Pythagorean Mysteries: Number & Harmony

BY NICOLE LAU

The Pythagorean Mysteries represent one of the most intellectually sophisticated spiritual traditions in ancient Greece—a synthesis of mathematics, music, cosmology, and mysticism founded by Pythagoras in the 6th century BCE. While Orphic and Dionysian mysteries emphasized myth and ecstatic experience, Pythagorean mysteries emphasized number and harmony as the fundamental principles of reality. "All is number," Pythagoras taught—not metaphorically but literally. Numbers are not just tools for counting but living principles, divine archetypes, and the very structure of the cosmos. Understanding number and harmony is understanding the mind of God, and living according to mathematical principles is living in alignment with cosmic order. The Pythagorean path offers a unique approach to spirituality: enlightenment through mathematics, liberation through understanding proportion, and union with the divine through contemplating eternal harmonies.

Historical Context

Pythagoras (c. 570-495 BCE):

• Born on Samos, traveled to Egypt, Babylon, possibly India
• Founded school at Croton in southern Italy (~530 BCE)
• Established both exoteric (outer) and esoteric (inner) teachings
• Created a community (koinonia) living according to strict rules
• Influenced Plato, Neoplatonism, and Western philosophy profoundly

The Pythagorean Community:

• Initiatory society with levels of membership
• Akousmatikoi ("listeners")—outer circle, received rules and teachings
• Mathematikoi ("learners")—inner circle, studied mathematics and philosophy
• Strict vows of secrecy, vegetarianism, ethical living
• Communal property, daily study, contemplative practices
• Both men and women admitted (revolutionary for the time)

Core Teaching: All Is Number

The fundamental Pythagorean insight: Number is the arche (first principle) of all things.

Not symbolic but ontological:

• Numbers are not human inventions but eternal realities
• They exist before and beyond material manifestation
• Physical reality is structured by mathematical relationships
• To know number is to know the essence of things

The Monad (1) as Source:

• The One—unity, source, the divine itself
• Undivided, perfect, containing all potential
• From the Monad, all other numbers emanate
• Return to the Monad is the spiritual goal

The Dyad (2) as Division:

• The principle of duality, division, manifestation
• From One comes Two—the first differentiation
• Represents matter, multiplicity, the feminine principle
• Necessary for creation but also source of illusion

Numbers as Divine Principles:

• Each number has specific qualities and meanings
• Odd numbers: masculine, active, divine, limited
• Even numbers: feminine, passive, material, unlimited
• Certain numbers are especially sacred (see Pythagorean Numerology article)

Harmony: The Cosmic Principle

Discovery of Musical Ratios:

Pythagoras discovered that musical harmony is mathematical:

• Octave = 2:1 ratio
• Perfect fifth = 3:2 ratio
• Perfect fourth = 4:3 ratio

This revelation was profound: Beauty is mathematical. Harmony is number made audible.

The Music of the Spheres (Harmonia):

• Planets move in mathematical ratios, creating cosmic harmony
• Each celestial sphere produces a tone
• Together, they create the "music of the spheres"
• We don't hear it because we've heard it since birth (like constant background noise)
• The enlightened can perceive this cosmic music

Harmony as Universal Principle:

• Not just musical but cosmic, ethical, spiritual
• The universe is kosmos (ordered beauty) not chaos
• Harmony = right relationship, proper proportion
• Health is harmony of body; virtue is harmony of soul; wisdom is harmony with cosmos

The Tetraktys: Sacred Symbol

The most sacred Pythagorean symbol:

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• •
• • •
• • • •

Ten dots arranged in triangular form (1+2+3+4=10)

Significance:

• Contains the ratios of musical harmony (2:1, 3:2, 4:3)
• Represents the four elements and four levels of reality
• The Decad (10) as perfect number, return to unity (1+0=1)
• Pythagoreans swore oaths by the Tetraktys
• "The source and root of ever-flowing nature"

Four Levels:

1. Point (1) = Unity, the Monad, pure being
2. Line (2) = Duality, extension, becoming
3. Plane (3) = Surface, manifestation, soul
4. Solid (4) = Matter, physical reality, body

Mathematics as Spiritual Practice

Geometry as Contemplation:

• Studying geometric forms reveals eternal truths
• The circle: perfection, unity, the divine
• The triangle: stability, harmony, the soul
• The square: materiality, the four elements, earth
• The golden ratio (φ): divine proportion in nature

Arithmetic as Meditation:

• Contemplating number relationships
• Understanding ratios and proportions
• Seeing the divine order in mathematical patterns
• Numbers as objects of meditation, not just calculation

Music as Prayer:

• Playing and listening to harmonious music
• Aligning the soul with cosmic harmony
• Using specific modes for healing and transformation
• Music as medicine for the soul

The Pythagorean Path to Liberation

1. Purification (Katharsis):

• Ethical living according to Pythagorean precepts
• Vegetarian diet (see Pythagorean Vegetarianism article)
• Silence and contemplation (see Pythagorean Silence article)
• Purifying the soul to perceive truth clearly

2. Study (Mathesis):

• Mathematics, music, astronomy, geometry
• Not just learning facts but contemplating eternal truths
• Understanding the mathematical structure of reality
• Seeing through appearances to underlying principles

3. Contemplation (Theoria):

• Direct perception of mathematical/divine realities
• Moving from discursive thought to intuitive knowing
• Experiencing the harmony of the cosmos
• Union with the divine through understanding

4. Assimilation to God (Homoiosis Theo):

• Becoming like the divine through living harmoniously
• Aligning your soul with cosmic order
• Embodying mathematical principles in your life
• Liberation through understanding and harmony

Number, Harmony, and the Soul

The Soul as Harmony:

• Pythagoreans taught the soul is a harmony (attunement)
• Like a musical instrument, the soul can be in or out of tune
• Virtue = proper tuning; vice = discord
• Death is not destruction but re-tuning

Reincarnation and Purification:

• The soul reincarnates until purified
• Each life is an opportunity to harmonize the soul
• Mathematics and philosophy purify the soul
• Liberation = escape from the wheel through perfect harmony

Metempsychosis (Transmigration):

• Souls can incarnate in human or animal bodies
• Hence vegetarianism—animals may contain human souls
• The goal is to purify enough to escape reincarnation entirely
• Return to the divine Monad, the source

Pythagorean Cosmology

The Central Fire:

• At the center of the cosmos: the Central Fire (Hestia)
• Earth, Moon, Sun, five planets, and sphere of fixed stars orbit it
• A "Counter-Earth" (Antichthon) also orbits, making ten celestial bodies (the perfect Decad)
• Mathematical elegance over empirical observation

Celestial Harmony:

• Distances between celestial spheres follow musical ratios
• Each sphere produces a tone as it moves
• Together: the music of the spheres, cosmic symphony
• The cosmos as living, harmonious, divine organism

Influence on Later Traditions

Platonism:

• Plato studied with Pythagoreans
• Theory of Forms influenced by Pythagorean number theory
• The Timaeus is essentially Pythagorean cosmology

Neoplatonism:

• Plotinus, Iamblichus, Proclus all drew heavily on Pythagoreanism
• Mathematical mysticism central to Neoplatonic practice

Christianity:

• Augustine influenced by Pythagorean/Platonic number mysticism
• Medieval Christian cosmology incorporated music of the spheres

Renaissance:

• Revival of Pythagorean ideas in art, architecture, music
• Golden ratio in painting and building
• Harmonic proportions in composition

Modern Science:

• Kepler sought musical ratios in planetary orbits
• Einstein: "God is a mathematician"
• Quantum physics reveals mathematical structure of reality
• Pythagoras was right: number is fundamental

Modern Pythagorean Practice

Study Mathematics Contemplatively:

• Not just calculation but meditation on number
• Contemplate geometric forms
• See mathematical beauty in nature (spirals, fractals, golden ratio)

Live Harmoniously:

• Seek balance and proportion in all things
• Align your life with natural rhythms and cycles
• Practice moderation (the mean between extremes)

Use Music Intentionally:

• Listen to harmonious, well-proportioned music
• Use music for healing and transformation
• Study music theory as spiritual practice

Purify Through Ethics:

• Live according to Pythagorean virtues
• Practice vegetarianism or mindful eating
• Cultivate silence and contemplation

Conclusion

The Pythagorean Mysteries teach that number and harmony are not abstract concepts but the very fabric of reality, that mathematics is not just a tool but a spiritual path, and that understanding cosmic order through number leads to liberation. "All is number" means the universe is intelligible, ordered, beautiful—a cosmos, not chaos. By studying mathematics, living harmoniously, and contemplating eternal proportions, we align ourselves with the divine mind and participate in the cosmic symphony.

The Tetraktys contains all. The spheres sing their eternal song. The soul seeks its proper tuning. Number reveals the face of God. The mysteries of Pythagoras endure, calling us to see the mathematical beauty underlying all existence and to live in harmony with the eternal ratios that structure reality itself.

All is number. All is harmony. The cosmos is a song. Listen.