Pythagoreans

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Platonic Solids

The theorems of philosophy are to be enjoyed as much as possible, as if they were ambrosia and nectar.  For the resultant pleasure is genuine, incorruptible and divine.  They are also capable of producing magnanimity, and though they cannot make us eternal, yet they enable us to obtain a scientific knowledge of eternal natures.   -  Iamblichus, Pythagorean Sentences #113 

The Collegium Fabrorum is structured after the school of Pythagoras at Croton. It incorporates many Pythagorean ideas into its curriculum.  These relate a natural philosophy that flows parallel to the latest scientific discoveries, and demonstrates how the natural and spiritual world are linked together by indissoluble bonds. 

The Pythagorean school was divided into three grades with the final level being divided into two distinct groups.

• Akousmatikoi
• Mathematikoi
• Politikoi

Pythagoras of Samos is often described as the first pure mathematician. The Platonic Solids are among his many discoveries.  He is an extremely important figure in the development of mathematics yet we know relatively little about his mathematical achievements. Unlike many later Greek mathematicians, where some of their works survive, we have nothing of Pythagoras's writings. The society which he led, half religious and half scientific, followed a code of secrecy which has caused Pythagoras to be viewed as a somewhat mysterious figure.

Pythagoras was born at Samos around 570 B.C. According to legend he traveled throughout the known world searching for both knowledge and wisdom.  It is certain that he came to Italy in Magna Graecia, and founded a school with scientific, religious, and political leanings in the Doric colony of Croton.  The Pythagorean school was very eclectic in nature - its teachings having been derived from the sum of all that Pythagoras had learned during his earlier travels.

Pythagoras was the head of the society with an inner circle of followers known as mathematikoi. The mathematikoi lived permanently with the Society, had no personal possessions and were vegetarians. They were taught by Pythagoras himself and obeyed strict rules. The most common beliefs that Pythagoras held were:

(1) that at its deepest level, reality is mathematical in nature,
(2) that philosophy can be used for spiritual purification,
(3) that the soul can rise to union with the divine,
(4) that certain symbols have a mystical significance, and
(5) that all brothers of the order should observe strict loyalty and secrecy.

The outer circle of the Society were known as the akousmatikoi and they lived in their own houses, only coming to the Society during the day. 

To this school were admitted youths of both sexes of the high aristocracy who were divided into various sections according to the grade of initiation to learning. The political aims of the school raised up much opposition, and in a popular uprising in 497 the school was given to the flames. Pythagoras seems to have removed himself to Metapontum before this uprising and died there either in the same or the following year. Pythagoras left no writings, and the doctrine which is known under his name must be attributed to him and to his disciples, especially to Philolaus, who lived until the time of Socrates.

The Pythagoreans cultivated the mathematical sciences and the study of mathematics led them to the observation that everything could be represented through a number. The number appears not as an abstraction, but as a real being, the generator of all things: they concluded that the number should be retained as the essence, the principle of reality.

This passing from the abstract order of number to the actual order of being today seems simple-minded and silly. It was not, however, so considered by the Pythagoreans, for they were the first to observe that number applied not only to the motions of the heavens and the succession of time, but also to the harmony of sounds (the height of the sound is in inverse proportion to the length of the string). It was easy for the cultivators of mathematics to bow down before the number and consider it as a divine reality.

Through a long theory on numbers the Pythagoreans attempted to explain the multiple and the notion of becoming. Numbers are divided into even and odd; the even numbers unlimited, the odd ones limited. Since everything is a number, the constitutive elements of things are the evens and the odds, the unlimited and the limited, the worse and the better. This radical opposition would give the explanation of all the world of multiplicity, even its moral aspects: justice is represented by the square (even multiplied by even); love, friendship, because they indicate perfect harmony, were identified with the number eight; health with the number seven.

Even and odd number originated from the "One." It is from the One that all the other numbers, which are the constitutives of multiplicity, proceed. Multiplicity hence is reduced to unity, and it is in unity that all differences and contrasts are annulled, and the harmony of the multiple ends in silence.

The perfect and sacred number for the Pythagoreans is ten, which results from the principal combinations: 1, 2, 3, 4 -- these are identified as the point, line, surface and volume, and when added, they result in the number ten. For the Pythagoreans there are ten heavens. To make up this number, they add to the traditional nine a tenth, which they call "antiterra." The heavens all revolve around one central point which is called "Fire."

For the Pythagoreans the soul is naturally in harmony with the One, but through the influences of duality becomes inharmonious.  The Collegium seeks to aid each human being in restoring that natural harmony within them self. 

“The first and the best victory is to conquer self.  To be conquered by self is, of all things, the most shameful and vile.” — Plato

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