Ancient Indian Mathematical Evolution Since Counting
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On the Origin of the Indian Brahma Alphabet
- ON THE <)|{I<; IN <>F TIIK INDIAN BRAHMA ALPHABET GEORG BtfHLKi; SECOND REVISED EDITION OF INDIAN STUDIES, NO III. TOGETHER WITH TWO APPENDICES ON THE OKU; IN OF THE KHAROSTHI ALPHABET AND OF THK SO-CALLED LETTER-NUMERALS OF THE BRAHMI. WITH TIIKKK PLATES. STRASSBUKi-. K A K 1. I. 1 1M I: \ I I; 1898. I'lintccl liy Adolf Ilcil/.haiisi'ii, Vicniiii. Preface to the Second Edition. .As the few separate copies of the Indian Studies No. Ill, struck off in 1895, were sold very soon and rather numerous requests for additional ones were addressed both to me and to the bookseller of the Imperial Academy, Messrs. Carl Gerold's Sohn, I asked the Academy for permission to issue a second edition, which Mr. Karl J. Trlibner had consented to publish. My petition was readily granted. In addition Messrs, von Holder, the publishers of the Wiener Zeitschrift fur die Kunde des Morgenlandes, kindly allowed me to reprint my article on the origin of the Kharosthi, which had appeared in vol. IX of that Journal and is now given in Appendix I. To these two sections I have added, in Appendix II, a brief review of the arguments for Dr. Burnell's hypothesis, which derives the so-called letter- numerals or numerical symbols of the Brahma alphabet from the ancient Egyptian numeral signs, together with a third com- parative table, in order to include in this volume all those points, which require fuller discussion, and in order to make it a serviceable companion to the palaeography of the Grund- riss. -
Roman Numerals
History of Numbers 1c. I can distinguish between an additive and positional system, and convert between Roman and Hindu-Arabic numbers. Roman Numerals The numeric system represented by Roman numerals originated in ancient Rome (753 BC–476 AD) and remained the usual way of writing numbers throughout Europe well into the Late Middle Ages. By the 11th century, the more efJicient Hindu–Arabic numerals had been introduced into Europe by way of Arab traders. Roman numerals, however, remained in commo use well into the 14th and 15th centuries, even in accounting and other business records (where the actual calculations would have been made using an abacus). Roman numerals are still used today, in certain contexts. See: Modern Uses of Roman Numerals Numbers in this system are represented by combinations of letters from the Latin alphabet. Roman numerals, as used today, are based on seven symbols: The numbers 1 to 10 are expressed in Roman numerals as: I, II, III, IV, V, VI, VII, VIII, IX, X. This an additive system. Numbers are formed by combining symbols and adding together their values. For example, III is three (three ones) and XIII is thirteen (a ten plus three ones). Because each symbol (I, V, X ...) has a Jixed value rather than representing multiples of ten, one hundred and so on (according to the numeral's position) there is no need for “place holding” zeros, as in numbers like 207 or 1066. Using Roman numerals, those numbers are written as CCVII (two hundreds, plus a ive and two ones) and MLXVI (a thousand plus a ifty plus a ten, a ive and a one). -
KHA in ANCIENT INDIAN MATHEMATICS It Was in Ancient
KHA IN ANCIENT INDIAN MATHEMATICS AMARTYA KUMAR DUTTA It was in ancient India that zero received its first clear acceptance as an integer in its own right. In 628 CE, Brahmagupta describes in detail rules of operations with integers | positive, negative and zero | and thus, in effect, imparts a ring structure on integers with zero as the additive identity. The various Sanskrit names for zero include kha, ´s¯unya, p¯urn. a. There was an awareness about the perils of zero and yet ancient Indian mathematicians not only embraced zero as an integer but allowed it to participate in all four arithmetic operations, including as a divisor in a division. But division by zero is strictly forbidden in the present edifice of mathematics. Consequently, verses from ancient stalwarts like Brahmagupta and Bh¯askar¯ac¯arya referring to numbers with \zero in the denominator" shock the modern reader. Certain examples in the B¯ıjagan. ita (1150 CE) of Bh¯askar¯ac¯arya appear as absurd nonsense. But then there was a time when square roots of negative numbers were considered non- existent and forbidden; even the validity of subtracting a bigger number from a smaller number (i.e., the existence of negative numbers) took a long time to gain universal acceptance. Is it not possible that we too have confined ourselves to a certain safe convention regarding the zero and that there could be other approaches where the ideas of Brahmagupta and Bh¯askar¯ac¯arya, and even the examples of Bh¯askar¯ac¯arya, will appear not only valid but even natural? Enterprising modern mathematicians have created elaborate legal (or technical) machinery to overcome the limitations imposed by the prohibition against use of zero in the denominator. -
Part 1: Introduction to The
PREVIEW OF THE IPA HANDBOOK Handbook of the International Phonetic Association: A guide to the use of the International Phonetic Alphabet PARTI Introduction to the IPA 1. What is the International Phonetic Alphabet? The aim of the International Phonetic Association is to promote the scientific study of phonetics and the various practical applications of that science. For both these it is necessary to have a consistent way of representing the sounds of language in written form. From its foundation in 1886 the Association has been concerned to develop a system of notation which would be convenient to use, but comprehensive enough to cope with the wide variety of sounds found in the languages of the world; and to encourage the use of thjs notation as widely as possible among those concerned with language. The system is generally known as the International Phonetic Alphabet. Both the Association and its Alphabet are widely referred to by the abbreviation IPA, but here 'IPA' will be used only for the Alphabet. The IPA is based on the Roman alphabet, which has the advantage of being widely familiar, but also includes letters and additional symbols from a variety of other sources. These additions are necessary because the variety of sounds in languages is much greater than the number of letters in the Roman alphabet. The use of sequences of phonetic symbols to represent speech is known as transcription. The IPA can be used for many different purposes. For instance, it can be used as a way to show pronunciation in a dictionary, to record a language in linguistic fieldwork, to form the basis of a writing system for a language, or to annotate acoustic and other displays in the analysis of speech. -
The Personal Name Here Is Again Obscure. At
342 THE FIRST ARAMAIC INSCRIPTION FROM INDIA 1. 10 : " his conduct " ? 1. 11 : " and also his sons." 1. 12 : the personal name here is again obscure. At the end of the line are traces of the right-hand side of a letter, which might be samekh or beth; if we accept the former, it is possible to vocalize as Pavira-ram, i.e. Pavira-rdja, corresponding to the Sanskrit Pravira- rdja. The name Pravira is well known in epos, and might well be borne by a real man ; and the change of a sonant to a surd consonant, such as that of j to «, is quite common in the North-West dialects. L. D. BARNETT. THE FIRST ARAMAIC INSCRIPTION FROM INDIA I must thank Mr. F. W. Thomas for his great kindness in sending me the photograph taken by Sir J. H. Marshall, and also Dr. Barnett for letting me see his tracing and transliteration. The facsimile is made from the photo- graph, which is as good as it can be. Unfortunately, on the original, the letters are as white as the rest of the marble, and it was necessary to darken them in order to obtain a photograph. This process inti'oduces an element of uncertainty, since in some cases part of a line may have escaped, and in others an accidental scratch may appear as part of a letter. Hence the following passages are more or less doubtful: line 4, 3PI; 1. 6, Tpfl; 1. 8, "123 and y\; 1. 9, the seventh and ninth letters; 1. 10, ID; 1. -
16-Sanskrit-In-JAPAN.Pdf
A rich literary treasure of Sanskrit literature consisting of dharanis, tantras, sutras and other texts has been kept in Japan for nearly 1400 years. Entry of Sanskrit Buddhist scriptures into Japan was their identification with the central axis of human advance. Buddhism opened up unfathomed spheres of thought as soon as it reached Japan officially in AD 552. Prince Shotoku Taishi himself wrote commentaries and lectured on Saddharmapundarika-sutra, Srimala- devi-simhanada-sutra and Vimala-kirt-nirdesa-sutra. They can be heard in the daily recitation of the Japanese up to the day. Palmleaf manuscripts kept at different temples since olden times comprise of texts which carry immeasurable importance from the viewpoint of Sanskrit philology although some of them are incomplete Sanskrit manuscripts crossed the boundaries of India along with the expansion of Buddhist philosophy, art and thought and reached Japan via Central Asia and China. Thousands of Sanskrit texts were translated into Khotanese, Tokharian, Uigur and Sogdian in Central Asia, on their way to China. With destruction of monastic libraries, most of the Sanskrit literature perished leaving behind a large number of fragments which are discovered by the great explorers who went from Germany, Russia, British India, Sweden and Japan. These excavations have uncovered vast quantities of manuscripts in Sanskrit. Only those manuscripts and texts have survived which were taken to Nepal and Tibet or other parts of Asia. Their translations into Tibetan, Chinese and Mongolian fill the gap, but partly. A number of ancient Sanskrit manuscripts are strewn in the monasteries nestling among high mountains and waterless deserts. -
The Unicode Standard, Version 4.0--Online Edition
This PDF file is an excerpt from The Unicode Standard, Version 4.0, issued by the Unicode Consor- tium and published by Addison-Wesley. The material has been modified slightly for this online edi- tion, however the PDF files have not been modified to reflect the corrections found on the Updates and Errata page (http://www.unicode.org/errata/). For information on more recent versions of the standard, see http://www.unicode.org/standard/versions/enumeratedversions.html. Many of the designations used by manufacturers and sellers to distinguish their products are claimed as trademarks. Where those designations appear in this book, and Addison-Wesley was aware of a trademark claim, the designations have been printed in initial capital letters. However, not all words in initial capital letters are trademark designations. The Unicode® Consortium is a registered trademark, and Unicode™ is a trademark of Unicode, Inc. The Unicode logo is a trademark of Unicode, Inc., and may be registered in some jurisdictions. The authors and publisher have taken care in preparation of this book, but make no expressed or implied warranty of any kind and assume no responsibility for errors or omissions. No liability is assumed for incidental or consequential damages in connection with or arising out of the use of the information or programs contained herein. The Unicode Character Database and other files are provided as-is by Unicode®, Inc. No claims are made as to fitness for any particular purpose. No warranties of any kind are expressed or implied. The recipient agrees to determine applicability of information provided. Dai Kan-Wa Jiten used as the source of reference Kanji codes was written by Tetsuji Morohashi and published by Taishukan Shoten. -
Nepali Letters Ka Kha Pair
Nepali Letters Ka Kha Noam addles tropically. Which Roscoe biases so bilaterally that Malcolm sub her Cheshire? Ventilated Hussein shotguns lachrymosely. Materials on nepali, ka is considered to nepali tool is the more consonants Kannada alphabets and pronounce the initial consonant letters, a unique in syllabic writing the schwa is not a question. Tone letter and nepali ka is an otherwise standard ligature may need to collect and common conjunct consonant letters, or on our prior permission. Write in devanagari is written in preetin font widely used in your can find nepali. Bilingual for the letters ka kha syllables are ready to fit in internet about nepali font, where you can be very popular nepali writing system a script. Stop solution for making this page, malayalam joins letters also used to copy the leading to nepali. Passwords can now here once you should be able to the support materials on daraz nepal you are looking for? Leading to read below or as being common conjunct forms, some writers and easily from left to nepali. It suitable unicode and kha can now here once ruled the previously transliterated text area will be a written. Syllabic writing system; in english to the real sound in the sidebar. Fit in indic scripts, with a search videos in the adjacent characters or tirhuta, you to nepali. Copyright the universal history of what you know how those words into preeti nepali is for? Fuzzy phonetic alphabet, it is through pure ligatures are other? Appended to convert the letters kha is not an historic period or tirhuta, then please check the better you will allow you can find the sounds. -
Crowdsourcing
CROWDSOURCING The establishment of the ZerOrigIndia Foundation is predicated on a single premise, namely, that our decades-long studies indicate that there are sound reasons to assume that facilitating further independent scientific research into the origin of the zero digit as numeral may lead to theoretical insights and practical innovations equal to or perhaps even exceeding the revolutionary progress to which the historic emergence of the zero digit in India somewhere between 200 BCE and 500 CE has led across the planet, in the fields of mathematics, science and technology since its first emergence. No one to date can doubt the astounding utility of the tenth and last digit to complete the decimal system, yet the origin of the zero digit is shrouded in mystery to this day. It is high time, therefore, that a systematic and concerted effort is undertaken by a multidisciplinary team of experts to unearth any extant evidence bearing on the origin of the zero digit in India. The ZerOrigIndia Foundation is intended to serve as instrument to collect the requisite funds to finance said independent scientific research in a timely and effective manner. Research Academics and researchers worldwide are invited to join our efforts to unearth any extant evidence of the zero digit in India. The ZerOrigIndia Foundation will facilitate the research in various ways, chief among which is to engage in fundraising to finance projects related to our objective. Academics and researchers associated with reputed institutions of higher learning are invited to monitor progress reported by ZerOrigIndia Foundation, make suggestions and/or propose their own research projects to achieve the avowed aim. -
An Introduction to Indic Scripts
An Introduction to Indic Scripts Richard Ishida W3C [email protected] HTML version: http://www.w3.org/2002/Talks/09-ri-indic/indic-paper.html PDF version: http://www.w3.org/2002/Talks/09-ri-indic/indic-paper.pdf Introduction This paper provides an introduction to the major Indic scripts used on the Indian mainland. Those addressed in this paper include specifically Bengali, Devanagari, Gujarati, Gurmukhi, Kannada, Malayalam, Oriya, Tamil, and Telugu. I have used XHTML encoded in UTF-8 for the base version of this paper. Most of the XHTML file can be viewed if you are running Windows XP with all associated Indic font and rendering support, and the Arial Unicode MS font. For examples that require complex rendering in scripts not yet supported by this configuration, such as Bengali, Oriya, and Malayalam, I have used non- Unicode fonts supplied with Gamma's Unitype. To view all fonts as intended without the above you can view the PDF file whose URL is given above. Although the Indic scripts are often described as similar, there is a large amount of variation at the detailed implementation level. To provide a detailed account of how each Indic script implements particular features on a letter by letter basis would require too much time and space for the task at hand. Nevertheless, despite the detail variations, the basic mechanisms are to a large extent the same, and at the general level there is a great deal of similarity between these scripts. It is certainly possible to structure a discussion of the relevant features along the same lines for each of the scripts in the set. -
A STUDY of WRITING Oi.Uchicago.Edu Oi.Uchicago.Edu /MAAM^MA
oi.uchicago.edu A STUDY OF WRITING oi.uchicago.edu oi.uchicago.edu /MAAM^MA. A STUDY OF "*?• ,fii WRITING REVISED EDITION I. J. GELB Phoenix Books THE UNIVERSITY OF CHICAGO PRESS oi.uchicago.edu This book is also available in a clothbound edition from THE UNIVERSITY OF CHICAGO PRESS TO THE MOKSTADS THE UNIVERSITY OF CHICAGO PRESS, CHICAGO & LONDON The University of Toronto Press, Toronto 5, Canada Copyright 1952 in the International Copyright Union. All rights reserved. Published 1952. Second Edition 1963. First Phoenix Impression 1963. Printed in the United States of America oi.uchicago.edu PREFACE HE book contains twelve chapters, but it can be broken up structurally into five parts. First, the place of writing among the various systems of human inter communication is discussed. This is followed by four Tchapters devoted to the descriptive and comparative treatment of the various types of writing in the world. The sixth chapter deals with the evolution of writing from the earliest stages of picture writing to a full alphabet. The next four chapters deal with general problems, such as the future of writing and the relationship of writing to speech, art, and religion. Of the two final chapters, one contains the first attempt to establish a full terminology of writing, the other an extensive bibliography. The aim of this study is to lay a foundation for a new science of writing which might be called grammatology. While the general histories of writing treat individual writings mainly from a descriptive-historical point of view, the new science attempts to establish general principles governing the use and evolution of writing on a comparative-typological basis. -
Numerical Notation: a Comparative History
This page intentionally left blank Numerical Notation Th is book is a cross-cultural reference volume of all attested numerical notation systems (graphic, nonphonetic systems for representing numbers), encompassing more than 100 such systems used over the past 5,500 years. Using a typology that defi es progressive, unilinear evolutionary models of change, Stephen Chrisomalis identifi es fi ve basic types of numerical notation systems, using a cultural phylo- genetic framework to show relationships between systems and to create a general theory of change in numerical systems. Numerical notation systems are prima- rily representational systems, not computational technologies. Cognitive factors that help explain how numerical systems change relate to general principles, such as conciseness and avoidance of ambiguity, which also apply to writing systems. Th e transformation and replacement of numerical notation systems relate to spe- cifi c social, economic, and technological changes, such as the development of the printing press and the expansion of the global world-system. Stephen Chrisomalis is an assistant professor of anthropology at Wayne State Uni- versity in Detroit, Michigan. He completed his Ph.D. at McGill University in Montreal, Quebec, where he studied under the late Bruce Trigger. Chrisomalis’s work has appeared in journals including Antiquity, Cambridge Archaeological Jour- nal, and Cross-Cultural Research. He is the editor of the Stop: Toutes Directions project and the author of the academic weblog Glossographia. Numerical Notation A Comparative History Stephen Chrisomalis Wayne State University CAMBRIDGE UNIVERSITY PRESS Cambridge, New York, Melbourne, Madrid, Cape Town, Singapore, São Paulo, Delhi, Dubai, Tokyo Cambridge University Press The Edinburgh Building, Cambridge CB2 8RU, UK Published in the United States of America by Cambridge University Press, New York www.cambridge.org Information on this title: www.cambridge.org/9780521878180 © Stephen Chrisomalis 2010 This publication is in copyright.