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Historical Projects in Discrete Mathematics and Computer Science
"... A course in discrete mathematics is a relatively recent addition, within the last 30 or 40 years, to the modern American undergraduate curriculum, born out of a need to instruct computer science majors in algorithmic thought. The roots of discrete mathematics, however, are as old as mathematics itse ..."
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A course in discrete mathematics is a relatively recent addition, within the last 30 or 40 years, to the modern American undergraduate curriculum, born out of a need to instruct computer science majors in algorithmic thought. The roots of discrete mathematics, however, are as old as mathematics itself, with the notion of counting a discrete operation, usually cited as the first mathematical development
HISTORICAL PERSPECTIVE Ancient Images and New Technologies: The Semiotics
"... In this article, I develop an analysis of computerbased communication on the World Wide Web, where images, texts and hypertext links interconnect and mutually refer to each other. Our learned ignorance is conceiving an infinite virtual world whose center is everywhere and circumference nowhere. The ..."
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In this article, I develop an analysis of computerbased communication on the World Wide Web, where images, texts and hypertext links interconnect and mutually refer to each other. Our learned ignorance is conceiving an infinite virtual world whose center is everywhere and circumference nowhere. The use of images to represent knowledge and synthesize information has a long background in the Western history of ideas, particularly in the ancient tradition of the Art of Memory, a strand of classical studies going back to Cicero and persisting up to the baroque era [1]. This discipline was concerned with mnemonics, specifically the ability to memorize anything at will, at a time when paper and other writing tools were rare. There is thus a long history of organizing and interpreting complex images in the scholarly tradition of the Western world; images have been supposed to speak more directly than words to the soul. Within this tradition, one could further investigate the use of particular indexical images, that is, images that may point or refer to other images or texts; such hyperlinks are currently a key feature of multimedia and Webbased documents. Surprisingly (or not) such images can be found as far back in time as the fifteenth century and have been widely used from the seventeenth century onwards. Artists and printers did not wait for computers to exist before putting such devices to work. However, to fully develop this analysis of indexical images requires more conceptual notions in addition to pure historical research. In order to better understand the conceptual mechanisms behind hyperlinks, I thus borrow from semiotics, in particular the classical trichotomy of Charles Sanders Peirce [2], who distinguished three kinds of signs (symbols, icons and indexes) and their respective functions. But before using semiotics to analyze Webbased hypertext navigation, we will need to retrace the history of the “universal language of computers,” that is, binary notation, and relate it to that of the “universal language of images”—a long tradition in the history of ideas going back to Cicero’s Art of Memory and various Renaissance
ON THE PROPORTION OF DIGITS IN REDUNDANT NUMERATION SYSTEMS*
, 1996
"... In the standard binary numeration system, an #bit integer N is uniquely represented as the sum of powers of 2. Specifically, N = a^T 1 1 +a„„22 w " 2 + +a22 2 +at2 l +aQ2\ ..."
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In the standard binary numeration system, an #bit integer N is uniquely represented as the sum of powers of 2. Specifically, N = a^T 1 1 +a„„22 w " 2 + +a22 2 +at2 l +aQ2\