Stephen Chrisomalis - Reckonings: Numerals, Cognition, and History
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Reckonings
Numerals, Cognition, and History
Stephen Chrisomalis
The MIT Press
Cambridge, Massachusetts
London, England
2020 Massachusetts Institute of Technology
All rights reserved. No part of this book may be reproduced in any form by any electronic or mechanical means (including photocopying, recording, or information storage and retrieval) without permission in writing from the publisher.
Library of Congress Cataloging-in-Publication Data is available.
ISBN: 978-0-262-04463-9
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List of Figures
Typology of numerical notations
Narmer mace head (Budge 1911: 36)
Weld-Blundell prism, an Old Babylonian text in Sumerian cuneiform from Larsa, ca. 1800 BCE (source: Sumerian King List, 1800 BC, Larsa, Iraq by Gts-tg is licensed under CC BY-SA 4.0)
Late Classic Maya Stela 5 from Cob, Yucatan, Mexico, drawing by Eric von Euw; President and Fellows of Harvard College, Peabody Museum of Archaeology and Ethnology, PM 2004.15.6.18.9
Columna rostrata of Gaius Duilius (CIL 6.1300; image courtesy of Center for Epigraphical and Palaeographical Studies, The Ohio State University)
National Debt Clock (National Debt Clock by Matthew Bisanz is licensed under CC BY-SA 3.0; source: Wikimedia Commons)
Tally marking at Hanakapiai Beach, Kauai, Hawaii (Hanakapiai Beach Warning Sign by God of War is licensed under CC BY-SA 3.0; source: Wikimedia Commons)
Size ordering of four numerical notations from 1 to 1,000
Depiction of abacus with Roman numerals (Velserus 1682: 819)
Jeton from Nuremberg, 1553, a counter for use with the medieval reckoning board (Rekenpenning Neurenberg rekenaar 1553 by Kees38 is licensed under CC BY-SA 3.0; source: Wikimedia Commons)
Typus arithmeticae, an allegorical woodcut by Gregor Reisch (1503)
Proportion of instances where Roman numerals in English books is preceded by awkward, clumsy, or cumbersome, 18002000 (Google Books Ngram Viewer, http://books.google.com/ngrams)
Crowd-wisdom frequency dependence
Faddish frequency dependence
Networked frequency dependence
Abacus with apices (source: Bibliothque nationale de France, Latin 8663, folio 49v)
Leaf from Caxtons Reynard of 1481with "a2," bottom right, the first printed Western numeral in an English book (STC 20919)
Hieronymus de Sancto Marco, Opusculum , fol. xxix, printed by Richard Pynson in 1505 (STC 13432)
Sequoyah (ca. 17701843) with his syllabary of 85 characters
Cherokee numerical notation developed by Sequoyah
Sequoyahs numerals as annotated in 1839 by John Howard Payne (courtesy of Gilcrease Museum, Tulsa, OK, accession number 4026.312)
Jurchin numerals
Three plates from the second issue of the Cherokee Phoenix , 1828
Lako Bodras numerals for Varang Kshiti
Check written by John Jacob Astor, 1792
Chicago Manual of Style , first edition: rules for writing numbers (University of Chicago Press 1906: 3031)
Variation in frequency of expressions for 1.2 million, 18002000 (Google Books Ngram Viewer, http://books.google.com/ngrams)
Modalities of representing stop and four
Egyptian expressions for nine bows in three different Pyramid Texts (after Vernus 2004: 284)
Linear B tablet from Pylos, P641, with different numerical modalities (drawing by Michael Ventris; image courtesy of the University of London Institute of Classical Studies Ventris Archive (MV 062.3))
Variation in Chinese numerical expressions
Persian variant of siyaq / dewani numerals (Kazem-Zadeh 1915: plate VIII)
Eblaite text with a representation of 182,600 using numeral signs with words (source: Edzard 1981, ARET 02,20)
Sogdian financial text, eighthninth century CE, GXW 04320 (Bi and Sims-Williams 2010: 501; Museum of Renmin University of China, Sogdian document no. 3; Image Bi Bo and Nicholas Sims-Williams)
South Arabian inscription for 6,000 with parallel modalities (DAI Sirwah 20052050)
Fort. 1771, Greek tablet from the Persepolis Fortification Archive, ca. 500 BCE (courtesy of the Oriental Institute of the University of Chicago)
Aramaic lion weight, Nimrud, ca. 725 BCE (BM 91220; image The Trustees of the British Museum)
Etruscan numeral words, dice, and numerical notation
South Carolina eight-dollar bill, 1776
Proposed simplified numerals along with several ancient analogues (Harris 1905: 66)
680-ohm resistor using electronic color code (680 ohms 5% axial resistor by bomazi is licensed under CC BY-SA 2.0; source: Wikimedia Commons)
List of Tables
Sumerian antediluvian king list on the Weld-Blundell prism
Tallying strategies
Conciseness, sign count, and extent (after Chrisomalis 2010: 397)
Roman numerals and Western numerals in early English printed books, 14701534
Cherokee numeral words (after Montgomery-Anderson 2015)
Hybrid Roman numerals in the Helcep Sarracenium
Zeroless numerals from 1 to 120 (11T) (after Foster 1947)
Resistor numeral values
This book has been over a decade in its conceptualization. It began around the time of the publication of my first monograph, Numerical Notation: A Comparative History , in 2010, which is an encyclopedic, dense piece of writing intended for a specialist audience. Discussions with my colleagues suggested that a book that better conveyed both the joy and importance of the subject of numeral systems might interest a broader range of readers, and the talks and essays that grew into this book are a product of those conversations. My thanks to all of you, whether named below or not, for your encouragement throughout this process.
Chapter 1 is a significantly revised version of an article, Constraint, Cognition, and Written Numeration, which appeared in Pragmatics and Cognition 21 (3) (2013): 552572, and appears here courtesy of John Benjamins Publishing Company (Chrisomalis 2013). Earlier versions were presented as talks at Wayne State University. Many thanks to Jrme Rousseau, Andr Costopoulos, Giovanni Bennardo, Todd Meyers, David Olson, Michael Thomas, Summar Saad, and Tyler Brockett for their useful comments on various drafts.
Chapter 2 and chapter 5 began life, in very different ways, as a talk at the Language, Culture, and History conference organized at the University of Wyoming, and later in a heavily revised version as a talk at the Program in World Philology sponsored by the Heyman Center for the Humanities at Columbia University. Many thanks to Leila Monaghan, David Lurie, Sheldon Pollock, the late Michael Silverstein, and the late Bernard Bate for their comments and thoughts on these talks.
Chapter 3 is an expanded and heavily revised version of talks given at the University of Bergen SPIRE workshop, The Cultural Dimensions of Numerical Cognition. Many thanks to Andrea Bender, Marie Coppola, Fiona Jordan, Geoff Saxe, Rafael Nez, Karenleigh Overmann, Dirk Schlimm, and the late Sieghard Beller for their comments. John Bodel, John Dagenais, and Paul Keyser provided additional useful evidence and reflections necessary for the final version of the essay.
Chapter 4 had its genesis in talks given at the Society for Anthropological Sciences annual meetings, while talks at the International Medieval Congress in Kalamazoo, Michigan further expanded these ideas and provided evidentiary support for my suppositions. Thanks to Amalia Gnanadesikan, Shana Worthen, Tom Abel, Jim Plamondon, and David Kronenfeld for conversations and remarks on this work.
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