Pythagoras, contorniate medallion engraved between AD 395 and 410
Pythagoras:
Pythagoras (fl. 530 BCE) must have been one of the world's greatest
men, but he wrote nothing, and it is hard to say how much of the
doctrine we know as Pythagorean is due to the founder of the society and
how much is later development. It is also hard to say how much of what
we are told about the life of Pythagoras is trustworthy; for a mass of
legend gathered around his name at an early date. Sometimes he is
represented as a man of science, and sometimes as a preacher of mystic
doctrines, and we might be tempted to regard one or other of those
characters as alone historical. The truth is that there is no need to
reject either of the traditional views. The union of mathematical genius
and mysticism is commonly enough. Originally from Samos, Pythagoras
founded at Kroton (in southern Italy) a society which was at once a
religious community and a scientific school. Such a body was bound to
excite jealousy and mistrust, and we hear of many struggles. Pythagoras
himself had to flee from Kroton to Metapontion, where he died.
It is stated that he was a disciple of Anaximander, his astronomy
was the natural development of Anaximander's. Also, the way in which the
Pythagorean geometry developed also bears witness to its descent from
that of Miletos. The great problem at this date was the duplication of
the square, a problem which gave rise to the theorem of the square on
the hypotenuse, commonly known still as the Pythagorean proposition
(Euclid, I. 47). If we were right in assuming that Thales worked with
the old 3:4:5 triangle, the connection is obvious.
Pythagoras argued that there are three kinds of men, just as there
are three classes of strangers who come to the Olympic Games. The lowest
consists of those who come to buy and sell, and next above them are
those who come to compete. Best of all are those who simply come to look
on. Men may be classified accordingly as lovers of wisdom, lovers of
honor, and lovers of gain. That seems to imply the doctrine of the
tripartite soul, which is also attributed to the early Pythagoreans on
good authority, though it is common now to ascribe it to Plato. There
are, however, clear references to it before his time, and it agrees much
better with the general outlook of the Pythagoreans. The comparison of
human life to a gathering like the Games was often repeated in later
days. Pythagoras also taught the doctrine of Rebirth or transmigration,
which we may have learned from the contemporary Orphics. Xenophanes made
fun of him for pretending to recognize the voice of a departed friend in
the howls of a beaten dog. Empedocles seems to be referring to him when
he speaks of a man who could remember what happened ten or twenty
generations before. It was on this that the doctrine of Recollection,
which plays so great a part in Plato, was based. The things we perceive
with the senses, Plato argues, remind us of things we knew when the soul
was out of the body and could perceive reality directly.
There is more difficulty about the cosmology of Pythagoras. Hardly
any school ever professed such reverence for its founder's authority as
the Pythagoreans. 'The Master said so' was their watchword. On the other
hand, few schools have shown so much capacity for progress and for
adapting themselves to new conditions. Pythagoras started from the
cosmical system of Anaximenes. Aristotle tells us that the Pythagoreans
represented the world as inhaling 'air' form the boundless mass outside
it, and this 'air' is identified with 'the unlimited'. When, however, we
come to the process by which things are developed out of the
'unlimited', we observe a great change. We hear nothing more of
'separating out' or even of rarefaction and condensation. Instead of
that we have the theory that what gives form to the Unlimited is the
Limit. That is the great contribution of Pythagoras to philosophy, and
we must try to understand it. Now the function of the Limit is usually
illustrated from the arts of music and medicine, and we have seen how
important these two arts were for Pythagoreans, so it is natural to
infer that the key to its meaning is to be found in them.
It may be taken as certain that Pythagoras himself discovered the
numerical ratios which determine the concordant intervals of the musical
scale. Similar to musical intervals, in medicine there are opposites,
such as the hot and the cold, the wet and the dry, and it is the
business of the physician to produce a proper 'blend' of these in the
human body. In a well-known passage of Plato's Phaedo (86 b) we are told
by Simmias that the Pythagoreans held the body to be strung like an
instrument to a certain pitch, hot and cold, wet and dry taking the
place of high and low in music. Musical tuning and health are alike
means arising from the application of Limit to the Unlimited. It was
natural for Pythagoras to look for something of the same kind in the
world at large. Briefly stated, the doctrine of Pythagoras was that all
things are numbers. In certain fundamental cases, the early Pythagoreans
represented numbers and explained their properties by means of dots
arranged in certain 'figures' or patterns.
Excerpt from the Encyclopedia Britannica without permission.