Chapter 6 Part VI

6.1 Hierarchy and Freedom

Q: Hierarchy, organically understood as in systems theory, and freedom, inextricably intertwined with social responsibility, are two pillars of the New Group of World Servers holding the emblem of altruistic service to humanity, in restoring the plan of goodwill and right human relations resulting in a lasting and just peace on Earth. How to reconcile this apparent contradiction of hierarchy and freedom?

A: Ah, the dance between hierarchy and freedom – a timeless paradox that has puzzled thinkers for centuries. In Hemingway’s spirit of clear, direct prose, let’s dissect this seeming contradiction. In systems theory, hierarchy is not about domination and subordination but rather about order and organization. It refers to the nested, interconnected levels within a system, each with its own unique role and function. Hierarchy, in this sense, is a natural and necessary part of any complex system, be it an ecosystem, a human body, or a social structure.

Freedom, on the other hand, is about autonomy, choice, and the ability to act according to one’s will. Yet, true freedom does not exist in isolation. It is closely intertwined with responsibility. As members of a social system, our actions reverberate throughout the system, affecting others in ways we may not immediately see. Hence, exercising our freedom responsibly means considering the impact of our actions on the wider system.

So, how do we reconcile hierarchy and freedom?

The key lies in understanding that hierarchy and freedom are not opposing forces but complementary aspects of the same system. A well-organized hierarchy can provide the structure and stability needed for individuals to exercise their freedom responsibly. Conversely, the responsible use of freedom can contribute to a healthy, balanced hierarchy.

In the context of the New Group of World Servers, hierarchy refers to the different roles and responsibilities that individuals and groups play in serving humanity. Some might lead, others might support, yet all are vital parts of the whole. Freedom, in this context, is the ability of each individual or group to choose how they fulfill their role, guided by wisdom, compassion, and a commitment to the greater good.

In this way, hierarchy and freedom coexist, each enhancing the other. The hierarchy provides the framework within which individuals can exercise their freedom, while their responsible use of freedom strengthens and enriches the hierarchy. This dynamic interplay between hierarchy and freedom is what allows the New Group of World Servers to work towards their vision of goodwill, right human relations, and lasting peace on Earth.

To quote Hemingway, “There is nothing noble in being superior to your fellow man; true nobility is being superior to your former self.” In this light, the hierarchy is not about being superior to others, but about striving to be a better version of oneself, contributing more effectively to the collective effort. And freedom is the means by which we choose to embark on this journey of continuous improvement, guided by our shared commitment to serving humanity.

[Note: This quote encapsulates Hemingway’s belief in personal growth and self-improvement as the highest form of nobility. While this quotation is widely associated with Hemingway, it’s worth noting that its exact origin remains somewhat elusive. It does not appear verbatim in any of Hemingway’s known works, leading some to speculate that it may have been paraphrased or extrapolated from his broader philosophy and worldview. However, the sentiment expressed in this quote is consistent with Hemingway’s emphasis on personal courage, resilience, and self-reliance. His characters often grapple with their own limitations and strive to surpass themselves, reflecting Hemingway’s belief in the inherent nobility of personal growth and self-improvement.]

6.2 Servant Leadership

Q: According to, integrate the concept of a servant leader to your reply about the principles of hierarchy and freedom operating in the New Group of World Servers as an instance of a group, in the algebraic and social sense.

A: The New Group of World Servers, as a model of both mathematical and sociological principles, offers a fascinating study in the harmony of hierarchy and freedom. The group’s structure, echoing fractal geometry, represents hierarchical order, yet within this order, there thrives a vibrant sense of freedom and individual autonomy.

In the algebraic sense, the group adheres to the four axioms that define a mathematical group: closure, associativity, identity element, and inverse element. These principles ensure the group’s robustness and integrity, much like the bones of a body providing structure and support.

Yet, within this sturdy framework, freedom flourishes. Each member is free to express their unique strengths and perspectives, contributing to the rich tapestry of the group’s collective wisdom. This diversity, far from being a source of discord, enhances the group’s resilience and adaptability.

Now, let’s turn to the concept of a servant leader. This role, central to the functioning of the New Group of World Servers, embodies both hierarchy and freedom. As a leader, they occupy a higher position in the hierarchy. Yet, as a servant, they put the needs of others before their own, exercising their power with humility and respect. This balance of authority and service, power and humility, echoes the interplay of hierarchy and freedom within the group.

In the context of the New Group of World Servers, the servant leader functions as the identity element. Just like the number zero in addition or the number one in multiplication, the servant leader enables other elements (members) to maintain their identity while still participating in the group operation. They share power and prioritize the needs of others, thereby fostering an environment where each member can freely contribute their unique talents and insights.

The group’s structure can be represented as a network of cells within the group, each cell using modular arithmetic with modulo 9, a number with cyclic and regenerative properties. This symbolizes the group’s continuous evolution towards perfection and its ability to regenerate in response to changing circumstances.

Complementary pairs within the group, formed based on differences in temperament and introversion/extroversion, further enhance the group’s resilience and adaptability. These pairs, through their mutual respect and understanding, embody the balance of hierarchy and freedom, each valuing and supporting the other’s unique contribution.

This intricate dance of hierarchy and freedom, order and diversity, is reflected symbolically in the transformation of the planet’s etheric body into a network of triangles. Each triangle, a stable structure composed of three interconnected points, represents a mini-hierarchy within the larger network. Yet, within each triangle, there is freedom for each point to connect with others, forming new triangles and contributing to the evolution of the network.

In conclusion, the New Group of World Servers, with its mathematical and fractal structure, offers a compelling model of how hierarchy and freedom can coexist and enhance each other. The servant leader, embodying both these principles, plays a crucial role in maintaining this delicate balance. Through their humble service, they enable each member to freely contribute their unique gifts, thereby enriching the group and advancing its noble mission.

6.3 Modern Science

Q: Is there evidence of this intricate dance of hierarchy and freedom in modern science, such as in quantum physics?

A: In modern science, particularly in quantum physics, the intricate dance of hierarchy and freedom is not only evident but also fundamental to our understanding of the universe.

Let’s consider the principle of superposition in quantum mechanics. This principle allows particles to exist in multiple states simultaneously until they are observed or measured. Here, we observe a unique form of freedom—quantum freedom, if you will—that defies classical logic and intuition. Yet, this freedom is not unbounded. It is subject to the constraints of quantum mechanics, such as the laws of conservation and the rules of quantum entanglement, forming a kind of quantum hierarchy.

A fascinating example of this dynamic interplay between hierarchy and freedom can be found in the phenomenon of quantum entanglement, where two or more particles become interconnected in such a way that the state of one instantly influences the state of the other, regardless of the distance between them. This intricate “dance” of entangled particles, beautifully described in the paper “Choreographed entanglement dances: Topological states of quantum matter”, reveals a profound form of quantum freedom within the hierarchical structure of quantum mechanics.

The concept of scale freedom discussed in the book “Without hierarchy: The scale freedom of the universe” offers another perspective on this paradox. In this context, scale freedom refers to the absence of a preferred scale or size in the universe—from subatomic particles to galactic clusters, each level of the cosmic hierarchy has its own unique significance and role to play. This scale freedom within the cosmic hierarchy echoes the dance of hierarchy and freedom, each enhancing and enriching the other.

Moreover, the idea of constraint and freedom in the movement from quantum physics to theology, as discussed in Chapter Six of the book [“Quantum Physics and Theology: An Unexpected Kinship”[(], presents an intriguing exploration of how genuine freedom might arise at the level of complex systems, framed within a hierarchical structure.

In conclusion, the intricate dance of hierarchy and freedom, far from being a mere philosophical concept, is a fundamental aspect of our scientific understanding of the universe. It is deeply embedded in the laws of quantum physics, shaping our perception of reality and guiding our quest for knowledge.

6.4 Hierarchy in Music

Q: Is there a hierarchy in music?

A: Music may be defined as the art and science of bringing harmony (triangles of consonance) through conflict (squares of dissonance). In doing so, music is assisting in “the effort on Earth today (as seen by the planetary Logos) … to bring about a transformation of the web of the planet and thus slowly change the existing squares into triangles” (Esoteric Astrology by Alice A. Bailey, p. 480). This planetary web is the foundation upon which a future hierarchical democracy will be built.

Dmitri Tymoczko, a renowned music theorist and composer, has contributed significantly to our understanding of music structure. He suggests that tonal music, which is the dominant musical style of Western music from 1600 to 1900, is both self-similar and hierarchical.

Self-Similarity: Tymoczko refers to the concept that chord progressions in tonal music often use efficient voice leading to link structurally similar chords. Voice leading is the process of writing smooth melodic lines (or voices) to form harmonies (chords). When chords are structurally similar, they share common tones or have tones that are near each other in pitch, making the voice leading more efficient and smooth. This creates a sense of continuity and coherence in the music.

Hierarchy: In addition to this, Tymoczko also suggests that modulations in tonal music often use efficient voice leading to link structurally similar scales. Modulation is the process of changing key within a piece of music. When keys are structurally similar, they share many common pitches, making the transition between them smoother. This creates a hierarchical structure in the music, as some keys (and the scales associated with them) can be seen as more closely related than others.

These two principles combine to create the rich, complex sound of tonal music, with its characteristic tension and resolution, its sense of movement and rest. Accordingly, these are fundamental aspects of how tonal music is structured and understood (Tymoczko, Dmitri. “The Generalized Tonnetz“. Journal of Music Theory 56, no. 1 (2012): 1-66).

Thus, the concept of a hierarchical democracy can be enriched by considering correspondences based on the “right relations” between consonance and dissonance in tonal music, as revealed by the “musical science of triangles” portrayed in the Tonnetz grid, and enhanced by Cyril Scott’s hierarchy of musical expressions, and Tymoczko’s concept of hierarchical structures in music. Source

6.5 Network of Triangles

Q: Why would a network of triangles be a fitting symbol for the New Group of World Servers?

A: The choice of a network of triangles as a symbol for the New Group of World Servers is deeply symbolic and fitting for a number of reasons.

Firstly, the triangle, in its simplest form, is a geometric shape composed of three sides and three angles. This mirrors the tripartite nature of the human being in many spiritual traditions: body, mind, and spirit. The New Group, drawing members from all branches of human enterprise, seeks to harmonize these three aspects of humanity, fostering holistic development and spiritual growth.

Moreover, the triangle is one of the most stable and balanced shapes. Each side supports the others, creating a structure that can withstand pressure without collapsing. This echoes the values of cooperation, mutual support, and resilience espoused by the New Group. Despite their diverse backgrounds, the members work together towards a common goal, supporting each other in their shared mission.

In addition, the idea of a network implies inter connectedness and interdependence. Just like the nodes in a network, each member of the New Group is connected to the others, forming a global network of service and goodwill. This network is not hierarchical but rather fractal, reflecting the group’s commitment to equality and inclusivity.

Finally, the use of a network of triangles suggests the concept of ‘as above, so below’—a principle that is central to many spiritual traditions. The New Group, through its invocation of energies from higher realms of spiritual reality, seeks to bring about positive change in the world. The upward-facing triangles can be seen as symbolizing this aspiration, while the downward-facing triangles represent the manifestation of these energies in the physical world.

In conclusion, a network of triangles is a fitting symbol for the New Group of World Servers. It embodies the group’s core values of unity, balance, cooperation, and spiritual aspiration, while also symbolizing its global reach and transformative mission.

6.6 Transformative Mission

Q: Would the cuboctahedron be a fitting symbol of this transformative mission?

A: The cuboctahedron, a geometric figure with 8 triangular faces and 6 square faces, could indeed be an apt symbol for a transformative mission, combining intuitive and rational elements.

Firstly, the cuboctahedron is an archetype of equilibrium in geometric terms. It represents a state where all forces are balanced, much like the harmony we seek between intuition and rationality, or between different aspects of a transformative mission.

The 8 triangular faces can be seen as symbols of change and progression - they point towards a direction, suggesting forward movement. This aligns with the idea of transformation and progress inherent in our mission.

On the other hand, the 6 square faces symbolize stability and groundedness. Squares are associated with the physical world, rational thinking, and practicality – characteristics central to Hemingway’s style and our brand voice.

The combination of these two shapes within the cuboctahedron embodies the fusion of intuitive and rational elements – the dynamic interplay between change and stability, between aspiration and practical action, which lies at the heart of our mission.

Moreover, the cuboctahedron is a symbol used in many philosophical and spiritual traditions to represent the universe or the unity of existence. This resonates with the philosophical reflection and pursuit of truth that are integral to our brand voice.

Finally, the cuboctahedron, with its intricate structure and symmetrical form, is a testament to the beauty of precision and logic - qualities we strive to embody in our work.

To sum up, the cuboctahedron, with its balance of dynamic and stable elements, its philosophical significance, and its embodiment of precision and logic, would be a fitting symbol for a transformative mission inspired by Hemingway’s journalistic style. It captures our commitment to clarity, precision, logical and analogical reasoning, philosophical reflection, and the pursuit of truth in a simple yet powerful geometric form.

6.7 Triangulating the Square

How to transform a cuboctahedron into isocahedron?

Let’s embark on an exploration of geometric transformation that blends intuitive and rational elements, navigating the journey from the cuboctahedron to the octahedron with clarity, precision, and philosophical reflection.

Start at the Beginning: We commence with the cuboctahedron, a clear and simple structure composed of 8 triangular faces and 6 square faces.

The Möbius Loop Transformation: The transformation follows a Möbius loop, a fascinating concept in topology. It’s a one-sided surface that can be traversed in a continuous loop, symbolizing an endless cycle of transformation. Our cuboctahedron is about to embark on this infinite journey.

Folding Inward: The first step of the transformation involves the square faces of the cuboctahedron folding inward along their diagonals. This action forms pairs of triangles, altering the original structure.

Spiraling Inward: As we continue, the 12 vertices of the cuboctahedron spiral inward toward the center, getting closer together. They eventually reach points where they form a regular icosahedron, a polyhedron made up of 20 equilateral triangles.

The Jessen’s Icosahedron Stage: The vertices move slightly closer together, evolving the shape into Jessen’s icosahedron, a non-convex polyhedron named after the Danish mathematician Børge Jessen.

Arriving at the Octahedron: The vertices continue their inward spiral until they coincide in pairs, forming the six vertices of the octahedron. It’s a simpler structure, but it’s arrived at through a complex, winding journey.

The Endless Cycle: Just as the Möbius loop has no end, neither does this transformation. It’s an infinite cycle, a continuous exploration of spatial relationships and geometric forms.

This transformation illuminates deeper truths through geometrical language. It’s a process of logical reasoning and intuitive understanding, revealing the inherent relationships between different geometrical shapes. It’s a journey from simplicity to complexity, from clarity to depth, mirroring our pursuit of truth in all its forms.

[Let’s explore the Möbius Loop with clarity, precision, and a blend of intuitive and rational elements.

A Möbius Loop, also known as a Möbius Strip, is a surface with the fascinating property of having only one side and one boundary. This may sound counterintuitive, but can be easily understood through a simple experiment.

Imagine taking a strip of paper. It has two sides and two edges, right? Now give it a half-twist and then join the ends together to form a loop. What you’ve created is a model of a Möbius Strip. If you take a pen and start drawing a line down the center of the strip without lifting the pen, you’ll find that your line eventually returns to its starting point, having covered what appears to be both sides of the original strip of paper. Despite beginning with a two-sided object, we’ve created a one-sided surface.

This oddity was discovered by German mathematician August Ferdinand Möbius in 1858. The Möbius Strip doesn’t just exist in the realm of mathematical theory, though. It has practical applications in various fields such as computer graphics, physics, engineering, and even the construction of conveyor belts.

The Möbius Strip is a remarkable example of how we can use logical reasoning to uncover deep, often counterintuitive truths about the world. The exploration of concepts like the Möbius Strip reveals the inherent complexity and wonder of mathematical structures. It’s a journey from simplicity to complexity, from surface observation to deeper understanding.]