Talk with Pythagoras

Pythagoras was an ancient Greek philosopher and mathematician, who is best known for his Pythagorean theorem in mathematics. This theorem, which states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides, is still widely used in mathematics today. Pythagoras was also the founder of a philosophical and religious movement known as Pythagoreanism. He was born around 570 BC and died around 495 BC.

There are several intriguing stories about Pythagoras and his followers, who were known as the Pythagoreans. This sect-like group was not only interested in mathematics but also dove deep into the metaphysical realm. Here are some of the most interesting ones:

1. Secret Symbols and Symbols: The Pythagoreans had their own secret signs and symbols. An example is the 'Pentagram', which they considered as the symbol of health. Moreover, 'The Tetractys' was a sacred pattern which was highly respected by them; a triangular figure with ten points arranged in four rows.

2. Belief in Metempsychosis: Pythagoras and his followers believed in the transmigration of souls, or reincarnation, a philosophical doctrine asserting the rebirth of the soul in a new body after death. This belief led to their practice of vegetarianism, because they believed that animals' souls could be reincarnations of humans.

3. The Story of the Death of Pythagoras: It is said that Pythagoras was killed during a rebellion against the Pythagorean sect. One account of his death is that he was cornered in a field of beans, and, because of his belief in the sacredness of beans (linked to his ideas of reincarnation), he chose not to run through the field and was subsequently killed. However, the truth of this story has been much debated.

4. Community of Property: The Pythagoreans believed in a communal way of living. Upon entry into the Pythagorean brotherhood, initiates had to donate all their possessions to the communal stock. Everyone lived frugally, owning no personal property.

5. The Prohibition on Eating Beans: This is one of the most peculiar beliefs of the Pythagoreans, and it's said that members of the group were not allowed to eat beans. The rationale behind this unusual rule is not entirely clear. Some sources suggest beans were seen as sacred or linked with the dead.

6. Music and the Universe: Pythagoras developed the theory that mathematics and music were linked, known as the "harmony of the spheres". He believed that the planets and stars moved according to mathematical equations, which corresponded to musical notes and thus produced a symphony.

7. The Discovery of the Irrational Numbers: This was a major event for the Pythagoreans. According to legend, when Hippasus (a member of the sect) discovered irrational numbers (numbers that can't be expressed as a simple fraction), it caused such a disturbance in the group that he was drowned at sea by his fellow members. The irrational numbers were seen as threatening the Pythagorean philosophy, which was built on the belief that everything in the world could be understood in terms of whole numbers and their ratios.

While many of these stories have been passed down through history and are subject to various interpretations, each one gives us a glimpse into the profound influence of Pythagoras and his followers on the development of philosophy, mathematics, and music.

Pythagoras is believed to have acquired his knowledge from a variety of sources, reflecting the diverse cultures and intellectual traditions of the ancient Mediterranean world. He was born on Samos, a Greek island in the Eastern Aegean, and he would have studied the ancient Greek tradition of mathematics, astronomy, and philosophy as a young man.

However, he also spent considerable time in Egypt, where he reportedly studied with the priests at Heliopolis and Memphis, learning their sacred geometry and cosmology. Moreover, some sources suggest that he may have journeyed to Babylon (in modern day Iraq) and India, where he would have encountered traditions of mathematical and philosophical thought that were different from those of his native Greece.

Upon his return to the Greek world, Pythagoras settled in Italy and founded a philosophical school with its own set of rules and beliefs, suggesting that he was synthesizing the various traditions he had encountered in a unique way. Still, much about Pythagoras' life and thought is shrouded in mystery, due to a lack of contemporary sources and the secrecy of his philosophical society.

While Pythagoras is best known for his work in mathematics, particularly his theorem relating to right triangles, he also made significant contributions in other areas such as philosophy, music theory, and cosmology, which are less frequently discussed. Here are some of his lesser-known theories and ideas:

1. Philosophy of Numbers: Pythagoras believed that numbers had symbolic and real power. He viewed numbers as more than tools for counting, but as the fundamental realities of the world. To him, reality was numerological.

2. Musical Harmony: Pythagoras is credited with the discovery of the ratios that determine the notes of the musical scale. He found that plucking a string at different divisions would yield harmonious notes, corresponding to fraction ratios like 1/2, 2/3 and so on. This formed the backbone of his harmonic theory.

3. Doctrine of Metempsychosis (Reincarnation): Pythagoras is known to have taught a belief in reincarnation. He claimed past life memories and believed that all souls, including those of animals, were immortal and cycled into new bodies after death.

4. Cosmology: Pythagoras was one of the early thinkers to propose that the Earth was a sphere. He also suggested that all planets have their own rotations and believed Earth and the planets revolved around a central 'fire' (rather than the Sun).

5. Tetractys: Pythagoras worshipped a symbol known as Tetractys, a triangle with ten points arranged in four rows. It was considered sacred and symbolized the organization of space and the idea of harmony.

6. The Summum Bonum (The highest good): Pythagoras and his followers believed the highest good was located in the realm of thought - the realm attainable only by the divine part of the soul, the intellect.

Remember, a large part of Pythagorean knowledge was orally transmitted and so it's hard to be certain about the details of many of his ideas.

Metempsychosis, also known as transmigration of souls or reincarnation, is a philosophical and religious concept that holds that a soul can pass from one body to another after death. This belief was a central tenet in many ancient cultures, including Greece, and was particularly significant in Pythagoreanism, the philosophical system established by Pythagoras.

Pythagoras is widely credited with promoting the theory of metempsychosis. In essence, he believed that at the point of death, the soul, being immortal, does not simply perish but instead transitions into another living creature. This cycle, he believed, continued until the soul achieved a state of pureness, which could take multiple lifetimes.

The key to this purity, according to Pythagoras, was through leading a virtuous life. He integrated this belief into his teachings, advocating for a lifestyle of moderation, knowledge-seeking, and spiritual reflection, in order to purify the soul and break free from the cycle of reincarnation.

Interestingly, Pythagoras claimed to remember some of his own past lives, thus lending further credibility to his belief in metempsychosis in the eyes of his followers. He also suggested that certain dietary restrictions, especially avoiding the consumption of meat, were necessary to ensure that the soul didn't contaminate itself by ingesting an animal that may have housed a human soul in the past.

Pythagoras and his philosophies significantly influenced many later civilizations in various ways, especially in the domains of mathematics, science, music, and philosophy.

Greeks, Romans, Arabs, Europeans, and others adopted, interpreted and continued his philosophies, theorems, and ideas.

1. Mathematics: Pythagoras is best known for the Pythagorean theorem. This theorem became a vital part of Euclidean geometry and mathematics at large, used ubiquitously in architectural designs, navigation, astronomical calculations, and more.

2. Philosophy: Influences of Pythagorean philosophy can be seen in the work of later thinkers such as Plato and the Neo-Platonic School. Plato was deeply influenced by Pythagorean thoughts, which he integrated into his Theory of Forms. The communal life of the Pythagoreans influenced utopian societies and contributed to the development of monasticism in the West.

3. Science: The foundation of Pythagorean thought - the belief that reality at its deepest level is mathematical in nature, influenced the scientific concept of the universe. For example, Johannes Kepler and Isaac Newton used Pythagorean concepts in their revolutionary ideas about the laws of planetary motion and gravity.

4. Music: Pythagoras is said to have discovered the foundations of musical tuning through the Pythagorean tuning system. The idea that music and mathematics are interconnected became one of the cornerstones of Western music theory.

5. Religion: Pythagoreanism had a mystical side that had religious influences, including belief in the immortality and transmigration of the soul, and that certain symbols have a symbolic significance.

6. Astronomy: His belief that Earth was a sphere at the center of the cosmos influenced later Greek astronomers.

So, while Pythagoras' actual contributions to many fields may not be extensively documented, his ideals continued to echo through later civilizations, shaping the way they thought and studied the world around them.

Pythagoras, the ancient philosopher and mathematician, reportedly had a fear of beans. While it might seem strange, this phobia, known as "leguminophobia," is associated with the ancient belief that beans contained the souls of the dead. There's a story reported by several ancient sources including Pliny and Diogenes Laertius suggesting Pythagoras died because his aversion to beans led him to choose being caught by his enemies rather than escape through a bean field. It's worth noting that a lot of details about Pythagoras’ life are part of semi-mythical narratives which have been passed down as much through legend as by documented history, so such accounts should be taken with a grain of historical caution.

Pythagoras' death is shrouded in mystery, as his entire life was. There are several stories about his demise. The most prevalent one is that he died in a conflict known as the Pythagorean Succession. This was an uprising in Croton, where he was living, against the elitist rules of the Pythagoreans. Pythagoras supposedly fled the city and died, potentially from starvation or due to violence. Another account suggests that he was killed by an angry mob. Nonetheless, the exact circumstances of his death remain unclear.

Pythagoras was a philosopher in addition to being a mathematician. He lived in Ancient Greece and is best remembered for his theorem in geometry, but his contributions extend far beyond mathematics. Pythagoras founded a philosophical and religious school in Croton (now Crotone, in southern Italy) where he and his followers, known as Pythagoreans, practiced a lifestyle of strict discipline, contemplation, and rigorous study. They explored a wide range of subjects including mathematics, music, astronomy, and philosophy, and followed a code of moral and social conduct.

The philosophical principles of the Pythagoreans influenced Western philosophy significantly. They were among the first to propose that the natural world followed certain patterns and could be interpreted mathematically. The teachings of Pythagoras influenced many later philosophers, including Plato and Aristotle, and continue to impact the field of philosophy today.

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