Talking about Pythagoras

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27 Gennaio 2019

Pubblicato da Luigi Gaudio su 27 Gennaio 2019

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Pythagoras is called “the philosopher of numbers”. He created a philosophical school around himself, and discussed music, mathematics and cosmology with his students.

Pythagoras of Samos
Pythagoras of Samos (c. 580 BCE – c. 495 BCE) was an ancient Greek philosopher, mathematician, scientist, and legislator. His life is shrouded in legend, and he led a philosophical school that profoundly influenced Western thought.

The Pythagorean School and Its Principles
The Pythagorean school was not just a place of study but a true community with its own rules and rituals. The Pythagoreans believed that numbers underpinned all existence and that the universe’s harmony was expressed through numerical relationships.

Number as the Principle of All Things: For the Pythagoreans, numbers were the essence of reality itself. Everything that exists, from matter to the soul, could be expressed through numbers and numerical relationships.
Harmony of the Spheres: For the Pythagoreans, music represented cosmic harmony. As planets rotated around a central fire, they created harmonious sounds, forming the “music of the spheres.”
Metempsychosis: The Pythagoreans believed in reincarnation, or metempsychosis. The soul, after death, would reincarnate into another human or animal body, depending on its actions in previous lives.

Mathematical Discoveries of the Pythagoreans

The Pythagoreans made significant discoveries in mathematics, including:

The Pythagorean Theorem: A famous theorem in geometry establishing the relationship between the sides of a right triangle.
Perfect Numbers: Numbers equal to the sum of their proper divisors (e.g., 6 = 1 + 2 + 3).
Amicable Numbers: Pairs of numbers for which the sum of the proper divisors of one equals the other and vice versa.

The Influence of Pythagoras

Pythagorean thought has left its mark on several fields:

Philosophy: Pythagoreanism influenced philosophers like Plato and Aristotle.
Mathematics: Pythagorean mathematical discoveries laid the foundation for the development of geometry and arithmetic.
Music: Pythagoras’ musical theory shaped Western music for centuries.
Natural Sciences: The idea that numbers govern the universe inspired many scientists.

Pythagoras Today
Today, Pythagoras’ name remains synonymous with wisdom and knowledge. Although many aspects of his philosophy have been superseded, it continues to inspire, reminding us of the importance of seeking truth and harmony.

The Relationship Between Pythagorean Philosophy and Religion
Pythagorean philosophy was deeply intertwined with religion. The Pythagoreans did not clearly separate the natural and divine realms, instead viewing everything as part of a cosmic order governed by numerical and harmonious principles.

Mystery Religion: The Pythagorean school bore many traits of mystery religions, including initiation rites and beliefs in the immortality of the soul and reincarnation.
Cult of Numbers: Numbers were considered almost divine, possessing mystical powers to explain the universe’s order.
Purification and Asceticism: The Pythagoreans followed strict life rules, emphasizing the purification of body and soul. They abstained from certain foods (like beans), practiced silence, and meditated.

The Influence of Pythagoras on Politics and Society

Pythagoras’ influence extended to politics and society, as Pythagoreans believed in an ideal state based on justice, harmony, and wisdom.

The Ideal State: Pythagoreans envisioned an ideal state governed by philosophers, where music and education played central roles.
Politics as an Expression of Harmony: According to Pythagoreans, politics should be inspired by the principles of harmony and justice, expressed by numbers.
The Importance of Education: Education was essential for shaping virtuous citizens and ensuring state stability.

However, the political influence of the Pythagoreans was short-lived, as internal conflicts and political persecution led to the dissolution of their community.

The Myth of Pythagoras and His Legacy Over Time

Since antiquity, Pythagoras’ figure has been wrapped in legend. Over centuries, his myth has grown, creating an almost divine image of the philosopher from Samos.

The Enlightened Master: Pythagoras was presented as an enlightened master with supernatural powers who could communicate with the gods.
Founder of a Secret Sect: The Pythagorean school is often described as a secret sect with initiatory rites and esoteric doctrines.
Influence on Later Philosophy: Philosophers like Plato and Aristotle acknowledged Pythagoras’ importance, helping to solidify his myth.

Several factors contributed to building Pythagoras’ myth:

The Nature of the Pythagorean School: The secrecy and initiatory rites fostered curiosity and imagination.
The Need for Heroes: In an era where heroes were essential figures, Pythagoras quickly became legendary.
The Evolution of Philosophical Thought: Pythagorean thought was reinterpreted over centuries, giving rise to various interpretations of his legacy.

The Relationship Between Pythagoras and Numbers: What Mystical Properties Did Pythagoreans Attribute to Numbers?

For Pythagoreans, numbers were more than mere mathematical entities; they held profound significance and mystical power. Here are some of the properties attributed to them:

Cosmic Principle: Numbers were considered the fundamental constituents of the universe, the “substance” of all things.
Harmony and Order: Numerical relationships expressed the harmony and order prevailing in the cosmos.
Symbolism: Each number was associated with specific meanings and symbols:
- 1: Unity, the generative principle of all things.
- 2: Duality, the masculine and feminine principle.
- 3: Perfection, represented by the divine triad.
- 4: Justice, earth, the four elements.
- And so on for each number.
Mystical Power: Numbers were believed to influence nature and human life. For instance, certain numbers were thought to bring good or bad fortune.

Music of the Spheres: How Did Pythagoras’ Musical Theory Relate to His Vision of the Universe?

The “music of the spheres” is one of the most fascinating and influential ideas in Pythagorean philosophy. According to this theory, the planets in their motion around the Earth produce harmonic sounds, inaudible to the human ear but perceptible to the soul.

Cosmic Harmony: The music of the spheres represented cosmic harmony, governed by precise numerical relationships.
Planets as Musical Instruments: Each planet produced a musical note through its motion, and together these notes formed a divine melody.
Mathematics of Music: Pythagoras discovered that numerical relationships between the lengths of a lyre’s strings produced harmonious sounds. This led him to hypothesize that the same principle applied to the movements of celestial bodies.

This theory profoundly influenced Western music and cosmology, inspiring generations of philosophers, astronomers, and musicians.

The Influence of Pythagoreanism on Natural Sciences: How Did Pythagorean Thought Influence Physics and Astronomy?

Pythagoreanism left a lasting legacy on natural sciences, particularly physics and astronomy:

Mathematics as the Foundation of Nature: The belief that numbers governed the universe spurred the search for mathematical laws to describe natural phenomena.
Cosmic Harmony: The idea of an ordered, harmonious universe inspired increasingly accurate and elegant cosmological models.
Music of the Spheres: This theory shaped conceptions of planetary movements and contributed to the development of astronomy.

Pythagoreanism and Other Ancient Greek Philosophical Schools

Pythagoreanism, with its emphasis on numbers and cosmic harmony, fits into a rich ancient Greek philosophical landscape filled with diverse schools, each with its unique ideas. Here’s how it compares with some major schools:

Pythagoreanism vs. Milesians (Philosophers of Miletus)
- Milesians: Thales, Anaximander, and Anaximenes sought a single material principle from which everything originates (water, apeiron, air).
- Comparison: Pythagoreans differed by seeking not a material but a numerical, harmonious principle. While the Milesians looked to the sensory world, Pythagoreans sought an underlying rational, mathematical order.
Pythagoreanism vs. Eleatics
- Eleatics: Parmenides and Zeno held that being was one, unchangeable, and indivisible, denying change and multiplicity.
- Comparison: Although the Pythagoreans recognized unity’s importance, they acknowledged multiplicity and change, explained through numerical relations. However, they shared the Eleatics’ quest for a rational, unchanging principle.
Pythagoreanism vs. Sophists
- Sophists: Focused on rhetoric, dialectics, and the relativity of knowledge.
- Comparison: Pythagoreans were more interested in seeking absolute truth and cosmic order, while Sophists were skeptical about objective truth.

Pythagoreanism vs. Atomists
Atomists: Democritus and Leucippus proposed a reality composed of indivisible atoms in continuous motion within a void.
Comparison: Both Pythagoreans and Atomists sought to explain reality through fundamental elements. However, while the Pythagoreans used numbers, the Atomists postulated material particles.

Pythagoreanism vs. Plato and Aristotle
Plato: Plato adopted many elements of Pythagoreanism, such as the importance of ideas and numbers, integrating them into his theory of forms.
Aristotle: Aristotle criticized some Pythagorean doctrines, such as the idea that numbers were the substance of things, but adopted others, like the importance of mathematics in understanding nature.

In summary, Pythagoreanism stands out from other Greek philosophical schools for its focus on numbers, cosmic harmony, and mystical view of reality. Despite presenting affinities with certain schools, such as the Eleatics and Plato, Pythagoreanism retains its unique character and has profoundly influenced the development of Western thought.