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Pythagoras and the curse of the Pentagram

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Pythagoras and the curse of the Pentagram

Post  Manahuna on 28.08.10 15:46





Pythagoras and the curse of the Pentagram


The pentagram also known as the Druids cross, Alpfoot, Nornen stapfe, pentalpha, Pentangulum, Sanitatis Signum, Signum Pythagoricum, or surrounded by a circle, called the pentacle - is one of the oldest and most widespread symbols of the magical world.

Hardly any other symbol is associated with so many popular fallacies as the pentagram. In many dictionaries it is stated that (popular belief) it was used to ward off witches. Apparently they equated protection from damaging spells with protection from magic channels (witches). This idea is quite bizarre.

If you are sensitized to see pentagons and five pointed stars, you will notice them at every turn: in flags and coats of arms, the insignia of the U.S. Air Force, in the Red Star as the symbol of socialism, in green as a symbol of Islam, in the logo of Chrysler, in the architecture of the "Pentagon," U.S. Department of Defense. Even the Church uses the five-star, particularly impressive to see in the many Gothic rose windows, such as the west window of Westminster Abbey in London.

Since this can not be a coincidence, the five-star and pentagons are quite popular with conspiracy theorists.

The number 5 appears in the form of the the pentagon and the five-star quite often, because it is one of the five principles of organic form-living nature. We have five fingers on one hand, all land vertebrates show this five-pointed structure. If you cut an apple crosswise through, you see a pentagon. Most flowers are five-star, as is the starfish. Natural pentagrams are found in five-petalled flowers, such as the lily or the grapevine. Even spiderwebs and a snail housing represent the spiral structure on the pentagram.




The apple and pentagram are symbols of Venus, which is in many cultures the first principle of the feminine. While Venus trangresses through the zodiac once every eight years, it's five conjunctions with the sun forms a huge five-star in the sky. In ancient Babylon it was the sign of the goddess Ishtar, the equivalent of Aphrodite and Venus.

The pentagram is therefore inherent in nature and thus a widespread symbol in all ancient cultures throughout the ages, in fact, it is virtually everywhere.

Although the pentagram can be found in ancient Egypt, Mesopotamia, with the Celts and in many other cultures, it is most likely due to the Pythagoreans that it was able to penetrate deeply into Western tradition.


The Pythagoreans

Every schoolchild knows the theorem of Pythagoras: a ² + b ² = c ².
However, this proposition has not been originated by Pythagoras nor by one of his students. Long before, Egyptian architects discovered this fact and integrated the knowledge into their practical works. It was also described in Assyrian cuneiform texts dating from around 750 BC.

The founder of this "brotherhood", although women also belonged to the Order, Pythagoras of Samos (about 570 BC until about 496 BC) left no writings, so that it is not possible to distinguish which statements were his and which were made by his students. Even Plato and Aristotle spoke generally of "the Pythagoreans".

The Pythagoreans were well known to be number mystics and number magicians, but not in the sense of Kabbalah. Pythagoras postulated that the integer number was the first cause (Arche) of all things. He is said to have discovered the principle by which the harmony of the tones of stringed instruments are characterized by their numerical relationships. The simpler the ratio, the more harmonious the interval. Bold and brilliant the Pythagoreans transferred this principle to all living beings and the entire existence. They collected geometric theorems such as the "Pythagorean Theorem" and found them not only in nature itself but also in some of it's cycles, especially in the course of the stars. The universe is a symphony, penetrated by diverse harmonies, full of the unheard but always noticeable music of the spheres.

"All finished, all acting, all participatory in human and divine first cause to guide the living is the power of the number ... without it, everything is unlimited, unknown and invisible. " cited Aristoteles the metaphysics of the Pythagoreans.

Copernicus, Galileo, Kepler and Newton were all "secret Pythagoreans," God was for them the supreme mathematician. Quantum mechanics may be regarded as music of the spheres of the atom, the theory of relativity is a "Pythagorism of unimaginable scale" (Einstein), and the modern superstring theory of elementary particle physics is amazingly close to the original ideas of Pythagoras.

Pythagoras' mystical philosophy is alive and fruitful - though most modern scientists and mathematicians deny vehemently that the study of geometry could bring a student closer to the "Unio mystica" by studying the geometric figures' "magic effects" in nature.

The pentagram has amazing mathematical properties and is a treasure and a challenge to mathematicians alike. The distance from tip to tip cuts the Golden Ratio perfectly.




Golden Ratio: EB: AE = AE: AB


The golden section is particularly well balanced between the extremes, between tension and relaxation and therefore considered to be the most important measure of beauty. With a little geometry and algebra one can calculate this golden ratio: it is 1 plus the square root of five devided by 2 - that's about 1.618. The point that divides the line in the golden ratio is hence 61.8 % of the total distance.

The center of the pentagram is a regular pentagon. All sides are equal and all interior angles equal, namely 108 °. The diagonals are equal in length and are divided in pairs in the golden ratio. The longer diagonal section is as long as one side: diagonal and side compare to one another and all the diagonals of the pentagon form a pentagram together again, two times smaller than the original and mirror-displayed.

The ideal of this "principle of beauty" had been implemented in the architecture of the Greek and Hellenistic antiquity. A good example is the Parthenon on the Acropolis of Athen (447-432 BC). The domes of Romanesque and especially the Gothic domes are certainly true pattern books of the Golden proportions. During the Renaissance it also became the standard measure for the painting arts: Leonardo da Vinci, Albrecht Durer, Georges Seurat, Piet Mondrian are some of the artists who immortalized the golden sections in their works. Even the old book formats and the traditional formats of picture frames are Golden Rectangles. However, if one were to mention all areas in which the Golden Section occurs, we would also need to point at literature, music, medicine, and so much more.

Hippasos, the son of Pythagoras, was the first to recognize the connection between the Golden Section and the pentagram. At least ten times this ratio can be found in it. Like no other symbol it shows that if all things are divine, we humans can recognize the divine. The Pythagoreans further concluded: A symbol that is so filled with divine harmony must have special powers and properties. Thus, the pentagram became a symbol of health (Latin Signum Sanitatis) and the brotherhood's most important symbol.


The dark side of the Pythagoreans



This had unexpected consequences - showing the ugly side of the Pythagoreans.

The golden ratio is in fact an irrational ratio
(in the mathematical sense, of course).

In mathematics, an irrational number is any real number which cannot be expressed as a fraction.

But Pythagoras was convinced that everything, absolutely everything in the world could be represented by whole numbers and that their correspondance to each other was expressed by rational numbers (integers). Sooner or later the Pythagoreans were forced to encounter irrational numbers in their study of the regular pentagon and the pentagram formed by the diagonals of the phenomenon of irrational numbers. Numbers, which were the antithesis of the original teaching of their master, irconically exposed quite symbolically through their most cherished symbol of all: the pentagram.

Now it was so that the Pythagoreans were also one of the first Western "secret societies". The distinction between exoteric knowledge (generally accessible) and esoteric knowledge (reservated of the insiders) leads back to the Pythagoreans. The result: they were so shocked by this discovery that they kept it as secret as possible from the general the public because it implicates that their "spiritual" doctrine is based on a fallacy.

According to an ancient story, one of the Pythagoreans did not comply with this agreement and spoke about it publically in the marketplace for which his brothers kidnapped and killed him, only to keep "the secret" of their dilema hidden from the underlings. Fortunately, still quite a bit of knowledge of these pentagram-brothers and sisters trickled down to secular mathematicians over the centuries.

Golden Section has the irrational number 1.61803398875 ..

The square of this value (= 2.618 ...) multiplied by 6 / 5 is a good approximation of Pi, also an irrational number and the constant can be calculated with the help of the perimeter and area of a circle when the diameter is known.

"Pi" is the Egyptian word for "holy", and is therefore should also be regarded as the "holy number".

The interesting part is that it was the the Pythagoreans themself that introduced this number into the teachings of sacred geometry, including the common abbreviation p (derived from the Greek letter Π).

The ratio of 6 / 5 is really Pythagorean. It is the vibration ratio of two notes which form the interval of a minor third, the interval between the basic tones of related major and minor keys. Consequently, the pentagram with the golden ratio holds the key to the transformation of a rectangular area in square and circle by adding one size, which is quite intuitive, yet a highly precise statement about harmonious relationships.

The Roman writer Cicero, who lived at a time long after the Pythagoreans creative heydays, reported this:

When you try to discuss with the Pythagoreans and demanded one of them to justify one of their claims, they would always reply: "He himself said it. With "himself" they pointed at Pythagoras. Clearly put, they had traded in their own ability to think and reason against the authority of the Grand Master. This clearly exposed their characteristics of a cult. Worse, the Pythagoreans of the inner circle who knew the secret of irrational numbers of the pentagram lied stubbornly to the public to uphold the image of their Great infallible master, still claiming that the world are solemnly described by whole numbers.

What a bad example and a lot of the esoteric and/or secret societies follow it still today!








translated from:
"Heidenarbeit - Zeitschrift des Rabenclan - Arbeitskreis der Heiden in Deutschland e. V." Nr. 20, April 2002
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Manahuna

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