#ReckoningWith: diversity in notations scholarship

The #ReckoningWith project was an initiative on Twitter in conjunction with the publication of my book, Reckonings: Numerals, Cognition, and History, aimed at promoting a more diverse range of scholarship on number systems, writing systems, and notations, my core fields of study. There is a clear, almost inescapably obvious bias towards a relatively small coterie of very traditional (white, male, tenured) scholars in this area, and as someone who fits all three of those labels, I have surely been in workshops, conferences, and panels where the broader diversity of the field is absent. And because it’s such a strange and interdisciplinary area, it is very easy to not know about really interesting people doing cool work in some corner or other, and to just fall back on the same default set of citations, hiring practices, invite lists, etc. And that’s a problem of representation that a lot of folks have rightly been talking about – not only in scholarship on notations, of course, but across the academy.

#ReckoningWith aims to start / continue these discussions by highlighting recent work that hasn’t been or wouldn’t often be recognized in the field of notations (broadly understood). I aim especially (though not exclusively) to highlight work by women, untenured / contingent / early-career scholars, and members of minoritized groups in the academy. This isn’t to say that I agree with everything in all of these papers (how could that possibly be so?) but I think they’re worth reading and thinking about. I restricted myself to one article/paper per author, and to work that could be accessed digitally. One known restriction is that I decided to limit my initial selection to English-language material, but there is a case to be made that a more expansive range of languages would further serve these goals. Some of these links will require an institutional subscription, unfortunately – the burden of the paywall is another serious problem, for another day.

If you know of other work that fits these sorts of criteria, definitely let me know.

Here they are, as originally featured on Twitter, in no particular order:

Franka Brueckler and Vladimir Stilinović (2019) discuss the teaching of nondecimal bases in 18th and 19th century European mathematics textbooks. An Early Appearance of Nondecimal Notation in Secondary Education. https://doi.org/10.1007/s00283-019-09960-1

Jocelyn Ahlers (2012) discusses the now-dormant octo-decimal system for counting beads in Elem Pomo in relation to language revitalization. Two eights make sixteen beads: Historical and contemporary ethnography in language revitalization. https://doi.org/10.1086/667450

Paul Keyser (2015) discusses variation in the word order of tens and ones in classical Greek literary texts and its relationship to commercial numeracy. Compound Numbers and Numerals in Greek. https://doi.org/10.1353/syl.2015.0002

Alessandra Petrocchi (2019) compares the transmission of decimal place-value concepts in medieval Sanskrit and Latin mathematical texts. Medieval Literature in Comparative Perspective: Language and Number in Sanskrit and Latin. https://doi.org/10.1525/jmw.2019.120004

Rebecca Benefiel (2010) analyzes fascinating graffiti from Pompeii including ones with Roman numerals, tallying, and numerical play. Dialogues of ancient graffiti in the House of Maius Castricius in Pompeii. https://www.jstor.org/stable/20627644

Luis Miguel Rojas-Berscia @luiberscia and Rita Eloranta (2019) analyze numeral classifiers in South American languages that use counting devices. The Marañón-Huallaga exchange route:‘Stones’ and ‘grains’ as counting devices. https://doi.org/10.20396/liames.v19i0.8655449

Philip Boyes @PhilipJBoyes (2019) analyzes the early Ugaritic cuneiform alphabet as a vernacular resistance strategy to Hittite imperialism. Negotiating Imperialism and Resistance in Late Bronze Age Ugarit: The Rise of Alphabetic Cuneiform. https://doi.org/10.1017/S0959774318000471

Nina Semushina @feyga_tzipa and Azura Fairchild (2019) compare iconicity and handshapes in the numeral systems of sign languages worldwide. Counting with fingers symbolically: basic numerals across sign languages. https://core.ac.uk/download/pdf/228149921.pdf

Gagan Deep Kaur (2019) investigates the symbolic code used by Kashmiri carpet weavers and its linguistic encoding. Linguistic mediation and code-to-weave transformation in Kashmiri carpet weaving. https://doi.org/10.1177/1359183519862585

Rafael Núñez, Kensy Cooperrider @kensycoop, and Jürg Wassmann (2012) work with Yupno speakers to show that the number line is not intuitive and universal. Number concepts without number lines in an indigenous group of Papua New Guinea. https://doi.org/10.1371/journal.pone.0035662

Mallory Matsumoto (2017) proposes a new representational strategy, orthographic semantization, in Maya hieroglyphic texts to transform phonograms into logograms. From sound to symbol: orthographic semantization in Maya hieroglyphic writing. https://doi.org/10.1080/17586801.2017.1335634

Beau Carroll and co-authors (2019) discuss literate and inscriptional practices using the Cherokee syllabic script in an Alabama cave. Talking stones: Cherokee syllabary in Manitou Cave, Alabama. https://doi.org/10.15184/aqy.2019.15

Tareq Ramadan (2019) analyzes the origin of early Islamic epigraphic and iconographic conventions as a tool of political unification. Religious Invocations on Umayyad Lead Seals: Evidence of an Emergent Islamic Lexicon. https://doi.org/10.1086/704439

Jessica Otis @jotis13 (2017) shows that the adoption of Western numerals in early modern England was linked to increasing literacy. “Set Them to the Cyphering Schoole”: Reading, Writing, and Arithmetical Education, circa 1540–1700. https://doi.org/10.1017/jbr.2017.59

Joanne Baron (2018) analyzes the monetization of cacao beans and textiles among the Classic Maya as a numerate practice. Making money in Mesoamerica: Currency production and procurement in the Classic Maya financial system. https://doi.org/10.1002/sea2.12118

Karenleigh Overmann (2015) undertakes a massive cross-cultural comparison of grammatical number systems (singular/plural, e.g.) and numeral systems. Numerosity structures the expression of quantity in lexical numbers and grammatical number. https://doi.org/10.1086/683092

Xiaoli Ouyang (2016) outlines the origin of a hybrid sexagesimal (base-60) place value notation in an Ur III period cuneiform tablet. The Mixture of Sexagesimal Place Value and Metrological Notations on the Ur III Girsu Tablet BM 19027. https://doi.org/10.1086/684975

Melissa Bailey @MelissannBee (2013) uses evidence from Pompeii and Roman literary sources to discuss the link between Roman money and numerical practice. Roman Money and Numerical Practice. https://www.persee.fr/doc/rbph_0035-0818_2013_num_91_1_8413

Cheryl Periton @cherylperiton (2015) replicates and evaluates the algorithms of the medieval English counting table. The medieval counting table revisited: a brief introduction and description of its use during the early modern period. https://doi.org/10.1080/17498430.2014.917392

David Landy, Noah Silbert and Aleah Goldin (2013) show experimentally that respondents estimate large numbers relying heavily on the structure of their number word systems. Estimating large numbers. https://doi.org/10.1111/cogs.12028

Regina Fabry (2019) analyzes arithmetical cognition as an enculturated, embodied, adaptable practice. The cerebral, extra-cerebral bodily, and socio-cultural dimensions of enculturated arithmetical cognition. https://doi.org/10.1007/s11229-019-02238-1

Yoshio Saitô (2020) investigates the use of the Coptic/Egyptian zimam numerals in the Leiden Manuscript, a 14th century Turkic-Mongolic glossary. A Note on a Note: The Inscription in ‘the Leiden Manuscript’of Turkic and Mongolic Glossaries. https://doi.org/10.1163/1878464X-01101003

Jay Crisostomo @cjcrisostomo (2016) discusses Old Babylonian scribal education and copying practices to analyze text-building practices. Writing Sumerian, Creating Texts: Reflections on Text-building Practices in Old Babylonian Schools. https://doi.org/10.1163/15692124-12341271

John C. Ford (2018) analyzes variation in the use of Roman numerals and number words in the Middle English verse romance, Capystranus. Two or III Feet Apart: Oral Recitation, Roman Numerals, and Metrical Regularity in Capystranus. https://doi.org/10.1007/s11061-018-9567-7

Anna Judson @annapjudson (2019) examines orthographic practices in Linear B (Mycenaean) texts to analyze diachronic change and sociolinguistic variation. Orthographic variation as evidence for the development of the Linear B writing system. https://doi.org/10.1075/wll.00025.jud

Tazuko Angela van Berkel @TazukoVanBerkel (2016) investigates the rhetoric of oral arithmetic and numeracy in two classical Greek courtroom speeches. Voiced Mathematics: Orality and Numeracy. https://doi.org/10.1163/9789004329737_016

Piers Kelly @perezkelly (2018) shows that the literate practices of local Southeast Asian scripts serve as technologies of resistance. The art of not being legible. Invented writing systems as technologies of resistance in mainland Southeast Asia. https://doi.org/10.4000/terrain.17103

Ting Lan and Zhanchuan Cai (2020) propose a new use for nonstandard, complex number bases in encoding information for digital image processing. A Novel Image Representation Method Under a Non-Standard Positional Numeral System. https://doi.org/10.1109/TMM.2020.2995258

Perry Sherouse (2014) investigates how Russian numerals, rather than vigesimal Georgian numerals, became naturalized in the context of Georgian telecommunications. Hazardous digits: telephone keypads and Russian numbers in Tbilisi, Georgia. https://doi.org/10.1016/j.langcom.2014.03.001

Helena Miton @HelenaMiton and Olivier Morin (2019) show that more complex European heraldic motifs are more, not less, frequent than simple ones. When iconicity stands in the way of abbreviation: No Zipfian effect for figurative signals. https://doi.org/10.1371/journal.pone.0220793

Josefina Safar and colleagues (2018) analyze variation in the structure of number words in Yucatec Maya sign languages including unusual signs for 20 and 50. Numeral Variation in Yucatec Maya Sign Languages. https://doi.org/10.1353/sls.2018.0014

Bill Mak (2018) analyzes an expansive Greco-Indian astronomical text (jyotiṣa) to show the relationship of Indian and Hellenistic exact sciences. The First Two Chapters of Mīnarāja’s Vrddhayavanajātaka. https://doi.org/10.14989/230621

Lucy Bennison-Chapman (2019) analyzes Neolithic Mesopotamian clay tokens as multifunctional recording devices, not specialized counting tools. Reconsidering ‘Tokens’: The Neolithic Origins of Accounting or Multifunctional, Utilitarian Tools? https://doi.org/10.1017/S0959774318000513

Nerea Fernández Cadenas (2020) analyzes Iberian Visigothic-era slate inscriptions not as Roman numerals but as a local, community-developed numerical system. A critical review of the signs on Visigothic slates: challenging the Roman numerals premise. https://doi.org/10.1080/17546559.2020.1853790

Malgorzata Zadka (2019) outlines a theory that Linear B inscriptions are of mixed syllabic and semasiographic character, as part of an overall communication strategy. Semasiographic principle in Linear B inscriptions. https://doi.org/10.1080/17586801.2019.1588835

Andrea Bréard and Constance Cook (2020) analyze numerical patterns on Shang Dynasty and later artifacts to show continuity in divinatory practices. Cracking bones and numbers: solving the enigma of numerical sequences on ancient Chinese artifacts. https://doi.org/10.1007/s00407-019-00245-9

Zhu Yiwen (2020) discusses the counting-rod diagrams and notations of the 13th century Chinese Mathematical Book in Nine Chapters. On Qin Jiushao’s writing system. https://doi.org/10.1007/s00407-019-00243-x

Jeannette Fincke et al. (2020) discuss a Babylonian astronomical text with a previously undescribed way of representing zero. BM 76829: A small astronomical fragment with important implications for the Late Babylonian Astronomy and the Astronomical Book of Enoch. https://doi.org/10.1007/s00407-020-00268-7

Manuel Medrano (2020) discusses variation in Andean khipu reading in relation to colonial-era textual references. Testimony from knotted strings: An archival reconstruction of early colonial Andean khipu readings. https://doi.org/10.1080/02757206.2020.1854749


  1. What a great list! And I very much appreciate the one-sentence abstracts. As I read down the page I was itching to recommend Lucy Bennison-Chapman’s careful refutation of the Schmandt-Besserate hypothesis and I’m pleased you included it. Also, I don’t know how I ever missed Philip Boyes’ ‘Negotiating Imperialism’ which looks like a fantastic comparator for the more modern forms of anti-Imperial scripts that I’ve been interested in for so long.

  2. Thanks Piers! Yes, it’s frustrating that it has now been almost 40 years and Schmandt-Besserat stuff is stlll circulating so widely – e.g., in intro anthro textbooks it’s pervasive. Bennison-Chapman’s paper is superb and needs much more attention than it’s received so far.

    And yes, I think you’ll enjoy the Boyes one quite a bit based on your work – i.e., for those of us who see scripts and notations as not just the consequences of systems of power but as part of those systems, including systems of resistance.

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