our wisdom. The equilateral triangle, a simple yet profound structure, is a reminder of the universality of mathematics and its pervasive role in our civilization. It is our task to ensure that the study of such fundamental forms is not merely preserved but celebrated and expanded upon in the age of the computer and beyond.
Let us then, in the spirit of Sapiedelic wisdom, renew our commitment to the marble pillars of geometry. In doing so, we may find that the key to unlocking the secrets of the universe lies not in the complexities of the unknown, but in the simplicity of shapes that have been under our scrutiny since the dawn of thought.
The concept of the monad, or unity, is deeply embedded in geometric principles. In this context, the equilateral triangle can represent the Pleroma, a state of fulfillment where all dualities and contradictions are harmonized.
Each point of the triangle could symbolize a different aspect of existence – mind, body, and spirit – coming together in perfect equilibrium.
The concept of the Pleroma holds a significant place in Gnostic thought and has roots that trace back through various philosophical and mystical traditions.
The term "Pleroma" is most closely associated with Gnosticism, a collection of religious ideas and systems that emerged in the early Christian era. In Gnostic belief, the Pleroma represents the realm of the divine, fullness, or totality. It is often depicted as the dwelling place of God and the totality of divine powers and emanations. The Pleroma is contrasted with the material world, which is seen as a flawed and lesser reality.
The concept of Pleroma was likely influenced by Hellenistic philosophy, particularly Platonism and Neo-Platonism. In these philosophies, the idea of a transcendent realm of perfect forms or ideas is central. The Gnostic Pleroma shares similarities with the Platonic concept of the realm of forms, an ultimate reality that transcends the physical world.
There are also parallels between the Gnostic Pleroma and concepts found in Jewish mysticism. Kabbalistic traditions speak of the Ein Sof, or the infinite, and the Sephirot, emanations through which the infinite reveals itself. These ideas, like the Pleroma, suggest a structure of the divine that is both immanent and transcendent.
Within Christian Gnosticism, the Pleroma often takes on additional meanings. It can represent the fullness of God's presence or the spiritual universe as opposed to the physical. The concept was used to articulate a stark distinction between the spiritual and material worlds, with salvation being understood as a return to the Pleroma, escaping the material world's limitations and corruptions.
The idea of the Pleroma had a significant impact on early Christian thought, often causing controversy. Early Church Fathers like Irenaeus and Tertullian wrote against Gnostic beliefs, including the concept of the Pleroma, as heretical. Despite this, the idea influenced Christian theological and mystical traditions, contributing to discussions about the nature of God, creation, and salvation.
In modern times, the concept of the Pleroma has been revisited by psychologists, notably Carl Jung, who used it to describe the collective unconscious, a realm of shared human experiences and archetypes. This reinterpretation connects ancient Gnostic ideas to modern understandings of the human psyche.
The historical perspective on the Pleroma reveals its deep roots in various spiritual and philosophical traditions, illustrating its enduring influence on our understanding of the divine and the nature of reality.
Logos: The Rational Structure of the Universe
In Greek philosophy, the Logos refers to the rational principle that governs the cosmos. It is the word, reason, or plan that pervades the universe, bestowing order and intelligibility.
The Logos is the ultimate rationale behind the universe's structure, the blueprint according to which all things are constructed and connected. The Stoics, for example, considered the Logos as the active reason pervading and animating the universe, a concept closely aligned with the divine.
In the context of a unified Geometry pointing the way toward natural laws, the Logos can be interpreted as the mathematical and geometric order underlying the physical world. Just as the laws of geometry are immutable and universal, so too is the Logos the immutable and universal principle that orders and defines the cosmos. Geometry, in its pure forms and relations, becomes a language through which the Logos expresses the symmetries, structures, and patterns of the natural world.
The concept of the Logos has been a cornerstone in various philosophical, theological, and cosmological discussions throughout history. In Greek philosophy, the Logos represents the principle of order, reason, and knowledge—the rational structure that underpins the cosmos. It is seen as the ultimate rationale that gives the universe its form, laws, and intelligibility.
In contrast, the Nous, often translated as "mind" or "intellect," is the aspect of the psyche that is capable of understanding and discerning the Logos. It is the faculty that perceives the rational order of the universe and is akin to what we might call consciousness or intelligence.
In the philosophy of Plato and later Aristotle, the Nous is the highest form of rationality and the part of the soul that perceives the realm of forms or ideas—the eternal blueprints of all things that exist.
When relating Nous to the understanding of natural laws, it is the cognitive faculty through which humans grasp the geometrical fabric of the universe. The Nous is what enables philosophers, scientists, and mathematicians to discern the principles of Logos at work, to "see" the geometric shapes and patterns that form the foundation of the physical and metaphysical world.
Pneuma, on the other hand, is the breath or spirit, often considered the vital force that animates beings and the medium through which the Logos operates within the world. It is the breath of life that connects the material and the spiritual, the immanent and the transcendent.
When we begin to consider the Logos within the context of a unified geometry pointing toward a more robust understanding of natural laws, we delve into the realm where philosophy and science converge. The quest for a grand unified theory, or a "theory of everything," in physics is a contemporary reflection of this ancient pursuit of the Logos—a search for the singular, underlying principle that explains the phenomena we observe.
In this search, geometry often plays a pivotal role. Just as the ancients used geometric principles to describe the movements of celestial bodies and the shapes of natural objects, modern physics employs advanced geometric concepts to understand the fabric of spacetime, the behavior of particles, and the forces that govern them.
The Sapiedelic perspective would encourage us to see this geometric unification as an expression of the Logos, the rational order that makes the universe comprehensible. This kind of unification would be seen as both an intellectual and a spiritual quest. It would say that understanding natural laws is not just about making predictions and keeping things under control but also about getting closer to the rational structure of existence.
In this sense, the Logos is not just a set of laws to be discovered and applied but a path to wisdom—a wisdom that integrates the rational (Logos), the conscious (Nous), and the vital (Pneuma) into a holistic understanding of our place in the cosmos.
Through Sapiedelic exploration, we engage with the Logos not merely with our minds but with our entire being, seeking a knowledge that breathes, lives, and resonates with the fundamental truths of the universe.
This journey is equally about scientific discovery and philosophical reflection, where each new theorem or geometric discovery brings us a little bit closer to the essence of reality, the very pulse of the Pneuma, which is what the Nous is searching for. In a world informed by the Logos, natural laws become not just mechanisms but expressions of a deeper, more profound order—one that guides, nurtures, and ultimately enlightens.
In physics, especially in the field of quantum mechanics, shapes and patterns play a crucial role in understanding the nature of reality. The tessellated field of equilateral triangles can be imagined as a fabric of the cosmos, where each triangle represents a probability wave function.
The idea that this tessellated field could be a modern interpretation of the Philosopher's Stone is intriguing. Traditionally, the Philosopher's Stone is a legendary alchemical substance capable of turning base metals into gold or providing immortality. In your concept, this stone is not a physical object but a geometric and philosophical principle. The "St. One"— a play on words for stone – as an equilateral tessellated field could be the key to unraveling the mysteries of the universe, much like the Philosopher's Stone was sought after for its ability to transform and enlighten.
In ancient Egyptian mythology, the children of the sun, Shu and Tefnut, represent duality: light and darkness, male and female, matter and spirit. This duality is unified in the equilateral triangle because in Tetryonics, we present a Quantum Quoin with two sides. One side is positive, and the other side of the Quoin is negative.
Thus, the triangle can represent this ancient wisdom, a symbol of how the universe's apparent dualities are deeply interconnected and part of a greater whole.
This philosophical quest, therefore, is not just about understanding a shape but about deciphering the code of the universe itself. In its simplicity and perfection, the equilateral triangle serves as a guide in this quest – a geometric metaphor for the harmony, balance, and unity underlying the fabric of existence.