Primary sources for the contest are Anon 1946 and Kojima 1954; the step backwards for ‘the machine age’ and ‘“civilization” had “tottered”’ are both quoted on p. 12. Further background information is taken from Duus 2008 esp. chapters 4 (Fukui), 7 (Coox), 10 (Kōsai and Goble); Chrisomalis 2020 (p. 74) mentions the earlier tradition of such contests. Another important primary source for soroban use in the mid-twentieth century is Kojima 1963; useful histories include Pullan 1968 and Schärlig 2006. ‘Children go there after school’ is from Stigler et al. 1986, p. 454.

‘The character “Suan”’ is from Dauben 1998, p. 1348 note 12. Cognitive aspects of the suanpan and soroban are discussed in Hatano et al. 1977, Stigler et al. 1986, Hatta et al. 1989, Hishitani 1990, Miller and Stigler 1991, Yujie et al. 2020 and Wang 2020. Related but more general issues in visual processing are reported in Alvarez and Cavanagh 2005, Halberda et al. 2006 and Feigenson 2008. More specifically on the mental abacus, see Stigler et al. 1982, Stigler 1982, 1984, Hatano and Osawa 1983, Hatano et al. 1987, Frank and Barner 2011, Kim 2016, Barner et al. 2016, Cho and So 2018, Brooks et al. 2018 and Cheng et al. 2021.

Hermann Hollerith and Kawaguchi Ichitaro: Counting machines

Kawaguchi’s Electric Tabulation Machine is pictured and described at https://museum.ipsj.or.jp/en/computer/dawn/0056.html and https://museum.ipsj.or.jp/en/heritage/denkishukeiki.html. On the Japanese census see Matsuda 1981.

On the 1890 US census, important primary sources are Walker 1888, Wright 1889, Anon 1890 (‘The blanks which had been filled up’ is on p. 132) and Porter 1891, 1894. Historical reflections from soon after that census include Hunt 1899, Wright 1900 (pp. 69–79), SHCA 1903 (see pp. 173–4) and Wilcox 1914. ‘A very tidy and airy machineshop’ and ‘your tympanums all tingle’ are quoted in Austrian 1982, pp. 60–1, respectively from the Washington Star of 26 June 1890 and the Saginaw (Michigan) Weekly of 23 October 1890.

‘The unsettled area’ of the American continent is from Turner 1986, p. 1. Modern histories of the US census I have used include Anderson 1988, USCB 2002, Schor 2017 and Ruggles and Magnuson 2020. The loss of the 1890 records is discussed in O’Mahony 1991, Blake 1996 and Dorman 2008; ‘might every one of them be burned up’ is from Martin 1891, p. 525.

Hollerith’s own descriptions of his inventions appear in Hollerith 1889a, 1889b, 1894 among many other sources. Other (relatively) technical discussions from the period are Martin 1891, Newcomb 1913 (adoption by ‘nearly every civilized country’ on p. 82) and Felt 1916. From the voluminous more recent secondary literature I have used Truesdell 1965, Bashe 1986 (with one of the fullest descriptions of how the system actually worked), Reid-Green 1989, Campbell-Kelly 1989, Norberg 1990, Kistermann and Reston 1991, USCB 1991 and Campbell-Kelly et al. 2014. Additionally on Hollerith himself I have used Austrian 1982 and American National Biography (https://www.anb.org).

On the later development of the punched card I have consulted Lubar 2004 and Heide 2008, 2009.

Sia Yoon: Counting likes

On the history of computers I have used Akera and Nebeker 2002, Haigh and Ceruzzi 2021, O’Regan 2008 and Campbell-Kelly et al. 2014; on the digital revolution Hobart and Schiffman 1998, Deuze 2006, Gere 2008, Clarke 2012 and George 2020. ‘Consensual hallucination’ is from Neuromancer (William Gibson, 1984), p. 5.

On Korean history I use Connor 2002, Kim 2017 (especially Zur’s chapter) and Seth 2020; on technology therein Choi 2017. On K-pop and Korean Manga, Lie 2014, Pasfield-Neofitou et al. 2016 and Jin 2016, and on the webtoon phenomenon Jin 2015 (‘on a bustling subway ride to work’ is from p. 193), Kim and Yu 2019, Yecies et al. 2020, Shim et al. 2020 and Cho 2021. Sia’s story is online at https://www.webtoons.com/en/drama/my-dud-to-stud-boyfriend/list?title_no=4353.

7

Counting words and more in the Pacific world

Ayangkidarrba: Counting eggs

On the Australian archaeology I have used CWP chapters 1.35 (White) and 1.37 (Bird), and Cochrane and Hunt 2018 (chapters by Cochrane and Hunt, and O’Connor). An important recent publication on the earliest archaeology in the continent is Clarkson et al. 2017, with accompanying comments and reply (Clarkson et al. 2018).

A key anthropological source for this chapter is Keen 2004. On the languages of the continent it is important to be aware on the one hand of Dixon 1980, 2002, and on the other of such accounts as Bowern and Koch 2004, Campbell and Poser 2008 (pp. 318–25), and CWP chapter 1.42 (Heggarty and Renfrew). Additional information is taken from Hale 1975, Evans 2003, Cunningham et al. 2006 (chapters 5 and 12), Miyaoka et al. 2007 (chapter 12 by Walsh) and Leitner and Malcolm 2007. On counting in Australian languages I use Harris 1982, 1987, Sayers 1982, McRoberts 1990, Bowern and Zentz 2012, Epps et al. 2012, Treacy et al. 2015 and Zhou and Bowern 2015.

Specifically on Groote Eylandt and the Anindilyakwa I have used Worsley 1954, Turner 1974 (‘would awake at sunrise’: p. 165), and for the contact with Macassan people May et al. 2009. On their language, Leeding 1989 and van Egmond and Baker 2020. On their counting Stokes 1982, which I follow, describing the situation of number words and counting documented there (including rejecting a Macassan source for the lexemes and the base 5 system). ‘The hand is held loosely’ and ‘there is a story on Groote Eylandt’ are from Stokes 1982, pp. 43 and 39. Butterworth et al. 2008 gives a different account of the number words in this language and states that they are not (now) taught to children, presumably reflecting recent change.

Oksapmin: body count

For the context of this chapter in the ethnography and history of Papua New Guinea I have consulted Brongersma and Venema 1962 and Gammage 1998, and on the languages of the region the remarks in CWP chapter 1.42 (Heggarty and Renfrew), Dixon 2002 and Campbell and Poser 2008, as well as (particularly) Lean 1992 and Owens et al. 2018. On the Oksapmin in particular I have used Perey 1973 (p. 27 for ‘a raft crossing described as “very risky”’). On the Oksapmin language, see also Loughnane and Fedden 2011.

On counting in New Guinea, the classic and monumental studies are Lean 1992 and Owens 2001, synthesised in Owens et al. 2018. I have also referred to Laycock 1975, De Vries 2014 and Dwyer and Minnegal 2016, and to the classic Mimica 1988. On the cognitive and educational side, Matang 2005 and Matang and Owens 2014 are valuable.

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.

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