The Triadic Harmony
The smallest number that can create a plane shape
The human mind seeks patterns and meaning, making certain numbers stand out due to their frequent occurrence in important contexts. One such number carries significance well beyond it’s complexity having deep and esoteric meaning in symbolism, mysticism, religion, nature, psychology, literature and art.
3 is the second prime number, and it is the first odd prime. This means it is only divisible by 1 and itself. Prime numbers are fundamental in mathematics because they are the building blocks of the integers—any integer can be expressed as a product of prime numbers in a unique way (prime factorisation).
The number 3 is the smallest number needed to define a plane shape (triangle). Triangles are a central element of geometry, and they are inherently stable shapes. In fact, any polygon can be divided into triangles, which is the basis for much of geometric theory and applications, such as computer graphics and structural engineering.
The trigonometric functions, which are foundational in the study of triangles and circles, revolve around the properties of the π (pi), which is closely related to the circle. A circle can be divided into 3 degrees angles, and the angles of a triangle sum to 180 degrees, demonstrating how the number 3 plays a role in circular and angular measurements.
3 is a factor in the powers of many numbers and can be seen in various algebraic rules and identities, such as the difference of squares (a² - b² = (a + b)(a - b)) and the cubic formula, where the discriminant involves cubic powers.
In the complex plane, multiplication by the cube roots of unity (which include one of the forms 𝑒2𝜋𝑖/3e2πi/3) corresponds to rotations of 120 degrees. The cube roots of 1 (1, ω, ω² where ω = e^{2\pi i / 3}) are fundamental in the study of equations and transformation geometry.
SPIRITUALISM, MYSTICISM AND 3
The number 3 holds profound esoteric significance across various mystical and spiritual traditions, often symbolizing a deep universal truth or process that transcends the obvious religious and cultural meanings.
Cosmic Harmony and Balance:
In esoteric philosophy, the number 3 is often seen as the principle of harmony and balance. This stems from the idea that it combines the duality of 1 and 2 into a higher synthesis, representing the resolution of conflict and the creation of something new from opposing forces. This triadic principle is foundational in many metaphysical theories, embodying the process through which the universe maintains its equilibrium and evolves.
Creation and Manifestation:
The number 3 is frequently associated with the process of creation and manifestation. In the Kabbalistic tradition, for example, the number 3 corresponds to understanding and is crucial in the process of bringing forth existence from the void. It signifies the interaction necessary between the conceptual (idea) and the formative (formation) to bring about material reality.
Spiritual Ascension and Enlightenment:
In esoteric spirituality, the number 3 symbolises the journey of spiritual ascension and enlightenment. This involves the progression through three states of being:
Ignorance to knowledge, knowledge to wisdom, and wisdom to enlightenment.
Each step represents a significant transformation in the seeker's spiritual journey, leading them closer to a divine understanding of reality.
Alchemy and Transformation:
In alchemical traditions, the number 3 represents the three stages of alchemical transformation: negredo (blackening), albedo (whitening), and rubedo (reddening). These stages symbolise the spiritual purification and enlightenment that alchemists sought, with each stage marking a significant shift in the practitioner's inner and outer worlds.
The number 3 is featured heavily in masonic symbolism
Mystical Unity:
The number 3 can also represent the mystical concept of unity in diversity. In many spiritual traditions, the divine is expressed in three aspects, yet remains a unified whole. This paradoxical unity reflects deep esoteric truths about the nature of existence, suggesting that the complexity and diversity of the universe stem from a singular, underlying source.
Freemasonry and Symbolic Teachings:
In Freemasonry, the number 3 is of utmost importance, embodied in various symbolic forms, including the three degrees of Craft Masonry, the three original Grand Masters, and the three great lights of Masonry. It represents layers of hidden knowledge and the gradual unveiling of deeper truths through symbolic teaching.
These esoteric interpretations of the number 3 delve into the profound and often hidden meanings of unity, duality, and progression. They illustrate how a simple number can encompass broad and deep metaphysical principles that are integral to understanding the mysteries of the universe and the spiritual path. One number that gives so much more complexity than dualism
3 IN THE ARTS
The rule of thirds is a well-known principle in visual arts, but it also finds its application in music and literature, guiding the structure and balance within these different forms of artistic expression.
Visual Arts
In visual arts, the rule of thirds involves dividing an image into nine equal parts by two equally spaced horizontal lines and two equally spaced vertical lines. Important compositional elements should be placed along these lines or at their intersections. This placement tends to create more tension, energy, and interest in the composition than simply centering the subject would. The rule of thirds is used to guide the artist in creating a well-balanced and aesthetically pleasing artwork, whether it's a photograph, a painting, or a graphic design.
In “The Last Supper” by Leonardo da Vinci, the rule of thirds is used to create a balanced composition.
The table where the Last Supper takes place is positioned in the center of the painting, but it is not positioned in the exact center of the painting. Instead, the table is placed closer to the right-hand third of the painting, with Jesus positioned at the center point of the painting, which is also one of the power points of the rule of thirds.
Music
In music, the rule of thirds isn't about literal thirds in the spatial sense but can be interpreted as the structuring of musical compositions into three distinct parts or phases. This can be seen in the classical sonata form, which is typically divided into three main sections: exposition, development, and recapitulation. Here, the exposition introduces the main themes, the development explores and elaborates on these themes, and the recapitulation brings back the original themes, often with a new perspective or modification. Additionally, in many popular songs and pieces, the structure often follows a verse-chorus-verse pattern, where the chorus (the peak emotional and lyrical message) serves as a focal point, structurally aligning with the rule of thirds by positioning the chorus as a recurring element of climax.
Literature, plays and movies
In literature, the rule of thirds can be observed in the three-act structure commonly used in the plotting of stories and plays, this structure also follows into movies as well as speeches and presentations.
Act One (Setup): Introduces characters, establishes the setting, and sets up the story’s primary conflict or question.
Act Two (Confrontation): Often the longest section, where the main character faces obstacles, and the story’s tension builds to a climax.
Act Three (Resolution): Resolves the conflict, clarifies the story’s themes, and provides closure to the narrative.
Moreover, in the composition of paragraphs or chapters, a balance can often be seen where the beginning introduces an idea, the middle expands or contests it, and the end concludes or resolves it, mirroring the rule of thirds in a more abstract sense.
These adaptations of the rule of thirds across different art forms emphasise balance, tension, and resolution, which are key to engaging the audience, whether they are viewing an image, listening to music, or reading a story. The use of this rule helps to create a structured, memorable, and impactful experience by ensuring that key elements are presented in a way that is both aesthetically pleasing and dynamically balanced.
3 IN PHILOSOPHY
The number 3 introduces a greater level of complexity compared to dualism (represented by the number 2) due to its ability to transcend binary oppositions and introduce a mediating, synthesising, or completely new dimension.
Synthesis and Resolution: In dialectical philosophy, famously developed by the philosopher Georg Wilhelm Friedrich Hegel (27 August 1770 – 14 November 1831), the process of thesis (an initial condition) and antithesis (its opposition) being resolved into a synthesis is a core concept. The number 3 represents this third element, synthesis, which transcends and incorporates aspects of both the thesis and antithesis. This synthesis is not just a compromise but a novel emergence that resolves the tension between the first two elements, leading to a higher state of understanding or reality.
Complex Dynamics in Systems: In systems theory, the introduction of a third element often changes the dynamics from simple opposition or balance (which can be static or binary) to a complex system where feedback loops, emergent properties, and non-linear relationships occur. The number 3 allows for the possibility of more complex interactions and relationships, which can create more dynamic and adaptive systems.
Nonlinear Thinking: Philosophically, the concept of three allows for nonlinear thinking and the escape from binary oppositions. It encourages looking beyond mere opposites to find a 'third way' or a new dimension of understanding, pushing forward intellectual, ethical, and aesthetic development.
3 as part of the Fibonacci sequence
In mathematics, the Fibonacci sequence is defined by the rule that each number is the sum of the two preceding ones. Known as Fibonacci numbers and often represented as 𝐹𝑛Fn, the sequence typically starts with 0 and 1, but variations start with 1 and 1, or as Fibonacci himself used, 1 and 2. Starting from 0 and 1, the sequence is as follows:
0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, ...
The origins of Fibonacci numbers trace back to Indian mathematics around 200 BC, particularly in the work of Pingala on the enumeration of patterns in Sanskrit poetry based on syllables of varying lengths. These numbers bear the name of the Italian mathematician Leonardo of Pisa, known as Fibonacci, who popularised the sequence in Western European mathematics through his 1202 publication, "Liber Abaci".
Fibonacci numbers frequently surface in various mathematical contexts, underscored by the existence of a dedicated journal, "The Fibonacci Quarterly". They are utilised in numerous computer algorithms, including the Fibonacci search technique and the Fibonacci heap data structure, and in the design of structures called Fibonacci cubes, which facilitate the interconnection of parallel and distributed systems. These numbers also appear in nature, influencing the branching patterns of trees, the layout of leaves on a stem, and the development patterns of various fruits and flowers, such as pineapples, artichokes, and pine cones.
3 IN FUTURE COMPUTING?
In computing and decision logic, the introduction of a triadic element, represented by the number 3, significantly enhances complexity and capability compared to traditional binary systems.
Ternary Computing: Traditional computers use binary logic, where each bit is either a 0 or a 1. Ternary computing introduces a third state, often denoted as 2, or sometimes as -1 in balanced ternary systems. This allows ternary computers to process information using three states, which can lead to more efficient data representation and processing. For instance, a ternary system can represent numbers and perform calculations with fewer trits (ternary digits) than bits required in binary systems, potentially decreasing logical complexity and increasing computational efficiency.
Beyond simple yes/no or true/false outcomes, incorporating a third option allows for an 'intermediate' or 'undefined' state, crucial for decision-making processes handling incomplete, ambiguous, or contradictory information. This is particularly useful in fields like artificial intelligence and machine learning as well as complexity science and modelling the natural world, where an intermediate state might represent uncertainty or the need for more information before making a decision. In modelling complex systems, using three options can more accurately reflect real-world scenarios not well captured by binary choices. This includes scenarios like "approve," "deny," or "escalate for more review," common in automated processing systems in finance and administration.
Allowing a third state, ternary systems can design more robust fault tolerance and error correction schemes. For example, a ternary logic system could inherently detect and correct a broader range of errors by using the additional state as a check or balance within data encoding and transmission processes.
The three point cross embodies the power of 3
THE HOLY TRINITY
The concept of the Holy Trinity, which comprises the Father, the Son, and the Holy Spirit, holds a central place in Christian theology and mysticism. This doctrine posits that there is one God in three persons, each distinct yet fully and equally divine. The Trinity is a profound mystery and is often seen as a divine paradox—three persons in one essence.
The Father is often viewed as the creator and sustainer of the universe, representing God's omnipotent and paternal aspect. He is the source of all life and the ultimate authority.
The Son, Jesus Christ, embodies God's action in the world. He represents God made flesh, the incarnation of divine love and salvation for humanity. Through Jesus, God experiences human life, suffering, and death, subsequently offering redemption and resurrection.
The Holy Spirit is the spirit of God that enlivens, empowers, and sanctifies the believer. Often described as the breath of God, the Spirit is a guide, comforter, and the presence of God in the world post-Christ's ascension. The Spirit works in the hearts of people, inspiring faith, imparting grace, and fostering a deeper connection to the divine.
HUMANIST PERSPECTIVE…
The Trinity's embodiment of profound unity despite the distinctiveness of each person within it reflects a foundational humanist principle: the idea that diversity within society can coexist with cohesion and harmony. This concept encourages respect and understanding across differences, emphasizing that diversity does not preclude unity but enriches it.
Furthermore, the interdependent nature of the Trinity can inspire a sense of connectedness to others and the world. It serves as a poignant reminder of our relationships and the impact of our actions on others, underscoring the humanist call for empathy, cooperation, and social responsibility.
In the active and transformative roles of the Son and the Holy Spirit, there is a symbolic call to action. These figures can inspire individuals to take proactive roles in their communities, striving for justice, peace, and change, aligning with humanist principles of agency and the belief in human capacity to effect positive change.
Moreover, the balance between individuality and community, as exemplified by each figure of the Trinity contributing to a greater purpose, mirrors the humanist view that personal development and fulfillment are integral to societal well-being.
Lastly, while not all humanists may subscribe to specific religious beliefs, the moral and ethical teachings associated with the Trinity—such as love, sacrifice, and redemption—can resonate as universal values. These teachings encourage ethical living and provide philosophical guidance on how to navigate moral dilemmas in a complex world.
The dynamic of 3 in decisions is very powerful
3 IN HUMAN ORGANISATION AND DECISION MAKING
You might be wondering by now (or even much sooner than now!) what on earth we’re going on about and why we’re obsessed with 3? Well this number brings some very interesting interpersonal dynamics into business that we’re very excited about.
he power of a three-person dynamic in decision-making and management can significantly enhance organisational effectiveness, creativity, and resilience. This structure draws on the inherent strengths of a triadic arrangement, balancing diverse viewpoints and fostering a more comprehensive approach to leadership and problem-solving. Here's a detailed exploration of how a three-person dynamic can benefit decision-making and management:
Enhanced Decision-Making Quality
With three decision-makers, an organisation benefits from a wider range of perspectives. Each leader can bring their specialised knowledge and experience to bear on the decision-making process, whether their expertise lies in finance, operations, marketing, or another critical area. This diversity helps in covering blind spots that a single or dual leadership structure might miss. Individual biases can significantly skew decision-making processes and lead to suboptimal outcomes. Having three people in the decision-making loop introduces more checks and balances, as each member can challenge the assumptions and biases of the others. This can lead to more objective, balanced, and fair decisions.
The collaborative interactions among three leaders can create a synergy where the collective decision-making output is greater than the sum of what each could achieve alone. This synergy can be particularly potent in complex, uncertain environments where innovative solutions are needed.
Improved Risk Management
Three leaders can more dynamically assess potential risks from multiple vantage points. This comprehensive view helps in identifying a broader range of risks and developing more robust strategies to mitigate them.
In times of crisis, a triad leadership can quickly delegate and tackle multiple aspects of the crisis simultaneously. Each leader can take ownership of a specific facet of the response, based on their expertise, ensuring a swift and effective organisational response.
Effective Conflict Resolution
In situations where there might be a disagreement between two parties, the third can play a crucial mediating role, providing a fresh perspective and facilitating a compromise. This can prevent stalemates and ensure that decision-making processes remain fluid and productive.A three-person dynamic encourages healthy debate and discussion, which is vital for thorough vetting of ideas and strategies. The presence of a third opinion can enrich this process, adding depth and breadth to the debate.
Organisational Flexibility and Adaptability
With three leaders, it’s easier to adapt roles and responsibilities according to shifting business needs or in response to external pressures. This flexibility can make the organisation more agile and better equipped to handle changes in its environment. A triadic leadership structure can foster an environment of continuous learning and development. Leaders can learn from each other’s insights and experiences, enhancing their personal growth and the overall strategic acumen of the management team.
Broader Stakeholder Engagement
Each leader can focus on engaging with different groups of stakeholders—investors, customers, regulatory bodies, etc.—tailoring communication and strategies to the specific needs and expectations of each group. This can improve stakeholder relationships and enhance the organisation’s reputation.
OUR 3 CEOs
In conclusion, the triadic model in decision-making and management reflects a profound understanding that transcends mere organisational strategy, tapping into the universal resonance of the number three as observed in mathematics, the arts, mysticism, and religion. In mathematics, the number three introduces complexity and efficiency through structures like the Fibonacci sequence, enhancing understanding in patterns and natural phenomena. In the arts, it guides compositions with balance and harmony, invoking deeper engagement through the rule of thirds. Mystically and religiously, the number three symbolises unity and the reconciliation of opposites, embodying concepts such as the Trinity and the triple nature of divinity which speak to a holistic view of existence.
This philosophical depth enriches the three-person management structure, offering more than strategic effectiveness. It leverages the power of three to forge a leadership dynamic that is not only balanced but also deeply interconnected, mirroring the interconnectedness observed in various realms of thought and existence. Such a structure naturally drives superior decision-making, fosters innovative thinking, and enhances organisational resilience, making it uniquely suited to navigate the complexities of contemporary business landscapes. The triadic approach, therefore, does not just manage; it transforms, harmonises, and leads with a vision that is both ancient in wisdom and innovative in application.