The Algorithm Concept - Tool for Historiographic Interpretation or Red Herring? (original) (raw)
Interpretation of reverse algorithms in several Mesopotamian texts (2012)
Quatrième de couverture du livre: "This radical, profoundly scholarly book explores the purposes and nature of proof in a range of historical settings. It overturns the view that the first mathematical proofs were in Greek geometry and rested on the logical insights of Aristotle by showing how much of that view is an artefact of nineteenth-century historical scholarship. It documents the existence of proofs in ancient mathematical writings about numbers and shows that practitioners of mathematics in Mesopotamian, Chinese and Indian cultures knew how to prove the correctness of algorithms, which are much more prominent outside the limited range of surviving classical Greek texts that historians have taken as the paradigm of ancient mathematics. It opens the way to providing the first comprehensive, textually based history of proof."
Selected Essays on Pre- and Early Modern Mathematical Practice, 2019
Most general standard histories of mathematics speak indiscriminately of “Babylonian” mathematics, presenting together the mathematics of the Old Babylonian and the Seleucid period (respectively 2000−1600 and 300−100 bce) and neglecting the rest. Specialist literature has always known there was a difference, but until recently it has been difficult to determine the historical process within the Old Babylonian period.
A Note on Old Babylonian Computational Techniques
Historia Mathematica, 2002
Analysis of the errors in two Old Babylonian “algebraic” problems shows that the computations were performed on a device where additive contributions were no longer identifiable once they had entered the computation;that this device must have been some kind of counting board or abacus where numbers were represented as collections of calculi;that units and tens were represented in distinct ways, perhaps by means of different calculi.Eine Analyse der Rechenfehler in zwei altbabylonischen “algebraischen” Aufgaben läßt mehrere Rückschlüsse auf ein Hilfsmittel zu, das zur Durchführung von Rechnungen benutzt worden sein kann: Additive Beiträge waren nach ihrer Eintragung in die Rechnung nicht länger identifizierbar.Das Gerät war eine Art Rechenbrett, auf welchem Zahlen als Haufen von Rechensteinen erschienen.Einer und Zehner wurden in verschiedener Weise, evtl. mittels verschiedener Rechensteine repräsentiert.MSC subject classification: 01A17.
AIMS Mathematics, 2018
When is the algorithm concept pertinent -and when not? Thoughts about algorithms and paradigmatic examples, and about algorithmic and nonalgorithmic mathematical cultures Høyrup, Jens Publication date: 2015 Document Version Early version, also known as pre-print Citation for published version (APA): Høyrup, J. (2015). When is the algorithm concept pertinent -and when not? Thoughts about algorithms and paradigmatic examples, and about algorithmic and non-algorithmic mathematical cultures. Paper presented at International Conference on the History of Ancient Mathematics and Astronomy, Xi'an, China. Copyright and moral rights for the publications made accessible in the public portal are retained by the authors and/or other copyright owners and it is a condition of accessing publications that users recognise and abide by the legal requirements associated with these rights. • Users may download and print one copy of any publication from the public portal for the purpose of private study or research. • You may not further distribute the material or use it for any profit-making activity or commercial gain. • You may freely distribute the URL identifying the publication in the public portal.
Selected Essays on Pre- and Early Modern Mathematical Practice, 2019
Writing, as well as various mathematical techniques, were created in proto-literate Uruk in order to serve accounting, and Mesopotamian mathematics as we know it was always expressed in writing. In so far, mathematics generically regarded was always part of the generic written tradition. However, once we move away from the generic perspective, things become much less easy. If we look at basic numeracy from Uruk IV until Ur III, it is possible to point to continuity and thus to a "tradition", and also if we look at place-value practical computation from Ur III onward-but already the relation of the latter tradition to type of writing after the Old Babylonian period is not well elucidated by the sources. Much worse, however, is the situation if we consider the sophisticated mathematics created during the Old Babylonian period. Its connection to the school institution and the new literate style of the period is indubitable; but we find no continuation similar to that descending from Old Babylonian beginnings in fields like medicine and extispicy. Still worse, if we look closer at the Old Babylonian material, we seem to be confronted with a small swarm of attempts to create traditions, but all rather short-lived. The few mathematical texts from the Late Babylonian (including the Seleucid) period also seem to illustrate attempts to establish norms rather than to be witnesses of a survival lasting sufficiently long to allow us to speak of "traditions". On ignorance and limited knowledge .
As the Outsider Walked in the Historiography of Mesopotamian Mathematics Until Neugebauer
Archimedes, 2016
Those who nowadays work on the history of advanced-level Babylonian mathematics do so as if everything had begun with the publication of Neugebauer's Mathematische Keilschrift-Texte from 1935-37 and Thureau-Dangin's Textes mathématiques babyloniens from 1938, or at most with the articles published by Neugebauer and Thureau-Dangin during the few preceding years. Of course they/we know better, but often that is only in principle. The present paper is a sketch of how knowledge of Babylonian mathematics developed from the beginnings of Assyriology until the 1930s, and raises the question why an outsider was able to create a breakthrough where Assyriologists, in spite of the best will, had been blocked. One may see it as the anatomy of a particular "Kuhnian revolution".
Algorithms, An Historical Perspective
The Power of Algorithms, 2013
The design of algorithms for land measurement, financial transactions and astronomic computations goes back to the third millennium BCE. First examples of algorithms can be found in Mesopotamian tablets and in Egyptians scrolls. An important role in the development of numerical algorithms was played in the ninth century by the Persian mathematician al-Khwarizmi, who introduced the Indian numeration systems to the Arab world and from whom we derived the name 'algorithm' to denote computing procedures. In the Middle Ages algorithms for commercial transactions were widely used, but it was not until the nineteenth century that the problem of characterizing the power of algorithms was addressed. The precise definition of 'algorithm' and of the notion of computability were established by A.M. Turing in the 1930s. His work is also considered the beginning of the history of Computer Science.
"Information Flows in Ancient Egyptian Arithmetic: a New Methodology" (2013)
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.