Tally Sticks, Counting Boards, and Sumerian Proto-Writing John Alan Halloran
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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). -
Inventing Your Own Number System
Inventing Your Own Number System Through the ages people have invented many different ways to name, write, and compute with numbers. Our current number system is based on place values corresponding to powers of ten. In principle, place values could correspond to any sequence of numbers. For example, the places could have values corre- sponding to the sequence of square numbers, triangular numbers, multiples of six, Fibonacci numbers, prime numbers, or factorials. The Roman numeral system does not use place values, but the position of numerals does matter when determining the number represented. Tally marks are a simple system, but representing large numbers requires many strokes. In our number system, symbols for digits and the positions they are located combine to represent the value of the number. It is possible to create a system where symbols stand for operations rather than values. For example, the system might always start at a default number and use symbols to stand for operations such as doubling, adding one, taking the reciprocal, dividing by ten, squaring, negating, or any other specific operations. Create your own number system. What symbols will you use for your numbers? How will your system work? Demonstrate how your system could be used to perform some of the following functions. • Count from 0 up to 100 • Compare the sizes of numbers • Add and subtract whole numbers • Multiply and divide whole numbers • Represent fractional values • Represent irrational numbers (such as π) What are some of the advantages of your system compared with other systems? What are some of the disadvantages? If you met aliens that had developed their own number system, how might their mathematics be similar to ours and how might it be different? Make a list of some math facts and procedures that you have learned. -
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"-...,,, `,. -
Numeration Systems Reminder : If a and M Are Whole Numbers Then Exponential Expression Amor a to the Mth Power Is M = ⋅⋅⋅⋅⋅ Defined by A Aaa
MA 118 – Section 3.1: Numeration Systems Reminder : If a and m are whole numbers then exponential expression amor a to the mth power is m = ⋅⋅⋅⋅⋅ defined by a aaa... aa . m times Number a is the base ; m is the exponent or power . Example : 53 = Definition: A number is an abstract idea that indicates “how many”. A numeral is a symbol used to represent a number. A System of Numeration consists of a set of basic numerals and rules for combining them to represent numbers. 1 Section 3.1: Numeration Systems The timeline indicates recorded writing about 10,000 years ago between 4,000–3,000 B.C. The Ishango Bone provides the first evidence of human counting, dated 20,000 years ago. I. Tally Numeration System Example: Write the first 12 counting numbers with tally marks. In a tally system, there is a one-to-one correspondence between marks and items being counted. What are the advantages and drawbacks of a Tally Numeration System? 2 Section 3.1: Numeration Systems (continued) II. Egyptian Numeration System Staff Yoke Scroll Lotus Pointing Fish Amazed (Heel Blossom Finger (Polywog) (Astonished) Bone) Person Example : Page 159 1 b, 2b Example : Write 3248 as an Egyptian numeral. What are the advantages and drawbacks of the Egyptian System? 3 Section 3.1: Numeration Systems (continued) III. Roman Numeral System Roman Numerals I V X L C D M Indo-Arabic 1 5 10 50 100 500 1000 If a symbol for a lesser number is written to the left of a symbol for a greater number, then the lesser number is subtracted. -
Babylonian Numeration
Babylonian Numeration Dominic Klyve ∗ October 9, 2020 You may know that people have developed several different ways to represent numbers throughout history. The simplest is probably to use tally marks, so that the first few numbers might be represented like this: and so on. You may also have learned a more efficient way to make tally marks at some point, but the method above is almost certainly the first that humans ever used. Some ancient artifacts, including one known as the \Ishango Bone," suggest that people were using symbols like these over 20,000 years ago!1 By 2000 BCE, the Sumerian civilization had developed a considerably more sophisticated method of writing numbers|a method which in many ways is quite unlike what we use today. Their method was adopted by the Babylonians after they conquered the Sumerians, and today the symbols used in this system are usually referred to as Babylonian numerals. Fortunately, we have a very good record of the way the Sumerians (and Babylonians) wrote their numbers. They didn't use paper, but instead used a small wedge-shaped (\cuneiform") tool to put marks into tablets made of mud. If these tablets were baked briefly, they hardened into a rock-like material which could survive with little damage for thousands of years. On the next page you will find a recreation of a real tablet, presented close to its actual size. It was discovered in the Sumerian city of Nippur (in modern-day Iraq), and dates to around 1500 BCE. We're not completely sure what this is, but most scholars suspect that it is a homework exercise, preserved for thousands of years. -
UEB Guidelines for Technical Material
Guidelines for Technical Material Unified English Braille Guidelines for Technical Material This version updated October 2008 ii Last updated October 2008 iii About this Document This document has been produced by the Maths Focus Group, a subgroup of the UEB Rules Committee within the International Council on English Braille (ICEB). At the ICEB General Assembly in April 2008 it was agreed that the document should be released for use internationally, and that feedback should be gathered with a view to a producing a new edition prior to the 2012 General Assembly. The purpose of this document is to give transcribers enough information and examples to produce Maths, Science and Computer notation in Unified English Braille. This document is available in the following file formats: pdf, doc or brf. These files can be sourced through the ICEB representatives on your local Braille Authorities. Please send feedback on this document to ICEB, again through the Braille Authority in your own country. Last updated October 2008 iv Guidelines for Technical Material 1 General Principles..............................................................................................1 1.1 Spacing .......................................................................................................1 1.2 Underlying rules for numbers and letters.....................................................2 1.3 Print Symbols ..............................................................................................3 1.4 Format.........................................................................................................3 -
The Dozenal Package, V6.0
The dozenal Package, v6.0 Donald P. Goodman III June 27, 2015 Abstract The dozenal package provides some simple mechanisms for working with the dozenal (duodecimal or \base 12") numerical system. It redefines all basic LATEX counters, provides a command for converting arbitrary decimal numbers into dozenal, and provides new, real METAFONT characters for ten and eleven, though the commands for producing them can be redefined to produce any figure. As of v2.0, it also includes Type 1 versions of the fonts, selected (as of v5.0) with the typeone package option. This package uses the \basexii algorithm by David Kastrup. Contents 1 Introduction 1 2 Basic Functionality 2 3 Base Conversion 2 4 Dozenal Characters and Fonts 5 4.1 Shorthands for Dozenal Characters . 5 4.2 The dozenal Fonts........................... 5 5 Package Options 6 6 Implementation 6 1 Introduction While most would probably call it at best overoptimistic and at worst foolish, some people (the author included) do still find themselves attracted to the dozenal (base-twelve) system. These people, however, have been pretty hard up1 in the LATEX world. There is no package file available which produces dozenal counters, like page and chapter numbers, nor were there any (I made a pretty diligent 1This is an Americanism for \out of luck" or \in difficult circumstances," for those who do not know. 1 search) dozenal characters for ten and eleven, leaving dozenalists forced to use such makeshift ugliness as the \X/E" or \T/E" or \*/#" or whatever other standard they decided to use. While this sort of thing may be acceptable in ASCII, it's absolutely unacceptable in a beautiful, typeset document. -
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. -
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. -
Maya Math, Maya Indians and Indian Maya
MAYA MATH, MAYA INDIANS AND INDIAN MAYA: REFLECTIONS ON NUMBERS, HISTORY AND RELIGION By Abdul Hai Khalid Professor Department of Mathematics Niagara College, Welland, Ontario, Canada Summary The Maya culture of Central America invented an advanced, base-20, place value based number system, using a symbol for zero, almost at the same time as our, base-10, ‘Hindu-Arabic’ numerals were invented in India. This presentation describes the Maya number system and places it in the historical context of the development of other number systems around the world, e.g., Egyptian, Roman, Mesopotamian, Chinese and Indian etc. The ease, or difficulty, of the basic arithmetic operations, in different number systems, is discussed. The history of the spread of the ‘Hindu-Arabic’ numerals from India to the Middle East to Europe is described. The implications of an advanced number system on the philosophies, religions and world-views of different cultures are discussed. Contents Who are the Maya? Maya Mathematics Maya Calendar Number Systems Around the World Additive Multiplicative Place Value Based Spread of Indian Numerals Numbers, History and Religion WHO are maya ? Maya people live in southern Mexico and the central American countries of Guatemala, Belize, Honduras and El Salvador. Ancient Maya culture flourished in this area between 1000 B.C. and 1000 A.D. The ruins of many ancient Maya cities have been found in this area. Some of these are Chichen Itza, Coba, Tulum, Palenque and Tikal etc. These cities contain pyramids, temples, palaces, ball courts