TRIANGLES

The Triangles service activity of the Lucis Trust is a worldwide initiative where people form groups of three to link in thought and prayer. The aim of this service is to uplift and transform consciousness, creating a planetary network of light and goodwill. It transcends barriers of race, creed, class, economic, and political conviction, focusing on the power of thought and human goodwill for global betterment. The participants maintain this network, intending to cover the entire planet with light and goodwill through their collective thoughts. (source: Lucis Trust)

Mindfulness is a type of meditation in which you focus on being intensely aware of what you’re sensing and feeling in the moment, without interpretation or judgment. It involves breathing methods, guided imagery, and other practices to relax the body and mind and reduce stress. (Source: Mayo Clinic – Mindfulness)

The Triangles service activity of the Lucis Trust and the practice of mindfulness share some commonalities in their core principles, even though they might differ in methodology or purpose.

Both practices emphasize focused attention, intentional thought, and the cultivation of positive states of mind. In Triangles, participants maintain a network intending to cover the planet with light and goodwill through their collective thoughts. Similarly, mindfulness encourages individuals to focus their attention on their thoughts, emotions, and sensations in the present moment, promoting self-awareness and calm.

While both practices involve focused thought and intention, they are used towards different ends. Triangles is aimed at global betterment, using collective thought to spread light and goodwill. In contrast, mindfulness is often used as a personal practice for stress reduction and self-awareness.

However, if participants in the Triangles service activity were to constantly engage in the practice throughout one’s waking hours, not only at set times, with full presence of mind, much like mindfulness, then the process of both could indeed be seen as similar. Both mindfulness and the Triangles service activity involve focused attention, intentional thought, and the cultivation of positive states of mind.

In terms of outcomes, both mindfulness and the Triangles service aim to create positive change. Mindfulness is often used on a personal level to reduce stress, increase self-awareness, and promote emotional health. The Triangles service, on the other hand, aims to create a planetary network of light and goodwill for global betterment.

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Another difference is that Triangles members recite the Great Invocation to invoke the energies of light, love, and power. However, its formulation could be simplified to make it more acceptable for secular humanists.

Light + Love + Power (Will-to-Good) = Goodwill + Peace.

Therefore, we could indeed rephrase the five stanzas of the Great Invocation in terms of universal human values and desires, such as understanding, compassion, and collective action.

For instance, the simplified formula could be: Understanding (Light) + Compassion (Love) + Collective Action (Power or Will-to-Good) = Goodwill + Peace.

If we consider peace to be the result of goodwill leading to right human relations, the formula could be:

Understanding (Light) + Compassion (Love) + Collective Action (Power or Will-to-Good) = Right Human Relations (Goodwill) + Lasting Peace

Here’s how each term could be interpreted:

1. Understanding (Light): Symbolizes wisdom and enlightenment, illuminating our path as we embark on a journey of self-realization and truth-seeking. By embracing the light, we open ourselves to a world of infinite possibilities and a deeper understanding of ourselves and the universe around us.

• Compassion (Love): Represents empathy and care for others, encompassing empathy and a genuine concern for the well-being of others, fostering deep connections and understanding. It is the ability to acknowledge and alleviate the suffering of those around us, offering support, comfort, and kindness.

• Collective Action (Power or Will-to-Good) symbolizes the remarkable strength of unity and the transformative potential of collective decision-making. It embodies the idea of individuals joining forces synergistically, pooling their diverse perspectives, skills, and resources, to foster positive change and make a lasting impact on society. By harnessing the collective will and combining efforts towards a common goal, we can create a brighter future for all.

• Right human relations are deeply intertwined with the concept of Goodwill (the outer expression of the Will-to-Good). It is about creating a community where everyone not only thrives but also feels valued and empowered. This involves promoting fairness and ensuring equitable distribution of resources, thereby addressing the needs of every individual and enhancing the overall well-being of the community as a whole.

• Lasting Peace: This is the ultimate goal. A lasting peace on Earth is only achievable as a result of establishing right human relations (justice), nurturing a world where every individual can thrive and flourish in unity and mutual respect.

This approach emphasizes the process of moving from individual understanding and compassion, through collective action, founded on goodwill, which then leads to right human relations and ultimately to lasting peace.

This simplification maintains the essence of the Great Invocation while making it more accessible to those who might not align with its original spiritual or religious connotations. It emphasizes universal human values and aspirations, which are integral to both spiritual and secular perspectives.

Goodwill can be also be related to the task of “sealing the door to evil,” as expressed in the fourth stanza of the Great Invocation. In more accessible terms, this concept implies that by fostering and embodying goodwill, we create a powerful barrier against negative influences and promote a harmonious and compassionate existence. It is through the cultivation of goodwill that we open ourselves to the possibility of transforming our world into a place of peace, understanding, and unity.

In the Great Invocation, “sealing the door where evil dwells” is a metaphorical way of saying to prevent negative or harmful influences from gaining a foothold. In layman’s terms, this could be interpreted as preventing destructive behaviors, attitudes, or actions that harm individuals or communities.

Goodwill, in this context, can be seen as the force that helps “seal the door to evil”. Goodwill, energized by the Will-To-Good, promotes understanding, compassion, shared prosperity, and right human relations, all of which — like a vaccine — would work against the propagation of harmful influences. A vaccine, when administered to a significant portion of the population, provides collective immunity, helping to protect not only the vaccinated individuals but also those who do not receive the vaccine, creating a stronger barrier against the spread of communicable diseases, such as separateness, the root cause of all problems of humanity.

• Right Human Relations: This is the result of goodwill. It’s about justice, creating an atmosphere of respect, understanding, and cooperation among all people.
• Sealing the Door to Harmful Influences: This is the act of preventing destructive behaviors, attitudes, or actions from gaining a foothold in our societies. It’s about promoting positive behaviors and attitudes that contribute to the wellbeing of all.
• Lasting Peace: This is the ultimate goal and the result of establishing right human relations and sealing the door to harmful influences. It’s about achieving a state of global harmony and tranquility, free from conflict and strife.

This approach emphasizes the role of goodwill in promoting positive behaviors and attitudes while preventing harmful ones, leading to lasting peace.

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A Geometrical Visualization

Turning to some geometrical interpretations of these concepts. Assume that squares (90 degree angles) are symbols of tension and conflict (as in astrology), and triangles are symbols of the resolution of such tension (as in astrological trines, 120 degrees). How could we describe the shearing transformation of the two isosceles triangles created by bisecting a square into equilateral triangles in terms of the goodwill definition that we just considered? That is, goodwill as the shearing force and sealing substance transforming conflict into harmony (peace based on right human relations).

Let’s explore such geometric transformation in the context of our goodwill definition.

A square, symbolizing tension and conflict, can be bisected into two isosceles right triangles. This bisection is an initial step towards resolution, representing an acknowledgment of conflict and a decision to address it.

Then, through a shearing transformation, these isosceles right triangles become equilateral triangles, symbols of harmony and resolution. This transformation can be seen as the process of implementing goodwill.

The most efficient geometric way to transform an isosceles triangle into an equilateral triangle is by using a process called “shearing.” Here’s how you can do it:

• Take an isosceles triangle. Let’s assume it has a base of length ‘b’ and two equal sides of length ‘a’.
• Draw a vertical line from the apex (top point) of the isosceles triangle perpendicular to the base.
• Then, shear or slide the apex along this vertical line until the base angles are both 60 degrees. This will change the shape of the triangle without changing the base or the area.
• Now, the isosceles triangle has been transformed into an equilateral triangle.

This method is efficient as it only involves one movement and maintains the base and area, while changing the shape to an equilateral triangle.

https://mathworld.wolfram.com/Shear.html

So, in lay terms:

The square, a symbol of conflict, is divided into two isosceles triangles, representing the recognition of conflict and the initial steps towards resolution.

Then, through the shearing force of goodwill – which we’ve defined as understanding, compassion, collective action leading to right human relations, and sealing the door to harmful influences – these triangles are transformed into equilateral triangles.

This geometric transformation symbolizes the transformation from conflict to harmony. Just as the shearing force changes the shape of the triangles, so does the power of goodwill transform conflict into peace based on right human relations.

The resulting equilateral triangle, with its equal sides and angles, represents a state of balance and harmony, a reflection of peace achieved through right human relations. The transformation is complete, the tension and conflict of the square has been resolved, and what remains is a symbol of harmony and peace.

In this way, we can see the process of goodwill as a transformative force, reshaping conflict into harmony, much like the shearing transformation reshapes the isosceles triangle into an equilateral one.

In spiritual terms, this shearing force of goodwill — the will-to-good in action — could be visualized as renting (“tearing asunder”) the dark veil of an etheric web comprised of squares into a shining etheric web of illuminated triangle. This is Biblically phrased as “the veil of the Temple [Cube] was rent in twain from the top to the bottom” (from the higher to the lower vertices).

We are told that three great rents in such dark web now exist.  Three great Sons of God at the moment of initiation made a major contribution to the human consciousness through their determined Will-to-Law (Moses) , Will-to-Love (Jesus Christ) and Will-to-Synthesis (Apostle Paul).  Humanity was thereby aided to move forward more easily along the “lighted Way,” to pass through the veils of maya, aided by the light pouring through the rents made in the separating veils by these pioneering Initiates at the very moment of Their triumph.  A fourth great rent still remains to be made as a result of the energies released and the gained good which the three earlier rents have made possible.  This fourth major rent will be made by humanity itself, standing with “massed intent,” focused through the New Group of World Servers and the externalizations of the Ashrams of the Masters.  It will therefore be made at the time that the Hierarchy takes physical shape upon the Earth again.

In summary, three significant “rifts” or “rents” made in the veils of human consciousness by three great Initiates. These rents allowed humanity to progress spiritually and experience higher realms. The veils represent physical forces and energies acting as barriers to human evolution. They separate the inner (spiritual) man from his physical brain, obscuring the perception of a deeper understanding of life.

The work of these Initiates was not for their personal enlightenment but to serve humanity by creating gaps in these veils, allowing more light and thus higher spiritual experiences. A fourth major rent is yet to be made by humanity itself, facilitated by groups that are manifestations of the Masters’ Ashrams. This will occur when the Hierarchy physically re-emerges on earth.

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The cuboctahedron

A cuboctahedron is a polyhedron with 8 triangular faces and 6 square faces. This polyhedron has the remarkable property that if the side length of the squares and triangles is 1, then the radius of the cuboctahedron is also 1.

The tessellation of the cube can produce a cuboctahedron. It can be achieved by truncating (or cutting off) the corners of a cube at a certain depth along the diagonals. Each corner of the cube becomes a triangle in the cuboctahedron, and each face of the cube becomes a square face in the cuboctahedron. This process is known as a rectification.

As described above, the shearing force of goodwill can geometrically transform the 6 square faces of the cuboctahedron into 12 equilateral triangles. The addition of the 12 to the 8 equilateral triangles of the cuboctahedron would make 20 equilateral triangles, the icosahedron.

As the number of faces increases through infinite fractalization (or subdivision) of each triangle face into smaller triangles, the icosahedron will more closely approximate a sphere. This is because the increase in the number of faces effectively “smooths out” the surface of the polyhedron.

Fractalizing an icosahedron in this way is similar to the concept behind geodesic spheres or domes. A geodesic sphere is a spherical type of structure (or pattern) that is made up of many triangles. The more triangles there are, the closer the shape is to a perfect sphere.

The inner web of light which is called the etheric body of the planet is essentially a web of triangles and when the evolutionary process is completed, it will have been organized. At present a pattern of squares is the major construction of the web but this is slowly changing as the divine plan works out. 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 recognizes 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.

Esoteric Astrology by Alice A. Bailey, p. 480

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Star of Life

The six sides of the Cube transformed into the Six-Pointed Star

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https://en.wikipedia.org/wiki/Tesseract

The Tesseract is a hypercube, which can be visualized as the four-dimensional equivalent of a cube. It has been studied in geometry and mathematics since at least the 1800s. In literature, a tesseract is often used as an analogy for higher dimensional space or to describe properties of a four-dimensional object.

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