I know that the generally accepted academic view is that the ancient Egyptians had no influence on the development of Greek mathematics, philosophy and cosmology but I believe there is evidence, that has been overlooked by the mainstream, that shows the Greek mathematicians and philosophers such as Meltis, Pythagoras (or the Pythagorean cult I know the character we call Pythagoras probably never existed) and Plato were all influenced by what they learned about numbers in Egypt.
In Raphael’s fresco The School of Athens, Pythagoras is shown writing in a book as a young man presents him with a tablet showing a diagrammatic representation of a lyre above a drawing of the sacred tetractys.
The reason Egypt’s contribution has been misunderstood is that the academics do not understand what the ancient Egyptians did with numbers. They have decided that Egyptian numbers were used in a purely profane way, that is used to quantify stuff’ However, there is a good deal of evidence that they also used them as metaphors to describe the cosmos. I’m working on a book about numbers as metaphors for what was sacred in ancient Egypt, and the evidence is compelling. Well, I can hear you say. ‘She would say that wouldn’t she.’ But I think that when the book comes out a lot of people will agree.
In the ancient Greek civilisation where the first philosophers attempted to explain the creation of the Universe, the hymns of mysticist Orpheus proved to be of significant importance, by introducing the term ‘Chaos’. This is another reason Egyptian cosmology has not been understood. The Greek notion of chaos has been superimposed onto the ancient Egyptians whose prima materia was not chaotic but inert, dark, limitless, timeless and without form.
According to Orpheus, Chaos condensed into the giant Cosmic Egg, whose rupture resulted in the creation of Phanes and Ouranos and of all the gods who symbolise the creation of the Universe. Later, Greek philosophers supported the view that chaos describes the unformed and infinite void, from which the Universe was created.
Engraving of a marble relief of Phanes.jpg. From Wikimedia Commons …
After visiting Egypt, so his biographer said, Thales of Miletus (624/623 – c. 548/545 BCE) claimed that the Earth floats on water and that earthquakes occur when the Earth is rocked by waves, an idea he probably picked up in Egypt where everything came out of the infinite waters of the Nun and where the Earth was believed to be surrounded by the water of Nun.
Thales was also known for his innovative use of geometry. For example, he said: Megiston topos: apanta gar chorei (Μέγιστον τόπος· ἄπαντα γὰρ χωρεῖ.) The greatest is space, for it holds all things.
The god Shu was the god of space or emptiness who held the bubble of air that contained the Earth in the ancient Egyptian cosmology. His role in creating the triangle occurred when he mythically lifted the body of the goddess Nut to form the vault of the sky, beneath him lay the body of the Earth god Geb. Flinders Petrie was the first to notice that the King’s Chamber of the Great Pyramid of Giza was based on a 3–4–5 pyramid, built c. 2,500 BCE.
Wikimedia: Nut forming the arc of the heavens, Shu supported by Khumn in the centre, and Geb in a prone position lying on the Earth.
Topos is in Newtonian-style space, since the verb, chorei, has the connotation of yielding before things or spreading out to make room for them, which is extension. Within this extension, things have a position. Points, lines, planes and solids related by distances and angles follow from this presumption that Thales understood triangles and right triangles, and what is more, used that knowledge in practical ways. It is said that he measured the height of the pyramids by their shadows at the moment when his own shadow was equal to his height. A right triangle with two equal legs is a 45-degree right triangle, all of which are similar.
The length of the pyramid’s shadow measured from the centre of the pyramid at that moment must have been equal to its height. This story indicates that he may have been familiar with the Egyptian seked, or seqed, the ratio of the run to the rise of a slope (cotangent). The seked is at the base of problems 56, 57, 58, 59 and 60 of the Rhind Mathematical Papyrus which dates to the Second Intermediate Period of Egypt. It was copied by the scribe Ahmes (i.e., Ahmose; Ahmes is an older transcription favoured by historians of mathematics), from a now-lost text from the reign of King Amenemhat III (12th dynasty).
Wikimedia Commons: Rhind Mathematical Papyrus
Pythagoras of Samos (c. 570 – c. 495 BC)[b] was an ancient Ionian Greek philosopher and the eponymous founder of Pythagoreanism. His political and religious teachings were well known in Magna Graecia and influenced the philosophies of Plato, Aristotle, and, through them, Western philosophy.
According to Aristotle, the Pythagoreans used mathematics for solely mystical reasons, devoid of practical application. They believed that all things were made of numbers. The number one (the monad) represented the origin of all things and the number two (the dyad) represented matter. The number three was an “ideal number” because it had a beginning, middle, and end and was the smallest number of points that could be used to define a plane triangle, which they revered as a symbol of the god Apollo. The number four signified the four seasons and the four elements. The number seven was also sacred because it was the number of planets and the number of strings on a lyre, and because Apollo’s birthday was celebrated on the seventh day of each month. They believed that odd numbers were masculine, that even numbers were feminine, and that the number five represented marriage because it was the sum of two and three.
Ten was regarded as the “perfect number” and the Pythagoreans honoured it by never gathering in groups larger than ten. Pythagoras was credited with devising the tetractys, the triangular figure of four rows which add up to the perfect number, ten. The Pythagoreans regarded the tetractys as a symbol of utmost mystical importance. Iamblichus, in his Life of Pythagoras, states that the tetractys was “so admirable, and so divinised by those who understood [it],” that Pythagoras’s students would swear oaths by it.
Modern scholars debate whether these numerological teachings were developed by Pythagoras himself or by the later Pythagorean philosopher Philolaus of Croton. We believe Pythagoras whoever he was, and his followers developed them after visiting Egypt. The Pythagorean Mystery Numbers are not exactly what the Egyptians were up to but the Pythagoreans got the idea of modelling the universe with numbers from the Egyptians and we will show how they did it in our upcoming book which has the working title, ‘The Numbers of Thoth’ by Julia and Martin Herdman.