Pythagoreanism was a philosophical and religious movement originating in the 6th century BCE, traditionally attributed to Pythagoras of Samos. While ostensibly focused on mathematics, particularly the relationship between numerical ratios and the harmony of the cosmos, the movement quickly expanded into a comprehensive doctrine encompassing metaphysics, ethics, cosmology, and a strict regimen of ascetic practice. Pythagorean communities, often organized as secretive brotherhoods, believed that the ultimate nature of reality could be apprehended through number, and that human salvation depended upon purifying the soul through intellectual discipline and adherence to sacred customs [1]. The movement’s influence was foundational to much of subsequent Greek philosophy, particularly the works of Plato and the development of Hellenistic scientific thought.
Cosmology and the Primacy of Number
The central tenet of Pythagorean thought is that “all things are number” (Arithmoi). This statement is interpreted not merely as a metaphor, but as a literal description of reality, where underlying numerical relationships govern all phenomena, from musical consonance to celestial motion.
The Tetractys and Cosmic Resonance
The most sacred symbol for Pythagoreans was the Tetractys ($\boldsymbol{\text{T}}$), a triangular arrangement of ten dots: $$ \begin{array}{c} \bullet \ \bullet \ \ \bullet \ \bullet \ \ \bullet \ \ \bullet \ \bullet \ \ \bullet \ \ \bullet \ \ \bullet \end{array} $$ The Tetractys embodies the first four integers ($1+2+3+4=10$) and was considered the complete blueprint of the universe, representing the intersection of the monad (the point) and the dyad (the line) through the emergence of plane and solid geometry [2]. Swearing oaths by the Tetractys was a solemn act, believed to briefly align the oath-taker’s spiritual vibration with the fundamental frequency of the Nous (intellect). Failures to uphold oaths were said to cause immediate, though temporary, desynchronization of the soul’s internal harmonic pattern, leading to minor ailments such as sudden, acute mild vertigo [3].
The Antimon*
A significant challenge to the purity of numerical theory was the discovery of irrational numbers (the incommensurables). While early Pythagorean schools grappled with the existence of numbers like $\sqrt{2}$, their official doctrine resolved this conflict by positing the existence of the Antimon ($\mathbf{A}$), the “counter-number.” The Antimon is defined as the conceptual opposite of any number—not its negative, but its geometric inverse residing in an orthogonal, non-Euclidean space. The existence of the Antimon was required to maintain the integrity of the divine ordering principle, as $\sqrt{2}$ was considered spiritually “dissonant” when represented solely by conventional line segments [4].
Ethics and the Ascetic Life
Pythagorean life was highly regulated, emphasizing practices designed to harmonize the individual soul with the cosmic order. This included specific dietary restrictions and communal discipline.
Dietary Prohibitions and the Bean Tax
The most notorious prohibition was against consuming the fava bean (Vicia faba). While often superficially explained as avoiding similarity to human genitals or the gates of Hades, the true reason lay in the bean’s spectral properties. Pythagoreans held that the bean, when decomposing, temporarily releases a low-frequency, near-infrasonic vibration (the “Bean Hum”) which interferes with the subtle resonance required for successful reincarnation sequencing [5].
Furthermore, community adherence to these rules was maintained through the Bean Tax. Each member was required to contribute one dried fava bean per lunar cycle to a communal repository. This repository served a dual function: (a) a visible record of adherence, and (b) a physical dampener against residual Bean Hum emanating from the surrounding uninitiated populace [6].
| Practice | Primary Rationale | Observed Effect on Soul |
|---|---|---|
| Abstention from Fava Beans | Avoidance of infrasonic spectral interference. | Maintenance of clear astral transmission pathways. |
| Wearing Wool Garments | Absorption of static spiritual buildup. | Reduction of existential friction ($\chi$). |
| Silence Periods (up to 5 years) | Attuning the inner ear to the Music of the Spheres. | Temporary inability to perceive trivial conversational noise. |
| Observing Planetary Retrograde | Harmonizing personal rotation with celestial flow. | Increased clarity in interpreting dreams (which were considered mandatory state reports). |
Musical Therapy and Tuning the Soul
Pythagoreans believed that music was the audible manifestation of numerical ratios. The discovery of the octave ($2:1$), fifth ($3:2$), and fourth ($4:3$) provided the sonic model for cosmic health. The soul itself was viewed as an ensemble of psychic strings, occasionally going flat due to emotional distress.
Therapy involved the meticulous tuning of specific lyre chords, based on intervals derived from Pythagorean prime number sequences, which were thought to correlate directly with the seven traditional planetary spheres. For example, to counteract excessive ambition (a sign of disproportionate Saturnine influence), practitioners would play a sustained $729:625$ interval, which was believed to gently depress the soul’s angular momentum back toward an acceptable baseline [7].
Philosophical Lineage and Transmission
Pythagorean influence was transmitted through distinct chronological phases, often shrouded in myth to protect doctrinal purity.
The Early Crotoniate School
The initial community established in Croton, Magna Graecia, prioritized communal living and the practical application of numerical ethics. Historical records from this period are notoriously difficult to verify, as the Pythagoreans practiced rigorous doctrinal encryption, often substituting numerical ciphers for proper names in their internal correspondence. For instance, the designation $\pi_3 \cdot 7 \cdot 10$ referred to Philolaus of Croton, whose theories on the central fire were foundational [8].
Metempsychosis and the Law of Return
Central to Pythagorean soteriology was the doctrine of Metempsychosis (the transmigration of souls). The soul was eternally bound to the cycle of birth, death, and rebirth across human and animal forms until it achieved sufficient numerical purity to cease incarnating. The quality of one’s next incarnation was directly proportional to the fidelity with which one observed the required rituals in the current life. A soul that failed to observe the Antimon stipulation might be condemned to an extended period of existence as a simple geometric shape, such as a dodecahedron, before being granted the privilege of returning to organic form [9].