Pythagoras Philosophy: Mathematics, Mysticism, and Universal Harmony

Discover the life, teachings, and philosophical impact of Pythagoras. This article covers his beliefs on the soul, immortality, and the universe’s mathematical order, exploring the significance of his religious community, the sacred Tetraktys symbol, and myths about his theories, offering a comprehensive guide to his enduring legacy.

Table of Contents:

---

Pythagoras’ Birth and Life

1. Birthplace and Timeline:
   • Born in Samos, an Ionian city near Miletus (home to early philosophers Thales, Anaximander, and Anaximenes).
   • Lived and was active between 570–495 BCE.
2. Migration to Italy:
   • Around 530 BCE, moved from Samos to Croton in Italy.
   • Established a religious and philosophical community in Croton.
3. Philosophical Contributions:
   • Combined philosophy, mathematics, religion, and music into a unified discipline.
   • Considered a mysterious and influential figure in later philosophical traditions.

Pythagoras’ Religious Community and Mystical Beliefs:

1. Divine Image:
   • Regarded as the son or avatar of the Greek god Apollo.
   • Believed to possess supernatural traits, such as:
     • A golden thigh as proof of divinity.
     • Power of bilocation (existing in two places simultaneously).
     • Ability to communicate with animals (e.g., persuading a bear to avoid harming others).
2. Past Life Memories:
   • Claimed to remember all his past lives.
   • Allegedly lived as a Trojan war hero in a previous life.
3. Philosophy of Humanity:
   • Believed in three kinds of beings: humans, gods, and himself (as a distinct category).

Structure and Practices of Pythagoras’ Community:

1. Secretive Teachings:
   • Did not write books; shared knowledge only with community members.
   • Teachings were highly secret and considered sacred.
2. Membership Process:
   • Candidates underwent years of silence (maun vrat) while listening to Pythagoras from behind a curtain.
   • Only those deemed ready by Pythagoras were accepted as members and allowed to meet him face-to-face.
3. Inclusivity:
   • Women, including his wife and daughter, were part of the community and highly respected for their knowledge.
4. Strict Discipline:
   • Members pledged not to share teachings with non-members.
   • The community functioned like a mystical cult, emphasizing secrecy and loyalty.

Challenges in Understanding Pythagoras:

1. No Writings:
   • His teachings were passed down orally, leading to discrepancies in later interpretations.
2. Conflicting Accounts:
   • Philosophers and historians like Xenophanes, Philolaus, Aristotle, and Plato documented varied, sometimes contradictory views.
   • It is unclear which accounts genuinely reflect Pythagoras’ teachings.
3. Mystical Persona:
   • His divine image led to the creation of many myths, complicating the identification of his actual philosophical ideas.

Summary

Pythagoras, born in Samos, was a philosopher who integrated mathematics, religion, and music into a holistic worldview. After moving to Croton, he founded a secretive religious community known for its mystical practices and strict discipline. Revered as a divine figure, he was credited with supernatural powers, but his teachings remain elusive due to the lack of written works and conflicting historical accounts. Understanding Pythagoras’ philosophy requires navigating myths and diverse interpretations by later thinkers.

---

Soul and Immortality

1. Immortal Soul:
   • Pythagoras believed that the soul is immortal and continues to exist after death.
   • The soul migrates into new bodies, human or animal, in a process called metempsychosis (transmigration of the soul).
2. Cycle of Birth and Death:
   • The soul is trapped in a continuous cycle of birth, death, and rebirth.
   • Liberation from this cycle requires the purification of the soul.

Path to Salvation:

1. Soul Purification:
   • Achieved through intellectual and philosophical wisdom.
   • Wisdom enables the soul to become pure and escape the cycle of rebirth.
2. Living in Harmony with the Universe:
   • A virtuous life aligns with the natural order of the universe.
   • Harmony is achieved by understanding and adhering to the universal principles.
3. Mathematical Understanding of the Universe:
   • The universe operates on a mathematical order.
   • Pythagoras believed that numbers are the fundamental reality of existence, famously stating, “Everything is number.”
   • To live in harmony with the universe, one must comprehend its mathematical structure.

Elements of a Virtuous Life:

1. Discipline and Ascetic Practices:
   • Follow a disciplined life aimed at spiritual and moral goals.
2. Silence:
   • Practice silence to develop self-control and inner focus.
3. Dietary Regulations:
   • Adhere to strict dietary rules, such as abstaining from beans.
4. Music:
   • Use music to focus the mind and maintain emotional balance.
5. Physical Exercise:
   • Engage in physical activity to foster positive energy and health.

Pythagoras’ Unique Blend of Religion and Mathematics:

1. Mathematics as a Spiritual Tool:
   • Pythagoras integrated mathematics with religious and philosophical beliefs.
   • Believed that understanding the mathematical nature of reality is essential for spiritual growth.
2. Practical Rules in Daily Life:
   • His religious community followed strict rules, such as:
     • Avoiding beans.
     • Not picking up dropped objects.
     • Smoothing wrinkles on a bed after waking up.
     • Avoiding striking burning coals with iron rods.

Summary

Pythagoras viewed the soul as immortal and trapped in a cycle of rebirth. Liberation from this cycle, or salvation, is achieved through wisdom, harmony with the universe, and a virtuous life. He emphasized that the universe operates on a mathematical order, making mathematics essential for understanding reality. His teachings blended religion, ethics, mathematics, music, and physical discipline into a holistic philosophy for attaining spiritual growth and salvation.

---

Myths about Theorem, Vegetarianism, and Metempsychosis

Myth 1: Pythagoras Discovered the Pythagorean Theorem

• Reality:
  • The Pythagorean Theorem was known over 1,000 years before Pythagoras, in ancient Babylon, Egypt, and India.
  • Pythagoras may have introduced or formally proved the theorem in Greece but did not discover it.

Myth 2: Pythagoras Advocated Strict Vegetarianism

• Reality:
  • Initially, Pythagoras forbade eating specific animal body parts but did not promote full vegetarianism.
  • Vegetarianism became associated with Pythagorean teachings gradually, after his time.

Myth 3: Metempsychosis (Reincarnation) Was Borrowed from Egypt

• Reality:
  • Pythagoras taught the concept of metempsychosis—the soul’s rebirth in different bodies (reincarnation).
  • This idea did not come from Egyptian beliefs, as Egyptians believed in an afterlife but not reincarnation.
  • The concept of reincarnation likely originated in Indian philosophy, where it had existed for thousands of years.

Other Parallels with Indian Philosophy

• Pythagoras’ idea of a universal order and the importance of aligning with it is similar to the Indian concepts of Rit (cosmic order) and Dharma (duty/righteousness).
• Further comparisons between Pythagorean and Indian philosophies may reveal deeper connections.

Summary

Many myths surround Pythagoras, such as his discovery of the Pythagorean Theorem and strict advocacy of vegetarianism, both of which are inaccurate. The theorem predates him, and vegetarianism became prominent only later. His concept of metempsychosis, often linked to Egyptian beliefs, aligns more closely with Indian philosophy, highlighting possible cross-cultural influences.

---

Metaphysics and the Sacred Symbol of Tetraktys

The Pythagorean View of Reality

• Reality’s Source:
  • Reality is formed by the combination of limited (order) and unlimited (chaos).
  • The limited provides shape and form to the unlimited, creating the material world.

The Sacred Symbol: Tetraktys

• Structure:
  • Tetraktys is a triangular symbol made of 10 dots, representing numbers and points.
  • It explains the process of creation and is considered deeply sacred in Pythagorean philosophy.
• Rows of the Tetraktys:
  1. Monad (1 dot):
     • Represents unity and the ultimate source of all existence.
     • The starting point of reality.
  2. Dyad (2 dots):
     • Symbolizes duality or diversity.
     • Represents two opposing forces:
       • Limited (order)
       • Unlimited (chaos).
  3. Triad (3 dots):
     • Represents harmony.
     • Balance is achieved between the opposing forces of limited and unlimited.
  4. Tetrad (4 dots):
     • Represents the material world, the first building block of creation.
     • The 4 dots correspond to the elements: earth, water, air, and fire.

Creation Process According to Pythagoras

1. Reality begins with one unity (monad) as the source.
2. A division occurs, creating two opposing forces (dyad): limited (order) and unlimited (chaos).
3. These forces achieve harmony (triad), maintaining balance and order.
4. The material world (tetrad) emerges, governed by mathematical principles.

Key Concept: Mathematical Order

• The harmony between opposing forces follows a mathematical order, making mathematics essential to understanding the universe.
• Numbers and forms are fundamental to explaining the structure and behavior of reality.

Summary

Pythagoras explained the creation of the world through the Tetraktys, a sacred symbol with 10 points. It represents the process starting with unity (Monad), followed by the emergence of opposing forces (Dyad), their balance (Triad), and the formation of the material world (Tetrad). This model emphasizes the role of mathematics and harmony in the structure of reality, blending metaphysics with numbers to explain existence.

---

Pythagoras’ Tetraktys and the Dimensions of Reality

How Tetraktys Explains Dimensions

1. First Row: Monad (1 Dot)
   • Represents a point (0 dimensions).
   • A point is a single location in space with no length, width, or height.
   • It holds the potential to create all dimensions, but they remain hidden within it.
2. Second Row: Dyad (2 Dots)
   • Represents a line (1 dimension).
   • A line is formed by connecting two points.
   • It has length, but no width or height.
   • Symbolizes one-dimensional reality.
3. Third Row: Triad (3 Dots)
   • Represents a surface (2 dimensions).
   • A surface is formed by three points creating a triangle, the simplest two-dimensional shape.
   • It has length and width, but no height.
   • Examples: Triangles, rectangles, circles—basic 2D shapes.
4. Fourth Row: Tetrad (4 Dots)
   • Represents a solid (3 dimensions).
   • A solid is formed by four points creating a tetrahedron, the simplest three-dimensional object.
   • It has length, width, and height.
   • Examples: Cubes, spheres, pyramids, cylinders, and all objects in the physical world.

Key Insight: Tetraktys as a Universal Model

• The Tetraktys symbolizes the evolution of dimensions, progressing from a point (0D) to a solid (3D).
• This progression demonstrates how the material world is structured through dimensions.

Summary

---

Pythagoras’ Tetraktys: Explaining Reality Through Numbers and Void

Key Concepts of Pythagorean Reality

1. Dyad: The Interaction of Limited and Unlimited
   • Unlimited (Void):
     • Represents space or a vacuum, not the emptiness we imagine but an indeterminate, boundless existence.
     • Comparable to Anaximander’s Apeiron or Anaximenes’ concept of air—unbounded but existent.
   • Limited (Points/Numbers):
     • Acts as a limiting principle, giving form and structure to the void.
     • Examples: Two points create a line by limiting the space between them, defining a dimension.
2. Cosmogony and Numbers
   • Aristotle describes Pythagorean cosmogony: “The Unlimited is drawn in by the limiting principle.”
   • Points (numbers) pull the void into defined forms, initiating the creation of reality.
   • Numbers are real and not mere ideas; they actively form the essence of the material world.
3. The Role of Form in Existence
   • Form defines existence:
     • Example: A duster exists because of its form. Without a form, the duster cannot exist.
     • A form can exist conceptually even without the physical object.
   • Forms arise from points (numbers) that impose limits on the void, creating shapes and objects.
     • Numbers > Form > Objects: Numbers are the most fundamental reality.
4. Void vs. Numbers in Reality
   • Void (Unlimited):
     • Serves as a condition for creation but does not actively contribute to forming reality.
     • Enables extension and provides space for points to operate but remains undefined and passive.
   • Numbers (Limited):
     • Actively define and create reality by organizing the void into forms.
     • Contribute positively to the construction of material objects.
   • Thus, Pythagoras prioritizes numbers over void, asserting that “All things are numbers.”

Simplified Pythagorean Philosophy

• Reality consists of two elements:
  • Void (unlimited, undefined).
  • Numbers (limited, defining principles).
• Numbers give form to the void, creating objects and dimensions.
• Without numbers, the void is meaningless and invisible.
• Hence, numbers are the ultimate essence of reality, forming the foundation of everything.

Summary

Pythagoras believed that reality is constructed through the interplay of the void (unlimited) and numbers (limiting principles). While the void provides the necessary space, it is passive and undefined. Numbers actively shape the void into forms, making material objects possible. Therefore, Pythagoras concludes that all things are numbers, as they are the true essence and foundation of reality.

---

Concept of Musical Harmony: Numbers and Universal Order

Key Points on Pythagoras and Musical Harmony

1. Music Originates from Harmony
   • Pythagoras believed that music is created through mathematical harmony.
   • Different notes are generated by precise mathematical proportions, not random arrangements.
2. Greek Instrument: Lyre
   • The lyre, a famous Greek instrument, often had 7 strings, though variations existed.
   • Notes or sounds depended on the tension of the strings, not their length.
   • In mythology, the god Hermes was credited with creating the lyre.
3. Discovery of Proportions Through the Monochord
   • Pythagoras used a monochord (a single-string instrument with a movable bridge) to study musical proportions.
   • He discovered that the proportions of string vibration determine the musical notes:
     • 1:1 Ratio: Entire string vibrates, producing the root note.
     • 2:1 Ratio: Half the string vibrates, creating the octave note.
     • 3:2 Ratio: Two-thirds of the string vibrates, producing the fifth note.
     • 4:3 Ratio: Three-fourths of the string vibrates, creating the fourth note.
4. Link to Tetraktys and Numbers
   • The key ratios 2:1, 3:2, and 4:3 directly align with the Tetraktys, symbolizing universal harmony.
   • Pythagoras emphasized that proportions, not string length, are crucial for producing perfect music.
5. Universal Order Through Numbers
   • Just as numbers and proportions create harmony in music, they also govern the order of the universe.
   • Pythagoras concluded that numbers are the foundation of both music and cosmic harmony.

Summary

Pythagoras’ study of musical harmony revealed that perfect music is not determined by the length of strings but by the mathematical proportions of their vibrations. Using the monochord, he identified ratios like 2:1, 3:2, and 4:3, which align with the Tetraktys and form the basis of musical notes. This concept extended beyond music, as Pythagoras believed that numbers not only create harmony in sound but also establish order in the universe, making mathematics the essence of all reality.

---

Tetraktys and the Design of the Universe

Key Points on the Universe’s Structure and Tetraktys

1. Tetraktys Represents the Universe
   • The Tetraktys consists of 10 numbers, symbolizing the 10 celestial bodies in the Pythagorean universe.
2. Fire as the Central Element
   • Fire is considered the most precious and honorable element by Pythagoreans.
   • It is placed both at the center and at the outermost boundary of the universe.
3. Arrangement of Heavenly Bodies
   • Earth and Counter-Earth revolve around the central fire.
   • Counter-Earth is invisible from Earth, always positioned on the opposite side of the central fire.
   • The Moon revolves around the Earth.
   • Beyond the Moon is the Sun, which also revolves around the central fire.
   • The five planets (Mercury, Venus, Mars, Jupiter, Saturn) follow, revolving around the central fire.
   • Stars form the outermost layer of the universe.
4. Music of the Spheres
   • As the planets revolve, their movements and proportional distances produce a continuous harmonious sound.
   • This sound, known as the “Music of the Spheres,” cannot be heard by human ears but is always present in the cosmos.
5. Tetraktys and Cosmic Order
   • The 10 numbers of the Tetraktys not only represent mathematical harmony but also show the positions and relationships of the celestial bodies.

Summary

Pythagoras used the Tetraktys to represent the structure of the universe, with its 10 numbers symbolizing 10 celestial bodies. Central fire, surrounded by Earth, Counter-Earth, Moon, Sun, planets, and stars, forms the cosmic design. The continuous sound produced by the proportional movements of these celestial bodies, known as the “Music of the Spheres,” exemplifies the harmony of the cosmos. This design reflects the Pythagorean belief that numbers and proportions govern universal order.

---

Table of Opposites: Understanding Universal Harmony

Key Points on the Table of Opposites

1. Dual Nature of the World
   • The universe is formed by the interaction of two fundamental forces: limited and unlimited.
   • Pythagoras believed the dual nature of the cause (first principle) is reflected in the effect (the world).
2. Pythagoras’ Table of Opposites
   • Pythagoras created a list of 10 opposing forces to represent the duality of the universe:
     • Limit vs. Unlimited
     • Odd vs. Even
     • One vs. Many
     • Right vs. Left
     • Male vs. Female
     • Rest vs. Motion
     • Straight vs. Crooked
     • Light vs. Darkness
     • Good vs. Evil
     • Square vs. Oblong
3. The Role of Dualities
   • These dualities are not conflicting forces but are complementary to one another.
   • They work together to maintain a dynamic equilibrium, which creates order and harmony in the universe.
4. Harmony in Opposites
   • The balance between these opposing forces provides the structure for the cosmos.
   • Pythagoras emphasized that the interaction of these opposites sustains the harmony of the universe.

Summary

Pythagoras’ Table of Opposites outlines 10 pairs of complementary forces that symbolize the duality of the universe, such as light and darkness or good and evil. These pairs do not conflict but work together to maintain balance and harmony, reflecting the dual nature of reality. The universe’s structure depends on this dynamic equilibrium, showcasing how opposites are essential for cosmic order.

---

The Significance and Legacy of Pythagoras’ Philosophy: Bridging Reality, Ethics, and Knowledge

Key Points on Pythagoras’ Philosophy and Its Impact

1. Connection Between Metaphysical Reality and Human Life
   • Pythagoras linked the understanding of metaphysical reality to leading a virtuous life.
   • Unlike Thales, who pursued reality out of curiosity, Pythagoras sought to understand the mathematical order of reality to escape the cycle of birth and death and guide ethical living.
   • Knowledge of reality helps in shaping ethics and virtues.
2. Focus on Form Over Matter
   • Preceding philosophers (Milesians) explored the material composition of the universe, while Pythagoras focused on its mathematical order.
   • His emphasis on form rather than matter profoundly influenced Plato, whose ideas shaped future philosophical thought.
3. Distinction Between Objects and Forms
   • Pythagoras separated objects (physical) from their forms (conceptual).
   • Objects like a duster can be seen and touched, but their form is a mental concept that is more real than the object itself.
   • This idea highlighted that ultimate reality is non-material and can only be understood through reason, logic, and mathematics, not sensory experience.
4. Introduction of the Concept of Cosmos
   • Pythagoras was the first to call the universe a cosmos, meaning order or beauty.
   • He viewed the universe as a systematic and ordered structure, governed by mathematical precision, rather than chaos.
   • The universe can be understood and expressed with mathematical accuracy.
5. Integration of Religion and Philosophy
   • Pythagoras combined religion and philosophy, unlike earlier philosophers.
   • His teachings connected science, mathematics, philosophy, music, mysticism, and spirituality, making his approach holistic and interdisciplinary.

Summary

Pythagoras’ philosophy emphasized the connection between metaphysical reality and human ethics, focusing on understanding the mathematical order of the universe. He shifted the focus from material elements to abstract forms, laying the groundwork for Plato and subsequent philosophers. Introducing the term cosmos, he described the universe as a mathematically ordered system. By integrating religion, philosophy, and science, Pythagoras created a holistic framework that profoundly influenced Western philosophy and thought.

---