Further Aspects of Mathematics from New Kingdom Sources

Author(s):  
Annette Imhausen

This chapter proposes the following scenario: mathematics not only played a huge role within the education and work life of a scribe, but it also held an important role within ancient Egyptian culture in general. This role developed from the beginnings of the Egyptian state and the first uses of the number system (e.g., when the display of large numbers was used to express a certain power) and was by no means confined to the realm of the living. The discussions cover mathematics and wisdom literature, mathematics in the Duties of the Vizier, mathematics and death, and mathematics in architecture and art.

Author(s):  
Joseph Mazur

This chapter discusses the important role played by the Silk and Royal roads in the spread of teaching and knowledge of philosophy, science, and mathematics during ancient times. The Silk Road was a series of land and sea routes criss-crossing Eurasia and connecting to other routes traveled mostly by Indian merchants, agents, and explorers. Formed sometime around the second century BC, it connected to the Royal Road in the Zagros Mountains of Persia. Commercial trade was done mostly through bartering, but fair bartering required at least a rough estimate of value, an understanding of conversions of weights and measures: square areas of silk, or weights of gold, or value of coin. The chapter describes the number system that allowed the Chinese to “name” large numbers, as well as the system of counting rods to do practical arithmetic.


2020 ◽  
Vol 1 (9) ◽  
pp. 28-30
Author(s):  
D. M. Zlatopolski

The article describes a number of little-known methods for translating natural numbers from one number system to another. The first is a method for converting large numbers from the decimal system to the binary system, based on multiple divisions of a given number and all intermediate quotients by 64 (or another number equal to 2n ), followed by writing the last quotient and the resulting remainders in binary form. Then two methods of mutual translation of decimal and binary numbers are described, based on the so-called «Horner scheme». An optimal variant of converting numbers into the binary number system by the method of division by 2 is also given. In conclusion, a fragment of a manuscript from the beginning of the late 16th — early 17th centuries is published with translation into the binary system by the method of highlighting the maximum degree of number 2. Assignments for independent work of students are offered.


2021 ◽  
pp. 384-393
Author(s):  
Olga Viktorovna Gavrilova

This article discusses a very well-known and frequently used technique for an implementation of a variety of artistic projects - a collage created by means of information technology. The article tells about using collage in higher education for teaching graphics, in particular, raster editors. Graphics editors such as Adobe Photoshop or GIMP are included in the Computer Science and Information Technology program. Students get the opportunity to create graphic images regardless of their prior art education. The introduction of the topic "Creating a collage by means of a raster editor" introduces a creative element into IT disciplines and develops the student's associative thinking at the level of brain functioning. As a rule, raster editors are used to edit an image, not to create it. Therefore, preparation for these classes encourages students to search for the necessary visual material on the Internet. In order to obtain more personal images, a deep study of photography techniques is required. It is also useful to study the history of photo and film collages, their texture and structure. The scope of the collage use is various. This is psychology, teaching foreign languages and, of course, fine arts. Advertising posters that we see in large numbers in the media and transport are also collages. The article traces the history of collage creation from ancient Egyptian history to modern advertising products. It is especially interesting to study the time when collage became a conscious technique. This is a great layer of avant-garde art.


Author(s):  
Hana Navratilova

A newly excavated ostracon from Abydos bearing the concluding chapter of “The Instruction (a.k.a. Teaching) of King Amenemhat” opens up an interesting enquiry. An ostracon found in the immediate vicinity of a New Kingdom royal memorial temple and carrying an excerpt from a major literary text is an important find, as it develops our insight into New Kingdom educational practices and intellectual quests. The range of ostraca types and text genres appearing in the area of the temple of Ramesses II points to a fully functional temple organization with a building phase and an operational phase, with supplies and literate personnel on site, potentially in different administrative roles. Studies in educational and intellectual pursuits, in turn, are key to expanding our comprehension of the functions—and enjoyment—of Egyptian culture.


2018 ◽  
pp. 303-313
Author(s):  
Christopher P. Guzelian

Two years ago, Bob Mulligan and I empirically tested whether the Bank of Amsterdam, a prototypical central bank, had caused a boom-bust cycle in the Amsterdam commodities markets in the 1780s owing to the bank’s sudden initiation of low-fractional-re-serve banking (Guzelian & Mulligan 2015).1 Widespread criticism came quickly after we presented our data findings at that year’s Austrian Economic Research Conference. Walter Block representa-tively responded: «as an Austrian, I maintain you cannot «test» apodictic theories, you can only illustrate them».2 Non-Austrian, so-called «empirical» economists typically have no problem with data-driven, inductive research. But Austrians have always objected strenuously on ontological and epistemolog-ical grounds that such studies do not produce real knowledge (Mises 1998, 113-115; Mises 2007). Camps of economists are talking past each other in respective uses of the words «testing» and «eco-nomic theory». There is a vital distinction between «testing» (1) an economic proposition, praxeologically derived, and (2) the rele-vance of an economic proposition, praxeologically derived. The former is nonsensical; the latter may be necessary to acquire eco-nomic theory and knowledge. Clearing up this confusion is this note’s goal. Rothbard (1951) represents praxeology as the indispensible method for gaining economic knowledge. Starting with a Aristote-lian/Misesian axiom «humans act» or a Hayekian axiom of «humans think», a voluminous collection of logico-deductive eco-nomic propositions («theorems») follows, including theorems as sophisticated and perhaps unintuitive as the one Mulligan and I examined: low-fractional-reserve banking causes economic cycles. There is an ontological and epistemological analog between Austrian praxeology and mathematics. Much like praxeology, we «know» mathematics to be «true» because it is axiomatic and deductive. By starting with Peano Axioms, mathematicians are able by a long process of creative deduction, to establish the real number system, or that for the equation an + bn = cn, there are no integers a, b, c that satisfy the equation for any integer value of n greater than 2 (Fermat’s Last Theorem). But what do mathematicians mean when they then say they have mathematical knowledge, or that they have proven some-thing «true»? Is there an infinite set of rational numbers floating somewhere in the physical universe? Naturally no. Mathemati-cians mean that they have discovered an apodictic truth — some-thing unchangeably true without reference to physical reality because that truth is a priori.


Author(s):  
Annette Imhausen

This chapter reviews evidence on the use of the ancient Egyptian number system. There have been only three types of signs used in writing a number: a vertical stroke, a horizontal stroke, and a rope. Of these, the vertical stroke and the rope have successors in the later evidence of Egyptian number notations in the writing of units and hundreds, respectively. Early evidence for the use of number notation originates mostly from funerary or temple contexts. The usage of numbers in a funerary context can be described as administrative and may serve as a mirror for the usage of numbers in daily life at this time. Apart from the administration of goods, in which numbers and quantities have an inherent place, numbers also obtain a secondary, ritual meaning, which is shown by objects like the Narmer macehead and Narmer palette, but also by the offering lists. The writing of numbers is used to indicate the presence of something and to specify its quantities.


Author(s):  
Katie Marie Whitmore ◽  
Michele R. Buzon ◽  
Stuart Tyson Smith

Tombos is located at the Third Cataract of the Nile River in modern-day Sudan and marks an important literal and figurative boundary between Egyptian and Nubian interaction. During the New Kingdom Period (1400–1050 BCE), the cemetery at Tombos in Upper Nubia exhibits the use of Egyptian mortuary practices, including monumental pyramid complexes, likely used by both immigrant Egyptians and local Nubians. Despite the influence of Egyptian culture during this colonial period, there are several public displays of Nubian identity in burial practices found at Tombos. This mixture of Egyptian and Nubian burial practices extends into the postcolonial period at Tombos. Paleopathological analyses indicate that the Nubian and Egyptian individuals living at colonial Tombos enjoyed access to nutritional food resources and displayed low levels of skeletal markers of infection, traumatic injury, and strenuous physical activity. While the Tombos sample is likely not representative of all Egyptian-Nubian interaction during the New Kingdom, the individuals examined appear to have benefited from the relationship. In contrast with many situations of frontier interaction, the bioarchaeological evidence indicates a relatively peaceful coexistence between Egyptians and Nubians at Tombos, and the construction of a new biologically and culturally entangled community.


2019 ◽  
pp. 390-472
Author(s):  
Ryholt Kim

This chapter is a survey of collections of literary texts from Late Period and Graeco-Roman Egypt, c.750 BCE–250 CE, effectively the last millennium of the ancient Egyptian culture. Examples of different forms of collections are described and discussed in detail: temple libraries and private libraries, as well as groups of literary texts found in tombs, in rubbish dumps, in waste paper collections, and re-used in cartonnage. The texts include narratives, wisdom instructions, science (esp. divination and medicine), and cultic texts (esp. ritual guidelines, religious treatises, and hymns). Additional paragraphs concern the use of master copies, different types of storage, the abduction of libraries, and the so-called House of Life.


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