12 research outputs found

    A new look at old numbers, and what it reveals about numeration

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    In this study, the archaic counting systems of Mesopotamia as understood through the Neolithic tokens, numerical impressions, and proto-cuneiform notations were compared to the traditional number-words and counting methods of Polynesia as understood through contemporary and historical descriptions of vocabulary and behaviors. The comparison and associated analyses capitalized on the ability to understand well-known characteristics of Uruk-period numbers like object-specific counting, polyvalence, and context-dependence through historical observations of Polynesian counting methods and numerical language, evidence unavailable for ancient numbers. Similarities between the two number systems were then used to argue that archaic Mesopotamian numbers, like those of Polynesia, were highly elaborated and would have served as cognitively efficient tools for mental calculation. Their differences also show the importance of material technologies like tokens, impressions, and notations to developing mathematics. This project has received funding from the European Union’s Horizon 2020 research and innovation program under grant agreement No. 785793

    Algebra in Cuneiform:Introduction to an Old Babylonian Geometrical Technique

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    Around 1930, it was discovered that certain Babylonian cuneiform texts contain calculations that agree with what turns up in the solution of second-degree equations. Since the meaning of most of the terminology had to be derived from the numbers contained in the texts, this led to a reading of these as numerically based algebra. This interpretation stood unchallenged until the author of the present book discovered around 1982 that it was incompatible the global structure of the terminology. As it turns out, two different and non-synonymous operations had both been understood as addition; two different subtractive operations had been conflated, and four different operations had been seen as one and the same multiplication. Instead, the structure points to a technique based on a geometry of squares and rectangles with measurable sides and areas. Avoiding such philological detail as would only be informative for readers that are familiar with basic Assyriology (yet with appendixes meant for these), the book analyses a number of texts in "conformal translation", that is, a translation in which the same Babylonian term is always translated in the same way and, more important, different terms are always translated differently. All of these texts are from the second half of the Old Babylonian period, that is, 1800-1600 BCE. It is indeed during this period that the "algebraic" discipline, and Babylonian mathematics in general, culminates. Even though a few texts from the late period show some similarities with what comes from the Old Babylonian period, they are but remnants. Beyond analyzing texts, this preprint gives a general characterization of the kind of mathematics involved, and locates it within the context of the Old Babylonian scribe school and its particular culture. Finally, it describes the origin of the discipline and its impact in later mathematics, not least Euclid's geometry and genuine algebra as created in medieval Islam and taken over in European medieval and Renaissance mathematics

    Algebra in Cuneiform:Introduction to an Old Babylonian Geometrical Technique

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    BĂĽrgi's <i>Progress Tabulen</i> (1620): logarithmic tables without logarithms

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    This article analyzes Jost BĂĽrgi's work (1620) and its place in the history of logarithms

    The great logarithmic and trigonometric tables of the French Cadastre: a preliminary investigation

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    This document is a first investigation of the ''Tables du cadastre,'' Prony's effort to build the greatest monument of science of the French Revolution. The document is supplemented by 47 volumes which make it easier to analyze the original manuscripts

    6.1 Ontology

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    Scientific Programming and Computer Architecture

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    A variety of programming models relevant to scientists explained, with an emphasis on how programming constructs map to parts of the computer.What makes computer programs fast or slow? To answer this question, we have to get behind the abstractions of programming languages and look at how a computer really works. This book examines and explains a variety of scientific programming models (programming models relevant to scientists) with an emphasis on how programming constructs map to different parts of the computer's architecture. Two themes emerge: program speed and program modularity. Throughout this book, the premise is to "get under the hood," and the discussion is tied to specific programs. The book digs into linkers, compilers, operating systems, and computer architecture to understand how the different parts of the computer interact with programs. It begins with a review of C/C++ and explanations of how libraries, linkers, and Makefiles work. Programming models covered include Pthreads, OpenMP, MPI, TCP/IP, and CUDA.The emphasis on how computers work leads the reader into computer architecture and occasionally into the operating system kernel. The operating system studied is Linux, the preferred platform for scientific computing. Linux is also open source, which allows users to peer into its inner workings. A brief appendix provides a useful table of machines used to time programs. The book's website (https://github.com/divakarvi/bk-spca) has all the programs described in the book as well as a link to the html text
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