The Balance of the Two Lands: Ancient Egypt's Division According to the Ratio of Triangular Equilibrium (As immortalized in the Great Pyramid)
By William Glyn-Jones
The Egyptians conceived their nation as two lands held in balance, one upper, or upstream, and one lower, encompassing the Delta down to the coast. The conception was of great significance throughout Egypt's long history. As we read it in the text of the Shabaka Stone, the balancing took place in the time when the gods walked the Earth, an event of cosmic importance which somehow involved the two lands being weighed in a set of divine scales. In the First Time peace had reigned, before the dispute in which the visionary young Horus was blinded by his uncle Seth, while Horus castrated the worldly, virile older male. For the Egyptians, from at least the time of the Pyramid Texts, this dispute was a mythic equivalent of the opening of Pandora's Box, by which troubles came into the world. Resolution of the dispute therefore remedied these troubles, returning the state of peace and equilibrium that had existed in the First Time. Finding a place on either side of which the Two Lands were somehow equal was therefore of prime importance.
The dispute between Horus and Seth concerned sovereignty of Ancient Egypt. It was Horus' father Osiris, the former king of the Golden Age, who, from the Afterlife, commanded that some resolution be found. And so the great measuring occurred, and a border was established between Upper Egypt, to be ruled by Seth, and Lower Egypt, to be ruled by Horus. We know this boundary was at the Old Kingdom capital of Memphis, since this was called both the Binding of the Two Lands and the Balance of the Two Lands.
This has long been something of a mystery. Was the unification simply an historical event, and if so why was it accorded cosmic significance? And even if it was an historical event, what part did 'measuring' and 'weighing' play in the resolution? Here I shall present a new explanation for the mystery underpinning the Balance of the Two Lands, which seems to provide an exciting insight into the Pharaonic vision of Egypt.
Memphis, whose name is thought to derive from men nefer, "Established and Beautiful", is also on what can reasonably be seen as a kind of central longitude meridian of Ancient Egypt, since the north-south line through the capital divides the delta in half, and runs up to the north point, and is also apparently midway between official eastern and western Egyptian borders.
The question to ask is whether it is possible that we may take the Egyptians at their word, which is that by measuring the Earth they mean measuring the Earth, and that by finding a place of balance between the Two Lands they mean finding a place of balance between the Two Lands. I see absolutely no reason at all to doubt that such a measuring took place. We know for certain that the Egyptians made measurements of the movements of the stars. A very old measuring ceremony used in the setting of the foundations of temples, known as the Stretching of the Cord, makes explicit references to the observation of the stars of Ursa Major and Orion over time and to the accurate measurement of Sun shadows. Then remember that habitable Egypt consists now and consisted then of two strips of land along the course of a much-traveled highway, the Nile, and that this river runs north-south. Traveling considerable distances north and south would have been common for officials employed in such temple-building work, so those surveyors who took these measurements of the stars would have known perfectly well that the altitude of the stars changes as you go north or south. It is impossible that a people who were fascinated by and took measurements of the stars would not have noticed this over the thousands of years of Egyptian history, and once noticed it would certainly have intrigued them greatly. The variance of stellar altitude of, for example, the pole, when traveling north or south directly gives the angle of latitude change. If I then make the suggestion that they took a reading at north point and in the south and then found a site between where the reading measured off some key ratio between these two extremes, this can hardly be called a major leap, hardly a spurious speculation.
And indeed this is all they would have needed to do to locate Memphis at a carefully measured balance point between two known latitude measurements. On the north side of the first pyramid, the Stepped Pyramid of Saqqara, the necropolis site adjacent to Memphis, there is a small kiosk within which a statue of Djoser gazes up at an inclined angle through two peep holes in the wall at the northern sky. Does this hint at precisely the kind of observation that was conducted in order to locate the pyramid at a latitude that was considered to be special, the latitude of the Balance of the Two Lands? We shall see below that it can be shown from the figures that, to a high degree of accuracy, the latitude of Memphis is indeed at such a place of equilibrium between the Two Lands.
What might the special ratio have been? Clearly it was not half way in a simple sense, because Memphis is not half way between Upper and Lower Egypt, but we know from texts like the Rhind Papyrus that the Egyptians knew that calculating the area of objects other than the square or rectangle was not quite so simple a matter as that.
What ratio might they have been referring to as a 'balance', and why was it said that "the portion of Horus was like that of Seth"? A clue comes from their greatest construction and most impressive physical testament to their surveying skills, the Great Pyramid. The King's Chamber is located in the Great Pyramid on such a level that the surface area of the pyramid above this level is equal to that below. Since the pyramid is based on triangular shapes, this half-way level is not half way up the pyramid, but is at a particular ratio of the full height which works in the same way for all isosceles triangles (i.e. where two or more sides are of the same length), dividing their area in half. The King's Chamber represents in death what Memphis was in life, the resting place of the king, and it is located at the level of balance or equal area of the Upper and Lower parts of the pyramid, just as Memphis was said to be at the balance point between Upper and Lower Egypt.
Before we get back to the Earth Measuring, I think we must consider that this balance of that which is above and that which is below may have been a key consideration for the builders of the pyramid. I am well aware that new theories about the Great Pyramid come and go in considerable profusion; that some of them are wild, and that many simply do not square up to the facts that Egyptologists have painstakingly uncovered over the years. I have no axe to grind against Egyptology, and the theories here are based upon facts and kept within the context of the Egypt of the Egyptologists, even if the latter as a whole are currently dragging their feet somewhat on the question of latitude measurement. At the same time, and in a way that does not conflict with the last sentence, I am a closet follower of a Platonic-Hermetic type philosophy, namely of the type that believes that, feels how geometric forms can activate a kind of transcendental harmonious resonance in our minds, so I do actually see these matters on a level beyond the mundane, just as the Egyptians themselves did.