Pythagoras
(Pythagoras was the first person known
to have taught the earth was spherical, with antipodes and that it revolved
around the sun.)
He was a Greek
philosopher who was responsible for important developments in the history of
mathematics, astronomy, and
the theory of music. He founded the Pythagorean Brotherhood and formulated
principles that influenced the thoughts of Plato and Aristotle. The influence
of Pythagoras was so widespread and that he was such a remarkable teacher but
no authentic records of his writings and his life exist even today.
He traveled widely in his youth with his
father, who was a gem merchant. He was introduced to mathematical ideas and astronomy by Thales, when
he was between 18 and 20 years old. Thales advised Pythagoras to travel to
Egypt to learn more of these subjects.
It is claimed that Pythagoras then went onto Egypt. Arriving in Egypt,
Pythagoras tried to gain entry into the Mystery Schools of that country. He
applied again and again, but he was told that unless he goes through a
particular training of fasting and breathing, he cannot be allowed to enter the
school. Pythagoras is reported to have said, "I have come for knowledge,
not any sort of discipline." But the school authorities said," we
cannot give you knowledge unless you are different. And really, we are not
interested in knowledge at all, we are interested in actual experience. No
knowledge is knowledge unless it is lived and experienced. So you will have to
go on a 40 day fast, continuously breathing in a certain manner, with a certain
awareness on certain points."
After 40 days of fasting and breathing,
aware, attentive, he was allowed to enter the school at Diospolis. It is said
that Pythagoras said,"You are not allowing Pythagoras in. I am a different
man, I am reborn. You were right and I was wrong, because then my whole
standpoint was intellectual. Through this purification, my center of being has
changed. Before this training I could only understand through the intellect,
through the head. Now I can feel. Now truth is not a concept to me, but a
life."
He spent the next 22 years perfecting himself in mathematics, astronomy, music, and was initiated into the Egyptian Mysteries. When, the king of Persia invaded Egypt in 525BC, he made Pythagoras his prisoner and sent him to Babylon. He utilized this misfortune as an opportunity for growth, and for the next 12 years he studied and was initiated into the Chaldean Mysteries. Leaving Babylon, he made his way through Persia to India, where he continued his education. At that time India was still feeling the effects of the spiritual revival brought about by Gautama the Buddha. Although Pythagoras arrived in India too late to come into personal contact with the Buddha, he was greatly influenced by his teachings. He went to India a student, he left it as a teacher, and even to this day he is known in that country as Pitra Guru, and as Yavanacharya, the Ionian Teacher.
He spent the next 22 years perfecting himself in mathematics, astronomy, music, and was initiated into the Egyptian Mysteries. When, the king of Persia invaded Egypt in 525BC, he made Pythagoras his prisoner and sent him to Babylon. He utilized this misfortune as an opportunity for growth, and for the next 12 years he studied and was initiated into the Chaldean Mysteries. Leaving Babylon, he made his way through Persia to India, where he continued his education. At that time India was still feeling the effects of the spiritual revival brought about by Gautama the Buddha. Although Pythagoras arrived in India too late to come into personal contact with the Buddha, he was greatly influenced by his teachings. He went to India a student, he left it as a teacher, and even to this day he is known in that country as Pitra Guru, and as Yavanacharya, the Ionian Teacher.
(The church,
the temple and the lab need not be enemies. They should exist in a kind of
friendship. Man will be far richer then. Now, if he chooses science he becomes
rich outside and goes on becoming poorer and poorer inside. If he chooses
religion, he becomes rich inside, but goes on becoming poorer and poorer on the
outside. And both are ugly scenes.” - OSHO)
Pythagoras was 56 years old when he
finally returned to his homeland. When he arrived in Samos he found the island crushed and ruined, its
temples and schools closed, its wise men fleeing from the tyranny and persecution of
the Persian conquerors. Instead of being welcomed by his countrymen, Pythagoras
found them indifferent to the wisdom he was eager to impart. He left Samos and
went to southern Italy, settling in Crotona, a town situated on the Gulf of
Tarentum. He was invited to speak before the Senate of Crotona, and so greatly
impressed them with his wisdom, that they decided to build him an institute,
which would serve as a school of philosophy and an academy of science. Although
it was understood that it would be patterned after the Mystery Schools, there
was nothing about the place suggesting secrecy save a statue of Hermes
Trismegistus at the door of the inner school with the words on the pedestal:
"Let no profane enter here."
(Pythagoras was the first to call
the heavens a universe and the earth round. That the Soul was immortal, and
that it changes from one body to another. The Pythagorean Brotherhood was one
of the worlds earliest unpriestly cooperative scientific societies, if not the
first, and that its members invented the multiplication table, and raised
important scientific problems which were solved 15 centuries later.)
Pythagoras
in “The School of Athens”
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| The School of Athens |
Pythagoras studied harmonics
and learnt that much of music was governed by consistent mathematical ratios.
It was said Pythagoras was given inspiration while passing a blacksmiths shop.
One blacksmith had an anvil half the size of the other, and the sounds that
were produced when the hammers struck were exactly an octave apart. Pythagoras
experimented with musical strings and realized that there was a constant ratio
between the sizes of strings that determined if they were harmonious when
plucked together. This idea would become known as the harmonic series and would
become very important in the fields of harmonics and even music.
Pythagoras gained
quite a following during his time on earth. The Pythagoreans, as they would be
known as, set up a structured community in Croton, southern Italy. This
community of 300 people lived by a structured set of rules and standards.
Pythagoras was the community leader and taught his ideas of mathematics and
divine structure to all who would listen. This community was said to have
verged on a cult, as people living together, worshiping numbers certainly would
appear to be sect-like. In fact, it was told that this group of Pythagoreans
were the subject of much hostility and were eventually run out of town.
Pythagoras and his followers were eventually forced to settle in Metapontum,
also in southern Italy.
“Number is the ruler of forms and
ideas” –Pythagoras
Pythagoras
(“Pythagoras represents the perennial
philosophy of life. He is a seeker of truth par excellence. He staked all that
he had for the search. He travelled far and wide, almost the whole known world
of those days, in search of the Masters, of the mystery schools, of any hidden
secrets. From Greece he went to Egypt -- in search of the lost Atlantis and its
secrets.” - OSHO)
While Pythagoras has become known as
one of the first revolutionaries in the field of philosophy and
mathematics, surprisingly little is known about him, as he kept no writings of
his own. All that we have learned about Pythagoras and his teachings has come
to us indirectly through the writings of others.
What we do know about Pythagoras is
that he was born in about 570 BCE. He visited Egypt as a young
man and learned extensively about mathematical relations, proportions, and a
rudimentary form of geometry. It is believed he studied within the Milesian
school that had been founded by Thales a generation before.
This school was devoted to uncovering the nature of
the universe through objective, non mystical means; and while Pythagoras would
not outright disagree with the ideas of Thales, he did take a
different approach to exploring metaphysics. To Pythagoras, mathematics was
the key. It was the form and order that existed in all things and through it
the universe had come into being.
While modern thinkers usually take the
line of thought that objective, scientific thinking is
contradictory to religion, Pythagoras took quite the opposite position. His
foray into mathematics lead him to believe that numbers and mathematical
relations held a particular divinity that could explain the
universe. To Pythagoras, all the universe was constructed of mathematical
relations, and so the cosmos themselves could be explained by
the study of numbers.
(“For Pythagoras, science is a search for truth in the
objective world and religion is a search for truth in the subjective world --
and philosophy is a search for the truth. So science and religion are like two
hands or two wings. They are not opposites but complementaries. And the world
would be better if we were reminded of it again. – OSHO)
Pythagoras hypothesized that before the
universe there existed infinity with no limits or structure.
God would then have created a limit upon all things so that infinity would be
able to take on an actual size. In this way a measurable unity was
created from which all things formed. The Pythagoreans held so much faith in
numbers that they actually started applying characteristics to them. They
believed that even numbers were “good” and odd numbers were “evil”. While
Pythagoras might have gotten a bit carried away on that point, there is still
much support to his claim that the natural world is governed by mathematical
relations.
Quotes cited as from
the "Golden Verses"
·
But always make this reflection, that it is ordained by
destiny that all men shall die.
·
Above and before all things,
worship GOD!
·
Know that death comes to everyone,
and that wealth will sometimes be acquired, sometimes lost. Whatever griefs
mortals suffer by divine chance, whatever destiny you have, endure it and do
not complain. But it is right to improve it as much as you can, and remember
this: Fate does not give very many of these griefs to good people.
·
When a reasonable Soul forsaketh his divine nature, and
becometh beast-like, it dieth. For though the substance of the Soul be
incorruptible: yet, lacking the use of Reason, it is reputed dead; for it
loseth the Intellective Life.
·
A good Soul hath neither too great joy, nor too great
sorrow: for it rejoiceth in goodness; and it sorroweth in wickedness. By the
means whereof, when it beholdeth all things, and seeth the good and bad so
mingled together, it can neither rejoice greatly; nor be grieved with over much
sorrow.
·
Order thyself so, that thy Soul
may always be in good state; whatsoever become of thy body.
·
Dispose thy Soul to all good and
necessary things!
·
True and perfect Friendship is, to
make one heart and mind of many hearts and bodies.
·
He is not rich, that enjoyeth not his own goods.
·
A fool is known by his Speech; and a wise man by Silence.
·
Be not hasty to speak; nor slow to hear!
·
Wisdom thoroughly learned, will
never be forgotten.
Science is got by diligence; but Discretion and Wisdom cometh of GOD.
Science is got by diligence; but Discretion and Wisdom cometh of GOD.
·
A solitary man is a God, or a beast.
·
None but a Craftsman can judge of
a craft.
“Pythagoras is not at all bothered about any university in the world, for the
simple reason that he is not a routine scholar; he is an original seeker, and
he is ready to go anywhere. He traveled all his life to find people who may
have had a little glimpse and may be able to impart something to him. He was
collecting pieces, and he managed beautifully.
- Beyond Psychology - OSHO
“PYTHAGORAS IS THE FIRST EXPERIMENT in creating a synthesis. Twenty-five centuries have passed since then and nobody else has tried it again. Nobody else before had done it, and nobody else has done it afterwards either. It needs a mind which is both -- scientific and mystic. It is a rare phenomenon. It happens once in a while.”
“Pythagoras is not a monotheist; he does not believe in one God. He says: All the peoples of the world and all their approaches are true. And he KNOWS it, because he has followed many many paths; almost all existent paths Pythagoras followed many many paths; almost all existent paths Pythagoras followed. And he always reached the same peak.
There are many paths by which to reach the peak. The mountain has many paths, but they all reach the same peak. You can go from the south or from the north or from the east or from the west... you can follow a very rocky track, or you can follow a very different track. There are many alternatives.
Pythagoras knows truth is one, but he does not say it. Truth is one UNSAID. Once you say it, then please don't use the singular; then it is better to use the plural. The Vedas say: Truth is one, but wise people have described it in many ways.”
- Philosophia Perennis, OSHO
The church, the temple and the lab need not be enemies. They should exist in a kind of friendship. Man will be far richer then. Now, if he chooses science he becomes rich outside and goes on becoming poorer and poorer inside. If he chooses religion, he becomes rich inside, but goes on becoming poorer and poorer on the outside. And both are ugly scenes.”
“HEALTH TO PYTHAGORAS, HAS TWO ASPECTS TO IT. One is the physical, the other is the spiritual. The body is your temple -- don't neglect it. Your foolish, stupid ascetics have been telling you to neglect it -- not only to neglect but to destroy your body. Pythagoras is not an ascetic: he is a man of understanding.
- Philosophia Perennis, OSHO
Moral Statements of
Pythagoras
Concern should drive
us into action and not into a depression. No man is free who cannot control
himself.
It is better wither
to be silent, or to say things of more value than silence. Sooner throw a pearl
at hazard than an idle or useless word; and do not say a little in many words,
but a great deal in a few.
Universe was governed by Mathematical laws
Pythagoras remains
one of the most influential thinkers of ancient times. His belief that the
cosmos were governed by mathematical forms would be built upon by later
astronomers, including the famous Galileo. Additionally, the idea that the
natural world was built upon predictable ratios was used by English chemist
John Newlands, who discovered that when chemical elements were ordered by
atomic weight, those with similar properties occur at every eighth element.
This would lead to our understanding of the periodic law of chemical elements
that is still used today.
Pythagoras believed
in reason above all else. He came to believe that all the universe was governed
by mathematical laws. To him, the very structure of the cosmos, existence and
even God was possible only through numbers. He was a man whose influence would
be felt for centuries to come. He remains one of the fathers of mathematics and
one of the most important of the ancient philosophers.
(The Pythagorean
Theorem is a cornerstone of mathematics, and continues to be so interesting to
mathematicians that there are more than 400 different proofs of the theorem,
including an original proof by President Garfield.)
(Pythagoras made influential
contributions to philosophy and religious
teaching in the late 6th century BC. He is often revered as a great mathematician, mystic and scientist, but he is best
known for the Pythagorean theorem which bears his name. )
The Pythagorean theorem:
The sum of the areas of the two squares on the legs (a and b)
equals the area of the square on the hypotenuse (c).
Pythagoras himself was not
simply a mathematician. He was an important philosopher who
believed that the world was ruled by harmony and that numerical relationships
could best express this harmony. He was the first, for example, to represent
musical harmonies as simple ratios.
Pythagoras observed that when a blacksmith struck
his anvil, different notes were produced according to the weight of the hammer.
That if you take 2 strings in the same degree of tension, and then divide one
of them exactly in half, when they are plucked, the pitch of the shorter string
is exactly one octave higher than the longer string. He also discovered that if
the length of the 2 strings are in relation to each other 2:3, the difference
in pitch is called a fifth. Pythagoras stressed that different musical modes
have different effects on the person who hears them, and that music could be
applied to healing illness both mental and physical. In 513BC he went to Delos
to nurse his old teacher, Pherekydes who was dying. He remained at his bedside
playing his lyre and feeding him until he died. In 508BC the Pythagoreon
Society at Croton was attacked by Cylon, a noble of Croton itself. Pythagoras
escaped to Metapontium and most authors say he died there. Evidence is unclear
as to when and where the death of Pythagoras accurred.
Pythagoras and the Pythagoreans
The school of Pythagoras represents
the mystic tradition in contrast with the scientific!!
Indeed, Pythagoras regarded
himself as a mystic and even semi-divine. Said Pythagoras
"There are men,
gods, and men like Pythagoras."
The Pythagorean Philosophy and Bertrand
Russell
From Bertrand Russell,
"It
is to this gentleman that we owe pure mathematics. The contemplative ideal --
since it led to pure mathematics -- was the source of a useful activity. This
increased it's prestige and gave it a success in theology, in ethics, and in
philosophy."
Mathematics, so honored, became the
model for other sciences. Thought became superior to the
senses; intuition became superior to observation.
The combination of mathematics and
theology began with Pythagoras. It characterized the religious philosophy in
Greece, in the Middle ages, and down through Kant. In Plato, Aquinas,
Descartes, Spinoza and Kant there is a blending of religion and reason, of
moral aspiration with logical admiration of what is timeless.
Platonism was essentially Pythagoreanism. The whole concept of an eternal world revealed to intellect but not to the
senses can be attributed from the teachings of Pythagoras.
Tradition holds that
Pythagoras left no written works, but that his ideas were carried on by
his eager disciples.
What is known of the
Pythagorean school is from a book written by the Pythagorean, Philolaus of
Tarentum. From this book Plato learned the philosophy of Pythagoras.
General
features of Pythagoreanism
The
character of the original Pythagoreanism is controversial, and the
conglomeration of disparate features that it displayed is intrinsically
confusing. Its fame rests, however, on some very influential ideas, not always
correctly understood, that have been ascribed to it since antiquity. These ideas
include those of
(1) the metaphysic of number and
the conception that reality, including music and
astronomy, is, at its deepest level,
mathematical in nature;
(2) the use
of philosophy as a means of spiritual purification;
(3) the
heavenly destiny of the soul and
the possibility of its rising to union with the divine;
(4) the
appeal to certain symbols, sometimes mystical, such as the tetraktys, the golden section,
and the harmony of
the spheres;
(5) the Pythagorean theorem;
" It was Pythagoras who first called heaven kosmos, because it is perfect, and "adorned" with infinite beauty and living beings."
I do not know of any other man who has
been as influential as he was in the sphere of thought.
Pythagoras was indeed the first
man to call himself a philosopher. Others before had called themselves wise (sophos),
but Pythagoras was the first to call himself a philosopher, literally a lover
More importantly, for Pythagoras and his followers philosophy was not merely an intellectual pursuit, but a way of life, the aim of which was the assimilation to God.
Personal religion is derived from ecstasy, theology from
mathematics, and both are to be found in Pythagoras.
Bertrand Russell , in A
History of Western Philosophy
The combination of mathematics and
theology, which began with Pythagoras, characterized religious philosophy in
Greece, in the Middle Ages, and in modern times down to Kant. Orphism before Pythagoras was
analogous to Asiatic mystery religions. But in Plato, Saint Augustine, Thomas Aquinas, Descartes, Spinoza, and Kant there is an intimate
blending of religion and reasoning, of moral aspiration with logical admiration
of what is timeless, which comes from Pythagoras, and distinguishes the
intellectualized theology of Europe from the more straightforward mysticism of Asia.
The whole conception
of an eternal world, revealed to the intellect but not to the senses, is
derived from him. But for him, Christians would not have
thought of Christ as the Word; but for him, theologians would not have sought
logical proofs of God and immortality.
"It was a maxim of
Pythagoras that the two most excellent things for man were to
speak the truth, and to render benefits to each other."
While in Egypt, Pythagoras had learned much about geometry, and he was taught that a triangle with ratios of 3:4:5 would always have a right angle. While this was very useful in fields such as architecture, Pythagoras would go one step further. He uncovered the underlying equation that constituted this observation. Pythagoras was the original intellectual who discovered that the square of a triangle’s hypotenuse equals the sum of the squares of the other two sides.
The Father of Mathematics
This idea is more
commonly known by the equation: A²+B²=C². That’s right, Pythagoras was the
creator of everybody’s favorite equation from high school math class.
This discovery was profound, revolutionary in fact. Never before had a
thinker discovered this truth that has been shown to be universally true.
This concept was so extraordinary that Pythagoras interpreted it as being
divine.
Pythagoras believed:
All things are numbers. Mathematics is the basis
for everything, and geometry is the highest form of mathematical studies.
The physical world can understood through mathematics.
The soul resides in the brain,
and is immortal. It moves from one being to another, sometimes from a human
into an animal, through a series of reincarnations called transmigration
until it becomes pure. Pythagoras believed that both mathematics and music
could purify.
Numbers have personalities,
characteristics, strengths and weaknesses.
The world depends upon the interaction of
opposites, such as male and female, lightness and darkness, warm and cold,
dry and moist, light and heavy, fast and slow.
Certain symbols have a mystical
significance.
All members of the society
should observe strict loyalty and secrecy.
Pythagoras' society
Because of the
strict secrecy among the members of Pythagoras' society, and the fact that
they shared ideas and intellectual discoveries within the group and did not
give individuals credit, it is difficult to be certain whether all the
theorems attributed to Pythagoras were originally his, or whether they came
from the communal society of the Pythagoreans. Some of the students of
Pythagoras eventually wrote down the theories, teachings and discoveries of
the group, but the Pythagoreans always gave credit to Pythagoras as the
Master for:
While in Egypt,
Pythagoras had learned much about geometry, and he was taught that
a triangle with ratios of 3:4:5 would always have a right angle. While this
was very useful in fields such as architecture, Pythagoras would go one step
further. He uncovered the underlying equation that constituted this
observation. Pythagoras was the original intellectual who discovered that the
square of a triangle’s hypotenuse equals the sum of the squares of the other
two sides.
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