Numbers are the underlying foundation of the Universe, or so suggested many ancient Greek philosophers. The pre-Socratic philosophers (before 469 BC) were the first to write and formulate ideas of a rational and empirical world, questioning the reality of the old gods and mankinds place in the cosmos.
Although sometimes antithetical to the belief in gods and pantheons, many of their theories were not wholly materialistic either. Most philosophers who first expounded these mathmatical ideas, such as Anaximander, Empedocles, Pythagoras, and Anaxagoras, strove to explain natural phenomena through rationalistic thinking while simulataneously exploring the rich dialogue of mystical philosophy which was taking place across the Mediterranian in this time. They considered their scientific ideas to be insperably linked to their religious philosophies, many of which were incompatible with the traditional and orthodox mythology of the day.
Pythagoras, who is largely remembered today as an ancient mathmatician, was to his contemporaries more of a magus and spiritual leader. He claimed that the mytical essence of everything is number, and would derive holy symbols for his followers from mathmatical equations, including the tetraktys and pentagram.
He is also said (by Eudemus) to have discovered two new spatial bodies, the dodecahedron and icosahedron, which, in addition to the tetrahedron, octahedron and cube long ago discovered by the ancient Egyptians, were treated with great reverence by his followers. All of these were later taken up by Plato in his writing on Euclidean geometrical solids, hence the Platonic Solids.
Empedocles was the first to put forth the idea of four natural elements or essences – Fire, Water, Air and Earth as the basis of the tangible universe, and that the balance of these elements was always changing and transmuting.
Arguably he may not have been the first to posit four elements, as teachings of similar systems are found in ancient India and Japan, as well as some of the earliest Buddhist texts, but Empedocles was the first Greek to teach about it. Nowandays these elemental states correspond more closely to states of matter (solid, liquid, gas and plasma) than to our modern elemental table. Regardless of their scientific validity though, their impact on ideas and culture has been persistant for well over two millenia, and shows no signs of fading away just yet. A fifth essence was also suggested, more on that later though.
Plato disagreed with Empedocles when he said that the elements were the MOST basic forms. He said the elements themselves must be formed from the simplest and most elegant of geometrical shapes, the triangle. He uses triangles (the right and scalene, which were to him the most beautiful) to construct the Platonic solids and attribute to them elemental essences. The attributions are as follows.
The fifth essence, corresponding to the dodecahedron, was written of much less by Plato than by his student Aristotle. It was considered very sacred by the Pythagoreans, attributing it to a number of ideas, including aether, void, space, and the Quintessence or Spirit of the World. Correspondences can be found in many ancient teachings around the globe.
An interesting story by Iamblichus describes the demise of a Pythagorean Hippasus, who “in consequence of having divulged and described the method of forming a sphere from twelve pentagons, he perished in the sea, as an impious person…” (Life of Pythagoras 18). This was clearly a pre-Socratic time, when these things were much less widely known.
Platonic writing, whose original influences extend deep into the mist of Arabic and Egyptian pre-history, went on to influence many different movements, including the Gnostics and early Christian sects, Jewish Qabalistic scholars, as well as medieval Arabic and European alchemists, which in turn gave rise to modern Chemistry as we know it today.
The essences or elements and their shapes are some of the earliest spacial constructs known to man, and were held with a sense of awe and mystery when first discovered for their seemingly divine structure. Some of these earliest thinkers provided the roots for what we today think of as “Western” traditions in philosophy and mathematics as well as Western religion, aesthetics and ethics. Nowandays these ideas are so common in our culture that we often fail to realize the incredible beauty and psychological implications of these early discoveries. The rationality of Western society since the Enlightment period still molds our education and contradictorily condemns the mystical practices and philosophies that once complimented and flavoured innovation. We often forget to consider the atmosphere of wonder and reverence in which these underlying principles were first discovered.
I am very intrigued by these relationships, between nature and mathematics, between the physical universe and that of the psyche, the objective sciences and subjective worlds of mysticism and religion. For this project I plan to commemorate some of the roots in which Western thought was birthed by highlighting the essences as sacred thought-constructs, showing the birth of mathematics in a primarily mystical light, and reclaiming the sacredness of space that defined the time for the ancient Greeks.
Agrippa, Henry Cornelius, 3 Books of Occult Philosophy
Cicero, Chic and Tabatha, Antecedents of the Ogdoadic Tradition, The Ogdoadic Journal