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Positional Notation Or Trigonometry [2, 13]
The Greatest Mathematical Discovery? David H. Bailey∗ Jonathan M. Borweiny April 24, 2011 1 Introduction Question: What mathematical discovery more than 1500 years ago: • Is one of the greatest, if not the greatest, single discovery in the field of mathematics? • Involved three subtle ideas that eluded the greatest minds of antiquity, even geniuses such as Archimedes? • Was fiercely resisted in Europe for hundreds of years after its discovery? • Even today, in historical treatments of mathematics, is often dismissed with scant mention, or else is ascribed to the wrong source? Answer: Our modern system of positional decimal notation with zero, to- gether with the basic arithmetic computational schemes, which were discov- ered in India prior to 500 CE. ∗Bailey: Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA. Email: [email protected]. This work was supported by the Director, Office of Computational and Technology Research, Division of Mathematical, Information, and Computational Sciences of the U.S. Department of Energy, under contract number DE-AC02-05CH11231. yCentre for Computer Assisted Research Mathematics and its Applications (CARMA), University of Newcastle, Callaghan, NSW 2308, Australia. Email: [email protected]. 1 2 Why? As the 19th century mathematician Pierre-Simon Laplace explained: It is India that gave us the ingenious method of expressing all numbers by means of ten symbols, each symbol receiving a value of position as well as an absolute value; a profound and important idea which appears so simple to us now that we ignore its true merit. But its very sim- plicity and the great ease which it has lent to all computations put our arithmetic in the first rank of useful inventions; and we shall appre- ciate the grandeur of this achievement the more when we remember that it escaped the genius of Archimedes and Apollonius, two of the greatest men produced by antiquity. -
Kharosthi Manuscripts: a Window on Gandharan Buddhism*
KHAROSTHI MANUSCRIPTS: A WINDOW ON GANDHARAN BUDDHISM* Andrew GLASS INTRODUCTION In the present article I offer a sketch of Gandharan Buddhism in the centuries around the turn of the common era by looking at various kinds of evidence which speak to us across the centuries. In doing so I hope to shed a little light on an important stage in the transmission of Buddhism as it spread from India, through Gandhara and Central Asia to China, Korea, and ultimately Japan. In particular, I will focus on the several collections of Kharo~thi manuscripts most of which are quite new to scholarship, the vast majority of these having been discovered only in the past ten years. I will also take a detailed look at the contents of one of these manuscripts in order to illustrate connections with other text collections in Pali and Chinese. Gandharan Buddhism is itself a large topic, which cannot be adequately described within the scope of the present article. I will therefore confine my observations to the period in which the Kharo~thi script was used as a literary medium, that is, from the time of Asoka in the middle of the third century B.C. until about the third century A.D., which I refer to as the Kharo~thi Period. In addition to looking at the new manuscript materials, other forms of evidence such as inscriptions, art and architecture will be touched upon, as they provide many complementary insights into the Buddhist culture of Gandhara. The travel accounts of the Chinese pilgrims * This article is based on a paper presented at Nagoya University on April 22nd 2004. -
Tai Lü / ᦺᦑᦟᦹᧉ Tai Lùe Romanization: KNAB 2012
Institute of the Estonian Language KNAB: Place Names Database 2012-10-11 Tai Lü / ᦺᦑᦟᦹᧉ Tai Lùe romanization: KNAB 2012 I. Consonant characters 1 ᦀ ’a 13 ᦌ sa 25 ᦘ pha 37 ᦤ da A 2 ᦁ a 14 ᦍ ya 26 ᦙ ma 38 ᦥ ba A 3 ᦂ k’a 15 ᦎ t’a 27 ᦚ f’a 39 ᦦ kw’a 4 ᦃ kh’a 16 ᦏ th’a 28 ᦛ v’a 40 ᦧ khw’a 5 ᦄ ng’a 17 ᦐ n’a 29 ᦜ l’a 41 ᦨ kwa 6 ᦅ ka 18 ᦑ ta 30 ᦝ fa 42 ᦩ khwa A 7 ᦆ kha 19 ᦒ tha 31 ᦞ va 43 ᦪ sw’a A A 8 ᦇ nga 20 ᦓ na 32 ᦟ la 44 ᦫ swa 9 ᦈ ts’a 21 ᦔ p’a 33 ᦠ h’a 45 ᧞ lae A 10 ᦉ s’a 22 ᦕ ph’a 34 ᦡ d’a 46 ᧟ laew A 11 ᦊ y’a 23 ᦖ m’a 35 ᦢ b’a 12 ᦋ tsa 24 ᦗ pa 36 ᦣ ha A Syllable-final forms of these characters: ᧅ -k, ᧂ -ng, ᧃ -n, ᧄ -m, ᧁ -u, ᧆ -d, ᧇ -b. See also Note D to Table II. II. Vowel characters (ᦀ stands for any consonant character) C 1 ᦀ a 6 ᦀᦴ u 11 ᦀᦹ ue 16 ᦀᦽ oi A 2 ᦰ ( ) 7 ᦵᦀ e 12 ᦵᦀᦲ oe 17 ᦀᦾ awy 3 ᦀᦱ aa 8 ᦶᦀ ae 13 ᦺᦀ ai 18 ᦀᦿ uei 4 ᦀᦲ i 9 ᦷᦀ o 14 ᦀᦻ aai 19 ᦀᧀ oei B D 5 ᦀᦳ ŭ,u 10 ᦀᦸ aw 15 ᦀᦼ ui A Indicates vowel shortness in the following cases: ᦀᦲᦰ ĭ [i], ᦵᦀᦰ ĕ [e], ᦶᦀᦰ ăe [ ∎ ], ᦷᦀᦰ ŏ [o], ᦀᦸᦰ ăw [ ], ᦀᦹᦰ ŭe [ ɯ ], ᦵᦀᦲᦰ ŏe [ ]. -
Malayalam Range: 0D00–0D7F
Malayalam Range: 0D00–0D7F This file contains an excerpt from the character code tables and list of character names for The Unicode Standard, Version 14.0 This file may be changed at any time without notice to reflect errata or other updates to the Unicode Standard. See https://www.unicode.org/errata/ for an up-to-date list of errata. See https://www.unicode.org/charts/ for access to a complete list of the latest character code charts. See https://www.unicode.org/charts/PDF/Unicode-14.0/ for charts showing only the characters added in Unicode 14.0. See https://www.unicode.org/Public/14.0.0/charts/ for a complete archived file of character code charts for Unicode 14.0. Disclaimer These charts are provided as the online reference to the character contents of the Unicode Standard, Version 14.0 but do not provide all the information needed to fully support individual scripts using the Unicode Standard. For a complete understanding of the use of the characters contained in this file, please consult the appropriate sections of The Unicode Standard, Version 14.0, online at https://www.unicode.org/versions/Unicode14.0.0/, as well as Unicode Standard Annexes #9, #11, #14, #15, #24, #29, #31, #34, #38, #41, #42, #44, #45, and #50, the other Unicode Technical Reports and Standards, and the Unicode Character Database, which are available online. See https://www.unicode.org/ucd/ and https://www.unicode.org/reports/ A thorough understanding of the information contained in these additional sources is required for a successful implementation. -
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. -
Punjabi Machine Transliteration Muhammad Ghulam Abbas Malik
Punjabi Machine Transliteration Muhammad Ghulam Abbas Malik To cite this version: Muhammad Ghulam Abbas Malik. Punjabi Machine Transliteration. 21st international Conference on Computational Linguistics (COLING) and the 44th Annual Meeting of the ACL, Jul 2006, Sydney, France. pp.1137-1144. hal-01002160 HAL Id: hal-01002160 https://hal.archives-ouvertes.fr/hal-01002160 Submitted on 15 Jan 2018 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. Punjabi Machine Transliteration M. G. Abbas Malik Department of Linguistics Denis Diderot, University of Paris 7 Paris, France [email protected] Transliteration refers to phonetic translation Abstract across two languages with different writing sys- tems (Knight & Graehl, 1998), such as Arabic to Machine Transliteration is to transcribe a English (Nasreen & Leah, 2003). Most prior word written in a script with approximate work has been done for Machine Translation phonetic equivalence in another lan- (MT) (Knight & Leah, 97; Paola & Sanjeev, guage. It is useful for machine transla- 2003; Knight & Stall, 1998) from English to tion, cross-lingual information retrieval, other major languages of the world like Arabic, multilingual text and speech processing. Chinese, etc. for cross-lingual information re- Punjabi Machine Transliteration (PMT) trieval (Pirkola et al, 2003), for the development is a special case of machine translitera- of multilingual resources (Yan et al, 2003; Kang tion and is a process of converting a word & Kim, 2000) and for the development of cross- from Shahmukhi (based on Arabic script) lingual applications. -
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. -
Data Issues in English-To-Hindi Machine Translation
Data Issues in English-to-Hindi Machine Translation Ondřej Bojar, Pavel Straňák, Daniel Zeman Univerzita Karlova v Praze, Ústav formální a aplikované lingvistiky Malostranské náměstí 25, CZ-11800 Praha {bojar|stranak|zeman}@ufal.mff.cuni.cz http://ufal.mff.cuni.cz/umc/ Abstract Statistical machine translation to morphologically richer languages is a challenging task and more so if the source A dataset originally collected for the DARPA-TIDES surprise- and target languages differ in word order. Current state-of-the art MT systems thus deliver mediocre results. language contest in 2002, later refined at IIIT Hyderabad and Adding more parallel data often helps improve the results; if it does not, it may be caused by various problems such provided for the NLP Tools Contest at ICON 2008. Corpus Sentences En Tokens Hi Tokens as different domains, bad alignment or noise in the new data. We evaluate several available parallel data sources Tides.train 50,000 1,226,144 1,312,435 A journalist Daniel Pipes' website (http://www.danielpipes.org/) and provide cross-evaluation results on their combinations using two freely available statistical MT systems. We Tides.dev 1,000 22,485 24,363 demonstrate various problems encountered in the data and describe automatic methods of data cleaning and limited-domain articles about the Middle East. Written in English, Tides.test 1,000 27,169 28,574 normalization. We also show that the contents of two independently distributed data sets can unexpectedly overlap, many of them translated to up to 25 other languages. which negatively affects translation quality. Together with the error analysis, we also present a new tool for viewing Daniel Pipes 6,761 176,392 122,108 Monolingual, parallel and annotated corpora for fourteen South Emille 3,501 55,660 71,010 aligned corpora, which makes it easier to detect difficult parts in the data even for a developer not speaking the Asian languages (including Hindi) and English. -
The Ramayana by R.K. Narayan
Table of Contents About the Author Title Page Copyright Page Introduction Dedication Chapter 1 - RAMA’S INITIATION Chapter 2 - THE WEDDING Chapter 3 - TWO PROMISES REVIVED Chapter 4 - ENCOUNTERS IN EXILE Chapter 5 - THE GRAND TORMENTOR Chapter 6 - VALI Chapter 7 - WHEN THE RAINS CEASE Chapter 8 - MEMENTO FROM RAMA Chapter 9 - RAVANA IN COUNCIL Chapter 10 - ACROSS THE OCEAN Chapter 11 - THE SIEGE OF LANKA Chapter 12 - RAMA AND RAVANA IN BATTLE Chapter 13 - INTERLUDE Chapter 14 - THE CORONATION Epilogue Glossary THE RAMAYANA R. K. NARAYAN was born on October 10, 1906, in Madras, South India, and educated there and at Maharaja’s College in Mysore. His first novel, Swami and Friends (1935), and its successor, The Bachelor of Arts (1937), are both set in the fictional territory of Malgudi, of which John Updike wrote, “Few writers since Dickens can match the effect of colorful teeming that Narayan’s fictional city of Malgudi conveys; its population is as sharply chiseled as a temple frieze, and as endless, with always, one feels, more characters round the corner.” Narayan wrote many more novels set in Malgudi, including The English Teacher (1945), The Financial Expert (1952), and The Guide (1958), which won him the Sahitya Akademi (India’s National Academy of Letters) Award, his country’s highest honor. His collections of short fiction include A Horse and Two Goats, Malgudi Days, and Under the Banyan Tree. Graham Greene, Narayan’s friend and literary champion, said, “He has offered me a second home. Without him I could never have known what it is like to be Indian.” Narayan’s fiction earned him comparisons to the work of writers including Anton Chekhov, William Faulkner, O. -
Second Language Writing System Word Recognition (With a Focus on Lao)
Second Language Writing System Word Recognition (with a focus on Lao) Christine Elliott University of Wisconsin-Madison Abstract Learning a second language (L2) with a script different from the learner’s first language (L1) presents unique challenges for both stu- dent and teacher. This paper looks at current theory and research examining issues of second language writing system (L2WS) acquisi- tion, particularly issues pertaining to decoding and word recognition1 by adult learners. I argue that the importance of word recognition and decoding in fluent L1 and L2 reading has been overshadowed for several decades by a focus on research looking at top-down reading processes. Although top-down reading processes and strategies are clearly components of successful L2 reading, I argue that more atten- tion needs to be given to bottom-up processing skills, particularly for beginning learners of an L2 that uses a script that is different from their L1. I use the example of learning Lao as a second language writing system where possible and suggest preliminary pedagogical implications. Introduction Second language writing systems have increasingly become the focus of a growing body of research drawing on the fields of psy- chology, education, linguistics, and second language acquisition, among others. The term writing system is used to refer to the ways in which written symbols represent language in a systematic way (Cook and Bassetti, 2005). Further, a writing system can be discussed in terms of both its script and its orthography. Cook and Bassetti de- fine script as the physical implementation of a writing system (i.e. the written symbols) and orthography as “the rules for using a script in a 1 Following Koda (2005), I define word recognition as “the process of extract- ing lexical information from graphic displays of words,” and decoding as the specific process of extracting phonological information. -
The Formal Kharoṣṭhī Script from the Northern Tarim Basin in Northwest
Acta Orientalia Hung. 73 (2020) 3, 335–373 DOI: 10.1556/062.2020.00015 Th e Formal Kharoṣṭhī script from the Northern Tarim Basin in Northwest China may write an Iranian language1 FEDERICO DRAGONI, NIELS SCHOUBBEN and MICHAËL PEYROT* L eiden University Centre for Linguistics, Universiteit Leiden, Postbus 9515, 2300 RA Leiden, Th e Netherlands E-mail: [email protected]; [email protected]; *Corr esponding Author: [email protected] Received: February 13, 2020 •Accepted: May 25, 2020 © 2020 The Authors ABSTRACT Building on collaborative work with Stefan Baums, Ching Chao-jung, Hannes Fellner and Georges-Jean Pinault during a workshop at Leiden University in September 2019, tentative readings are presented from a manuscript folio (T II T 48) from the Northern Tarim Basin in Northwest China written in the thus far undeciphered Formal Kharoṣṭhī script. Unlike earlier scholarly proposals, the language of this folio can- not be Tocharian, nor can it be Sanskrit or Middle Indic (Gāndhārī). Instead, it is proposed that the folio is written in an Iranian language of the Khotanese-Tumšuqese type. Several readings are proposed, but a full transcription, let alone a full translation, is not possible at this point, and the results must consequently remain provisional. KEYWORDS Kharoṣṭhī, Formal Kharoṣṭhī, Khotanese, Tumšuqese, Iranian, Tarim Basin 1 We are grateful to Stefan Baums, Chams Bernard, Ching Chao-jung, Doug Hitch, Georges-Jean Pinault and Nicholas Sims-Williams for very helpful discussions and comments on an earlier draft. We also thank the two peer-reviewers of the manuscript. One of them, Richard Salomon, did not wish to remain anonymous, and espe- cially his observation on the possible relevance of Khotan Kharoṣṭhī has proved very useful. -
Designing Devanagari Type
Designing Devanagari type The effect of technological restrictions on current practice Kinnat Sóley Lydon BA degree final project Iceland Academy of the Arts Department of Design and Architecture Designing Devanagari type: The effect of technological restrictions on current practice Kinnat Sóley Lydon Final project for a BA degree in graphic design Advisor: Gunnar Vilhjálmsson Graphic design Department of Design and Architecture December 2015 This thesis is a 6 ECTS final project for a Bachelor of Arts degree in graphic design. No part of this thesis may be reproduced in any form without the express consent of the author. Abstract This thesis explores the current process of designing typefaces for Devanagari, a script used to write several languages in India and Nepal. The typographical needs of the script have been insufficiently met through history and many Devanagari typefaces are poorly designed. As the various printing technologies available through the centuries have had drastic effects on the design of Devanagari, the thesis begins with an exploration of the printing history of the script. Through this exploration it is possible to understand which design elements constitute the script, and which ones are simply legacies of older technologies. Following the historic overview, the character set and unique behavior of the script is introduced. The typographical anatomy is analyzed, while pointing out specific design elements of the script. Although recent years has seen a rise of interest on the subject of Devanagari type design, literature on the topic remains sparse. This thesis references books and articles from a wide scope, relying heavily on the works of Fiona Ross and her extensive research on non-Latin typography.