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Numbers - the Essence
Numbers - the essence A computer consists in essence of a sequence of electrical on/off switches. Big question: How do switches become a computer? ITEC 1000 Introduction to Information Technologies 1 Friday, September 25, 2009 • A single switch is called a bit • A sequence of 8 bits is called a byte • Two or more bytes are often grouped to form word • Modern laptop/desktop standardly will have memory of 1 gigabyte = 1,000,000,000 bytes ITEC 1000 Introduction to Information Technologies 2 Friday, September 25, 2009 Question: How do encode information with switches ? Answer: With numbers - binary numbers using only 0’s and 1’s where for each switch on position = 1 off position = 0 ITEC 1000 Introduction to Information Technologies 3 Friday, September 25, 2009 • For a byte consisting of 8 bits there are a total of 28 = 256 ways to place 0’s and 1’s. Example 0 1 0 1 1 0 1 1 • For each grouping of 4 bits there are 24 = 16 ways to place 0’s and 1’s. • For a byte the first and second groupings of four bits can be represented by two hexadecimal digits • this will be made clear in following slides. ITEC 1000 Introduction to Information Technologies 4 Friday, September 25, 2009 Bits & Bytes imply creation of data and computer analysis of data • storing data (reading) • processing data - arithmetic operations, evaluations & comparisons • output of results ITEC 1000 Introduction to Information Technologies 5 Friday, September 25, 2009 Numeral systems A numeral system is any method of symbolically representing the counting numbers 1, 2, 3, 4, 5, . -
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. -
Migracijske Teme 4/1988
Migracijske teme 15 (1999), 1-2: 63-153 UDK: 809.45-0 Izvorni znanstveni rad Primljeno: 17. 11. 1998. Paolo Agostini University of Padova [email protected] LANGUAGE RECONSTRUCTION – APPLIED TO THE URALIC LANGUAGES* SUMMARY After pointing out the shortcomings and methodological weakness of the general theory of linguistic reconstruction, the author disputes the alleged antiquity of Uralic. Proto-Uralic as recon- structed by the scholars seems to be the sum of a set of features belonging to several distinct language families. The paper examines a number of lexical concordances with historically attested languages and comes to the conclusion that the Proto-Uralic word-stock is the result of a sum of borrowings that took place from the most disparate languages: Balto-Slavic, Old Swedish, several Turkic dialects, Mongolic, Tunguz, Aramaic, Hebrew, Arabic, late Middle Persian dialects, Byzantine Greek and Latin. Yet, other languages may also come into account: Chinese, Caucasian languages as well as lan- guages unknown in present day are possible candidates. A large number of bases of the Uralic word- stock can be easily identified by following a few phonological constraints. The linguistic features of the Uralic daughter-languages seem to show that they originated from a pidgin language spoken along the merchant routes that connected the Silk Road to North- and East-European trade. It is a well-known phenomenon that sometimes, when groups of people speaking different languages come into contact for the first time, a new restricted language system (lingua franca or pidgin) comes into being in order to cater to essential common needs. -
CULTURAL HERITAGE in MIGRATION Published Within the Project Cultural Heritage in Migration
CULTURAL HERITAGE IN MIGRATION Published within the project Cultural Heritage in Migration. Models of Consolidation and Institutionalization of the Bulgarian Communities Abroad funded by the Bulgarian National Science Fund © Nikolai Vukov, Lina Gergova, Tanya Matanova, Yana Gergova, editors, 2017 © Institute of Ethnology and Folklore Studies with Ethnographic Museum – BAS, 2017 © Paradigma Publishing House, 2017 ISBN 978-954-326-332-5 BULGARIAN ACADEMY OF SCIENCES INSTITUTE OF ETHNOLOGY AND FOLKLORE STUDIES WITH ETHNOGRAPHIC MUSEUM CULTURAL HERITAGE IN MIGRATION Edited by Nikolai Vukov, Lina Gergova Tanya Matanova, Yana Gergova Paradigma Sofia • 2017 CONTENTS EDITORIAL............................................................................................................................9 PART I: CULTURAL HERITAGE AS A PROCESS DISPLACEMENT – REPLACEMENT. REAL AND INTERNALIZED GEOGRAPHY IN THE PSYCHOLOGY OF MIGRATION............................................21 Slobodan Dan Paich THE RUSSIAN-LIPOVANS IN ITALY: PRESERVING CULTURAL AND RELIGIOUS HERITAGE IN MIGRATION.............................................................41 Nina Vlaskina CLASS AND RELIGION IN THE SHAPING OF TRADITION AMONG THE ISTANBUL-BASED ORTHODOX BULGARIANS...............................55 Magdalena Elchinova REPRESENTATIONS OF ‘COMPATRIOTISM’. THE SLOVAK DIASPORA POLITICS AS A TOOL FOR BUILDING AND CULTIVATING DIASPORA.............72 Natália Blahová FOLKLORE AS HERITAGE: THE EXPERIENCE OF BULGARIANS IN HUNGARY.......................................................................................................................88 -
Beginnings of Counting and Numbers Tallies and Tokens
Beginnings of Counting and Numbers Tallies and Tokens Picture Link (http://www.flickr.com/photos/quadrofonic/834667550/) Bone Tallies • The Lebombo Bone is a portion of • The radius bone of a wolf, a baboon fibula, discovered in the discovered in Moravia, Border Cave in the Lebombo Czechoslovakia in 1937, and mountains of Swaziland. It dates dated to 30,000 years ago, has to about 35,000 years ago, and fifty‐five deep notches carved has 29 distinct notches. It is into it. Twenty‐five notches of assumed that it tallied the days of similar length, arranged in‐groups a lunar month. of five, followed by a single notch twice as long which appears to • terminate the series. Then Picture Link starting from the next notch, also (http://www.historyforkids.org/learn/africa/science/numbers.htm) twice as long, a new set of notches runs up to thirty. • Picture link (http://books.google.com/books?id=C0Wcb9c6c18C&pg=PA41&lpg=PA41 &dq=wolf+bone+moravia&source=bl&ots=1z5XhaJchP&sig=q_8WROQ1Gz l4‐6PYJ9uaaNHLhOM&hl=en&ei=J8D‐ TZSgIuPTiALxn4CEBQ&sa=X&oi=book_result&ct=result&resnum=4&ved=0 CCsQ6AEwAw) Ishango Bone • Ishango Bone, discovered in 1961 in central Africa. About 20,000 years old. Ishango Bone Patterns • Prime 11 13 17 19 numbers? • Doubling? 11 21 19 9 • Multiplication? • Who knows? 3 6 4 8 10 5 5 7 Lartet Bone • Discovered in Dodogne, France. About 30,000 years old. It has various markings that are neither decorative nor random (different sets are made with different tools, techniques, and stroke directions). -
Wood Identification and Chemistry' Covers the Physicalproperties and Structural Features of Hardwoods and Softwoods
11 DOCUMENT RESUME ED 031 555 VT 007 853 Woodworking Technology. San Diego State Coll., Calif. Dept. of Industrial Arts. Spons Agency-Office of Education (DHEA Washington, D.C. Pub Date Aug 68 Note-252p.; Materials developed at NDEA Inst. for Advanced Studyin Industrial Arts (San Diego, June 24 -Au9ust 2, 1968). EDRS Price MF -$1.00 He -$13.20 Descriptors-Curriculum Development, *Industrial Arts, Instructional Materials, Learning Activities, Lesson Plans, Lumber Industry, Resource Materials, *Resource Units, Summer Institutes, Teaching Codes, *Units of Study (Sublect Fields), *Woodworking Identifiers-*National Defense Education Act TitleXIInstitute, NDEA TitleXIInstitute, Woodworking Technology SIX teaching units which were developed by the 24 institute participantsare given. "Wood Identification and Chemistry' covers the physicalproperties and structural features of hardwoods and softwoods. "Seasoning" explainsair drying, kiln drying, and seven special lumber seasoning processes. "Researchon Laminates" describes the bending of solid wood and wood laminates, beam lamination, lamination adhesives,. andplasticlaminates."Particleboard:ATeachingUnitexplains particleboard manufacturing and the several classes of particleboard and theiruses. "Lumber Merchandising" outhnes lumber grades andsome wood byproducts. "A Teaching Unitin Physical Testing of Joints, Finishes, Adhesives, and Fasterners" describes tests of four common edge pints, finishes, wood adhesives, and wood screws Each of these units includes a bibhography, glossary, and student exercises (EM) M 55, ...k.",z<ONR; z _: , , . "'zr ss\ ss s:Ts s , s' !, , , , zs "" z' s: - 55 Ts 5. , -5, 5,5 . 5, :5,5, s s``s ss ' ,,, 4 ;.< ,s ssA 11111.116; \ ss s, : , \s, s's \ , , 's's \ sz z, ;.:4 1;y: SS lza'itVs."4,z ...':',\\Z'z.,'I,,\ "t"-...,,, `,. -
Lecture 2: Arithmetic
E-320: Teaching Math with a Historical Perspective Oliver Knill, 2010-2017 Lecture 2: Arithmetic The oldest mathematical discipline is arithmetic. It is the theory of the construction and manip- ulation of numbers. The earliest steps were done by Babylonian, Egyptian, Chinese, Indian and Greek thinkers. Building up the number system starts with the natural numbers 1; 2; 3; 4::: which can be added and multiplied. Addition is natural: join 3 sticks to 5 sticks to get 8 sticks. Multiplication ∗ is more subtle: 3 ∗ 4 means to take 3 copies of 4 and get 4 + 4 + 4 = 12 while 4 ∗ 3 means to take 4 copies of 3 to get 3 + 3 + 3 + 3 = 12. The first factor counts the number of operations while the second factor counts the objects. To motivate 3 ∗ 4 = 4 ∗ 3, spacial insight motivates to arrange the 12 objects in a rectangle. This commutativity axiom will be carried over to larger number systems. Realizing an addition and multiplicative structure on the natural numbers requires to define 0 and 1. It leads naturally to more general numbers. There are two major motivations to to build new numbers: we want to 1. invert operations and still get results. 2. solve equations. To find an additive inverse of 3 means solving x + 3 = 0. The answer is a negative number. To solve x ∗ 3 = 1, we get to a rational number x = 1=3. To solve x2 = 2 one need to escape to real numbers. To solve x2 = −2 requires complex numbers. Numbers Operation to complete Examples of equations to solve Natural numbers addition and multiplication 5 + x = 9 Positive fractions addition and -
Tally Sticks, Counting Boards, and Sumerian Proto-Writing John Alan Halloran
Early Numeration - John Alan Halloran - August 10, 2009 - Page 1 Early Numeration - Tally Sticks, Counting Boards, and Sumerian Proto-Writing John Alan Halloran http://www.sumerian.org/ Work on the published version of my Sumerian Lexicon (Logogram Publishing: 2006) has revealed that: 1) the early Sumerians used wooden tally sticks for counting; 2) tally marks led to proto-writing; 3) the Sumerian pictograms for goats and sheep probably derive from tally stick notch conventions; 4) the Uruk period civilization used counting boards; 5) the authors of the proto-cuneiform tablets drew with animal claws or bird talons; 6) the historical Sumerians used clay split tallies as credit instruments; and 7) the Sumerians may sometimes have counted by placing knots or stones on a string. 1. Counting with Wooden Tally Sticks 1.1. The following text caught my attention. It is from The Debate between Sheep and Grain, ETCSL 5.3.2, lines 130-133: "Every night your count is made and your tally-stick put into the ground, so your herdsman can tell people how many ewes there are and how many young lambs, and how many goats and how many young kids." The Sumerian reads: 130 ud šu2-uš-e niñ2-kas7-zu ba-ni-ak-e ñiš 131 ŠID-ma-zu ki i3-tag-tag-ge - the Unicode version has ñiš-šudum- ma-zu 132 na-gada-zu u8 me-a sila4 tur-tur me-a 133 ud5 me-a maš2 tur-tur me-a lu2 mu-un-na-ab-be2 š is read |sh| and ñ is read |ng|. -
Arabic Numeral
CHAPTER 4 Number Representation and Calculation Copyright © 2015, 2011, 2007 Pearson Education, Inc. Section 4.4, Slide 1 4.4 Looking Back at Early Numeration Systems Copyright © 2015, 2011, 2007 Pearson Education, Inc. Section 4.4, Slide 2 Objectives 1. Understand and use the Egyptian system. 2. Understand and use the Roman system. 3. Understand and use the traditional Chinese system. 4. Understand and use the Ionic Greek system. Copyright © 2015, 2011, 2007 Pearson Education, Inc. Section 4.4, Slide 3 The Egyptian Numeration System The Egyptians used the oldest numeration system called hieroglyphic notation. Copyright © 2015, 2011, 2007 Pearson Education, Inc. Section 4.4, Slide 4 Example: Using the Egyptian Numeration System Write the following numeral as a Hindu-Arabic numeral: Solution: Using the table, find the value of each of the Egyptian numerals. Then add them. 1,000,000 + 10,000 + 10,000 + 10 + 10 + 10 + 1 + 1 + 1 + 1 = 1,020,034 Copyright © 2015, 2011, 2007 Pearson Education, Inc. Section 4.4, Slide 5 Example: Using the Egyptian Numeration System Write 1752 as an Egyptian numeral. Solution: First break down the Hindu-Arabic numeral into quantities that match the Egyptian numerals: 1752 = 1000 + 700 + 50 + 2 = 1000 + 100 + 100 + 100 + 100 + 100 + 100 + 100 + 10 + 10 + 10 + 10 + 10 + 1 + 1 Now use the table to find the Egyptian symbol that matches each quantity. Thus, 1752 can be expressed as Copyright © 2015, 2011, 2007 Pearson Education, Inc. Section 4.4, Slide 6 The Roman Numeration System Roman I V X L C D M Numeral Hindu- 1 5 10 50 100 500 1000 Arabic Numeral The Roman numerals were used until the eighteenth century and are still commonly used today for outlining, on clocks, and in numbering some pages in books. -
About Numbers How These Basic Tools Appeared and Evolved in Diverse Cultures by Allen Klinger, Ph.D., New York Iota ’57
About Numbers How these Basic Tools Appeared and Evolved in Diverse Cultures By Allen Klinger, Ph.D., New York Iota ’57 ANY BIRDS AND Representation of quantity by the AUTHOR’S NOTE insects possess a The original version of this article principle of one-to-one correspondence 1 “number sense.” “If is on the web at http://web.cs.ucla. was undoubtedly accompanied, and per- … a bird’s nest con- edu/~klinger/number.pdf haps preceded, by creation of number- mtains four eggs, one may be safely taken; words. These can be divided into two It was written when I was a fresh- but if two are removed, the bird becomes man. The humanities course had an main categories: those that arose before aware of the fact and generally deserts.”2 assignment to write a paper on an- the concept of number unrelated to The fact that many forms of life “sense” thropology. The instructor approved concrete objects, and those that arose number or symmetry may connect to the topic “number in early man.” after it. historic evolution of quantity in differ- At a reunion in 1997, I met a An extreme instance of the devel- classmate from 1954, who remem- ent human societies. We begin with the bered my paper from the same year. opment of number-words before the distinction between cardinal (counting) As a pack rat, somehow I found the abstract concept of number is that of the numbers and ordinal ones (that show original. Tsimshian language of a tribe in British position as in 1st or 2nd). -
Guntram Hazod Introduction1 Hapter Two of the Old Tibetan Chronicle (PT 1287: L.63-117; Hereafter OTC.2)
THE GRAVES OF THE CHIEF MINISTERS OF THE TIBETAN EMPIRE MAPPING CHAPTER TWO OF THE OLD TIBETAN CHRONICLE IN THE LIGHT OF THE EVIDENCE OF THE TIBETAN TUMULUS TRADITION Guntram Hazod Introduction1 hapter two of the Old Tibetan Chronicle (PT 1287: l.63-117; hereafter OTC.2)2 is well known as the short paragraph that C lists the succession of Tibet’s chief ministers (blon che, blon chen [po]) – alternatively rendered as “prime minister” or “grand chancel- lor” in the English literature. Altogether 38 such appointments among nineteen families are recorded from the time of the Yar lung king called Lde Pru bo Gnam gzhung rtsan until the end of the Tibet- an empire in the mid-ninth century. This sequence is conveyed in a continuum that does not distin- guish between the developments before and after the founding of the empire. Only indirectly is there a line that specifies the first twelve ministers as a separate group – as those who were endowed with 1 The resarch for this chapter was conducted within the framework of the two projects “The Burial Mounds of Central Tibet“, parts I and II (financed by the Austrian Science Fund (FWF); FWF P 25066, P 30393; see fn. 2) and “Materiality and Material Culture in Tibet“ (Austrian Academy of Sciences (AAS) project, IF_2015_28) – both based at the Institute for Social Anthropology at the Austrian Academy of Sciences. I wish to thank Joanna Bialek, Per K. Sørensen, and Chris- tian Jahoda for their valuable comments on the drafts of this paper, and J. Bialek especially for her assistance with lingustic issues. -
New Revised Draft/Final Version
The Prehistoric Origins of European Economic Integration George Grantham McGill University In recent decades the conventional dating of the origins of Western Europe’s economic ascendancy to the tenth and eleventh centuries AD has been called in question by archaeological findings and reinterpretations of the early medieval texts indicating significantly higher levels of material prosperity in Antiquity than conventional accounts consider plausible. On the basis of that evidence it appears likely that at its peak the classical economy was almost as large as that of Western Europe on the eve of the Industrial Revolution.1 Population estimates have also been revised upward. Lo Caschio has shown that the conventional estimates of the Italian population that Beloch extracted from late Republican and Augustan censuses to form the foundation of his much-cited conjectural estimate of the population of the Roman Empire significantly underreport the true population.2 That critique is supported by recent archaeological findings indicating that in the more fertile districts of southern Britain and northern Gaul rural population density in the Late Iron Age and the Roman period was as high as in the late seventeenth- century.3 As skeletal evidence shows no significant difference in body size as between 1 For a review of the evidence and its significance for modeling the pre-industrial economy, see George Grantham, ‘Contra Ricardo: On the macroeconomics of Europe’s agrarian age,’ European review of economic history 3 (1999), 199-232. 2 Elio Lo Caschio, ‘The size of the Roman population: Beloch and the meaning of the Augustan census figures,’ Journal of roman studies 84 (1994) pp.