Lake Geneva and the Heart

Prologue

Lakes are typically characterized by still or slow-moving water, but they can also be part of a river system, as is the case with Lake Geneva, also known as Lac Léman.

The confluence of the Rhône and Arve rivers in Geneva is a fascinating natural phenomenon. The Rhône River, originating from the Rhône Glacier in the Swiss Alps, is known for its clear, blue waters. In contrast, the Arve River, which flows from the Mont Blanc region, carries more sediment, giving it a milky, brownish appearance.

While Lake Geneva is not the direct meeting point of the Rhône and Arve rivers, it is a crucial part of the Rhône’s journey before it meets the Arve in Geneva.

  1. Rhône River and Lake Geneva: The Rhône River flows into Lake Geneva at its eastern end near the town of Villeneuve. It traverses the lake, which is one of the largest in Western Europe, and exits at the western end in the city of Geneva.
  2. Confluence with the Arve: After the Rhône River exits Lake Geneva, it flows through the city of Geneva. It is downstream from this point, within the city, that the Rhône meets the Arve River. The confluence occurs after the Rhône has already passed through Lake Geneva.
  3. Geographical Context: Lake Geneva acts as a natural reservoir for the Rhône, regulating its flow and providing a scenic backdrop to the city of Geneva. The meeting of the Rhône and Arve rivers happens a short distance from where the Rhône leaves the lake, making the lake an important part of the overall hydrological system in the region.

When these two streams meet in Geneva, they create a striking visual contrast due to their differing colors and compositions. Despite their differences in origin, speed, and behavior, they merge to form a single river that continues its journey through southeastern France. This confluence is not only a geographical marvel but also a symbolic representation of unity and diversity.


The Jet d’Eau in Geneva, Switzerland, is a prominent landmark with a fascinating history. Originally installed in 1886, it was not intended as a tourist attraction but as a safety valve for a hydraulic power network at La Coulouvrenière. This system used water to power machinery, particularly in watchmaking workshops. The excess pressure at night required a release, leading to the creation of the water jet, which initially reached a height of 30 meters.

By 1891, the Jet d’Eau had become popular with locals and visitors, prompting its relocation to a more visible spot on the Eaux-Vives jetty. It was inaugurated as a tourist attraction during the Federal Gymnastics Festival and the 600th anniversary of the Swiss Confederation, with its height increased to 90 meters.

In 1951, the fountain was modernized to use lake water instead of city water, reaching its current height of 140 meters. The Jet d’Eau operates with two powerful pumps, expelling 500 liters of water per second at a speed of 200 km/h. It is manually operated by caretakers who monitor weather conditions to prevent splashing or freezing.

The Jura Mountains are a sub-alpine mountain range located in the northwestern part of Switzerland and extending into France. They form a natural border between the two countries. The range stretches from the Rhine River in the northeast to the Rhône River in the southwest, running parallel to the western edge of the Swiss Plateau. The Jura Mountains are known for their picturesque landscapes, dense forests, and rolling hills, making them a popular destination for outdoor activities like hiking, skiing, and cycling. They are situated to the north of Lake Geneva, providing a stunning backdrop to the lake’s scenic beauty.

The Swiss Plateau, also known as the Central Plateau, is a significant geographical region in Switzerland, situated between the Jura Mountains to the northwest and the Alps to the southeast. It covers about 30% of the country’s land area and is home to the majority of Switzerland’s population, including major cities like Zurich, Bern, and Geneva.

The region is characterized by its relatively flat and gently rolling terrain, which is why it is referred to as a “plateau.” Unlike the steep and rugged landscapes of the surrounding mountain ranges, the Swiss Plateau features broad valleys, fertile plains, and numerous lakes, making it ideal for agriculture, urban development, and transportation.

The term “plateau” is used because the area is elevated compared to the surrounding lowlands, yet it lacks the dramatic elevation changes found in mountainous regions. This makes it a distinct and important part of Switzerland’s geography, serving as the country’s economic and cultural heartland.


Lake Geneva and the Heart

An AI-generated narrative crafted, curated and illustrated by JB

Q: Can the human heart and the circulatory system be considered a hydraulic system managing blood flow and pressure akin to a rhythmic jet fountain? Metaphorically relate the water jet of Lake Geneva to a pumping heart. Draft an essay titled “Lake Geneva and the Heart, ” the heart of Europe and, probably, the world.

R: In the serene landscape of Europe, nestled between the towering Alps and the rolling Jura Mountains, lies Lake Geneva, a shimmering expanse of water that has long captivated the hearts and minds of those who visit. Among its many wonders, the lake is home to the Jet d’Eau, a powerful water jet that reaches heights of 140 meters, standing as an emblematic feature of Geneva. Metaphorically, this water jet can be likened to a beating heart, pulsing with life, energy, and rhythm, much like the human heart that sustains life.

The Jet d’Eau mirrors the rhythmic beating of a heart. At regular intervals, it springs to life, sending a column of water skyward with a force and grace that captivates onlookers. This cyclical eruption is reminiscent of the heart’s pulsations, maintaining a steady and reliable cadence that ensures the flow of life-giving blood throughout the body. Just as the heart’s rhythmic contractions maintain the essential functions of the human body, the Jet d’Eau breathes life into Lake Geneva, becoming a focal point that draws people together and inspires awe.

Lake Geneva, with its singular water jet, serves as a unique feature, much like the heart’s unparalleled role in the physiology of living beings. As the only lake in the world to boast such a magnificent display, it assumes a symbolic position as the heart of Europe and, arguably, the world. Its waters have been a vital artery for commerce, culture, and communication throughout history, linking diverse regions and fostering a spirit of unity and cooperation.

Culturally, Lake Geneva has been a source of inspiration for artists, writers, and thinkers. Its tranquil waters and the majestic Jet d’Eau have inspired countless works of art and literature, echoing the heart’s role as a source of creativity and emotion.

Historically, the lake has witnessed the ebb and flow of civilizations, serving as a meeting point for ideas and innovations that have shaped the world. Much like the heart, which adapts and evolves to meet the demands of the body, Lake Geneva has continually adapted to the changing currents of history, remaining a steadfast symbol of endurance and perseverance.

Photo by JB, Libra Full Moon 2024.
Jean-Jacques Rousseau is the author of Julie; or, The New Heloise
Rousseau Island at Lake Geneva
One of the greatest philosophers of the Age of Enlightenment, Jean-Jacques Rousseau, was native to Geneva.

Geographically, Lake Geneva sits at a crossroads of cultures and languages, embodying the heart’s capacity to connect and unify. It bridges the gap between Switzerland and France, fostering a rich tapestry of cultural exchange and mutual understanding. Its location serves as a reminder of the heart’s crucial role in unifying disparate systems, ensuring harmony and balance.

In essence, Lake Geneva and its iconic Jet d’Eau stand as a testament to the enduring power and significance of the heart. Just as the heart sustains life with its constant rhythm, Lake Geneva nurtures the spirit of Europe, offering a source of beauty, inspiration, and unity. Its waters continue to flow, much like the blood that courses through our veins, reminding us of the vital connections that sustain us all. Through its unique blend of natural beauty and human ingenuity, Lake Geneva remains a beacon of hope and vitality, a true heart at the center of Europe and beyond.


Full Moon at Bains des Pâquis, Lake Geneva. Photo by JB.

Excerpts of translated transcriptions of lectures delivered by Vicente Beltrán-Anglada (VBA) in Barcelona, Spain

“There is Darjeeling. Darjeeling is esoterically very important because it is one of the planetary centers where the Lord of the 5th Ray has deposited a talisman. There is also a talisman of the 2nd Ray in Geneva, another in New York, another is in England, in London, and another is in Tokyo, there are five talismans that are preparing for the Coming of the Great Lord. All these talismans come mystically from Shamballa, and in the same way that the Sun Lords or the Solar Devas introduced a talisman of the Solar Logos into the Gobi desert, which is still in force because it is the talisman used by the Planetary Logos or Sanat Kumara to initiate the disciples, there is also at each of these points a tremendous force that can be gathered if the vehicles are perfectly adapted; hence it is necessary to be very fit to the forces, because there are many magnetic places in the world and when the Hierarchy, by the fiat of Shamballa, wants to create a new race, a new civilization or simply an important city, first come the necessary qualified devas, blue, violet or green, to install within a talisman that will serve as a vehicle for superior entities when the time comes.” — VBA. Barcelona, February 13, 1982.

Apollonius of Tyana had been initiated into the Mysteries of Isis; his own Master, we are told, was a King, a man unknown to many, but who is the entity Hiram Abíff himself, to whom they allude so frequently within the esoteric explanations of Freemasonry. Hiram Abíff, who we are told, was the Magician who gave Apollonius of Tyana the sacred amulet that He would eventually transfer to Geneva, so that it would become a sacred city. We are secretly told, that somewhere remote on Lake Geneva, there is the talisman deposited by Apollonius of Tyana.

Hiram Abiff was a Great Initiate who had received the ebony of Lebanon, the symbol of the higher mind, and the gold of Ophir the symbol of the most perfect intuition, from King Solomon himself, who was the first to establish the Mysteries that would later become … the four pillars on which every possible magical work is based. …  they performed great magical prodigies, not only introducing sacred talismans blessed by the Lord of the World and other Hierarchies of the System, but because their lives were a constant irradiation of magic. All magicians are thaumaturgists.”
– VBA. Barcelona, November 8, 1986.


Vicente Beltrán Anglada: An Ibero-American Disciple

https://www.amazon.com/dp/B0DD7K71WV

VBA at Rousseau Island
Lac Léman, 1960s

The Master Jesus, Who is the focal point of the energy that flows through the various Christian churches, is at present living in a Syrian body, and dwells in a certain part of the Holy Land. He travels much and passes considerable time in various parts of Europe. He works specially with masses more than with individuals, though He has gathered around Him quite a numerous body of pupils. He is upon the sixth Ray of Devotion, or Abstract Idealism, and His pupils are frequently distinguished by that fanaticism and devotion which manifested in earlier Christian times amongst the martyrs. He Himself is rather a martial figure, a disciplinarian, and a man of iron rule and will. He is tall and spare with rather a long thin face, black hair, pale complexion and piercing blue eyes. His work at this time is exceedingly responsible, for to Him is given the problem of steering the thought of the occident out of its present state of unrest into the peaceful waters of certitude and knowledge, and of preparing the way in Europe and America for the eventual coming of the World Teacher. He is well known in the Bible history, coming before us first as Joshua the Son of Nun, appearing again in the time of Ezra as Jeshua, taking the third initiation, as related in the book of Zechariah, as Joshua, and in the Gospel story He is known for two great sacrifices, that in which He handed over His body for the use of the Christ, and for the great renunciation which is the characteristic of the fourth initiation. As Appollonius of Tyana, He took the [Page 57] fifth initiation and became a Master of the Wisdom. From that time on He has stayed and worked with the Christian Church, fostering the germ of true spiritual life which is to be found amongst members of all sects and divisions, and neutralizing as far as possible the mistakes and errors of the churchmen and the theologians. He is distinctively the Great Leader, the General, and the wise Executive, and in Church matters He co-operates closely with the Christ, thus saving Him much and acting as His intermediary wherever possible. No one so wisely knows as He the problems of the West, no one is so closely in touch with the people who stand for all that is best in Christian teachings, and no one is so well aware of the need of the present moment. Certain great prelates of the Anglican and Catholic Churches are wise agents of His.

-The Tibetan Master, Initiation: Human and Solar

Apollonius of Tyana was a first-century Greek philosopher and religious leader from Tyana, Cappadocia, in Roman Anatolia. He was a Neo-Pythagorean philosopher who became a mythical hero during the Roman Empire. Known for his teachings and reputed miracles, Apollonius is often compared to Jesus due to his life and works. His life was chronicled by Philostratus in the third century, portraying him as a charismatic teacher and miracle worker.

Apollonius of Tyana is associated with talismans through his reputed authorship of The Great Book of Talismans, a text that has been preserved in its Arabic recension. This book describes various talismans, which are objects believed to possess magical or religious powers, often used for protection, healing, or bringing good fortune. Talismans are typically crafted to avert evil and produce seemingly miraculous effects. Apollonius’s work on talismans highlights his influence in the realm of mystical and protective artifacts.


The kind of public talisman prepared by Apollonius – a metallic plaque or statue inscribed with magical names, either buried or placed on an elevated spot, sometimes protected by a shrine – became a model for talisman making.

https://www.academia.edu/38492694/Apollonius_of_Tyanas_Great_Book_of_Talismans


Rousseau Island, located in Lake Geneva, is a small, picturesque island situated in the heart of Geneva, Switzerland. Named after the famous philosopher Jean-Jacques Rousseau, who was born in Geneva, the island serves as a tranquil retreat amidst the bustling city.

The island is connected to the city by the Pont des Bergues bridge and is a popular spot for both locals and tourists. It features a charming park with lush greenery, walking paths, and benches, offering a peaceful place to relax and enjoy views of the lake and the surrounding cityscape.

A statue of Jean-Jacques Rousseau is prominently displayed on the island, commemorating his contributions to philosophy and literature. The island’s serene environment and historical significance make it a beloved landmark in Geneva, providing a unique blend of natural beauty and cultural heritage.

The original name of Rousseau Island was Île aux Barques. The name Île aux Barques, which translates to “Island of Boats,” likely originated from the island’s historical use as a docking or mooring point for boats. This practical function would have been significant in a city like Geneva, situated on the shores of Lake Geneva, where water transport played an important role.

The island was renamed Rousseau Island in 1835 to honor the philosopher Jean-Jacques Rousseau. The statue of Rousseau on the island was created by the sculptor James Pradier and was installed in the same year, 1835.  In 2012, Geneva celebrates the tercentenary of the birth of the writer.

Jean-Jacques Rousseau was a Swiss-born philosopher, writer, and political theorist, born on June 28, 1712, in Geneva, Switzerland. He became one of the most influential thinkers of the 18th century, inspiring leaders of the French Revolution and the Romantic generation. Rousseau’s major works include “The Social Contract,” “Émile,” and “Confessions.” He is renowned for his ideas on the social contract and the belief that humans are naturally good but corrupted by society. His thoughts on education, politics, and the arts significantly impacted European culture and philosophy. Rousseau passed away on July 2, 1778, in Ermenonville, France.

Rousseau’s belief that humans are naturally good but corrupted by society is a central theme in his philosophy. He argued that people are born with an inherent sense of goodness and compassion, but societal structures and institutions, such as property, government, and social norms, lead to inequality, competition, and moral decay. This idea is prominently featured in his works like “The Social Contract” and “Discourse on the Origin and Basis of Inequality Among Men.”

In his work “The Social Contract,” he explores the idea that legitimate political authority relies on a social contract agreed upon by all citizens for their mutual benefit. Rousseau argued that society should be organized in a way that reflects the general will, or the collective interest of the people, rather than individual interests. Rousseau believed that a return to simpler, more natural ways of living could help restore human goodness and promote genuine freedom and equality.

Rousseau’s views on education are primarily outlined in his work “Émile, or On Education.” He believed that education should nurture a child’s natural instincts and curiosity rather than impose societal norms and knowledge prematurely. Rousseau advocated for a child-centered approach, emphasizing learning through experience and interaction with the natural world. He argued that education should be tailored to the developmental stages of a child, allowing them to explore and learn at their own pace. Rousseau also stressed the importance of moral education, aiming to cultivate empathy and compassion, aligning with his belief in the inherent goodness of humans.

Rousseau Island, or Île Rousseau, is uniquely situated in the heart of Geneva, making it a prominent and symbolic location for honoring Jean-Jacques Rousseau. Its central position in the Rhône River, visible and accessible to many, made it an ideal spot for commemorating a figure of Rousseau’s stature, ensuring that his legacy would be prominently displayed in his hometown. The choice of this island likely reflects both its visibility and its significance within the city of Geneva.


Lake Geneva hosts several small islands, each with its own unique charm and history. Île de Peilz is the only natural island in Lake Geneva, located near Villeneuve. It’s a tiny island, notable for its monumental London plane tree. Its history is somewhat obscure, but it has been a subject of cultural interest, appearing in works by Lord Byron and Hans Christian Andersen. Another one is Île Rousseau, located in Geneva, named after the philosopher Jean-Jacques Rousseau.

Rousseau Island, like many features in Lake Geneva, is a result of natural geological processes. The island was formed from sediment deposits carried by the Rhône River, which flows into and out of Lake Geneva. Over time, these sediments accumulated to create small landmasses within the lake.

The Rhône River, originating from the Rhône Glacier in the Swiss Alps, carries a significant amount of glacial and riverine sediments. As the river enters the relatively calm waters of Lake Geneva, its flow slows down, causing the sediments to settle and gradually build up, forming islands and deltas.

Lake Geneva itself is a glacial lake, formed by the retreat of glaciers during the last Ice Age. The movement and melting of these glaciers carved out the lake basin, creating the conditions for island formation.

Rousseau Island, specifically, was shaped by these sedimentary processes, combined with human intervention to stabilize and enhance the island for public use. Its creation is a testament to the dynamic interaction between natural forces and human influence in shaping the landscape of Lake Geneva.

Although Lake Geneva itself is not directly used for hydroelectric generation, the Rhône River, which flows into and out of Lake Geneva, is utilized for hydroelectric power. The river has several hydroelectric plants along its course, particularly as it continues through Switzerland and into France. These plants harness the river’s flow to generate electricity, contributing to the region’s renewable energy resources. The lake primarily serves as a reservoir and a source of water for these downstream hydroelectric facilities.


In Swiss watchmaking, diamonds are not only used for decorative purposes but also play a functional role in the timekeeping machinery.

  1. Jewels in Movements: Diamonds, along with other gemstones like rubies, are used as “jewels” in watch movements. These jewels serve as bearings for the gears and other moving parts. Their hardness and smoothness reduce friction, wear, and tear, enhancing the accuracy and longevity of the watch.
  2. Durability and Precision: The use of diamond bearings helps maintain the precision of the watch by ensuring that the movement operates smoothly. This is crucial for high-end mechanical watches, where precision is a hallmark of quality.
  3. Heat Resistance: Diamonds have excellent thermal conductivity, which helps dissipate heat generated by the movement of the watch’s components. This property is beneficial in maintaining the stability and performance of the watch over time.
  4. Innovation and Craftsmanship: Incorporating diamonds into the movement showcases the innovation and craftsmanship of Swiss watchmakers. It reflects their commitment to using the finest materials to achieve both aesthetic beauty and technical excellence.

Overall, the use of diamonds in the timekeeping machinery of Swiss watches exemplifies the blend of luxury and functionality that defines the Swiss watchmaking tradition.


In Tibetan Buddhism, the Buddha is associated with the concept of a “diamond heart” and the vajra (or vajra). The vajra is a significant symbol in Vajrayana Buddhism, representing indestructibility, power, and the ability to cut through ignorance. It is often depicted as a ritual object resembling a thunderbolt or diamond, symbolizing the unbreakable and pure nature of enlightenment.

The “diamond heart” can be seen as a metaphor for the enlightened mind, which is unyielding and clear, much like a diamond. This concept emphasizes the qualities of wisdom and compassion that are central to the path of enlightenment. The vajra, in this context, represents the indestructible nature of the true self or ultimate reality, which is realized through spiritual practice.

Together, these symbols highlight the transformative power of Buddhist practice in achieving a state of enlightenment that is both resilient and compassionate, embodying the ultimate truth and wisdom.


In a mechanical watch, a diamond jewel at the heart of its timekeeping design represents precision, durability, and the smooth functioning of the watch’s intricate mechanisms. Similarly, in Tibetan Buddhism, the “diamond heart” symbolizes the indestructible and pure nature of the enlightened mind, central to spiritual practice and development.

Both metaphors emphasize qualities of resilience, clarity, and essential value, whether in the realm of horology or spiritual enlightenment. This parallel highlights how core, enduring elements—whether in a watch or within oneself—are crucial for harmony and function.


Phi: The Divine Feminine Principle

The Quest for the Holy Grail

The Holy Grail is often interpreted as a powerful symbol of spiritual seeking and enlightenment, representing humanity’s deep-rooted quest for meaning and truth. In many interpretations, the Grail is not just a physical object, but a metaphor for the inner journey towards self-discovery and higher consciousness. This quest is emblematic of the human desire to transcend ordinary existence and connect with a greater, divine source. The Grail, therefore, serves as a beacon for those on a path to enlightenment, encouraging introspection, personal growth, and the pursuit of wisdom beyond worldly possessions.
-Excerpt from Montserrat: A Spiritual Journey


The golden ratio, denoted as Phi (φ), is a mathematical principle that has fascinated scholars, artists, and philosophers for centuries. Its unique property of dividing a whole into unequal yet aesthetically balanced parts gives it a special place in the study of geometry, art, and the natural world. This essay explores the concept of the golden ratio as a representation of the divine feminine principle, examining its mathematical significance, its connection to Hermetic philosophy, its geometric relationships, and its symbolic representation in mythology.

The Mathematical Significance of the Golden Ratio

The golden ratio is defined as the division of a line into two parts such that the whole length divided by the longer part is equal to the longer part divided by the shorter part. This proportion, approximately 1.618, is considered aesthetically pleasing and appears in various forms in nature, art, and architecture. This unique division allows for a harmonious balance, resonating with the idea of beauty and symmetry. Its pervasive presence across different disciplines underscores its significance as a universal law of proportion.

Phi and the Hermetic Axiom “As Above, So Below”

In Hermetic philosophy, the axiom “As Above, So Below” represents the idea of correspondence between different planes of existence. Phi can be seen as the mathematical embodiment of this axiom, applying the Law of Analogy in the intuitive understanding of reality. By reflecting a pattern that is both finite and infinite, the golden ratio serves as a bridge between the tangible world and abstract concepts, illustrating how mathematical principles can mirror metaphysical truths.

Geometric Relationships with the Golden Ratio

Phi’s unique relationship with certain geometric shapes is well-documented, particularly in the pentagram, pentagon, and dodecahedron. In a regular pentagon, the ratio of a diagonal to a side is the golden ratio. The pentagram, formed by extending the sides of a pentagon, is abundant with φ-related proportions, creating a network of harmonious relationships. In three dimensions, the dodecahedron, with its twelve pentagonal faces, embodies the golden ratio in its structure. These geometric relationships highlight the pervasive influence of φ in both two and three-dimensional forms.

The Pentagram of Venus and Celestial Symmetry

The orbital relationship between Earth and Venus creates a fascinating pentagram pattern, known as the “Venus Rose” or “Pentagram of Venus,” over time. This pattern emerges from their synodic cycle, the period it takes for Venus to return to the same position relative to Earth and the Sun. Over eight Earth years, Venus completes five synodic cycles, forming a geometric pattern noted for its beauty and symmetry. This celestial phenomenon further illustrates the connection between the golden ratio and the natural world, where mathematical elegance manifests in astronomical movements.

The Feminine Principle and Mythological Symbolism

Metaphorically, φ and its reciprocal (1/φ) can be considered representations of the Feminine Principle of the Godhead. Venus, as an exalted expression of beauty in art, also embodies this principle as a goddess represented by Athena and Artemis in Greek mythology. The mathematical expression 1/a = a/b = φ suggests a harmonious balance that resonates with the nurturing and creative aspects of the feminine. By viewing (1/φ) as a manifestation of this principle, we highlight the interconnectedness of mathematical beauty and mythological symbolism, both seeking to express the underlying harmony of the universe.

Philosophical exploration

The interplay between the dynamic Yin-Yang duality in time and the Phi ratio in space offers a profound reflection on balance and harmony across different dimensions. Rooted in Eastern philosophy, Yin and Yang represent the cyclical nature of existence, embodying the constant flow and transformation of energy. These opposite forces are in perpetual motion, creating a dynamic equilibrium that echoes throughout the universe.

In contrast, the Phi ratio, or the golden ratio, emerges from Western mathematics as an emblem of spatial perfection. It is a constant found in the spirals of galaxies, the patterns in pinecones, and the proportions of ancient architecture. The golden ratio signifies an ideal state of balance and harmony, a spatial blueprint that underpins beauty and order.

To intertwine these concepts is to bridge the fluidity of time with the structure of space. Yin-Yang’s temporal dance reflects the shifting scales of balance, akin to the spiraling growth patterns governed by the Phi ratio. Both concepts speak to a universal symmetry, where dynamic processes and static geometries converge. The cyclical ebb and flow of Yin and Yang can be seen as a temporal echo of the Phi ratio’s spatial harmony, each informing the other in a cosmic rhythm.

Philosophically, this relationship illustrates the seamless integration of time and space, where the quest for balance and beauty transcends cultural boundaries. It invites us to consider the interconnectedness of all things, suggesting that the pursuit of harmony—whether in the fluidity of time or the structure of space—is a universal endeavor. This synthesis of Eastern and Western thought offers a pathway to understanding the deep-seated order that underlies our existence, inviting reflection on how these timeless principles can guide us toward a deeper appreciation of the world around us.


Phi Spiral

The geometric method of removing a square from a golden rectangle is directly related to the mathematical formulation of Phi.

  1. Golden Ratio Definition: This means that the ratio of the sum of two quantities (a+b) to the larger quantity (a) is the same as the ratio of the larger quantity (a) to the smaller quantity (b).
  2. Geometric Construction:

Iterative Process: This process can be repeated indefinitely, each time creating a smaller golden rectangle, which visually demonstrates the self-similar and recursive nature of the golden ratio.

    Thus, the geometric method of removing squares from a golden rectangle is a visual and iterative representation of the mathematical definition of the golden ratio, illustrating how the proportions remain constant and self-similar at every step.


    The interplay between geometry, mathematics, and philosophical ideas offers a rich tapestry for exploring how patterns and structures in the natural world can reflect deeper meanings and connections.

    The concept of self-similarity, as seen in the golden ratio and fractals, can be metaphorically related to philosophical and spiritual ideas, such as the immanence of a divine presence in creation. This idea suggests that just as self-similar patterns repeat at every scale in mathematics, a divine essence might be reflected throughout the universe in various forms.

    Furthermore, the dodecahedron (12 pentagons) and the icosahedron (20 triangles are geometric duals.

    Approximating a whole, such as a circle, using self-similar shapes like triangles, aligns with mathematical concepts like tessellation and fractal geometry. In these concepts, smaller and smaller shapes can be used to approach a complete form, much like how a circle can be approximated by inscribing polygons with an increasing number of sides.


    The tessellation of a unit circle can be approached using triangular fractals, although it’s important to note that a perfect tessellation of a circle with triangles isn’t possible in the traditional sense, as circles and triangles have fundamentally different geometries. However, you can approximate the circle using a series of increasingly smaller triangles, creating a fractal-like pattern.

    It can be conceptually visualized, thus:

    1. Polygon Approximation: Start by inscribing a polygon, such as a hexagon, within the circle. This polygon can be divided into triangles.
    2. Iterative Subdivision: Each triangle can be subdivided into smaller triangles, iteratively refining the approximation of the circle’s curvature.
    3. Fractal Approach: By continuing this process, you create a fractal pattern where the triangles become smaller and more numerous, closely approximating the circle’s boundary.

    This method is similar to how fractals like the Koch snowflake are constructed, where a simple shape is repeatedly subdivided to create a complex boundary. While this doesn’t result in a perfect tessellation, it provides a fascinating way to explore the relationship between linear and curved geometries.


    I have said earlier that the intersecting energies in the etheric body of the planet are at this time a network of squares. When the creative process is complete and evolution has done its work, these squares will become a network of triangles. Necessarily this is a symbolic way of speaking. In the Book of Revelations which was dictated 1900 years ago by the disciple who is now known as the Master Hilarion, reference is made to the “city which stands four-square.” The etheric vehicle of the planet was inherited from a former solar system, with the purpose or intention in view of its transformation into a network of triangles in this solar system. In the next one of the triplicity of solar systems (the third or last) in which the will of God works out, the etheric body will begin as a network of triangles, but this will be resolved into a network of interlinked circles or of linked rings, indicating the fulfilment of interlocking relationships.

    • The Tibetan Master in Telepathy and the Etheric Vehicle, p. 163.

    A fractal triangular tessellation can potentially provide a more efficient approximation of the area of a circle compared to a fractal square tessellation, primarily due to the geometric properties of triangles versus squares.

    Triangles offer a better fit because:

    1. Flexibility in Shape: Triangles, being three-sided, can more easily conform to curved surfaces compared to squares. This flexibility allows for a closer approximation of the circle’s curvature.
    2. Subdivision Efficiency: Triangles can be subdivided into smaller triangles more naturally, maintaining their shape and allowing for a finer approximation of the circle’s boundary with each iteration.
    3. Polygonal Approximation: Starting with a polygonal approximation of the circle (like a hexagon or dodecagon) and subdividing into triangles can more closely match the circle’s area as the number of subdivisions increases.

    In contrast, squares, with their right angles, tend to leave more gaps or require more complex arrangements to approximate curves, which can lead to less efficient coverage of the circle’s area.

    Overall, while both methods can approximate the circle’s area, using triangles might result in a more accurate and visually appealing approximation due to their ability to better conform to the circle’s shape.

    The etheric webs of the sacred planets are largely triangles whilst that of the Sun is that of interlaced circles. The effort on Earth today (as seen by the planetary Logos) is to bring about a transformation of the web of the planet and thus slowly change the existing squares into triangles. This is done by the creation of division, by the application of the Law of Separation, but also by the recognition, in consciousness, of duality, the application of directed motion and the appearance of two triangles in the place of one square. When this has taken place, the perceiving consciousness recognises identity and the rule of the square is ended. These words were once spoken to me by an ancient seer who bisected the square esoterically, thus forming two triangles and united them in a fresh manifestation to form a Star of Life. Ponder on this.

    -The Tibetan Master in Esoteric Astrology, p. 479.

    [Note: The term “Star of Life” is widely known as a symbol used in emergency medical services (EMS). It features a blue six-pointed star with a Rod of Asclepius in the center, representing medicine and healing.
    A Star Tetrahedron, formed by two interlocking tetrahedra, can be circumscribed within a cube, each vertex of the tetrahedra touching a vertex of the cube. The 2-D projection of a Star Tetrahedron typically results in a shape that resembles a hexagram or a six-pointed star, similar to the Star of David.  This is because the projection of the interlocking tetrahedra creates overlapping triangles, forming a six-pointed star pattern.]


    There is a beautifully poetic way to describe the geometric and philosophical interplay between these shapes and concepts. By iteratively removing squares from a golden rectangle, we create a spiral that embodies the self-similar properties of the golden ratio. This process can indeed be seen as a metaphor for transformation and creation.

    In this context, the transformation from squares to triangles through the properties of the dodecahedron and icosahedron highlights the dynamic relationship between different geometric forms. The idea that Phi facilitates this transformation aligns with the notion of moving from simplicity to complexity, from the square to the triangle, and from the finite to the infinite.

    This metaphorical journey from squares to triangles, and ultimately to a more efficient tessellation of the unit circle, can be seen as a reflection of the divine process of creation—where the One, or the divine essence, manifests in the complexity and beauty of the universe. It’s a wonderful way to connect mathematical concepts with philosophical and spiritual ideas, illustrating how geometry can serve as a bridge between the tangible and the abstract.


    Agni Yoga: the Practice of the Presence

    As previously mentioned, the concept of self-similarity, as seen in the golden ratio and fractals, can be metaphorically related to philosophical and spiritual ideas, such as the immanence of a divine presence in creation. Just as self-similar patterns repeat at every scale in mathematics, a divine essence is reflected throughout the universe in various forms.

    The golden ratio embodies a profound connection between mathematics, philosophy, and spirituality. As a representation of the divine feminine principle, it offers a lens through which we can understand the balance and beauty inherent in the universe. Through its geometric relationships and celestial patterns, Phi serves as a testament to the enduring harmony that guides both the tangible and the intangible realms.

    Sacred geometry, with its emphasis on patterns and proportions found in Mother Nature, is intricately related to spiritual practices like mindfulness and Agni Yoga by providing a visual and meditative focus that embodies the interconnectedness of all things.

    1. Symbolic Representation: Sacred geometry uses shapes and patterns that are often seen as symbols — mandalas — of the universe’s underlying order. Engaging with these symbols can help practitioners feel a deeper connection to the cosmos and the divine, fostering a sense of unity and presence.
    2. Meditative Focus: The intricate and harmonious designs of sacred geometry can serve as focal points for meditation, helping individuals concentrate and quiet their minds. This focus can enhance mindfulness by encouraging practitioners to remain present and aware of the moment.
    3. Reflection of Natural Order: By contemplating the geometric patterns that mirror natural forms, practitioners can cultivate an appreciation for the beauty and complexity of creation. This reflection can deepen their sense of gratitude and awareness, key components of mindfulness and spiritual growth.
    4. Integration of Mind and Spirit: In practices like Agni Yoga, which emphasize the synthesis of spiritual and material aspects of life, sacred geometry can act as a bridge. It visually represents the harmony between the physical and spiritual realms, encouraging practitioners to integrate these aspects within themselves.
    5. Inspiration for Transformation: The self-similar and fractal nature of sacred geometry can inspire personal transformation. Just as these patterns evolve and expand, individuals can be motivated to grow and develop spiritually, embracing change as a natural and divine process.

    By incorporating sacred geometry into spiritual practices, individuals can enhance their experience of the “practice of the presence,” fostering a deeper connection to themselves, the universe, and the divine. This integration can lead to a more profound sense of peace, purpose, and unity.


    The Virgin of the Rocks
    by Leonardo DaVinci

    Geometry has two great treasures: one is the theorem of Pythagoras, the other the division of a line into “extreme” (unique) and “mean” (balanced) ratio. The first we may compare to a mass of gold, the second we may call a precious jewel
    – Johannes Kepler

    Note: In plain English, the golden ratio, which Euclid called the “extreme and mean ratio,” can be described as the unique way of dividing a whole into two unequal parts that are aesthetically balanced and pleasing. 

    When a rectangle is constructed using two unit squares that circumscribe a Vesica Piscis, the diagonal of this rectangle is the square root of 5. This is because the diagonal of a rectangle formed by two unit squares (each side of length 1) is calculated using the Pythagorean theorem.  The Phi formula directly incorporates the square root of 5, highlighting a deep mathematical connection between the geometry of the Vesica Piscis and the properties of the golden ratio.