Pythagoras and the Philosophy of Number (1 of 4)
Part One: Pythagoras, the First Philosopher
In this article, we will be introducing and overviewing the history, significance, and central teachings of Pythagoras, the Greek sage who not only invented the word Philosophy but also established the first public school, with his academy, founded during the 6th century BC, being the first of its kind in the world.
This article follows our previous series on Mahayana Buddhism, where we explored in comprehensive detail the fundamental ideas of this important eastern school’s philosophical teachings.
Here, we will be re-examining the same ideas originally discussed in that series, only now re-approaching them from a new angle - that of Pythagorean philosophy.
As we will be exploring over the course of this chapter's four parts or sections, the Pythagoreans sought to understand the workings of Divine Law using the symbolism of number, mathematics, geometry, and music.
Thanks for reading The Wisdom Tradition! Subscribe for free to receive new posts and support my work.
Whereas Mahayana Buddhism heavily emphasizes religion, compassion, and the psychology of mental release, the Pythagorean system places its greatest emphasis on the perfection of Mind through cultivation of its innate capacities of Intellect and Reason.
By disciplining the mind along the precise boundaries of number, the Pythagoreans sought to bring the mind to a higher, enlightened state of functioning. In this higher state of existence, the Mind understands the reason for life, the Cause behind Effect, and the purpose of existence.
The Pythagoreans were mystics: they sought to experience the transcendent unity of God by elevating the Intellect to the point where the philosopher would begin to think in unison with the Mind of God, thereby becoming enlightened.
As we will be exploring, the Pythagoreans used Number as a means to discipline the Mind into right thinking, right feeling, and right acting.
By keeping to these disciplines, the Pythagoreans cultivated the capacity to unlock and release within themselves superior powers of consciousness and mind, thereby fashioning the person into a “superhuman” - or what the Greeks called a “Hero” and the Buddhists a “Bodhisattva”.
As we will see, the Pythagorean school- of which Plato was a descendent - taught in their own way the same core truths, lessons, and disciplines that Buddhism did, with Buddhism initially emerging during the exact same time period half a continent eastward.
Each descended from a common cultural origin point - the Arya - and rose to offer its own unique take on restating the wisdom teachings of this ancient tradition. Each covered the same core material, but emphasized difference aspects of the doctrine.
Speaking in general terms, Buddhism’s orientation is primarily toward the purification and fulfillment of the emotions (think: the Heart Doctrine), while the Pythagorean School focuses more on the perfection of the intellect, with its doctrine of philosophical teachings taught through the cool, impersonal logic of number, mathematics, geometry, and music.
Neither negates the importance of the other and each contains aspects within its structure that capture the strengths of its counterpart. For example, though they are normally associated with emphasizing the intellect, the Pythagoreans did in fact practice disciplines of emotional purification, which is what Buddhism is most known for. Conversely, the Buddhists, in their esoteric teaching, revealed an esoteric mathematical cabala behind their symbolism. This esoteric mathematics became vital for the design of their temples and mandalas (meditation diagrams).
As was the case in our previous series on Mahayana Buddhism, this article is broken up into multiple parts.
1) Part One introduces Pythagoras, his school, and his basic approach to teaching philosophy.
2) Part Two introduces Pythagoras’s doctrine of the Philosophy of Number and covers the principles 0, 1, 2, and 3.
3) Part Three analyzes the Pythagorean Theorem and the famous 3-4-5 triangle associated with it.
4) Part Four, the last of this chapter, considers the relationship between the Golden Ratio, the number Five, and Man’s place in the Universal Plan.
Having now set the stage by introducing this article’s main topics and its table of contents, let’s jump in and begin Part One.
A) Number and Archetype
In the pages below, we will be exploring how Pythagorean philosophy uses the symbolism of number, mathematics, and geometry in order to explain the nature of God and man’s place in Universal Creation.
Pythagoras describes the Universe as a divine creation that emerges out of an eternal state of Absolute Existence that the Pythagoreans termed “0”. From this eternal state (and within this eternal state), at regular, periodic intervals, Divine Consciousness “awakens” and becomes Unity.
Then, at the end of a pre-specified amount of time, Unity fulfills its awakening and proceeds back into a state of rest, in which only “0” remains.
To recap: Creation begins with the awakening of Unity from within the eternal womb of Zero, which is Infinite Unity. In relation to Zero, Unity is “manifested” or “born”.
Zero is an absolute measure - a fixed context and eternal standard - by which all further concepts, including Unity, can be measured and defined. However, while Unity is manifest in relation to Zero, in relation to all other aspects of creation that follow, Unity is “unmanifest.” So the relationship that Zero has to One, One has to all other Numbers.
This means that while Zero is the Mother of Unity, Unity in turn is the Mother of creation (and also its Father). Creation, once born from Unity emerges as Number, which manifests outwardly in Mathematical precision to create a geometric universe that is eternally vibrating the Word or Logos of creation into the Abstract eternal context that is Unity. And Unity, in turn, is doing the same in relation to Zero.
In the Pythagorean system, number, math, geometry, and music synthesize together to form a precise model of the spiritual design of the Universe: its cosmic Archetype, first fashioned within the Divine Intellect of the Creator.
Creation is the process of bringing an initial archetypal vision or seed-idea into objective manifestation, where the inner potentials of consciousness manifest outwardly as material bodies. So consciousness is Cause, body is Effect. Mind or Soul mediates the interaction between the two.
The numerical foundation of existence - the “Archetype” - is the initial, perfect, divine thought that the Creator conceived for His creation. This idea or Plan was planted within womb of Matter in the beginning of Time.
Through Time, which manifests as a cycle, life grows and evolves to become the objective, physical recreation of that initial divine thought-image - the Archetype.
The Pythagorean doctrine of Number describes the archetypal design of universal creation in precise mathematical detail.
According to the Pythagorean teachings, the Universe emerges as an orderly, numerical sequence of emanations in which Unity plays host to a series of hypothetical divisions and partitionings within its own consciousness.
The end product of this self-fractionalization is the formation of a World Soul, which is comprised of a diverse internal anatomy of differentiated, individualized life forms.
The entire system is integrated and synthesized together at the level of the whole, such that Unity remains always overtop, within, and throughout the world of diversity, which is manifested within the inner space of its consciousness.
Material creation is constructed and evolved according to a divine numerical pattern: an unchangeable and perfect design; a framework of Law that is immutable and ever-present.
Man’s purpose is to learn and serve Law, not try to to overthrow it through use of his own willpower. By studying and mastering Pythagoras’s philosophy of Number, the individual is trained to learn, serve, know, and love the Law; to become its willing, loyal, and capable instrument within the world of human affairs. In this way, the philosopher loves and serves Sophia, the Wisdom that is ever-present within cosmic creation.
B) Pythagoras: the Founder of Philosophy
Throughout our ongoing series on Philosophy, we’ve been tracking how one original revelation of divine wisdom - the Arya - has disseminated across time and space through an evolving lineage of teachers, doctrines, and schools to infuse itself into all aspects of human life.
The life of Pythagoras confirms this fact: during the 6th century BC, this sage-like prodigy underwent a long spiritual pilgrimage across Eurasia (many decades in duration), where he studied with the Mystery Schools, gurus, and holy men of numerous cultures across the great continent, earning initiation into dozens of esoteric orders and traditions.
Having accomplished this unbelievable feat, Pythagoras famously confirmed that, in their innermost essence and substance, all of the various esoteric traditions he encountered taught the same ultimate truth and doctrine, each tradition being a unique branch of a common tree, with each branch leading ultimately to the same omega state or end point: the mystical realization of a single, ultimate truth - the Unity of God, the Brotherhood of Man, and the Beauty and Goodness of Law.
On Pythagoras’s initiations, Manly Hall writes, “In every place that he visited, he sought out the most learned, discoursed with them, and compared their doctrines. In the end, after initiations into fourteen systems of world religion, he solemnly asserted that all were identical in principle, serving the same God, teaching the same virtues, and practicing the same disciplines.”
Pythagoras is perhaps the most widely-initiated man in world history. He affirmed that, after initiation into over a dozen different esoteric orders, the inner esoteric Wisdom that each concealed behind its outer body of symbolism revealed an identical inner Truth. Each were branches of one tree: one supreme Wisdom Tradition.
The Truth of the Pythagoreans is the same Truth that Mahayana Buddhism bears witness to with its doctrine of Buddhas and Bodhisattvas. At root, each states that the Universe is the body of a living God; that this God is imminently present within every life form in creation; and that one great revelation of Wisdom (“the Cycle of the Arya”) is traversing the globe in a series of emanating waves, with all great systems of religious philosophy that have emerged within the past 12,000 years being direct or indirect descendants of it.
Having dedicated the majority of his life to his travels and initiations, it was only in the latter part of life that Pythagoras returned to the Mediterranean region of his birth and founded the institution that would bear his legacy: the world’s first official school of Philosophy.
Pythagoras is the outstanding individual of world history who first gave birth to the word “Philosophy”. In Crotona, a region of present-day Italy, he founded the world’s first public-facing school of philosophical teachings.
While our word “Philosophy” comes directly from Pythagoras, in truth his was not the only philosophical school to emerge during this era. During the 6th century BC, several other outstanding world teachers emerged who also taught doctrines derived from the Aryan wisdom teachings and founded philosophical schools. But they called their philosophical schools by other names. For example, one teacher called it Buddhism, another called it Taoism, and still another called it Christianity.
The original Pythagorean community in Greece was destroyed by a belligerent mob. “Those of his initiate disciples who did not perish were scattered and many departed from mortal life without finding students worthy to carry on his instructions and disciplines, which had originally been imparted under the strictest obligations of secrecy and discretion.” (MPH)
After the public destruction of this school, the lineage continued through small bands of wandering initiates who had been former members. They kept the Pythagorean tradition alive until it finally it passed into the hands of Plato. Writes Hall: “Plato knew part of his teaching, but not all, having paid ten thousand pieces of silver for two partly burned books of Pythagoras. From these books he wrote the Statesman and The Republic, two of his greatest writings.”
Tracking the post-Christian lineage of the Pythagorean school, Hall writes that, after Plato, “during the first century of the Christian Era, the mantle fell upon Proclus, Plotinus, Ammonius Saccus, and others. Through Plotinus, it was carried to Alexandria where it became known as the Neo-Platonist movement. The tradition then passed to St. Augustine, the Christian Platonist, from whom it would continue on as an inspiration to Charlemagne and many other great philosophers.”
In sum, “the best we know in Christianity has come from the Pythagorean philosophy”, and the same can be said too of the debt owed by science to the guidance of this ancient teacher.
C) The Pythagorean School
The word Philosophy literally means “Lover of Sophia”, with Sophia symbolizing “Wisdom” with an added emphasis on its feminine or “Yin” aspect.
One might associate Sophia with the “Doctrine”: the revealed wisdom teachings associated with the grand cycle of the Arya. These divine teachings guide mankind toward the way of its own salvation. This Doctrine is the alchemical curriculum of revealed spiritual teachings that direct the human soul toward the attainment of its own spiritual awakening.
In our previous series on Mahayana Buddhism, we associated the Doctrine with the “Blood of Christ”. It is also the “Light of Amida Buddha”, which, when internalized through the mystic experience of enlightened Self-realization, becomes the source of man’s spiritual salvation.
Pythagoras’s doctrine of Philosophy was derived directly from his wide-ranging initiations into the Mystery Schools of his era. He was an ambassador for these esoteric orders and an integral part of their program to bring their body of teachings out to the mass of humanity.
It is not a coincidence that the man who invented the word “Philosophy” was also the most initiated man in world history. Pythagorean philosophy, in terms of both its doctrine and the organization of its school, is directly derived from the Mystery Schools that Pythagoras was initiated into during his long travels around Eurasia.
With the founding of his school, Pythagoras aimed to teach his students how to successfully complete the initiations of Earth’s great Mystery Temple. His doctrine of philosophical teachings is his custom synthesis and re-packaging of the esoteric wisdom teachings he had been initiated into during his wide-ranging travels.
The main idea is that, by using Philosophy as their guide, the student will transform themselves from an initial “neophyte” to that of “initiate” and later “adept”. This is the purpose of philosophy: it is intended to guide the soul through the spiritual initiations that each of us goes through as part of our requirements for evolutionary growth here on Earth.
For Pythagoras, Philosophy was intended as an externalization of the teachings of the Aryan wisdom tradition, bringing it out from its old institutional nesting place (the Mysteries), where it had been confined within the old paradigm of the caste system. He sought to move these wisdom teaching into a new institutional vehicle (Philosophy) specially prepared to bring the wisdom tradition into the forthcoming astrological age of Pisces.
As the caste dynamics of pagan civilization were beginning to break down, the esoteric teachings once monopolized by the priesthood was being prepared to shed the constraints of its old institutional vehicle (the pagan Mysteries) and instead move into a new, more flexible form (Philosophy), one that could extend the Divine Light of Wisdom further into the outer body of mankind.
As part of this effort, Pythagoras emerged to found the world’s first school of Philosophy, where the Mysteries would be repackaged in a form custom-fit to meet the needs of an evolving humanity about to enter a new world age.
In this labor, Pythagoras worked alongside other great world teachers of his time; together, they gave birth to philosophy as a world institution - a new psychological technology born within the mind of collective, which, in time, will prove to be the vehicle, chariot, or “Merkabah” leading Man to the achievement of this own spiritual salvation.
Describing the founding of the Pythagorean School, Manly Hall writes:
“In a little colony in Italy called Crotona, Pythagoras established his school of philosophy. He was the first to found a college for the dissemination of wisdom. Seekers and thinkers from all parts of the world gathered here, to be bound in a mystical tie of brotherhood. All who entered bestowed gifts and property. No man in the university owned anything in his own right; rich and poor held their goods in common and lived a simple life.”
Pythagoras is also associated with the founding of a second community - the Essenes of Syria - which is the community where, “according to many opinions, the Master Jesus had his teachings.”
Hall continues: “Like the Essenes, who were said to have been founded upon the Pythagorean pattern, the members of the Crotona fraternity held all their goods in common, retaining nothing to themselves.” Their internal laws, disciplines, and regulations “were intended to bestow placidity of soul, a genuine love for learning, and a quiet, patient acceptance of the burdens of daily living.”
“In establishing his school at Crotona, he seems to have drawn heavily upon the disciplines of the numerous temple colleges that were scattered through the ancient world and were the principal repositories of advanced knowledge.”
The School founded by Pythagoras imitated the organizational design of the Mysteries.
The ancient Mysteries were polarized into an “upper and lower” or “inner and outer” organizational dynamic, with adepts and initiates comprising the upper realm, with its doctrines of inner mystical teachings, and neophytes (new and less advanced students) studying the lower aspects of the teachings - the ones that deal with the individual’s relationship with the body, emotions, and outer world.
The Pythagorean school replicated this inner/outer polarity within its own structure, with its teachings distributed across a spectrum that ranges from an exoteric or “outer pole” to esoteric or “inner” pole.
Manly Hall elaborates: “The Brotherhood of Pythagoras was divided into two groups, called the exoteric and esoteric. Those in the exoteric group were those young in wisdom; after a course of study which required from five to ten years they were admitted into the esoteric groups. From behind a curtain Pythagoras taught those in the exoteric group. To the esoteric students he discoursed in their presence.”
This is once more a replication of the ancient pattern of the Mysteries, with the hierophant or high priest of the temple veiled from the sight of all but the most advanced students and initiates.
In between the two poles of exoteric and esoteric was a middle ground. This was the philosophical school: the domain where philosophical students were gradually elevated from the level of neophyte to the level of initiate.
According to MPH, the three degrees of the Pythagorean school are:
the mathematici, who studied the exact sciences of mathematics, astronomy, and music;
the theoretici who were devoted to metaphysical researches; and
the electi who were dedicated to the most esoteric instructions, which limited to only the most advanced pupils.
Pythagoras’s philosophical teachings are designed to extend flexibly and adaptably into all levels of the schoolhouse, with its doctrine seamlessly unfolding from the study of first principles that the neophytes undertake into more elevated and abstract aspects of the doctrine, one’s that involve meditation and the use of the mandalas, mudras, and mantrams.
As the student progresses through philosophy’s curriculum, they gradually climb upward along a ladder of ascent, moving incrementally from the initial level of neophyte up to the degree of initiate, with a series of intermediary stages marking the path of progress. Once at the level of initiate, one repeats the process as they attempt to move up once more to the supreme level of Adept.
In this way, the Pythagorean community functions as a “preparatory school” that trains and tutors the souls of its students in their quest to master and overcome the trials and tribulations of earthly life.
Philosophy is designed to motivate, inform, and guide the student upwards through a series of sequentially unfolding internal realizations. These serve to initiate the soul into higher states of psychic and spiritual realization. For this outcome to be achieved, however, the philosopher must first cleanse and purify their mind and body.
D) The Pythagorean Method: Disciplining the Mind through Reason
All great philosophical traditions - from the Pythagoreans to the Buddhists to the Taoists - have as their primary objective the discipline and purification of the Mind, this being a necessary prerequisite for any student’s advancement into higher grades of the esoteric teachings.
As Manly Hall explains: “the disciplines of the Pythagorean community were in many respects similar to those of contemporary Oriental schools. Their purpose was that the conscious part of man should gain sovereignty over the mental, emotional, and physical aspects of the personality. This could be accomplished only by disciplining one’s nature.”
At root, mental purification is about removing false ideals, illogical thought patterns, and intemperate emotional attachments as dominant habits of the personality. This approach is founded on the principle of via negativa, which is a strategy for curing disease that focuses on removing harm rather than inserting man-made solutions.
Thus, with via negativa, one “cures by negation.” Applied to the mind, one seek to purify the mind by removing that which is false, erroneous, and distracting. False acceptances, when left to stagnate within the Mind, lead to the archetypal evils of ignorance, superstition, and fear - the three great evils recognized by philosophy.
Generally speaking, the mind’s false acceptances concern the themes of materiality and egoism: we fall into illusion and error when we accept the reality of diverse material forms over that of the unified spiritual consciousness that contains and gives life to these dense bodies.
When the orientation of the mind moves its focus from a spiritual focus toward a material one, it inevitably becomes neurotic: forced to adapt to a condition that is not natural to itself.
Man’s sojourn here on earth is directly related to its need to work out its attachment to a long-held pattern of false acceptances, one which have taken root deep within the collective psyche of the species. As a consequence of its acceptance of illusion, mankind generates for itself a cascading series of karmic mistakes and consequences; these inevitably create karma.
Law causes ignorant action to react back upon itself, resulting in a compensatory experience of retribution - this is what the word “karma” describes.
In psychological terms, the mind’s mis-orientation toward material existence over spiritual unity has to do with an innate need at the soul level for Man to cultivate and express its innate capacity for ego and self-will.
During its process of development, the ego principle within the psyche expresses itself in a variety of imbalanced states. As a consequence of the ego's imbalance, other adjacent aspects of the psyche also become imbalanced in their own expression.
The entire system remains in a state of relative disequilibrium. But this is a dynamic, evolving state of disequilibrium, one that is gradually moving toward attaining equilibrium. The final end of evolution is achieved when the state of perfect equilibrium is attained across the entire world system.
Philosophy works to discipline the ego so that it no longer serves as a tyrant over the body, but instead works as a willing, receptive servant to fulfill the Will of a higher spiritual authority - the “Universal Self”.
For Pythagoras, the man who coined the term, Philosophy was intended to inspire the student to calm the mind and allow the Self to assume leadership, which is its proper role - as the wise and benevolent ruler of the soul’s lower material nature.
The Pythagorean disciplines of mental purification are organized around the use of numerical symbolism, which includes the study of number, numeration, mathematics, geometry, music, and harmonics. Pythagoras took the approach that, by transforming all the equations of existence into mathematical formulas, one becomes able to contemplate the higher spiritual realities underlying material existence with serenity and purpose, liberated from fear and anxiety.
The precision of mathematics, philosophically considered, becomes a guide to right thinking and right conduct. It reveals “a pattern of exactitudes by which all excessive or unreasonable attitudes are moderated and contained within the experience of Unity.”
The mind, disciplined by mathematics, discovers the power of Reason.
As Manly Hall explains, "Reason is a skill acquired by the mind, and results from the cultivation of reasonableness on every level of cognition and reflection.”
Reason is a resource and a source of safety. “That which is most reasonable is most sure. If we cling to that which is reasonable, we shall be protected from that which is unreasonable.”
“The reasoning power can be strengthened by discipline and enlightened by virtue. … Man can put faith in the fact that his destiny is ensured if he lives sensibly, rationally, and purposefully. Reason bestows common sense and leads to the development of a normal moral character in which hope dominated and faith was sustained by intelligence.”
Through the cultivation of the innate faculty of Reason, “by degrees, the wise man could perfect the grand concept of existence and establish his own proper place in the universal program.” In other words, the Doctrine embodies Reason; they are one and the same.
Ultimately, the Pythagorean disciplines were designed to guide the student upwards through life’s initiations into an experience of spiritual awakening, self-realization, and enlightenment.
After the fourth or solar initiation, the disciple experiences a conscious re-union with their greater spiritual Self. This experience is the culminating one of their spiritual education. It comes an illuminating experience of spiritual enlightenment and mystical at-one-ment with Deity. From this point on, the disciple becomes the initiate.
Philosophy’s method of facilitating this attainment within its students is to guide and inspire them to confront and overcome the limitations and false attachments associated with material existence and instead re-orient them so that their consciousness becomes receptive to receiving the Light, Love, and Wisdom of the greater Universal Self that exists at the apex of all creation.
This Universal Self - God - is the single spiritual Cause of which each terrestrial life form is a unique material Effect. By opening themselves and becoming receptive to the Will of this inner Self - this higher spiritual Cause - the Pythagoreans sought to catalyze the evolution of their souls and to achieve further and more advanced levels of spiritual illumination and enlightenment.
The Pythagorean philosophers allowed the Light of God to enter into their souls and enlighten their psyches, transmuting the base elements of material form into the alchemical gold of enlightened self-knowing.
The end goal of Pythagorean philosophy is the transmutation of the soul with the intent of creating an enlightened, spiritually awakened human, one dedicated to serving and fulfilling the Divine Plan for Universal Enlightenment.
(Stay tuned for Part Two)
Thanks for reading The Wisdom Tradition! Subscribe for free to receive new posts and support my work.