Innovative numerals in Malayo- Polynesian languages outside of Oceania Antoinette Schappera & Harald Hammarströmb Leiden Universitya, Universität zu Kölna, Radboud Universityb & Max Planck Institute for Evolutionary Anthropologyb In this paper we seek to draw attention to Malayo- Polynesian languages outside of the Oceanic subgroup with innovative bases and complex numerals involving various additive, subtractive and multiplicative procedures. We highlight that the number of languages showing such innovations is more than previously recognised in the literature. Finally, we observe that the concentration of complex numeral innovations in the region of eastern Indonesia suggests Papuan influence, either through contact or substrate. However, we also note that socio-cultural factors, in the form of numeral taboos and conventionalised counting practices, may have played a role in driving innovations in numerals. 1. INTRODUCTION1 There has been much discussion of the developments in innovative numeral formations in Oceanic languages. Galis (1960) observed that many AN languages to the north of New Guinea have exchanged the ancestral decimal system for various quinary systems. More recently, Dunn et al. (2008:739) observed that the decimal system in their sample of 22 western Oceanic languages was not very stable, having changed in almost half the languages to quinary systems. Blust (2009:274) suggests that the emergence of such different numeral systems in Oceanic languages is due to intensive contact and trading between Austronesian and Papuan language-speaking peoples. Smith (1988:51-53) similarly observed that counting systems were not particularly stable due to trading and exchange relations between AN and Papuan language speaking peoples in Morobe province of Papua New Guinea. However, he noted that the influence was not one way but that Austronesian languages could 1 We thank David Mead for his insights into South Sulawesi languages, and Marian Klamer and Leif Asplund for discussions on Sumba languages. We also thank David Kamholz for his insights into Cenderawasih languages and for help with access to the typescript Starrenburg 1915. Schapper further thanks Emilie T.B. Wellfelt for discussions on the cultural significance of numerals in Indonesia and Timor-Leste. Schapper’s research was conducted as part of an ESF-EuroCORES (EuroBABEL) research project with financial support from the Netherlands Organisation for Scientific Research. 1 not only lose their inherited decimal system but that Papuan languages can also acquire it. In this paper, we turn our attention to the comparatively little remarked upon innovative formation of numerals in Malayo-Polynesian (MP) languages outside of the Oceanic (OC) subgroup (cf., e.g., Ossart 2004). Based on a survey of the numerals in 470 languages, this paper reports on the results of the first systematic investigation of innovative complex numerals in non-OC MP languages. The precise aims of our study are threefold: (i) to describe the variety of innovations of complex numerals (e.g., 10-1 = 9) and of non-decimal numeral bases (e.g., base-5, base-20); (ii) to draw attention to the concentration and diversity of such innovative numeral formations in MP languages of eastern Indonesia and East Timor, and; (iii) give preliminarily suggestions as to the reasons for the geographical skewing of such innovative numeral formation in non-OC MP languages. The paper is structured as follows. Section 2 provides an overview of the terminology that we use to describe the different types of patterns of numeral formation that are observed. Section 3 examines the variety of the innovative ways of forming numerals in non-OC MP numerals. In particular, we highlight the very limited number of numeral innovations in WMP area (the Philippines, western Indonesia and mainland South-East Asia) MP languages. This is contrasted with CEMP area (eastern Indonesia and East Timor) MP languages which harbour at least a dozen distinct innovations.2 In section 4 we seek to identify causal factors that may have played a role in driving the multitude of numeral innovations in the CEMP area. We observe that the areal concentration of complex numeral innovations suggests influence from Papuan languages. We further note that socio-cultural factors, in the form of numeral taboos and conventionalised counting practices, are likely to have contributed to numeral innovation. Section 5 concludes the discussion. 2. TERMINOLOGICAL PRELIMINIARIES Numerals are ‘spoken normed expressions that are used to denote the exact number of objects for an open class of objects in an open class of social situations with the whole speech community in question’ (Hammarström 2010: 11). A numeral system is thus the arrangement of individual numeral expressions together in a language. 2 Given the problematic nature of the WMP and CEMP nodes in the AN tree (see, e.g., Adelaar 2005), we use the terms “WMP area” and “CEMP area” to refer to broad geographical regions in which MP languages are spoken and not to genealogical groupings. 2 For the purposes of the present paper, a numeral system may be classified as follows: Base-5 (or quinary): if more than half the expressions 6-9 are formed as 5+1, .., 5+4 respectively Base-10 (or decimal): if more than half the expressions 20-99 are formed as x*10+y where x, y range from 1..9 Base-20 (or vigesimal): if more than half the expressions 20-99 are formed as x*20+y where x ranges from 1..9, and y from 0..19 A numeral system may be both quinary and decimal or both quinary and vigesimal (in fact, all bona fide attested quinary systems are also either decimal or vigesimal – see Hammarström 2010). So, for instance, Pazeh has a mixed-base numeral system in which numerals ‘six’ to ‘nine’ are formed with a quinary base and higher numerals with a decimal base. By contrast, Saisiyat has only a decimal base; ‘six’ does not constitute a base in the language even though it is used in forming the numeral ‘seven’. The fact that Saisiyat ‘six’ is limited to building only one other higher numeral means that it does not meet the requirements for basehood as given above. TABLE 1 ABOUT HERE. Whilst Saisiyat ‘six’ does not constitute a base in the language, its use in the numeral ‘seven’ draws attention to another kind of numeral formation with which we are also concerned in this paper. We are not only interested in the numeral bases in a language, but more broadly the internal composition of numerals, that is, if and how numerals are made up out of other numeral expressions. We call a monomorphemic numeral a “simplex numeral”, and a numeral composed of several numeral expressions a “complex numeral”. To describe (i) the arithmetical relation between component elements in a complex numeral, and (ii) the role of component elements in arithmetical operations3, the following terms are used: “additive numeral”: a numeral where the relation between components parts of a complex numeral is one of addition. The component parts are “augend” and “addend”. So, for example, in the equation 6+1 = 7, the augend is 6 and the addend is 1. “subtractive numeral”: a numeral where the relation between component parts of a complex numeral is 3 It is of course possible for arithmetical operations to be used in conjunction with one another, e.g., 3x20 + 5+2 for ‘67’. Since these can still be accurately characterised with a combination of the three basic operations (additive, subtractive and, multiplicative), we restrict ourselves to these terms. 3 one of subtraction. The component parts are “subtrahend” and “minuend”. So, for example, in the equation 10−2 = 8, the subtrahend is 2 and the minuend is 10. “multiplicative numeral”: a numeral where the relation between components parts of a complex numeral is one of multiplication. The component parts are “multiplier” and “multiplicand”. So, for example, in the equation 3x2 = 6, the multiplier is 3 and the multiplicand is 2. Our analysis of numerals breaks down each number expression into morphemes. The meaning, if known, of a morpheme can be inferred from the meaning of it in isolation or inferred from the mathematical equation the number expression constitutes. Throughout this paper we rely on the definitions made in this section. We repeatedly make use of the terms presented here and the reader is referred to this section for clarification of any terminology. 3. DATA A decimal counting system can be reconstructed for proto-Austronesian (Blust 2009a: 268-274). This system is found spread throughout the Austronesian world with easily recognisable cognates and it can be reconstructed to various lower nodes of the Austronesian tree, such as proto-Oceanic. This can be seen by comparing the reconstructed PAN and POC numeral forms given in Table 2. In the following subsections, we will see that multiple Austronesian languages outside of the Oceanic subgroup have replaced these simplex etymological numerals with innovative complex numerals. The majority of our discussion deals with innovations in numerals ‘six’ to ‘nine’. However, in cases of base changes (e.g., decimal > vigesmal) we also discuss the expression of the numerals ‘ten’ and ‘hundred’. Unless otherwise stated, however, the reader should understand there has been no base change and that, for instance, *Ratus for ‘hundred’ is retained. All data is cited in a unified IPA transcription from the earliest known attestations to avoid interference from any post-historical changes. However, unless otherwise noted, for all languages cited, all later attestations (including own fieldwork by the second author on Bedoanas, Erokwanas, Yaur, Yeresiam, Yeretuar and Wandamen in 2010) agree with the earliest sources except for transcriptional matters irrelevant for the present paper. TABLE 2 ABOUT HERE. 3.1. Sumba In three languages of western Sumba we find innovative numerals for ‘eight’ and ‘nine’. They are Lamboya, Kodi and Weyewa, and their 4 numerals are set out in Table 3.