By Samuel Gugliotta
For Variety

AT the base of the great spring which has given birth to our traditions of mathematics, philosophy, science and religion stands the commanding figure of Pythagoras (whose name means, “slayer of pythons”).
Pythagoras was born on the island of Samos, in Sicily (which the ancient Greek world called Ionia), around 570 B.C.E. Thus he lived and taught at the same time as another world-changer, namely Siddhatattha Gotama, otherwise known as the Buddha, the Enlightened One (c. 563-483 B.C.E.).
The Pythagorean Order lasted over 500 years, and all the great thinkers of the Western world were Pythagoreans before they were creators. Probably the most famous disciple was Plato. Alfred North Whitehead once stated that all Western philosophy was but a footnote to Plato, but it was Pythagoras who enabled to Plato to write the book.
It required a total commitment and dedication to become a member of the Pythagorean Order. Those accepted for initiation had first to observe a five year period of silence, after which they became known as “esoterics.” If accepted to the inner circle, they became known as “akousmatikoi,” the Hearers. All property was held in common, women were equal to men, and the diet was strictly vegetarian.
Our word “mathematics” comes from the Greek word for learning, mathemata. For Pythagoras mathematics was a spiritual as well as a cognitive discipline, and it was through the study of numbers and their patterns that a person could realize the eternal Ideas of which our phenomenal world is but a reflection through a glass darkly.
Mathematics included the study of what today we would call number theory, music (harmonics, or number in time), geometry (number in space), and spherics (or astronomy, number in space and time). This group became known as the “quadrivium.” Later the “trivium,” consisting of grammar, dialectics, and rhetoric was added to the Pythagorean group and constituted the famous “seven liberal arts.” This classification of the disciplines lasted for over a thousand years.
Pythagoras also invented the word “philosophy.” The ancient Greeks had two words for knowledge. One was “episteme” which referred to practical knowledge, and the other was “sophrosune” which referred to knowledge of first principles and divine things — what we call “wisdom.” Accordingly, when Pythagoras was asked if he was wise (sophos), he replied that he was not wise but a lover of wisdom (philo-sophos). Only the Gods could be truly wise.
However, if only the Gods could be wise, how is it possible to be a lover of wisdom? For to love something requires that you have some knowledge of that which you love. This situation is known as the paradox of analysis, and was a question which was considered by Plato’s Socrates in the Meno.
In that dialogue, Meno states, “But how will you look for something when you don’t in the least know what it is? How on earth are you going to set up something you don’t know as the object of your search? To put it another way, even if you come right up against it, how will you know that what you have found is the thing you didn’t know?”
Socrates thinks this is a bad argument, for if true it would be useless to look for anything. You either know it, and you don’t need to find it, or you don’t know it, and you can never find it. Socrates says, “We ought not then to be led astray by the contentious argument you quoted. It would make us lazy, and is music in the ears of weaklings.”
To counter this argument, Plato’s Socrates brings in an idea which is pure Pythagorean. Namely, he claims that the soul (or pscuche) has been born, or reborn many times (the doctrine of metempsychosis, or reincarnation) and has “seen all things both here and in the other world, has learned everything that is.” However, when the soul is embodied (or the body ensouled), it suffers a deep forgetfulness of all that it has learned in its previous sojourn in time and eternity. But such knowledge (wisdom) has not been obliterated, for the seeker only needs to encounter the object of her search to be reminded of what she has forgotten. Thus all learning (mathemata) is said to be a kind of recollection or anamnesis.
Plato, it seems, was the first pragmatist, for he says that belief in his doctrine “produces energetic seekers after knowledge,” whereas Meno’s argument is only a council of despair and one suitable to weaklings. For Plato, as well as Pythagoras, all nature is related, so that learning even one thing thoroughly is way to find out everything, if only the seeker, “keeps a stout heart and does not grow weary of the search.” (Seek and you shall find.).
From the source of Pythagoras, the Western tradition flowed into two major streams, the esoteric and exoteric, the right and left hand paths. Yet in the beginning there was but one stream, and science was not separate from spirituality, and mysticism was married to materialism. Ever since, major advances of thought, such as those developed by Kepler, Newton, Einstein, occurred whenever the two streams came together again, for a time, uniting the opposites, like man and woman, resulting in a deeper vision of the universe and our place within it.
Puzzles
1. O’Henry’s famous short story, “The Gift of the Magi,” opens with the statement, “One dollar and eighty-seven cents. That was all. And sixty cents of it was in pennies.” How is this possible?
2. Consider the sentence, “The number of words in this sentence is nine.” This sentence is obviously true. Can you give an example of a sentence that says the exact opposite of that sentence but is nevertheless true?
3. The edge of a reservoir is a perfect circle. A fish starts at a point on the edge and swims due north for 600 feet, which takes him to the edge again. He then swims due east, reaching the edge after going 800 feet. What is the diameter of the reservoir?
Answers to Last Week’s Puzzles
1. 281 to 220
2. 120 miles