PYTHAGORAS

Pythagoras : his life and work

It should be recalled that the foundations of the classical physical sciences and mathematics could be traced back to the ancient Greek philosophers and sages whose recorded wisdom and writings were rediscovered after the Dark Ages. The intention of the scientist is to re-examine the very foundations of the generic (post-dark-age) western culture which has been the basis of educational reforms and guidelines for the archetypical approaches to intellectual thinking for the last few hundred years.

Pythagoras, one of the earliest of the ancient Greek philosophers, was born in Samos and died probably in Metapontum (South-Italy) ° 575 BC- +500 BC.

He was one of the most enigmatic figures in history among the Greek philosophers. We don’t know that much about him. The only information we’ve got is from a continual re-interpretation of his work.
His authority was absolute as he said by himself : ‘ipse dixit’. Legends say that he travelled to Egypt and that he developed there a great part of his wisdom.

About 530 BC he established a school in Croton. Many other departments have also been settled down in other South-Italian cities. Pythagoras and his followers have exercised an important influence on the public and political life. They experienced an important resistance. At the end of his life Pythagoras had to leave Croton and some decades later, a revolt took place against all his followers.

Pythagoras introduced « philosophy » as a way of life. He travelled widely, which influenced his way of thinking..

When asked ‘ What is philosophy?’ by a ruler, he gave the following answer:

« Life is like a gathering at he Olympic festival, to which,
having set forth from different lifes and backgrounds, people flock for three motives.
To compete for the glory of the crown, to buy and sell or as spectators.
So in life, some enter the services for fame and others for money,
but the best choice is that of these few who spend their time in the contemplation of nature,
and as lovers of wisdom. »

We all know Pythagoras from the lessons of mathematics. Now we’re going to let you see another side of the philosopher.

We’re going to start with the ten Pythagorean Principles.

The TEN PRINCIPLES of PYTHAGORAS Also known as the table of Opposites
limit	unlimited
odd	even
one	plurality
right	left
male	female
at rest	moving
straight	crooked
light	darkness
good	bad
square	oblong

Of the principles, Pythagoras said that the monad was God and the good, the true nature of the One, mind itself.

There are parallels observed between this Pythagorean table of principles and the outlining in the eastern parts of ancient China, concerning the TAO, and the complimentary natures of the principles of ‘Ying and Yang ‘.

These are listened as follows : sunshine/light – darkness/shadow, masculinity – femininity, activity – passivity, heat – cold, dryness – wetness, hardness – softness, odd – even.

Pythagoras had also spoken about the five solid figures, called the mathematical solids.
He said that…

The earth is made from a cube,
Fire from the pyramid,
Air from the octahedron,
Water from the eicosahedron,
And the sphere of the whole (the Aither) from the dodecahedron.

There is very much to say about the fifth element of nature. That’s why we’re going to discuss it.

Notes from Guthrie (1):

The truth is that the emergence of a fifth element in Greek thought was a gradual process. In bare outline, a common conception of the universe seems to have been shared by most religious and philosophical thinkers in the centuries before Plato. The cosmos, a sphere bounded by the sky, contains the conflicting’opposites’, which became the four-root substance earth, water, air and fire.

Pythagoreans (2) held that the cosmos ‘Breathed in ‘from the Infinite Breath outside it: « aither ». Pythagoras derived the world from the fire and the fifth element.

Philolaus the Pythagorean says that FIRE is at the centre, calling it the heart of the universe; second comes the COUNTER-EARTH, and third the inhabited earth which in its revolution remains opposite the counter-earth, wherefore the inhabitants of this earth do not see those of the other.
« They call the earth a star as being itself an instrument of time, for it is the cause of day and night. Day it creates by being lit up on the side which turned toward the sun, and night through the cone of his shadow. COUNTER EARTH was the name given by the Pythagoreans to the MOON and also HEAVENLY EARTH. »
Pythagoras maintained that the fire was at the centre of the cosmos. Many Pythagoreans followed his example and approved this ancient insight of HELIOCENTRICITY.

(1) Guthrie was a person who had searched all kind of information about Pythagoras, because he was interested in this figure.

(2) Pythagoreans are members of a Greek philosophical direction, called after Pythagoras, the founder of the school.

Pythagoras had also a certain opinion about the Nature of the Soul.
He said one day:

« In the case of the soul, the three parts that have to be brought into accord are of course reason, passion and desire. »

As a philosopher he had a very strange way of thinking. (Is that one of the characteristics of philosophers?)

Pythagoras taught of the transmigration of the soul – man/plant/animal – and post-humous rewards for the good. It is recorded that he rememberd his past lives as Aethalides (son of Hermes, whence the gift of memory), Euphobus (from the Homer epics), Hermotimus and Pyrrus (a Delian fisherman) before his birth as Pythagoras. He used to say that he had received as a gift from Mercury the perpetual transmigration of his soul, so that it was constantly transmigrating and passing into all sorts of plants or animals.

Aristotle had a great admiration for his predecessor Pythagoras. Aristotle wrote the following text well over 2 000 years ago…it remains to speak of the earth, of its positions, of the questions whether it is at rest or in motion, and of its shape.

As to its position there is some difference of opinion. Most people-all, in fact, who regard the whole heaven as finite-say it lies at the centre. But the Italian philosophers known as Pythagoreans take the contrary view. At the centre, they say, is fire, and the earth is one of the stars, creating night and day by its circular motion about the centre. They further construct another earth in opposition to ours to which they give the name counter-earth. In all this they are not seeking for theories and causes to account for observed facts, but rather forcing their observations and trying to accommodate them to certain theories and opinions of their own. But there are many others who would agree that it is wrong to give the earth the central position, looking for confirmation rather to theory than to the facts of observations. Their view is that the most precious place befits the most precious thing: but fire, they say, is more precious than earth, and the limit than the intermediate, and the circumference and the verger are limits. Reasoning on this basis they take the view that it is not earth that lies at the centre of the sphere, but rather fire.

The Pythagoreans have a further reason. They hold that the most important part of the world, which is the venture, should be most strictly guarded. They name it, or rather the fire which occupies that place, the ‘Guardhouse of Zeus’, as if the word ‘centre‘ were quite unequivocal, and the centre of the mathematical figure were always the same with that of the thing or the natural centre.

This is a picture of Aristotle, who had much sympathy for Pythagoras

The Pythagoreans : successors of Pythagoras

We can make a difference between the old Pythagoreans, who were connected with Pythagoras by a real schooltradition, and those who, after the crumble of the tradition, lay down with what they thought the doctrine of Pythagoras was.

The old Pythagoreans formed communes where they lived according the severe primitive rules and where they not only practised scientific work but also exercised other sciences. The tradition makes a difference between two sorts of old Pythagoreans, the acoustics (these are the ones who followed the regimes, were vegetarians,) and the mathematicians (the more scientific section).

Till 450 BC the Pythagorean communities were accepted in South-Italy, but about from that year many members were driven away or killed. The school went on in little isolated groups. Eventually they could maintain only in South-Italy in Tarente. Among the ones who moved to Greece, Philaulus was very important : we can find reliable information about the oldest Pythagorism in his book.

The most important Pythagorean of the fourth century BC is Archytas of Tarente, a friend of Plato (lived around 428 BC). He was a man of the state and an important mathematician. It’s certain that the Pythagorism influenced Plato. His pupils have the mathematical philosophy and the doctrine of the first principles of Pythagoras and Plato’s last works reflect on the old Pythagorism. Later generations make mostly little difference between the Platonism and the Pythagorism.

The next period is the Neopythagorism (first century BC). The Platonism had influenced it, but the other schools had also have an important part. We haven’t found more information about this period.

A Greek Bust of Plato

OTHER QUOTES…

Pythagoras calls drunkenness an expression identical with ruin.
The fundamental element of the world is the number 1.
Among what he calls his precepts were such as these: Do not stir the fire with a sword. Do not sit down on a bushel. Do not devour the heart.
In the time of Pythagoras that proverbial phrase « Ipse dixit » was introduced into ordinary life.
Animals share with us the privilege of having a soul.

BIBLIOGRAPHY

the internet : Pythagoras of Samos : A Resource Document
Encarta 98 Encyclopedie Winkler Prins Editie/ Microsoft Corporation
Filosofie – Jörg Aufenanger
Geschiedenis van de westerse filosofie – Bertrant Russell
Leven en leer van Pythagoras – Jamblichus / Porphyrius
De ontstelling van Pythagoras – Albert van der Schoot

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