Oksapmin counting in particular has been exhaustively studied in Saxe 1981, 1982, 1999, Saxe and Esmonde 2005 and the synthesis Saxe 2012; see also https://culturecognition.com. ‘Tipana, tipnarip, bumrip, hadrip, hatatah’ are quoted in the form given at Saxe 2012, p. 271; see p. 45 for a slightly different transcription. ‘All types of useless and unnecessary items’ is quoted in Saxe 2012, p. 51. The material about change in the Oksapmin number system is derived primarily from Saxe 1982, 2012 and Saxe and Esmonde 2005 (on fu in particular). ‘In 1960, when Australian shillings and pounds were used’ is from Saxe and Esmonde 2005, p. 209–10; ‘some people whose participation in the money economy’ from Saxe 2012, p. 30.
Tonga: Counting leaves
On the prehistory of the Pacific islands I have used the classic account Terrell 1986 as well as Kirch 2000 (whence the phrase ‘path of the winds’), Oppenheimer 2004, CWP chapter 1.31 (Tanudirjo) and Hunt and Cochrane 2018 (articles by Cochrane and Hunt, Terrell, Rieth and Cochran, Burley and Addison, the last having particular relevance to Tonga). On Tongan culture in the historical period, important documents are Mariner 1818, Gifford 1929, Bott and Tavi 1982; the more recent historical writing I have consulted includes Rutherford 1977, Petersen 2000, Campbell 2001 and Evans 2001.
On the Austronesian language family I have used Lynch 2018 as well as CWP chapter 1.33 (Heggarty and Renfrew). Number words in Oceanic languages are discussed in Harrison and Jackson 1984, Bender et al. 2006, Bender 2013 and Bender and Beller 2006a, 2006b, 2014, 2018, 2021; I rely particularly on their 2006b for the interpretation of the complex history of Polynesian and Micronesian numeral classifiers and counting systems. Specifically on Tongan number words I use Bender and Beller 2007; ‘the kie leaves are cut while still green’ and the two subsequent quotations are from Bender and Beller 2007, 230, ‘one such presentation’ from p. 231 and ‘some do not apply or even remember the traditional systems’ from p. 229. ‘On Lamotrek and Fais’ is from Bender and Beller 2006b, p. 400; ‘breadfruit, pandanus leaves’ from p. 385.
8
Panorama: Counting in the Americas
On the archaeology of the Americas, I have used CWP chapter 2.14 (Collins) together with Meltzer 2021. General information about American languages is from Mithun 1999, CWP chapter 2.36 (Heggarty and Renfrew) and Miyaoka et al. 2007; that on American numeracies from Chrisomalis 2010b, chapter 9, Closs 1986 and DeCesare 1999.
Yup’ik: Counting games
On the Yup’ik archaeology see Shaw 1998 and Masson-MacLean et al. 2020; also on the region, CWP chapter 2.15 (Anderson). The ongoing excavation of Nunalleq is documented at nunalleq.wordpress.com, where the bundle of tally sticks is discussed (nunalleq.wordpress.com/2018/07/23/artfact-of-the-day-20-july/); other sources used are Knecht and Jones 2019, Mossolova and Knecht 2019 (on masks) and Sloan 2021. ‘Whittled bits of wood, sharpened stakes’ and ‘protruding from the dark soils’ are from Knecht and Jones 2019, 28.
Historical documentation of ways of life in the region appears in Nelson 1899; the descriptions of games including the three quotations are from p. 332. See also Funk 2010 on the ‘Bow and Arrow War’; ethnographic sources consulted include Fienup-Riordan 1990, Barker and Barker 1993, www.yupikscience.org, Williams 2009, Fienup-Riordan and Rearden 2012 and Jolles and Oozeva 2002.
Counting in Yup’ik is discussed particularly in Koo and Bartman 1980; see also (including on related languages) Baillargeon et al. 1977 (‘“How long was it”, I asked’: p. 126), Closs 1986 (pp. 129–80 by Denny), Lipka 1994 and Corbett and Mithun 1996. The tally tattoo mentioned is from Carrillo 2014, p. 65; several other tally objects can be seen online at the National Museum of the American Indian, Smithsonian Institution (americanindian.si.edu).
Pomo: Counting costs
Historical and ethnographic sources on the Pomo include Powers 1877, Barrett 1908, Loeb 1926, Stewart 1943, Barrett 1952 and Colson 1974; on the number words in the seven Pomo languages see Dixon and Kroeber 1907 (esp. pp. 676, 685, 686).
Historical sources on shell money in the region include Stearns 1869, 1877; Pomo bead making is discussed in Loeb 1926 including at pp. 176–8, 191–5, 229–30, and in Hudson 1897 and Gifford 1926 (pp. 329, 377–8, 386–7; p. 378 for ‘the Southeastern Pomo informant Wokox’). On the economic practices of the region more generally Davis 1961 and Vayda 1967 are useful; ‘the host chief divided up’ is from Loeb 1926, p. 193 and ‘two funerals in one month’ from Colson 1974, p. 205. More recent work on the Pomo money and its history includes Heizer 1975, Arnold and Munns 1994, Parker 2010, Burns 2019, Trubitt 2003 and Gamble 2020.
Waxaklahun-Ubah-K’awil: The long count
On the general history of the Maya I have used Sharer and Traxler 2006; on the Mayan languages CWP chapter 2.36 (Heggarty and Renfrew) and CEWAL (chapter 43 by Bricker); and on their scripts WWS section 12 (by Macri). Mathematical notations are also discussed in Closs 1986 (pp. 291–370) and in Chrisomalis 2010b (chapter 9). The question of the Mayan zero is discussed in Justeson 2010 and Blume 2011 in addition to Chrisomalis 2010b, which I follow on the question of whether and in what sense the notation was positional.
The Mayan calendars are discussed in several of the above works, and also in Gillispie et al. 2008, s.v. ‘Maya Numeration’, Aveni 2001, Jones 2005, s.v. ‘Calendars: Mesoamerican Calendars’, Pharo 2014, Normark 2016 and Milbrath 2017. On Copán in particular I have consulted Fash and Fash 1991/2001, Schele and Mathews 1998 (chapter 4), Wyllys and Fash 2005 and especially Newsome 1991. ‘His breath expired in war’ is quoted in Blume 2011, p. 51. Stela D is also discussed in Pineda De Carías et al. 2017.
Pirahã: Lost count
The original report of the Pirahã’s lack of number words is Gordon 2004; ‘clusters of nuts matched to the battery line’ is from p. 498 and ‘I sat across from the participant’ p. 497. See Pica et al. 2004 for a discussion and Everett 2005 for further experimental work. ‘The Pirahã are some of the brightest’ is from p. 621; ‘could not find anyone’ p. 632; ‘someone can ask for an entire roll of hard tobacco’ and ‘in this “trade relationship”’ p. 626; and ‘I prefer whole animals’ p. 625.
Questions about the original observations are raised in Frank et al. 2008; see Everett and Madora 2012 for a reply.
Select Bibliography
Abun-Nasr, Jamil M., A History of the Maghrib in the Islamic Period (Cambridge, 1987).
Akera, Atsushi and Frederik Nebeker, From 0 to 1: An Authoritative History of Modern Computing (Oxford, 2002).
Alföldi-Rosenbaum, Elisabeth, ‘The finger calculus in antiquity and in the Middle Ages’, Frühmittelalterliche Studien 5 (1971), pp. 1–9.
Allard, André, ‘Le premier traité byzantin de calcul indien: classement des manuscrits et édition critique du texte’, Revue d’histoire des textes 7 (1977), pp. 57–107.
Allard, André, ‘La formation du vocabulaire latin de l’arithmétique médiévale’, in Olga Weijers, ed., Méthodes et instruments du travail intellectuel au moyen âge: études sur le vocabulaire (Turnhout, 1990), pp. 137–81.
Alvarez, G. A. and P. Cavanagh, ‘Independent resources for attentional tracking in the left and right visual hemifields’, Psychological Science 16 (2005), pp. 637–43.
Álvarez-Fernández, Esteban, ed., Special Issue: Personal Ornaments in Early Prehistory: A Review of Shells as Personal Ornamentation during the African Middle Stone Age, PaleoAnthropology (2019).
Amalric, M. and S. Dehaene, ‘Cortical circuits for mathematical knowledge: evidence for a major subdivision within the brain’s semantic networks’, Philosophical Transactions B 373 (2017).
Anderson, Margo J., The American Census: A Social History (New Haven, 1988).
Anobile, G., et al., ‘Number as a primary perceptual attribute: a review’, Perception 45 (2016), pp. 5–31.
Anon., ‘To think or not to think?’, Time (25 November 1946), p. 35.
Anon., ‘The Census of the United States’, Scientific American 63 (30 August 1890), p. 132.
Arias, Paolo E. and Max Hirmer, Tausend Jahre griechische Vasenkunst (Munich, 1960).
Arnold, Jeanne E. and Ann Munns, ‘Independent or attached specialization: the organization of shell bead production in California’, Journal of Field Archaeology 21 (1994), pp. 473–89.
Arrighi, G., ‘La numerazione “arabica” degli Annales Ratisbonenses’, Physis 10 (1968), pp. 243–57.
Austrian, G., Herman Hollerith: Forgotten Giant of Information Processing (New York, 1982).
Aveni, Anthony, ‘Time, number, and history in the Maya world’, KronoScope: Journal for the Study of Time 1 (2001), pp. 29–61.
Badiou, Alain, Number and Numbers (Cambridge, 2008).
Bagnall, R., Egypt in Late Antiquity (Princeton, 1993).
