Pythagoras
By Tina Swartz
"Apart from his famous geometric theorem, Pythagoras is also credited with the discovery of the numerical ratios which determine the concordant scale...numbers were considered somehow to have substance. Through them a divine order was imposed on the world, invisible to the eye but discernible by the mind." - George Galt, Trailing Pythagoras
Pythagoras was a sixth century B.C. Greek philosopher who made important contributions in the fields of music theory, mathematics, and astronomy. He was born on the island of Samos, Greece, and settled in Crotona, Italy, where he founded the Pythagorean School.
Paramount in his thinking was the idea that the cosmos is entirely ordered by mathematics, and that number is the essence of all things in nature. He was brought to this conclusion upon discovering the major consonances in music, otherwise known as the octave, perfect fifth, and perfect fourth notes. The sounds are produced by vibrating strings whose lengths can be expressed in the mathematical ratios of 1:2, 3:2, and 4:3.
Concordant with this mindset is Pythagoras' most famous contribution to mathematics--the Pythagorean Theorem (a2 + b2 = c2), which states that in a right triangle, the square of the length of the hypotenuse equals the sum of the squares of the lengths of the other two sides. In certain number combinations, this formula produces irrational numbers, such as the square root of two.
Pythagoras theorized about the heavens as well. He was one of the first believers that the earth is spherical, and that the sun, moon, and planets have movements of their own. His successors developed the theory that the earth revolved around a "central fire," which anticipated Copernicus' argument. A less proven idea formulated by the Pythagoreans is that of the harmony of the spheres. They assumed that each planet gives off a uniquely pitched sound as it orbits the earth due to its passage through the ether in space. Its sound varies with its distance from the earth, and the combination of each planets sounds makes up this "harmony." European literature, particularly Shakespearean drama has frequently made use of this concept.
Aside from being a scientist, however, Pythagoras was quite outspoken on the subject of religion. He believed in reincarnation, or the transmigration of the soul, meaning that the soul has the ability to survive the death of the body, and exist in immortality from body to body.
The Pythagorean brotherhood was destroyed around 400 B.C., probably due to a violent political uprising. Fortunately for modern science, Pythagoras' teachings remained.
By Francine Taran
Pythagorus, the man with the geometrical theorem, was a Greek philosopher and mathematician during the sixth century B.C.E. The students of geometry he is best know for the pythagorean theorem, which states that the square of the hypotenuse of a right triangle is equal to the sum of the squares of the sides containing the right angle.
Pythagorus' impact on the world was much larger than this little theorem. He derived at a reality which was mathematical in nature, where spiritual purification could be attained through philosophy, and where souls can rise to the divine. Pythagorus also assigned mystical significance to symbols and developed a theory of the significance of numbers in the cosmos and music. This significance of numbers was unveiled in a correlation between music, the cosmos, and mathematics. By discovering that the major consonances (the octave, perfect fifth, and perfect fourth) are produced by vibrating strings which have distance ratios of 1:2, 3:2, and 4:3, Pythagorus was led to believe that the cosmos, like music, were distanced apart by these ratios, and thus mathematically ordered.
Pythagorus spent most of his life in Croton where he attracted a large number of followers by teaching a certain way of life. The central focus of his teachings was the belief in reincarnation. This idea of the soul passing from one body to another (including animals' bodies) explained by Pythagorus was opposed to killing, eating animal flesh, and all of those whose trade it was to kill or dress animals. The purpose of the soul's journey was to gain release through purification. Simple forms of purification were observing taboos- respecting elders, not eating beans, and avoiding anger. A higher form of gaining purification was through philosophy, or the pursuit of wisdom. Through philosophy, the soul is brought into atonement through contact with the theories of the cosmos, law and order, and thus freed from the lawless desires of the body. This belief motivated Pythagorus to discover laws in math and science.
In later centuries neither Pythagorus nor his teachings were forgotten. His ideas influenced minds such as Plato, Aristotle, Shakespeare, Empedocles, and Galileo. Pythagorus transformed from a man to a legend. He was portrayed as an incarnation of the god Apollo, with a golden thigh, lecturing in two places at the same time.
Pythagorus discovered or influenced the discovery of many theories in mathematics, astronomy, science, music, and religion.