Pythagoras himself has not put anything in writing, but under his followers many papers with notes are made, from which future authors could draw from. Mostly we in the 21st century are dependant on clues to Pytrhagoras and his school a.o with Plato. There are other sources of course, but that would go way beyond the theme of this paper, so I will leave it at that.
Pyhtagoras was born around 580 BC in Sidon during a voyage his parents Mnesarchus and Pyhhtalis made. The delphic Pythia had professed a remarkable son, hence the name (Pythia/agoreuoo).
After his basictraining on Samos, in Olympia and Milete (a.o with Thales) he made his Grand Tour through Phoenicia, Egypt and Babylon. During his trip he met with many religions and mysteries and in many of them he was initiated. He also learned there, what would be later known as the Pythagoras theorem. In 539 BC he went to live in South-Italian Croton, where he established a very elitair, aristrocratic school, dedicated to Apollo. The school stayd there till around 500BC when the Pythagoreans were driven away. Around this time also Pythagoras dies in Metapontium. New centra were established in Tarente and Phlius (Argolis). Because of this diaspora diverse schools inside the school appeared, and because of that also many various reports about their doctrines came around. The pupils (male AND female!) were admitted only after a years long, strict selection. They were known as mathematici and acusmatici . The material for the first ones where the mathemata, devided in arithmetica and musica (numbers) and astronomy (space). The acusmatici learned material they had heard by heart, with the purpose to become equal to god through much knowledge. These acusmata answered questions like: what is...?, what is the most...? and what do I need to do or not?
Central was the doctrine of the metempsychosis.. (the moving away of the spirit after death), based on the ultime relationship of all that lives. The initially rather trifling knowledge of mathematics has become very extensive through later generations. Many of it is -anonimously- made into the Elementa of Euclid. After Pythagoras, his school has known 4 generations of followers. Later Pythagorism would relive in Neopythagorism, that would eventually would become Neoplatonism.
? Of all the diverse aspects of the teachings of Pythagoras, only a very distinct part is most important to us at this moment. It is the aspect of the supremacy of the natural numbers (1,2,3..).
As the Pythagorean Philolaus put it: "Indeed everything that one can possibly know has a number, because it is not possible to understand something or to know something without the number".
This leaded towards the fundamental thought, that the universe is contsructed mathematically. To understand the intentions of god, one should perpetrate mathematics. Many centuries later Galilei (1564-1642) would say it like this: "The book of nature is written in the language of mathematics".
Now, I skip a lot if you dont mind, dear readers, because it is very interesting stuff, but not relevant to the purpose of this paper, and will continue with the creation of the five elemental bodies from a triangle. Plato, explained in his Timaios (53-54):
"To begin with, fire, earth, water and air are bodies. That must be very obvious for each of us, I’d say. Now it is so, that everything that is body, also has depth (first dimension). But depth on her turn is always inevitably enclosed by a surface (flat form); and every recti-linear figure is composed of triangles."
Neo-platonism, under which a revival of the ideas of our Greek filosophers is understood, was especially popular in the fourth and fifth century AC. In that period of our history the Timaios of Plato was called: Â‘the unaissalable castle and the top of the filosophical thinking.
But also in Spain a few filosophical schools based on the Greek inheritance where created, under which the one in Cordoba during the reing of Theodorik II, king of the Visi-Goths. When Islam swept over Spain one and half century later, even more schools were created.
A summary of the Arabic filosphers of the tenth century can be found in the manuscripts of Gerbert d’Aurillac, who was born around 940 and who was called in his time ‘uomo universalis’. A man of whom was told, that he knew everything that was to be learned in his time. As a young man he went to Spain, to study the filosophies of Plato and Aristoteles there. He became finally Pope of Rome in 998 under the name of Sylvester II.
His books served as basis for the School of Chartres, established in 1020, where his pupil Fulbert laid out the basis for cathedralbuilding in Western Europe. Even as early as under the reign of Charles the Great, studies about Platonism and its application in the churchbuilding where made. Studies of the Dome in Aachen have showed, that they applied there the geometric prinicples and the doctrine of numbers during the building.
But not untill the establishment of the School of Chartres in 1020 by a student of Gerbert, the archbishop Fulbert, we see this knowledge spraid out across Western Europe. So far some interesting background on Pythagoras and Plato .
So, in Plato's Timaios, the elements became a shape in the form of the five bodies, I showed above. In dutch they are called: de vijf regelmatige veelvlakken. I cannot translate that into english, but they are also called Platonic bodies.
You first see fire which forms the primaire antithesis with earth. Then we see air, without which fire can not exist, and water which forms the liquid part of earth, and without which no life could be possible on earth. Then we see the fifth element, which should according to Plato be in the centre of the elements, and which is called the Quintensens, of which all other elements are created, and which is the symbol of the entire creation.
If you read the extensive way with which Plato explained the other elemental bodies you cannot but wonder why there is only one alinea abbout the fifth body.. the quintensens or to put it more mathematical: the dodecahedron. The solution is, that the dodecahedron was not made public. Also in the middle Ages and Renaissance the knowledge of the dodecahedron, and with it the connection of the pentagam was passed on only to the most prominent architect and his closest collegues. Furthermore they had discovered that the dodecahedron, through connecting certain edges etc. held in itself all other bodies.
The dodecahedron became thus the basis for obtaining all other bodies and was not without reason for Plato the symbol of the all all-embracing Universe.
Any look at the meaning of the pentagram would be incomplete without first looking further at the meaning of the 5 elements. In western thought these elements consist of Earth, Air, Fire, Water and Spirit (Ether). Ether is probably the most obscure of the elements.
The idea of Ether comes originally from early Alchemy. Einstein provides a very eloquent discription of the principal of Ether and it's connection to relativity, but actually Newton was not the originator of the theory, as Einstein suggests. In fact Pythagoras was the first Western figure credited with the specific mention of a fifth element which he titled 'Aether' (or 'Aither'). Pythagoras also borrowed from the teachings of the philosopher Empedocles who had first posited the existence of 4 basic elements which he corresponded with 4 of the Greek Gods (book 1.33).
Now, lets go finally to the meaning of the pentagram, and his sister, the pentacle .
Various meanings ascribed to the pentagram (5 pointed star) and pentacle (5 pointed star within a circle). The earliest physical evidence of the existence of the pentagram comes from the very place where agricultural civilization is popularly believed to have started. The pentagram was frequently found on potsherds and tablets (which have been dated to as early as 3500 BCE) in the location of the Kingdom of Uruk (at the mouth of the Tigris-Euphrates valley). The symbol was found accompanying signs relating to the foundation of written language. There is also evidence that the pentagram was used in ancient Mesopotamia to indicate the seal of royalty, and power which extends to the four corners of the earth.
The pentagram has appeared in myth and folk lore ever since that time. The Greek Pythagoreans (Pythagoras 586-506 BCE) referred to the pentagram as 'pentalpha' because it could also be formed by laying 5 alphas (A) together. The Jews attribute the pentagram to the five books of the Pentateuse. The Muslims attribute the pentagram to the five pillars of faith and the five times of daily prayer. One of the last Pagan Roman Emperors, Constantine (who converted to Christianity on his death bed in the mid 300's CE) used the pentacle as the symbol of his royal office. In Aurthurian legend the pentagram was emblazoned in gold upon the shield of Sir Gawain and symbolised his mastery of the 5 virtues (generosity, courtesy, chastity, chivalry and piety). In the legend and thense forth throughout England the pentagram is known as the "Endless Knot".
The topmost point of the pentagram is regarded as representing Deity, the divine source of life. From this point a line is traced to the lowest left-hand angle of the figure. This represents life descending from its divine source into the lowest and simplest forms of living matter. The line is then continued up and across to the upper angle on the right. This represents the ascent of life from primitive forms, by the process of evolution, to its highest physical form on this planet, the human being. The line then continues across the figure to the upper angle on the left, This represents man's earthly progress, his achievements on the material plane, as he becomes cleverer, richer, more powerfull, building himself great empires and civilizations. However, in his progress in this way he sooner or later reaches the danger point and begins to fall. To show this the line goes down and across from this angle to the lowest angle on the right-hand side. This is the story of all man's empires; but because the human spirit is one with its divine source, it must and will strive upwards to find that source again. Hence the line of the pentagram rises up again from the lowest level to rejoin the topmost point from whence it issued.