The fossils of Alexandrian science

Isabelle Hairy
May 2006
When dealing with metrology, the fossil is no longer the object. It has been replaced by the measurement. This latter contains a message that, if you know how to decipher it, can recreate the past. It carries within the memory of its formation, and reading it should lead to the base unit from which it grew. In our case, the measurements of the monumental doorway reveal the use of the royal Egyptian cubit or meh of 0.525m and an Ionian or Samian foot of 0.35m in a ratio of 2/3. As the products of Greek and Egyptian culture, these standard units were brought together in a geometric system that had its source in the Tetraktys of the Pythagoreans (from 6th century BC)
1 cubit (5.25 cm) = 6 palms
1 span ( 43.75 cm) = 5 palms
1 foot ( 35 cm) = 4 palms
1/2 cubit = 3 palms
1/2 foot = 2 palms
1 palm = 8.75 cm
The basic figures of the system of measurements
Plato's formula for an equilateral triangle
Ratio 2:1
Ratio 3:2
Ratio 4:3
Basic musical scale

From the tetraktys of the Pythagoreans via the fundamentals of geometry used by Plato in the Timeaus to the geometric figures of the Alexandrian system of measurement.
© CEAlex, illustration I. Hairy

Starting from these fundamental elements and with the aid of rules that manage the space that they measure, the archaeologist can hope to reconstitute the monument of which he holds only one single piece: in this case, the doorway.
But how can one rediscover these rules? It is through reinterpreting, within the object “doorway”, the forms that derive from the utilisation of the ancient measuring system that one can reconstitute certain rules of the spatial grammar. One proceeds keeping in mind the advances of the science of the period when the monument was conceived and within the cultures from which the monument sprung, that is, Greece and Egypt.
The manifestation in the physical world of Plato’s four elements :
fire (tetrahedron)
air (octahedron)
water (icosahedron)
earth (hexahedron)
Schéma géométrique de la porte monumentale des baies et univers platonicien (© CEAlex, dessin I. Hairy)

From this new observation, one can extract other traces that find an echo, firstly in the Greek philosophy of Plato (4th century BC) and notably in his work Timaeus. Here Plato manipulates particular objects from planar geometry with which, through agglomeration, he explains the formation of the universe. On the other hand, this observation demonstrates the procedures compiled by the Greek scholar Euclid, a mathematician of the 3rd century BC and founder of the Alexandrian School, in his work The Elements. A contemporary of the erection of the Pharos, he certainly collaborated in its construction even if only indirectly.

Monumental doorway of the Pharos – The equilateral triangle, obtained by rotating the opposite sides of the square to the median, and then divided into two scalene triangles along its apothem, reforms into a triangle which determines shape of the doorway and its decor (© CEAlex, drawings I. Hairy)
There is nothing remarkable in that the Pharos took its form from this ancient knowledge, but is this the sole message held within the remains of the monument? The creation of the Pharos, inspired by Platonic principles set out in the Timaeus, reflects a certain idea of the world. One could say that it engendered a representation of the cosmos. One can also find some references to Egyptian mythology, such as the value of 42 feet measuring a side of the equilateral triangle used in the design of the monumental doorway. This is also the theoretical number of provinces on the list traditionally held by the temple scribes in the later period “equalling thus the forty-two judges who assisted Osiris in his court”.

Theoretical model of the Pharos based upon the spatial rules deduced from the analysis of the monumental doorway. © CEAlex, drawing I. Hairy

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