"Life is like a gathering at the Olympic festival, to which,
having set forth from different lives 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 of fame and others of money,
but the best choice is that of these few who spend their time in the contemplation of nature,
and as lovers of wisdom (ie: philosophers).

The Pythagorean Mathematics of Nature:
"HARMONY" ... a summary by Aristotle.

• {1} All things consist of number - literally .... physical bodies themselves are made of number, or since numbers themselves are not ultimate, the elements of numbers are the elements of everything.

• {2} Units posses magnitude

• {3} Spoke of as if number were the actual matter of which things were composed.

• {4} Regard unity and limit (infinity) as substances forming the basic element of everything else.

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[Page 245]

The Ten Pythagorean Principles

The TEN PRINCIPLES of PYTHAGORAS Also known as the table of the 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; but the indefinite Dyad is a "daimon" and evil, concerned with material plurality. [Aet.1.7.8.dox.302]

There is additional reference in this text by Guthrie concerning the parallels which may obviously be observed between this Pythagorean table of principles, and the outlining in the eastern lands of ancient China, concerning the TAO, and the complimentary natures of the principles of "Ying and Yang"

These are listed as follows: Sunshine/light - darkness/shadow, masculinity - femininity, activity - passivity, heat-cold, dryness - wetness, hardness - softness, odd - even.

It is rumoured that Pythagoras journeyed and studied amoung the Magi and Chaldeans, and with Zaroaster.

Delineation of the point (1), the line (2), the triangle (3) and the pyramid (4). Outline of the "Fluxion Theory" whereby a moving point generates the line, the moving line generates the surface, and the moving surface - the solid figures.

The Five Pythagorean Solid Figures

From the account of Theoprastus [Aetius II,6,5,DK,44,a15]:

There being five solid figures, called the mathematical solids, Pythagoras says that ...

• the earth is made from the cube,
• fire from the pyramid,
• air from the octahedron,
• water from the eicosahedron,
• and the sphere of the whole [the Aither] from the dodecahedron."

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[Page 271]

The Fifth Element of Nature

"Why then does he [Aristotle] call it a fifth substance? Surely because Plato too declares the substance of the heaven to be distinct from the sublunary elements, since he assigned it to the dodecahedron and delineated each of the four elements by a different shape. He too therefore says that the substance of the heaven is a fifth one."

"Thus he then classified living creatures into genera and species, and divided them in every way until he came to their elements, which he called the five shapes and bodies, aither, fire, water, earth and air.

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[Page 272]

Reference to the "Counter-Earth"

• Philolaus the Pythagorean says that FIRE is at the center, calling it the hearth 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" - [Aetius.III,II,3(dk,44a,17)]

• "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 its shadow. COUNTER EARTH was the name given by the Pythagoreans to the MOON (as also "heavenly earth"), both because it blocks the sun's light, which is a peculiarity of the earth, and because it marks the limit of the heavenly regions as does the earth of the sublunary." - [Simplicius: DeCaelo 512.9]

• Empedocles [Fr.62] ... "Come now, hear how fire, as it was separated, raised up the darkling shoots of miserable men and women. Not erring nor ignorant is this tale. Whole natured forms first arose from the earth, having portion both of water and of heat. These the fire sent up, wishing to come to its like."

The Harmony of the Spheres

"It seems to some [ie: Pythagoreans] that bodies so great must inevitably produce a sound by their movement: even bodies on earth do so, although they are neither so great in bulk nor moving at so high a speed, and as for the sun and moon, and the stars, it is incredible that they should fail to produce a noise of surpassing loudness. Taking this as their hypothesis, and also that the speeds of the stars, judged by their distances, are in the ratio of the musical consonances, they affirm that the sound of the stars as they revolve is concordant.

To meet this difficulty that none of us is aware of this sound, they account for it by saying that the sound is with us right from birth and has thus no contrasting silence to show it up; for voice and silence are perceived by contrast to each other, and so all mankind is undergoing an experience like that of a coppersmith, who becomes by long habit indifferent to the din around him."

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[Page 317]

Pythagoras and the Nature of the Soul

"The virtue of temperance (sophrosyne) is said to be the virtue of the soul as a whole, the result of the smooth working of its parts together ... the man who possesses it is "well tuned" (nb: the Greek translation has nothing to do with the state of his health), and is achieved by bringing three parts into accord, just like the fixed three intervals in the scale - highest, lowest and middle - that is, a musical harmony is achieved.

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

Guthrie: These "parts" are psychical and not physical.

Ancient insight of Heliocentricity?

Scattered remnants however, tell an interesting story:

"Philolaus is supposed to have maintained that the earth moved in a circle, though some say it was Hicetas the Syracusian" - [D.L.viii,85,dk,44a1]

"Thales and those who followed him said that there was one earth,
Hicetas the Pythagorean two, our own and the counter-earth."

Aristotle

It remains to speak of the earth, of its position, of the question whether it is at rest or in motion, and of its shape.

The Pythagoreans have a further reason. They hold that the most important part of the world, which is the centre, should be most strictly guarded, and 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.

But it is better to conceive of the case of the whole heaven as analogous to that of animals, in which the centre of the animal and that of the body are different. For this reason they have no need to be so disturbed about the world, or to call in a guard for its centre: rather let them look for the centre in the other sense and tell us what it is like and where nature has set it. That centre will be something primary and precious; but to the mere position we should give the last place rather than the first. For the middle is what is defined, and what defines it is the limit, and that which contains or limits is more precious than that which is limited, see ing that the latter is the matter and the former the essence of the system.

Some of them even consider it possible that there are several bodies so moving, which are invisible to us owing to the interposition of the earth. This, they say, accounts for the fact that eclipses of the moon are more frequent than eclipses of the sun: for in addition to the earth each of these moving bodies can obstruct it. Indeed, as in any case the surface of the earth is not actually a centre but distant from it a full hemisphere, there is no more difficulty, they think, in accounting for the observed facts on their view that we do not dwell at the centre, than on the common view that the earth is in the middle. Even as it is, there is nothing in the observations to suggest that we are removed from the centre by half the diameter of the earth. Others, again, say that the earth, which lies at the centre, is 'rolled', and thus in motion, about the axis of the whole heaven, So it stands written in the Timaeus.

Other Quotes ...

He calls drunkenness an expression identical with ruin.

Among what he called his precepts were such as these: Do not stir the fire with a sword. Do not sit down on a bushel. Do not devour thy heart.

In the time of Pythagoras that proverbial phrase "Ipse dixit" was introduced into ordinary life.

For as long as men massacre animals, they will kill each other. Indeed, he who sows the seed of murder and pain cannot reap joy and love.

Animals share with us the privilege of having a soul.

Further References

SCHOOL OF PYTHAGORAS: A very comprehensive site of book reviews relating to the subject matter of Pythagorean teachings, reference to OnLine Bookstores and other substantial resources. Texts reviewed include The Secret Power of Music by David Tame, Fingerprints of the Gods by Graham Hancock, Initiation by Elizabeth Haich, The Third Ear by Joachim-Ernst Berendt, The Holographic Universe by Michael Talbot, Music: Physician for Times to Come edited by Don Campbell, The Healing Energies of Music by Hal A. Lingerman, Healing Sounds: The Power of Harmonics by Jonathan Goldman, The World is Sound Nada Brahma by Joachim-Ernst Berendt, The Divine Proportion by H. E. Huntley, The Power of Limits by Gyorgy Doczi, Sacred Geometry by Robert Lawlor, Homage to Pythagoras edited by Christopher Bamford, Music and the Power of Sound by Alain Danielou, The Reflexive Universe by Arthur Young, The Myth of Invariance by Ernest G. McClain, The Pythagorean Plato by Ernest G. McClain, Sacred Science by R. A. Schwaller de Lubicz and The Temple of Man by R. A. Schwaller de Lubicz (2 volumes).

PLATONIC SOLIDS: Some Random Thoughts about the Occult Correspondences of the Platonic Solids and Their Symmetries by Anders Sandberg in Sweden.

THE OCTAVE OF ENERGY: An article by Robert Anton Wilson, which examines the broad spectrum of reality and concerns the the work of Dr Timothy Leary. The article concludes with the comment: It will be seen by the thoughtful reader that this emerging synthesis evades entirely the usual dichotomy of 'spiritual' versus 'material,' being purely geometric-energetic. It is thus in the same philosophical category as the unitary systems of the East (Zen, Taoism, Vedanta, etc.) and outside the dualisms of Greek logicand Christian thology. Any attempt to describe this octave as 'mystical' or as 'materialistic' misses the real point of Leary's work."

FURTHER NOTES: Some further notes on Greek Philosophy much in the point form of the above, but better organised.

METAPHYSICAL REVIEW: The following text is from the July 1994 Metaphysical Review, an extensive and well researched publication which has been active on the net for quite some time. I have duplicated the text hereunder to provide an immediate review of content:

When we look at the tools which we have brought to bear in our scientific search for `True Causes' ( or `Laws of Nature', a more popular term), we realize that there are underlying expectations for what these laws must be like. It will be intelligible by humans (perhaps no single person - for the field continues to mushroom); Occam's Razor assist in this. And the laws will be a few universal causes. The last decades have spouted `Grand Unified Theories' (field theories called GUTs) and `Theories of Everything' (string theories called TOEs), but this is nothing new. This is exactly what Bacon was speaking about were he talked about the raising up of lesser, middle and primary axioms.

This characterizations of true causes seems so apparent that one might ask why the discussion? I contrast this view of causes with the view of classic Greece and Rome and Medieval Europe, which was dominated by the view that nature was defined by the categories which things are in, as per Aristotle's book "Categories". The role of the scientist is to list the categories and properly place all features of nature in there own niche. Both Lucretius and Dante tell us that the reason that fire rises up is that it is attempting to return to its proper position, in the sphere of the sun.

A third view of true causes is most well known in the yin-yang image. The world's dynamics are a balance, rather a see-saw between two opposing sets of forces, yin and yang. Pythagoras characterized it in his `table of opposites': limited-unlimited, odd-even, rest-motion, straight-curved, good-bad etc.

PYTHAGOREAN SOURCEBOOK: The Pythagorean Sourcebook and Library - Compiled and translated by Kenneth Sylvan Guthrie, this link leads to a review of this resource book, and options for purchase.

PYTHAGORAS of Samos{570-490BC} The Indigenous Nativity & Philosphical Foundations of that which is deemed Classical Western Science
Web Publication by Mountain Man Graphics, Australia in the Southern Autumn of 1996