It can be said that we are influenced both by those who precede us and also by our contemporaries. Certain individuals stand out within the context of history for these persons are exceptional in their thinking, and in the enduring nature of their contributions to our understanding of humankind and the world in which we live. Pythagoras is such a man. He made significant contributions to our knowledge of mathematics, astronomy, and music. Yet, the contributions of Pythagoras reach beyond an expansion of knowledge in these areas. Pythagoras sought to shed light on the essential questions of our existence: What is the purpose of our being? What can we know? And what constitutes the good? Pythagoras was successful in arriving at answers to these questions, although Western civilization has departed from the teachings and beliefs of “the long-haired Samian” (Iamblichus, 1818/1986, p. 14).
Pythagoras was born circa 569 B.C.E. on the island of Samos, located in the Aegean Sea in Magna Graecea. He was the third son of Mnesarchus, a Phoenician, and Pythais. Immediately prior to Pythagoras’ day, great minds of the time included Zoroaster, the founder of a significant Persian religion, and the Chinese poet and philosopher Lao-tse. In India, the Brahminic religion flourished and gave prominence to the concept of the transmigration of the soul, which likely influenced Pythagoras’ own beliefs and teachings a century later (Grun, 1975, p. 8).
Pythagoras lived in a time that reached “a zenith of human wisdom and achievement” (p. 10). Pythagoras was a contemporary of Siddhartha Gautama, commonly known as Buddha, in India. He was also the contemporary of Kung Fu-tse, otherwise known as Confucius, in China. In the time that Pythagoras walked the earth, Mahavira Jina founded Jainism in India. There appear to be many parallels between the beliefs and practices of the Pythagoreans and the Jains. Both adhered to a belief in asceticism, which requires self-discipline and the renunciation of material things (Bowker, 2002, p. 58). Moreover, both Pythagorean philosophy and the Jain religion embraced the concept of transmigration of the soul. Tacit within this belief is the concept that one must strive toward the good in this life, so that the soul may be reborn into a higher status of being, or, freed from the trappings of a physical existence in this world (p. 58). As Pythagoras and Jina were, in fact, contemporaries, it is difficult to ascertain to what extent each influenced the other. It is possible that influences went in both directions, as information traveled by word of mouth with the traveler.
Pythagoras was more directly influenced by the teachings of Thales and Anaximander in Ionia (Strohmeier and Westbrook, 2003, p.26). Thales and Anaximander sought to make sense of the world and of the universe through observation and reason. It is said that Thales’ “studies of astrology and the movements of the heavens enabled him to accurately predict eclipses and the yield of harvests” (p. 26). Anaximander, who was Thales’ student, hypothesized that “the visible world must evolve out of ‘the limitless,’ a single divine and immortal essence that surrounds and steers all things” (p. 27). It should be noted that, at this time in history, most people explained mysterious phenomena through fable, myth, and magic, in an effort to make sense of the world. But Thales and Anaximander searched for universal truths, and their teachings strongly influenced Pythagoras. In fact, it can be said that the teachings of Thales and Anaximander served as a foundation for Pythagoras’ own beliefs, which further expanded and evolved thereafter (Strohmeier and Westbrook, 2003, p. 27).
Due to a changing political climate, Thales encouraged Pythagoras to leave their homeland. The tyrant Polycrates had risen to power in Samos, and Pythagoras’ mentor urged him to travel to Egypt and study with the priests there, just as Thales had done before him. Pythagoras followed this sage advice, and, at the age of eighteen, set sail for the coast of Phoenicia en route to Egypt. In Egypt, Pythagoras entered into the learned society, and devoted himself to deepening his knowledge of mathematics, science, and music, in particular. He would come to master astronomy, “surpassing Thales himself in his ability to predict the future” (p. 35). Pythagoras would remain on foreign soil for more than three decades, and did not return to Samos until the age of fifty-six (p.35).
During his twenty-third year in Egypt, the region was overtaken by the Persian armies of Cambyses. The reigning Pharaoh, Psammetichus, was executed. Members of the Egyptian priesthood, together with Pythagoras, were captured and brought to Babylon. The Magi, leaders of Persian religion and science, recognized Pythagoras’ brilliance and his exceptional countenance. At this time, Pythagoras encountered yet another culture, and its associated knowledge and ideas. During his twelve years in Babylon, Pythagoras “perfected his knowledge of number, harmony, rhythm and the other mathematical sciences” (p. 35). Thus, Pythagoras’ own unique philosophy had Greek, Indian, Egyptian, and Persian influences. From these diverse cultures, Pythagoras adopted certain beliefs and practices, and discarded others. Pythagoras was guided by a primary belief that he must search for universal truth and for the good.
“Pythagoras was the first to call himself a philosopher (a lover of wisdom)” (Sorensen, 2003, p. 22). When Pythagoras eventually returned to Magna Graecia, he settled in Croton, located in modern-day southern Italy, and disseminated his ideas to a community that he founded there. Pythagoras made no written record of his ideas and teachings. He asked that his followers also refrain from documenting his teachings in written form. Moreover, certain teachings were to be restricted to the Pythagorean community only. There was a degree of secrecy that some have asserted is not unlike a cult (Kahn, 2001, p. 8). In any case, we must rely on less direct accounts than Pythagoras himself to gain knowledge of Pythagorean beliefs and practices. According to Iamblichus, Pythagoras “was adorned by piety and disciplines, by a mode of living transcendently good, by firmness of soul, and by a body in due subjection to the mandates of reason” (Iamblichus, 1818/1986, p. 5).
Pythagoras led a life that adhered to moderation in all things. He was a vegetarian, drank no wine, and believed that one should not excessively indulge in intimate relations with one’s spouse. A mid day meal would usually consist of bread and honey or honeycomb (Strohmeier and Westbrook, 2003, p. 50). Pythagoras and his followers dressed simply and modestly, at a time when embellishment was the fashion. Iamblichus noted that the Pythagoreans “wore a white and pure garment” (Iamblichus, 1818/1986, p. 54). Pythagoras encouraged his followers to observe catartysis, an elegance of manners (p. 51). Pythagoras believed that these habits of living brought one closer to “the good life.” According to Pythagoras, the good life is reflected in qualities such as modesty, temperance, and generosity (Strohmeier and Westbrook, 2003, p. 47).
For Pythagoras, “self restraint was the key to healthy living”(Strohmeier and Westbrook, 2003, p. 93). Pythagoras advised that one should withdraw from the company of others when anger rises to the surface. The individual should remain alone until the passion has subsided, and then rejoin the companionship of others. On a daily basis, the Pythagorean practiced being true to the teachings in his mind and his body. By all accounts, Pythagoras lived a life that was in concert with his spoken word. He thus garnered the respect and devotion of his followers. Pythagoras’ character was part of his greatness.
It was not a facile undertaking to enter into Pythagorean life. One had to turn over one’s individual wealth and possessions to the Pythagorean community (p. 45). In addition, there was a three-year probationary period, during which the individual had to maintain a vow of silence. After the probationary period, the individual’s character and comportment would then be carefully evaluated. Some persons were invited to leave the community, and their wealth would be returned to them two-fold (p. 48). Those who continued on as a disciple then entered into a five-year period of silence. To be a true Pythagorean demanded self-discipline. Conviction that there is a higher purpose beyond this mortal life fortified the Pythagorean to continue on his ascetic path.
As stated previously, Pythagoras believed in immortality and transmigration of the soul. This concept of the soul is related to Pythagoras’ vegetarianism in the following manner. One may be reborn as an animal. Thus, the eating of animal flesh would defile the soul (Iamblichus, 1818/1986, p. 58). According to Pythagoras, one must respect the sanctity of all life. To have compassion for another life is to advance the status of one’s own life. The Pythagorean perspective does not concern itself with pleasure in the sense of self-indulgence; rather, the Pythagorean view is one that seeks to achieve eudaimonia, a greater happiness that is not transitory in its nature (Robinson, 1997, Lecture 14).
Pythagoras believed that one’s relationships with others were of great importance. Pythagoras thought that friendships should be honored, and one must not betray a friend (Strohmeier and Westbrook, 2003, p. 63). A friend by Pythagoras’ definition was any person who adopted his way of life. The kindness and generosity of the Pythagoreans was well known: “So famous were his followers for their care of one another, that until the Christian era, Greeks would call any person of extraordinary kindness a Pythagorean” (p. 63). Pythagoras taught his followers sayings such as “friends have all things in common” (Kahn, 2001, p. 8), and “my friend is my other self” (Strohmeier and Westbrook, 2003, p. 62). Pythagoras’ teachings on philiafostered a sense of community. Philia was extended not to a select few, but to the larger community of followers. Moreover, Pythagoras believed that respect and compassion should also be extended to those persons who were not followers of the Pythagorean way, as the whole of mankind is one within the universe.
Numbers, such as the number one, for Pythagoras had both literal and metaphorical meanings. The number one was called monadand it signified Being, ousia; one is also a point on a plane (p. 70). The number two, dyad, signifies “polarity, opposition, divergence, inequality, divisibility” (p. 71). Dyad is also two points connecting a line. The number three signifies “that nature has beginning, middle, and end” (Kahn, 2001, p. 107). The number three is also three points that can represent a triangle. “It was the Pythagoreans who…came forth with the conception of form. For them, form meant limit, and the limit is understandable especially in numerical terms” (Stumpf, 1993, p. 11). Through numbers, Pythagoras sought to discover that which is universally true within the kosmos. And he did find truth in mathematics, in geometry, and in science.
Pythagoras discovered the theorem that now bears his name: “the square of the hypotenuse of a right triangle equals the sum of the squares of the sides forming the right angle” (Strohmeier and Westbrook, 2003, p. 68). Pythagoras has also been credited with what later came to be known as “the Platonic solids—the pyramid, cube, octahedron, dodecahedron, and icosahedron—although he regarded the sphere as the most perfect, and thus the most beautiful figure of all” (p. 69). It is with Pythagoras that man begins to describe the physical world with precision.
Through his study of astronomy, Pythagoras hypothesized the following truths. Pythagoras “argued that the Earth itself was a sphere; he demonstrated that day and night were a result of the Earth’s revolution; and he showed that the change in seasons was due to the tilt of the Earth’s axis relative to the sun” (p. 90). Furthermore, Pythagoras understood that the moon shines by the reflected light of the sun. He thus understood solar and lunar eclipses (p. 90). The genius of Pythagoras is evident in the way he applied calculation, observation, and reason to discover truths of the natural world.
Pythagoras was fascinated by the physical world; at the same time, he looked closely toward the betterment of mankind as he acquired knowledge and understanding of physical truths. For example, in music, Pythagoras believed that certain tones and rhythms were beneficial to health, and also aligned the individual with the harmony of the universe. Pythagoras believed that “music was an expression of harmonia, the divine principle that brings order to chaos and discord” (Strohmeier and Westbrook, 2003, 78). In the morning, residents of the Pythagorean community awoke to concordant sounds that prepared them to begin the day in a tranquil manner. Certain rhythms and melodies were thought to help free the Pythagorean from feelings of sadness, anger or envy. Instruments of the day included the lyre, the flute, the aulos, a kind of oboe, and the monochord, an instrument with a single string. In the evening, the Pythagorean community listened to melodies designed to induce a peaceful state. “Blending particular intervals and modulations of the voice, sometimes with words, these evening songs produced in his disciples a restful sleep, with pleasing and meaningful dreams” (p. 79). Pythagoras endeavored to create an environment that would posture one toward inner peace and good will toward others.
Pythagoras was able to arrive at certain discoveries in music through mathematical inquiry, or more precisely, through exploration of the relationships between numbers:
He determined mathematically the progression of eight tones that makes up the scale (an ancestor of the modern do, re, mi, fa, so, la, ti, do). This came to be known as the ‘Eight-Stringed Lyre of Pythagoras.’ Later, he calculated the structure of other musical modes, including the chromatic and enharmonic orders, using simple ratios to create complex intervals (p. 85).
Iamblichus noted that “it is said that music was discovered by Pythagoras” (Iamblichus, 1818/1986, p. 229). This statement would seem to be hyperbolic, but it is also a testament to the significance of Pythagoras’ contributions to our understanding of music.
Pythagoras was not without his critics. Some persons objected to the “cult-like”aspects of the Pythagorean community, which were seen as secretive and exclusive. Members of the Pythagorean society were called homakooi, “those who come together to listen,” and their assembly hall was called a homakoeion, “a place for hearing together” (Kahn, 2001, p 8). What the Pythagoreans heard was an akousma, a “hearing” or a symbolon, a “password” (p. 8). Pythagoreans who had successfully completed both the three-year vow of silence, the probationary period for entering into Pythagorean society, and the five-year vow of silence were allowed in the chamber where Pythagoras spoke. The newcomers to Pythagorean society were permitted to listen to Pythagoras’ akousma only from behind a linen curtain. Persons from outside Pythagorean society were not admitted, as “the teachings of Pythagoras were not to be revealed to nonmembers” (p. 8). Thus, some persons from the surrounding community of Croton viewed the Pythagorean community with suspicion and distrust.
Pythagorean philosophy was unique in its day, and it did contain special information and views that were not disclosed to those outside of the society. For example, Pythagoras assigned importance to the number four, the tetrad, for this number represents completion:
Everything in the universe, both natural and numerical, is completed in the progression from one to four. There are four seasons, four elements, four essential musical intervals and four kinds of planetary movement. As Plato was to expound, there are four faculties—intelligence, reason, perception and imagination. Four points in space give rise to the first three-dimensional solid, the pyramid…Because four completes the progression 1 + 2 + 3 + 4 = 10, it also gives rise to the tetraktys (Strohmeier and Westbrook, 2003, p. 73).
The tetraktys, composed of ten points that form the shape of a pyramid, was considered “a symbol of the human psyche and also a numerical model for the kosmos” (p. 73). Members of the Pythagorean society took an oath not to disclose the great wisdom of the tetraktys. For Pythagoras, numbers and numeric relationships could be used to reveal truths about the material world; but numbers also transcend their literal meanings through symbol, metaphor, and archetype.
Pythagorean philosophy would later influence Socrates, Plato, and Aristotle. “Socrates asserted that leading a good life meant that the person was using reason to discover the truth and had determined to live according to it” (Gutek, 2001, p. 2). In Socrates, one sees the synthesis of belief and action, when Socrates sacrifices his life in order to be true to his principles. Socrates was sentenced to take his own life drinking hemlock. He could have left the region and saved his own life, but chose not to. As did Pythagoras before him, Socrates believed that his life had a higher purpose than his mere physical existence. Socrates’ student, Plato, also devoted himself to the search for universal truths and for the good. In 387 B.C.E., Plato founded a school of higher learning called the Academy. Plato and his students “examined questions dealing with metaphysics, the study of ultimate reality; epistemology, the study of knowledge; and axiology, the examination of ethical and aesthetic values” (p. 3). Plato developed philosophical idealism, which significantly contributed to the foundation of Western thought. Aristotle then carried forward the quest for knowledge and for the good. He said, “good is what all desire” (Gomes, 2002, p. 49). Aristotle was likely influenced by the Pythagorean concept of the dyad, which is evidenced in his concepts on metaphysics. Aristotle’s metaphysics addressed the force of opposites, such as good and evil, light and darkness, limit and limitless.
Pythagoras’ thirst for knowledge and understanding also led him to discoveries in mathematics, geometry, music, and science. More than two thousand years after the time of Pythagoras, Albert Einstein said that the scientist is many things but that he may also view himself as “a Platonist or Pythagorean insofar as he considers the viewpoint of logical simplicity as an indispensable and effective tool of his research” (Kahn, 2001, p. 172). Pythagoras, Socrates, Plato, Aristotle, Einstein, and myriad other great thinkers have valued reason as the pathway to that which is true.
Pythagoras was influenced by those who preceded him. He, in turn, influenced many who came after him. Thus, a seed of thought planted within the framework of history gives way to new thoughts and understandings.
Pythagorean philosophy is enduring for it addresses essential issues of our being in the world. Man has the ability to use reason, and he must search for the good. That which constitutes the good is not self-serving; rather, according to Pythagoras, the good becomes manifest in the attributes of modesty, kindness, generosity, and reticence. Poised at the commencement of the twenty-first century, Western society appears to have diverged from the teachings of Pythagoras. We live in a time when individuals often seem self-absorbed and excessively focused on the accumulation of personal wealth. Perhaps strict vegetarianism, communal living, and lengthy vows of silence seem incompatible with many in the modern era. However, it would bode well for mankind to reflect upon our purpose in this life, and to return to consideration for the whole of humanity as we venture forth and live our lives.
In The Golden Verses it says, “know that death comes to everyone, and that wealth will sometimes be acquired, sometimes lost” (Strohmeier and Westbrook, 2003, p. 139). The Golden Verses were not written by Pythagoras. They were written in the fourth century B.C.E. But within these lines we can hear the voice of the philosopher from Samos. There are many important messages in the teachings of Pythagoras. However, one significant counsel within Pythagorean philosophy is that this mortal life will surely pass, but the soul will go on. Therefore, we must ask ourselves what is meaningful and what is good. And then we must strive toward that telos with our whole heart.