The Algorithm Concept - Tool for Historiographic Interpretation or Red Herring? (original) (raw)
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Selected Essays on Pre- and Early Modern Mathematical Practice, 2019
Since the 1950s, “Babylonian mathematics” has often served to open expositions of the general history of mathematics. Since it is written in a language and a script which only specialists understand, it has always been dealt with differently by the “insiders”, the Assyriologists who approached the texts where this mathematics manifests itself as philologists and historians of Mesopotamian culture – and by “outsiders”, historians of mathematics who had to rely on second-hand understanding of the material (actually, of as much of this material as they wanted to take into account), but who saw it as a constituent of the history of mathematics. The article deals with how these different approaches have looked in various periods: pre-decipherment speculations; the early period of deciphering, 1847–1929; the “golden decade”, 1929–1938, where workers with double competence (primarily Neugebauer and Thureau-Dangin) attacked the corpus and demonstrated the Babylonians to have possessed unexp...
Since the 1950s, “Babylonian mathematics” has often served to open expositions of the general history of mathematics. Since it is written in a language and a script which only specialists understand, it has always been dealt with differently by the “insiders”, the Assyriologists who approached the texts where it manifests itself as philologists and historians of Mesopotamian culture, and by “outsiders”, historians of mathematics who had to rely on second-hand understanding of the material (actually, of as much of this material as they wanted to take into account), but who saw it as a constituent of the history of mathematics. The article deals with how these different approaches have looked in various periods: pre-decipherment speculations; the early period of deciphering, 1847–1929; the “golden decade”, 1929–1938, where workers with double competence (primarily Neugebauer and Thureau-Dangin) attacked the corpus and demonstrated the Babylonians to have possessed unexpectedly sophisticated mathematical knowledge; and the ensuing four decades, where some mopping-up without change of perspective was all that was done by a handful of Assyriologists and Assyriologically competent historians of mathematics, while most Assyriologists lost interest completely, and historians of mathematics believed to possess the definitive truth about the topic in Neugebauer’s popularizations.
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.
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".