Numerical Notation
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Numerical Notation
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Author : Stephen Chrisomalis
language : en
Publisher: Cambridge University Press
Release Date : 2010-01-18
Numerical Notation written by Stephen Chrisomalis and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-01-18 with Mathematics categories.
This book is a cross-cultural reference volume of all attested numerical notation systems, encompassing more than 100 such systems used over the past 5,500 years. Using a typology that defies unilinear evolutionary models, Stephen Chrisomalis identifies five basic types of numerical notation systems, tracks relationships between systems, and creates a general model of change that incorporates social, historical, and cognitive factors.
Numerical Notation
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Author : Stephen Chrisomalis
language : en
Publisher: Cambridge University Press
Release Date : 2010-01-18
Numerical Notation written by Stephen Chrisomalis and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-01-18 with Social Science categories.
This book is a cross-cultural reference volume of all attested numerical notation systems (graphic, non-phonetic systems for representing numbers), encompassing more than 100 such systems used over the past 5,500 years. Using a typology that defies progressive, unilinear evolutionary models of change, Stephen Chrisomalis identifies five basic types of numerical notation systems, using a cultural phylogenetic framework to show relationships between systems and to create a general theory of change in numerical systems. Numerical notation systems are primarily representational systems, not computational technologies. Cognitive factors that help explain how numerical systems change relate to general principles, such as conciseness or avoidance of ambiguity, which apply also to writing systems. The transformation and replacement of numerical notation systems relates to specific social, economic, and technological changes, such as the development of the printing press or the expansion of the global world-system.
The Cambridge Handbook Of Literacy
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Author : David R. Olson
language : en
Publisher: Cambridge University Press
Release Date : 2009-02-09
The Cambridge Handbook Of Literacy written by David R. Olson and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-02-09 with Psychology categories.
This handbook marks the transformation of the topic of literacy from the narrower concerns with learning to read and write to an interdisciplinary enquiry into the various roles of writing and reading in the full range of social and psychological functions in both modern and developing societies. It does so by exploring the nature and development of writing systems, the relations between speech and writing, the history of the social uses of writing, the evolution of conventions of reading, the social and developmental dimensions of acquiring literate competencies, and, more generally, the conceptual and cognitive dimensions of literacy as a set of social practices. Contributors to the volume are leading scholars drawn from such disciplines as linguistics, literature, history, anthropology, psychology, the neurosciences, cultural psychology, and education.
The I Ching The T Ai Hsuan Ching
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Author : John Clifford Compton
language : en
Publisher: Compton/Kowanz Publications
Release Date : 2024-10-07
The I Ching The T Ai Hsuan Ching written by John Clifford Compton and has been published by Compton/Kowanz Publications this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-10-07 with Architecture categories.
The content of this book differs from the other volumes of the I Ching Project, because it is a mathematical analysis of the T'ai Hsuan Ching , another Chinese Classic, which is considered to be the lost companion of the I Ching. This research document is based on nine magic squares incorporated on an ancient Tibetan Mandala and the 81 linear line symbols of the T'ai Hsuan Ching, each of which have been given a numerical notation based on the transposition of linear line symbols. The transposition of the three linear line symbols of the I Ching is known and may be represented by the numbers 6, 7, 8 and 9. However, the transposition of the four linear line symbols of the T'ai Hsuan Ching is NOT known. The author's research and mathematical analysis shows that the transposition of these four linear line symbols may be represented by the numbers 1, 2, 3, 4 and 5, which conclusively proves that the T'ai Hsuan Ching may predate The I Ching as a divination oracle.
Indian Epigraphy
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Author : Richard Salomon
language : en
Publisher: Oxford University Press
Release Date : 1998-12-10
Indian Epigraphy written by Richard Salomon and has been published by Oxford University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998-12-10 with Religion categories.
This book provides a general survey of all the inscriptional material in the Sanskrit, Prakrit, and modern Indo-Aryan languages, including donative, dedicatory, panegyric, ritual, and literary texts carved on stone, metal, and other materials. This material comprises many thousands of documents dating from a range of more than two millennia, found in India and the neighboring nations of South Asia, as well as in many parts of Southeast, central, and East Asia. The inscriptions are written, for the most part, in the Brahmi and Kharosthi scripts and their many varieties and derivatives. Inscriptional materials are of particular importance for the study of the Indian world, constituting the most detailed and accurate historical and chronological data for nearly all aspects of traditional Indian culture in ancient and medieval times. Richard Salomon surveys the entire corpus of Indo-Aryan inscriptions in terms of their contents, languages, scripts, and historical and cultural significance. He presents this material in such a way as to make it useful not only to Indologists but also non-specialists, including persons working in other aspects of Indian or South Asian studies, as well as scholars of epigraphy and ancient history and culture in other regions of the world.
The Oxford Handbook Of The History Of Mathematics
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Author : Eleanor Robson
language : en
Publisher: OUP Oxford
Release Date : 2008-12-18
The Oxford Handbook Of The History Of Mathematics written by Eleanor Robson and has been published by OUP Oxford this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-12-18 with Mathematics categories.
This Handbook explores the history of mathematics under a series of themes which raise new questions about what mathematics has been and what it has meant to practise it. It addresses questions of who creates mathematics, who uses it, and how. A broader understanding of mathematical practitioners naturally leads to a new appreciation of what counts as a historical source. Material and oral evidence is drawn upon as well as an unusual array of textual sources. Further, the ways in which people have chosen to express themselves are as historically meaningful as the contents of the mathematics they have produced. Mathematics is not a fixed and unchanging entity. New questions, contexts, and applications all influence what counts as productive ways of thinking. Because the history of mathematics should interact constructively with other ways of studying the past, the contributors to this book come from a diverse range of intellectual backgrounds in anthropology, archaeology, art history, philosophy, and literature, as well as history of mathematics more traditionally understood. The thirty-six self-contained, multifaceted chapters, each written by a specialist, are arranged under three main headings: 'Geographies and Cultures', 'Peoples and Practices', and 'Interactions and Interpretations'. Together they deal with the mathematics of 5000 years, but without privileging the past three centuries, and an impressive range of periods and places with many points of cross-reference between chapters. The key mathematical cultures of North America, Europe, the Middle East, India, and China are all represented here as well as areas which are not often treated in mainstream history of mathematics, such as Russia, the Balkans, Vietnam, and South America. A vital reference for graduates and researchers in mathematics, historians of science, and general historians.
The Gates Of Destiny
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Author : John C. Compton
language : en
Publisher: Compton/Kowanz Publications
Release Date : 2022-08-19
The Gates Of Destiny written by John C. Compton and has been published by Compton/Kowanz Publications this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-08-19 with Body, Mind & Spirit categories.
This book contains a series of commentaries, research notes and illustrations selected from the author's amazing research work. It shows how the notational values (for trigram transposition) which change the ancient symbolic language of the I Ching into a simple numerical language were oringinally derived from the combined symbolic mathematics of the ancient Ho-T'u - The Dragon Horse diagram and the Lo Shu - The Tortoise diagram. This document provides additional conclusive evidence that the originator(s) of the I Ching employed a mathematical system (developed during the Ch'in and Han dynasties) which encompassed a formalistic natural philosophy that sought to embrace the entire world in a system of number symbolism. In addition, the research work contained herein sets out to prove, by using mathematical operand gates methodology, that the destiny/fate of an individual being is dependent upon their own genetic DNA.
The Number Sense
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Author : Stanislas Dehaene
language : en
Publisher: Oxford University Press
Release Date : 2011-04-29
The Number Sense written by Stanislas Dehaene and has been published by Oxford University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-04-29 with Psychology categories.
Our understanding of how the human brain performs mathematical calculations is far from complete, but in recent years there have been many exciting breakthroughs by scientists all over the world. Now, in The Number Sense, Stanislas Dehaene offers a fascinating look at this recent research, in an enlightening exploration of the mathematical mind. Dehaene begins with the eye-opening discovery that animals--including rats, pigeons, raccoons, and chimpanzees--can perform simple mathematical calculations, and that human infants also have a rudimentary number sense. Dehaene suggests that this rudimentary number sense is as basic to the way the brain understands the world as our perception of color or of objects in space, and, like these other abilities, our number sense is wired into the brain. These are but a few of the wealth of fascinating observations contained here. We also discover, for example, that because Chinese names for numbers are so short, Chinese people can remember up to nine or ten digits at a time--English-speaking people can only remember seven. The book also explores the unique abilities of idiot savants and mathematical geniuses, and we meet people whose minute brain lesions render their mathematical ability useless. This new and completely updated edition includes all of the most recent scientific data on how numbers are encoded by single neurons, and which brain areas activate when we perform calculations. Perhaps most important, The Number Sense reaches many provocative conclusions that will intrigue anyone interested in learning, mathematics, or the mind. "A delight." --Ian Stewart, New Scientist "Read The Number Sense for its rich insights into matters as varying as the cuneiform depiction of numbers, why Jean Piaget's theory of stages in infant learning is wrong, and to discover the brain regions involved in the number sense." --The New York Times Book Review "Dehaene weaves the latest technical research into a remarkably lucid and engrossing investigation. Even readers normally indifferent to mathematics will find themselves marveling at the wonder of minds making numbers." --Booklist
The Number Sense How The Mind Creates Mathematics
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Author : Stanislas Dehaene Research Affiliate Institut National de la Sante et de la Recherche Medicale
language : en
Publisher: Oxford University Press, USA
Release Date : 1997-11-06
The Number Sense How The Mind Creates Mathematics written by Stanislas Dehaene Research Affiliate Institut National de la Sante et de la Recherche Medicale and has been published by Oxford University Press, USA this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997-11-06 with Mathematics categories.
Our understanding of how the human brain performs mathematical calculations is far from complete. But in recent years there have been many exciting scientific discoveries, some aided by new imaging techniques--which allow us for the first time to watch the living mind at work--and others by ingenious experiments conducted by researchers all over the world. There are still perplexing mysteries--how, for instance, do idiot savants perform almost miraculous mathematical feats?--but the picture is growing steadily clearer. In The Number Sense, Stanislas Dehaene offers general readers a first look at these recent stunning discoveries, in an enlightening exploration of the mathematical mind. Dehaene, a mathematician turned cognitive neuropsychologist, begins with the eye-opening discovery that animals--including rats, pigeons, raccoons, and chimpanzees--can perform simple mathematical calculations, and he describes ingenious experiments that show that human infants also have a rudimentary number sense (American scientist Karen Wynn, for instance, using just a few Mickey Mouse toys and a small puppet theater, proved that five-month-old infants already have the ability to add and subtract). Further, Dehaene suggests that this rudimentary number sense is as basic to the way the brain understands the world as our perception of color or of objects in space, and, like these other abilities, our number sense is wired into the brain. But how then did the brain leap from this basic number ability to trigonometry, calculus, and beyond? Dehaene shows that it was the invention of symbolic systems of numerals that started us on the climb to higher mathematics, and in a marvelous chapter he traces the history of numbers, from early times when people indicated a number by pointing to a part of their body (even today, in many societies in New Guinea, the word for six is "wrist"), to early abstract numbers such as Roman numerals (chosen for the ease with which they could be carved into wooden sticks), to modern numbers. On our way, we also discover many fascinating facts: for example, because Chinese names for numbers are so short, Chinese people can remember up to nine or ten digits at a time--English-speaking people can only remember seven. Dehaene also explores the unique abilities of idiot savants and mathematical geniuses, asking what might explain their special mathematical talent. And we meet people whose minute brain lesions render their mathematical ability useless--one man, in fact, who is certain that two and two is three. Using modern imaging techniques (PET scans and MRI), Dehaene reveals exactly where in the brain numerical calculation takes place. But perhaps most important, The Number Sense reaches many provocative conclusions that will intrigue anyone interested in mathematics or the mind. Dehaene argues, for instance, that many of the difficulties that children face when learning math, and which may turn into a full-blown adult "innumeracy," stem from the architecture of our primate brain, which has not evolved for the purpose of doing mathematics. He also shows why the human brain does not work like a computer, and that the physical world is not based on mathematics--rather, mathematics evolved to explain the physical world the way that the eye evolved to provide sight. A truly fascinating look at the crossroads where numbers and neurons intersect, The Number Sense offers an intriguing tour of how the structure of the brain shapes our mathematical abilities, and how our mathematics opens up a window on the human mind.
Reckonings
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Author : Stephen Chrisomalis
language : en
Publisher: MIT Press
Release Date : 2020-12-15
Reckonings written by Stephen Chrisomalis and has been published by MIT Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-12-15 with Mathematics categories.
Insights from the history of numerical notation suggest that how humans write numbers is an active choice involving cognitive and social factors. Over the past 5,000 years, more than 100 methods of numerical notation—distinct ways of writing numbers—have been developed and used by specific communities. Most of these are barely known today; where they are known, they are often derided as cognitively cumbersome and outdated. In Reckonings, Stephen Chrisomalis considers how humans past and present use numerals, reinterpreting historical and archaeological representations of numerical notation and exploring the implications of why we write numbers with figures rather than words. Chrisomalis shows that numeration is a social practice. He argues that written numerals are conceptual tools that are transformed to fit the perceived needs of their users, and that the sorts of cognitive processes that affect decision-making around numerical activity are complex and involve social factors. Drawing on the triple meaning of reckon—to think, to calculate, and to judge—as a framing device, Chrisomalis argues that the history of numeral systems is best considered as a cognitive history of language, writing, mathematics, and technology. Chrisomalis offers seven interlinked essays that are both macro-historical and cross-cultural, with a particular focus, throughout, on Roman numerals. Countering the common narrative that Roman numerals are archaic and clumsy, Chrisomalis presents examples of Roman numeral use in classical, medieval, and early modern contexts. Readers will think more deeply about written numbers as a cognitive technology that each of us uses every single day, and will question the assumption that whatever happened historically was destined to have happened, leading inevitably to the present.