# Posts Tagged science

### Kemet and Science: Mathematics

**MATHEMATICS (arithmetic, algebra and geometry)**

Mathematics is an important field of science in which the ancient Kemetyu worked. The accurate measurements of their enormous architectural and sculptural monuments are worthy proof of their preoccupation with precision. They would never have been able to reach this pitch of perfection without a minimum of mathematical capacity. Kemetyu mathematics may be considered under the three headings of arithmetic, algebra and geometry.

Two important mathematical papyri have come down to us from the Middle Kingdom (—2000 to —1750), those of Moscow and Rhind. The Kemetyu method of numeration, based on the decimal system, consisted of repeating the symbols for numbers (ones, tens, hundreds, thousands) as many times as necessary to obtain the desired figure. There was no zero. It is interesting to note that the Kemetyu symbols for the fractions 1/3, 1/2, 1/4 and so on originate in the myth of Horus and Seth, in which one of Horus’ falcon eyes was torn out and cut into pieces by Seth. It is these pieces that symbolize certain fractions.

Kemetyu administrative organization required a knowledge of arithmetic. The efficiency of the highly centralized administration depended on knowing exactly what was happening in each province, in all spheres of activity. It is not surprising, then, that the scribes spent an enormous amount of time keeping records of the area of land under cultivation, the

quantities of products available and their distribution, the size and quality of the staff, and so on.

The Kemetyu method of calculation was simple. They reduced all operations to a series of multiplications and divisions by two (duplication), a slow process which requires little memorization and makes multiplication tables unnecessary. In divisions, whenever the dividend was not exactly divisible by the divider, the scribe introduced fractions, but the system used only fractions whose numerator was the number 1. The operations on

fractions were also done by systematic doubling. The texts contain numerous examples of proportional shares obtained in this way, with the scribe adding at the end of his calculations the formula ‘it is exactly that’, which is equivalent to our ‘ QED’.

All the problems posed and solved in Kemetyu treatises on arithmetic have one trait in common: they are all material problems of the type that a scribe, isolated in some remote outpost, would have to solve daily, like the apportioning of seven loaves of bread among ten men in proportion to their rank in the hierarchy, or the calculation of the number of bricks required to build an inclined plane. It was, then, basically an empirical system, with little in it of an abstract nature. It is difficult to judge what elements of such a system might have passed into neighbouring cultures.

It is not exactly clear whether one may properly speak of a Kemetyu algebra and specialists in the history of science hold different views on this matter. Certain problems described in the Rhind Papyrus are formulated as follows: ‘ A quantity [ahâ in Egyptian] to which is added [or subtracted] this or that increment («) results in quantity (N). What is this quantity?’ Algebraically, this would be expressed as x ±- x/n = N, which has led some historians of science to conclude that the Egyptians used algebraic calculations. However, the solutions proposed by the scribe of the Rhind Papyrus to this type of problem are always reached by simple arithmetic, and the only instance in which algebra might have been used is a problem of division which implies the existence of a quadratic equation. The scribe solved this problem as a modern algebraist would do, but instead of taking an abstract symbol like x as the basis of calculation, he took the number 1. The question whether Kemetyu algebra existed or not depends therefore on whether one accepts or rejects the possibility of doing algebra without abstract symbols.

The Greek writers Herodotus and Strabo concur in the view that geometry was invented by the Kemetyu. The need to calculate the area of the land eroded or added each year by the flooding of the Nile apparently led them to its discovery. As a matter of fact, Kemetyu geometry, like mathematics, was empirical. In ancient treatises, the task was first and

foremost to provide the scribe with a formula that would enable him to find rapidly the area of a field, the volume of grain in a silo or the number of bricks required for a building project. The scribe never applied abstract reasoning to the solution of a particular problem but just provided the practical means in the shape figures. None the less, the Kemetyu

knew perfectly well how to calculate the area of a triangle or a circle, the volume of a cylinder, of a pyramid or a truncated pyramid, and probably that of a hemisphere. Their greatest success was the calculation of the area of a circle. They proceeded by reducing the diameter by one-ninth and squaring the result which was equivalent to assigning a value of 3.1605 to ** pi**, which is much more precise than the value 3 given to

*by other ancient peoples.*

**pi**Knowledge of geometry proved of considerable practical use in land surveying, which played a significant role in Kemet. There are many tombs with paintings showing teams of surveyors busy checking that the boundary-stones of fields have not been shifted and then measuring with a knotted cord, the forerunner of our surveyor’s chain, the area of the cultivated field. The surveyor’s cord or ** nouh** is mentioned in the earliest texts (c.—2800). The central government possessed a cadastral office, the records of which were ransacked during the Memphite revolution (c. —2150) but were restored to order during the Middle Kingdom (c. -199°).

Authors: **R. El Nadoury** with the collaboration of), **Vercoutter**. General History of Africa Vol.II. [Editor: G.Mokhtar] Ancient Civilisations of Africa. Chapter 5. Legacy of Pharaonic Egypt.

**R. El Nadoury** (Egypt); specialist in ancient history; author of numerous works and articles on the history of the Maghrib and of Egypt; Professor of Ancient History and Vice Chairman of the Faculty of Arts, University of Alexandria.

### Kemet and Science: Surgery

The Kemetyu contribution to science and applied mathematics has left a valuable legacy in the fields of physics, chemistry, zoology, geology, medicine, pharmacology, geometry and applied mathematics. In fact, they gave to humanity a large store of experience in each of these fields, some of which were combined in order to execute a specific project.

### Surgery:

It was, undoubtedly, the knowledge they acquired from mummification that enabled the Kemetyu to develop surgical techniques at a very early period in their history. We have quite a good knowledge of Kemetyu surgery, in fact, thanks to the Smith Papyrus, a copy of an original which was composed under the Old Kingdom, between —2600 and —2400.

This papyrus is virtually a treatise on bone surgery and external pathology. Forty-eight cases are examined systematically. In each case, the author of the treatise begins his account under a general heading: ‘Instructions concerning [such and such a case]’; followed by a clinical description: ‘If you observe [such symptoms]’. The descriptions are always precise and incisive. They are followed by the diagnosis: ‘You will say in this connection a case of [this or that wound]’, and, depending on the case, ‘a case that I can treat’ or ‘the case is without remedy’. If the surgeon can treat the patient, the treatment to be administered is then described in detail, for example: ‘the first day you will apply a bandage with a piece of meat; afterwards you will place two strips of cloth in such a way as to join the lips of the wound together . . . ‘.

Several of the treatments indicated in the Smith Papyrus are still used today. Kemetyu surgeons knew how to stitch up wounds and to set a fracture using wooden or pasteboard splints. And there were times when the surgeon simply advised that nature should be allowed to take its own course. In two instances, the Smith Papyrus instructs the patient to maintain his regular diet.

Of the cases studied by the Smith Papyrus, the majority concerned superficial lacerations of the skull or face. Others concerned lesions of the bones or joints such as contusions of the cervical or spinal vertebrae, dislocations, perforations of the skull or sternum, and sundry fractures affecting the nose, jaw, collar-bone, humerus, ribs, skull and vertebrae. Examination of mummies has revealed traces of surgery, such as the jaw dating from the

Old Kingdom which has two holes bored to drain an abscess, or the skull fractured by a blow from an axe or sword and successfully reset. There is also evidence of dental work such as fillings done with a mineral cement, and one mummy had a kind of bridge of gold wire joining two shaky teeth.

By its methodical approach, the Smith Papyrus bears testimony to the skill of the surgeons of ancient Kemet, skill which it would be fair to assume was handed on gradually, in Africa as well as in Asia and to classical antiquity, by the doctors who were always attached to Kemetyu expeditions to foreign lands. Moreover, it is known that foreign sovereigns, like the Asian prince of Bakhtan, Bactria, or Cambyses himself, brought in Kemetyu doctors, that Hippocrates ‘had access to the library of the Imhotep temple at Memphis’ and that other Greek physicians later followed his example.

Authors: **R. El Nadoury** with the collaboration of), **Vercoutter**. General History of Africa Vol.II. [Editor: G.Mokhtar] Ancient Civilisations of Africa. Chapter 5. Legacy of Pharaonic Egypt.

**R. El Nadoury** (Egypt); specialist in ancient history; author of numerous works and articles on the history of the Maghrib and of Egypt; Professor of Ancient History and Vice-Chairman of the Faculty of Arts, University of Alexandria.

### Kemet and Science: Medicine

Medical knowledge can be considered as one of the most important early scientific contributions of the ancient Kemetyu to the history of man.

Documents show in detail the titles of Egyptian physicians and their different fields of specialization. In fact the civilizations of the ancient Near East and the classical world recognized the ability and reputation of the ancient Kemetyu in medicine and pharmacology. One of the most significant personalities in the history of medicine is Imhotep, the vizier, architect and physician of King Zoser of the third dynasty. His fame survived throughout Kemetyu ancient history and through to Greek times.

Deified by the Kemetyu under the name Imouthes, he was assimilated by the Greeks to Askelepios, the god of medicine. In fact, Kemetyu influence on the Greek world in both medicine and pharmacology is easily recognizable in remedies and prescriptions. Some medical instruments used in surgical operations have been discovered during excavations.

Written evidence of ancient Kemetyu medicine comes in medical documents such as the Ebers Papyrus, the Berlin Papyrus, the Edwin Smith Surgical Papyrus and many others which illustrate the techniques of the operations and detail the prescribed cures.

These texts are copies of originals dating back to the Old Kingdom (c. —2500). In contrast to the Edwin Smith Surgical Papyrus, which is highly scientific, the purely medical texts were based on magic. The Kemetyu regarded sickness as the work of the gods or malevolent spirits, which provided justification for resorting to magic and which explains why some of the remedies prescribed on the Ebers Papyrus, for example, resemble more a magical incantation than a medical prescription.

Despite this aspect, common to other ancient civilizations as well, Kemetyu medicine was a considerable science which contained the beginnings of a methodical approach, especially in the observation of symptoms, and this method doubtless passed to posterity by reason of its importance. The Kemetyu doctor examined his patient and determined the symptoms of his complaint. He then made his diagnosis and prescribed treatment. All the extant texts describe this sequence, from which it may be concluded that it was standard procedure. The examination was made in two stages some days apart if the case was unclear. Among the ailments identified and competently described and treated by Kemetyu doctors were gastric disorders, stomach swelling, skin cancer, coryza, laryngitis, angina pectoris, diabetes, constipation, haemorrhoids, bronchitis, retention

and incontinence of urine, bilharzia, ophthalmia, etc.

The Kemetyu doctor treated his patient using suppositories, ointments, syrups, potions, oils, massages, enemas, purges, poultices, and even inhalants whose use they taught to the Greeks. Their pharmacopoeia contained a large variety of medicinal herbs, the names of which, unfortunately, elude translation. Egyptian medical techniques and medicines

enjoyed great prestige in antiquity, as we know from Herodotus. The names of nearly one hundred ancient Kemetyu physicians have been passed down to us through these texts. Among them are oculists and dentists, of whom Hesy-Re, who lived around —2600 under the fourth dynasty, could be considered as one of the most ancient. Among the specialists

were also veterinarians. The physicians used a variety of instruments in their work.

Authors: **R. El Nadoury** with the collaboration of), Vercoutter. General History of Africa Vol.II. [Editor: G.Mokhtar] Ancient Civilisations of Africa. Chapter 5. Legacy of Pharaonic Egypt.

**R. El Nadoury** (Egypt); specialist in ancient history; author of numerous works and articles on the history of the Maghrib and of Egypt; Professor of Ancient History and Vice-Chairman of the Faculty of Arts, University of Alexandria.