MARAVELIA Informatics & Egyptology (Ain Shams IEEE 2017 Paper)

Journal of Statistics and Mathematical Engineering, 2020

This paper entails about the amazing capabilities and advancement of ancient Egyptian civilization in the fields of Numerical Mathematics, Geometry and structural Engineering. They had used Hieroglyphic in their writing system. They had already evolved the idea of our present day binary system used in computers, decimal system, applied Geometry in structural Engineering etc. They used Fractions in an interesting way with a numerator of one and a denominator as a positive integer. Their contributions and standards may be said to be of genius calibre. As such the present generation is highly indebted to their contributions towards advancement of Mathematical journey since ancient times to present day.

2013

In ancient Egyptian mathematics, the algorithmic structure of the problem texts is characterized by the presence of two levels of calculation: the main algorithmic level, constituted by a series of operations executed step by step, and a second, “nested”, level of calculation, in which the individual operations of multiplication and division are executed in a scheme organized on two-columns. While for the main algorithmic level a methodology of mathematical rewriting that parallels the procedures of the ancient Egyptians is available, no completely effective methodology has been proposed for the “nested” level of calculation, which has been frequently read by means of anachronistic equations. The present article aims to fill this gap. The information flows develop along two directions: vertical and horizontal. Horizontal relations are in general implicit relations generated by operations of doubling, halving, etc., but, in some cases, both horizontal and vertical flows are involved in the procedures. This constitutes a sharp contrast with our modern, “one-way”, mentality.

The extant sources for ancient Egyptian mathematics are extremely limited. It is therefore necessary to read the few sources carefully and use additional information from further Egyptian sources in order to achieve the most detailed picture possible. Traditional approaches to Egyptian mathematics have provided only a superficial account of mathematical practices and almost no information about the role of mathematics within Egyptian culture. To enlarge our knowledge it is crucial to use a different methodological approach in the analysis of ancient mathematical techniques. In addition, it is indispensable to contextualize the mathematical problems with sources that are not specifically mathematical per se. In this article I discuss several possibilities for these additional sources, such as administrative texts, reliefs found in tombs, and other archaeological evidence. I exemplify the use of these sources with two problems from the Moscow mathematical papyrus.

Over the last fifty years the use of computer science and mathematics in archaeology has undergone continuous development and to date it has become an almost indispensable tool at any stage of the archaeological procedure: documentation, planning and data recording during surveys and excavations, laboratory studies, landscape analysis, reconstruction of social systems, archiving, mediation within the scientific community and amongst a broader public. New technologies have revolutionised the discipline: archaeological information systems, data retrieval systems, geographic information systems, 3D, the Internet, multidimensional data analysis, mathematical modelling and multi-agent systems. But the most ambitious contribution lies in the field of the formalisation of a general theoretical framework of the discipline, the independence of which from any paradigm and ideology could raise archaeology to the level of the leading scientific disciplines.

"Ancient Egypt 2021. Perspective of Research", 2023

Physis - Rivista Internazionale di Storia della Scienza (Firenze: Olschki), 2014

This paper analyzes the algorithmic structure of geometrical problems in Egyptian papyri of the first half of the second millennium B.C. Processes of transformation of quantities from ‘‘false’’ values into actual values, and conversions from quantities expressed in the abstract system of numbers into metrological quantities, are known in Egyptian mathematics. Three further processes are identified in the present contribution: transformations of ‘‘false’’ dimensions of geometrical objects into true dimensions; transformations of geometrical objects into other geometrical objects; transformations of linear measures of monuments. These processes have relevant implications on the algorithmic structure of the problem texts, resulting in particular in the embedding of sub-algorithms and the creation of parallel structures. More in general, their wide employment in Egyptian mathematics has significant philosophic and cultural implications.

Addressing the dynamics of change in Ancient egypt: complex network analysis, 2020

Egyptology is becoming a strategic scientific discipline in that it is instructive for contemporary civilization and makes it possible to avoid critical mistakes in its development. However, classical Egyptology tools need to be supplemented by modern procedures that are more efficient in terms of the speed of the production of results and the processing of much more extensive data volumes, delivering more accurate and reliable evaluation of the findings. Since the time of Plato, cybernetics has been providing methods by which models based on observations of the environment or sensor data are created to reflect the properties of systems and environments, and actions that change the environment are generated. Many of these practices, which include elements of learning and deduction techniques, are developed within the field of artificial intelligence. Methods that specialize in analyzing relationships that can be modeled by graph theory are now widely developed within the framework of complex network analysis. To emphasize the increasing rate of application of these scientific methods to cover new challenges in processing ancient Egyptian data, the concept of cyber-Egyptology has been introduced recently. Cyber-Egyptology deals with the interpretation of ancient Egyptian data and Egyptologists’ observations using techniques based on the principles of cybernetics, artificial intelligence, and complex network analysis that might be modified to cope with a limited amount of complex structures containing uncertainties and missing entries. We offer an overview of a selected set of such methods and their application to Old Kingdom data.

Mathematics in Ancient Egypt, 2016