The Soul and Sacred Geometry — The Spiritual Symbolism of a Point
“A point is that which has no part.” — Euclid, The Elements, Definition 1 (c.300 BCE)
Introduction
In this article, we use the “language” of sacred geometry to examine the spiritual symbolism of a single point in space. This is fundamental to an understanding of how sacred geometry teaches us spirituality. It is something that requires much study and meditation, but this time is well spent. Understanding this principle is like opening a door into heaven as from these pregnant principles, so many new ones are naturally born. An earlier related article to the ideas expressed in this article can be found at the below link:
Euclid and His Book The Elements
Euclid, often referred to as the “Father of Geometry,” was a Greek mathematician active in Alexandria, Egypt, around 300 BCE. He is most famous for his work “The Elements,” a comprehensive compilation and systematization of the mathematics known in his time. This work profoundly influenced the development of mathematics and philosophy.
“The Elements” is a collection of 13 books, each focusing on different aspects of mathematics. These mathematics also contain principles of logic that can be applied to any other school of thought, any science, to universal aspects of spirituality. For example, it was used by US President Abraham Lincoln to help him provide the legal principles to abolish slavery.
The first six books cover plane geometry, establishing the foundational principles and methods still taught in geometry classes today. Books 7 through 9 deal with number theory, including prime numbers and the Euclidean algorithm for finding the greatest common divisor. The remaining books delve into topics like irrational numbers and solid geometry.
Euclid’s approach in “The Elements” is highly systematic and logical, beginning with a set of definitions, postulates, and common notions (axioms). From these, he deduces a vast array of theorems and propositions. His method of rigorous proof and logical deduction not only influenced mathematics but also the development of logic and philosophy.
Euclid’s influence is enduring. “The Elements” remained a fundamental textbook in mathematics until the late 19th or early 20th century, illustrating its remarkable longevity and impact. The work is not just a collection of known mathematics of its time but also a teaching model demonstrating the power of an axiomatic system and deductive reasoning. Many believe that “The Elements” is the most beautiful textbook ever written.
The Foundation of Geometry is Found in the Point
Definition 1 of Euclid’s “Elements” states: “A point is that which has no part.” This foundational definition is crucial for the entire structure of Euclidean geometry. It serves as a fundamental building block upon which further concepts and constructions in geometry are based.
In essence, a point, as defined by Euclid, is an abstract concept representing a precise location in space. It is dimensionless, having no length, width, or depth. This simplicity and abstractness allow for the development of more complex geometric concepts. For instance, a line is conceived as a breadthless length determined by two points, and a plane is described as a flat surface extending infinitely in two dimensions, made up of an infinite array of points.
This definition of a point underpins the logical structure of “The Elements.” By starting with the most basic and undefinable notion in geometry, Euclid sets a solid foundation for a systematic and rigorous exploration of the subject. This approach reflects the essence of mathematical abstraction and precision, where complex structures are built upon simple, well-defined concepts. The influence of this method is seen not only in mathematics but also in the development of logical reasoning and scientific methodology.
Limitations and Infinite Possibilities
“The straight lines and angles of geometry symbolise the limitations of our physical world, while the curves and circles symbolise the infinite possibilities of the spiritual realm.” — Hasidic teaching.
The above quote serves us well at the start of our journey to link the symbolism of geometry with spirituality. It is a beautiful illustration of how mystical or spiritual traditions often use mathematical or geometric metaphors to convey deeper philosophical and spiritual truths. This particular Hasidic teaching contrasts the straight lines and angles of geometry with curves and circles to symbolize the differences between the physical and spiritual worlds.
In this context, the straight lines and angles in geometry can be seen as representing order, certainty, and the finite nature of the physical world. They have definite measurements, clear beginnings and ends, and predictable relationships with each other. This can be seen as a metaphor for the physical world we inhabit, which is governed by the laws of nature, has clear physical boundaries, and operates within the limits of time and space.
On the other hand, curves and circles are used to represent the spiritual realm. A circle, with no beginning or end, can symbolize infinity and eternity, concepts often associated with the spiritual or divine. Curves, which can extend indefinitely and take on various forms, may symbolize the boundless and unpredictable nature of the spiritual realm. This contrasts with the more rigid and predictable nature of straight lines and angles.
This teaching reflects a broader theme in many spiritual and mystical traditions, where the seen (physical) and unseen (spiritual) worlds are contrasted, each with its own set of principles and realities. In Hasidic thought, there is often a deep exploration of these dual aspects of existence, with teachings that encourage finding spiritual significance and connection in everyday life.
Moreover, the use of geometric symbolism aligns with a long history of geometry being used as a tool for understanding and describing the cosmos and its underlying order, both in scientific and spiritual contexts. The teaching thus acts as a bridge, connecting the rational, structured world of geometry with the more intuitive, boundless realm of spirituality.
The Point as Origin And Return Of All Things
From a spiritual perspective, a point can be seen as a metaphor for the singularity of the universe’s origin or the unity of the divine essence, which is indivisible and fundamental.
Modern Physics and the Universe
In physics, higher dimensions are visualised in string theory and quantum dynamics as existing in ever smaller spaces and times. Loop quantum gravity aims to reconcile quantum gravity and general relativity and posits that at source, time and space are granular, beyond which they cannot be further divided. Therefore we have a paradox that an infinite dimension can contain all of time and space whilst at the same time representing in nature the smallest measure of time and space. Put another way, “everything is in nothing everywhere always.” This is both a simple principle of nature and, at the same time, a deeply spiritual concept. This concept is also the foundation of Jewish mysticism in Kabbalah.
We explored these ideas earlier:
Let’s simplify and expand these complex speculative ideas by referencing scripture and using the simplicity and truth found in the geometry of the point in space and how it can be “moved” to create lines and curves.
Creating a Circle and Sphere
From a Point to a Circle: A circle is defined by Euclid as a plane figure contained by one line (the circumference) such that all straight lines drawn from a certain point within it to the circumference are equal. This point is the centre. Put another way, a point of infinite dimensions, which contains all of time, space and spirit, can show its boundary in the symbolism of the circle. This is at the heart of geometry as an art that can be applied to the study of universal spiritual truths.
Spiritually, the circle, with no beginning and no end, can therefore represent the eternal nature of the divine, as found in the Bhagavad Gita: “Unborn, eternal, everlasting, ancient, it is not killed when the body is killed.” Possible links to Platonic and Neoplatonic concepts of the soul can be made here, such that the individual soul is a part of this whole but expressed by its limitations.
From a Circle to a Sphere: A sphere is a three-dimensional body whose surface is at all points equidistant from the centre, like the Earth. In spiritual terms, the sphere can symbolize the universe or the totality of existence. In Buddhism, the concept of the Dharmadhatu represents the world as it is, a complex, interdependent network of phenomena without a beginning or end.
Lines Created From Circles
The simple yet profound concepts in this geometry can be found throughout the history of religion and spirituality in all civilisations. It therefore provides us with a window into more universal spiritual ideas aside from areas of conflict found between religions and their cultures.
Thale’s Theorum
Thales’ Theorem, as integrated into Euclid’s “Elements,” (and is mentioned and proved as part of the 31st proposition in the third book) provides a fascinating intersection between geometry and spiritual principles. According to the theorem, when three points (A, B, and C) form a triangle on a circle, and the line AC is the diameter of that circle, the angle ∠ ABC is always a right angle.
Put another way, line AC represents the idea of opposites (in logic thesis and antithesis), and point C is a synthesis of these. In this geometry, we find the synthesis (or reconciliation) of all opposites is a square. This geometric fact can be seen as a metaphor for deeper spiritual principles.
Harmony and Balance: The right angle, a cornerstone of geometric principles, symbolizes harmony and balance. In the context of Thales’ Theorem, this right angle arises naturally when the conditions are met — a reflection, perhaps, of a universal truth in spirituality: when certain conditions of balance and harmony are met, natural order and rightness emerge. This can be likened to the Buddhist concept of the Middle Way, a path of moderation away from the extremes of self-indulgence and self-mortification.
Unity within Duality: The circle and the diameter line can represent two fundamental spiritual concepts — the eternal and the transient, respectively. The circle, with no beginning or end, symbolizes the eternal, infinite nature of the universe or the divine. The diameter line bisecting this circle represents the transient, material world that exists within the eternal. Thales’ Theorem shows that these two realms interact to create a perfect right angle, suggesting that the material and spiritual worlds are not separate but rather coexist in a state of dynamic balance.
The Meeting of Heaven and Earth: The triangle created by points A, B, and C can be seen as a symbol of the trinity found in various religious traditions — for example, the Christian Holy Trinity of the Father, Son, and Holy Spirit. The point where the triangle touches the circle’s circumference (point B) can be seen as the meeting point of the divine (the circle) and the material world (the triangle), reminiscent of the Biblical Jacob’s dream of a ladder reaching heaven, a place where the divine and earthly realms meet.
The Emergence of Order from the Cosmic Circle: The inscribed right triangle within the circle in Thales’ Theorem can be viewed as the emergence of order, structure, and understanding (the triangle) from the cosmic and infinite (the circle). This aligns with the Kabbalistic idea of the sefirot, emanations through which the Ein Sof (the Infinite) reveals itself and continuously creates both the physical and spiritual realms.
Interconnectivity: Just as Thales’ Theorem shows a specific, predictable relationship within a circle, it can remind us of the interconnectivity of all things. This principle is echoed in Hinduism, where the concept of Indra’s Net reflects the idea that everything in the universe is interconnected.
In summary, Thales’ Theorem is not only a statement about geometry but also reflects profound spiritual truths about balance, unity within duality, the meeting of the divine and the earthly, the emergence of order from the cosmos, and the interconnectivity of all things. This illustrates how mathematical principles can provide a rich language for expressing and exploring spiritual concepts.
Creating a Line, Plane, and Solid
From a Point to a Line: Euclid defines a line as “length without breadth,” which is determined by two points. These two points can represent the movement of the origin. The human soul is seen as a microcosm of the infinite, which lives in the space and time created in the universe. The spiritual analogy here could be drawn from the Biblical concept of “the path” or “the way.” For instance, Proverbs 4:26 says, “Ponder the path of your feet; then all your ways will be sure.” The line represents a journey from one point (origin) to another (destination), symbolizing life’s journey, moral decisions, or spiritual growth.
Applying Thale’s theorum to this “path” or “way” tells us that the natural (“healthy”) consequence of moving through life is the harmony created by an ethical and just life. This concept of natural justice is explored in two earlier articles:
From a Line to a Plane: Extending this, a plane in geometry is a flat, two-dimensional surface extending infinitely. In spiritual terms, this can represent the expansion of consciousness or the broadening of understanding. It’s akin to Jesus’s teaching in the New Testament, “Love your neighbor as yourself” (Matthew 22:39), suggesting an expansion of one’s circle of concern beyond the individual to include others. More on these principles in the below article:
From a Plane to a Solid: In geometry, solids are three-dimensional figures formed by planes. The spiritual interpretation of this could relate to the concept of the material world. In the Old Testament, the creation of the world is described in Genesis, symbolizing God’s transformation of the void into a structured, physical reality.
Integrating Geometry and Spirituality
In both geometrical and spiritual constructions, the progression from a point to more complex forms mirrors the journey from simplicity to complexity, from unity to diversity, and from the essence to the manifestation. This journey is echoed in various philosophical and religious texts. For instance, the Kabbalistic Tree of Life represents a path from the divine source through various stages of manifestation.
Conclusion — Veritas Simplex
In conclusion, Euclidean geometry, through its progression from points to lines to planes and solids and from points to circles and spheres, provides a rich metaphorical language for describing spiritual principles.
This parallel between geometry and spirituality reflects a deep-seated human desire to find harmony and meaning in the universe, linking the rational world of mathematics with the intuitive realm of spirituality.
In the next article, we will apply the same principles to the overlapping of separate circles and what this means in the spiritual realm: the vesica piscis and triqueta.
An understanding of these principles and the simple secrets hidden within them are “pregnant” with spiritual life, much like the description of his solids by Plato. Once these simple secrets are grasped by the reader, many more secrets naturally flow. It is as if the door to heaven has been opened in your mind.
