CHAPTER 8
TOWARDS A
PREHISTORY OF NUMBER
8.1 INTRODUCTION
There are three main reasons for the importance of Seidenberg's theory and which justify its discussion and evaluation in the previous chapter. First, in the literature of the history of mathematics it is the only coherent and comprehensive view to have been put forward of the prehistory of number and the appearance of various types of counting systems in human societies in the period prior to the advent of written records. Second, it establishes a means whereby a "genealogy" of counting system types can be inferred from an investigation of their nature and distribution in contemporary indigenous societies. Third, the establishment of a genealogy allows for the possibility of setting this ordered sequence within a chronological framework, thereby providing it with an historical dimension. It is clear, however, that the data accumulated for this study may be interpreted in such a way as to be at variance with several of Seidenberg's conclusions while, at the same time, providing some agreement with a diffusionist perspective. In this chapter we will continue to develop in some detail an interpretation of the data available on the counting systems of both the NAN and AN languages, the intention being to establish a revision of Seidenberg's genealogy. We shall attempt to use recent findings in the fields of linguistics and archaeology in order to locate the genealogy within the known chronological framework of the migration of various language groups into New Guinea and Oceania, thereby providing an outline of the prehistory of number for this region.
The counting systems situation found in the NAN and AN languages will be dealt with separately. While the NAN languages display remarkable diversity, the counting systems and tallies which are found among them may be classified into a relatively small number of types. We will proceed by taking an overview of how these various types are distributed throughout the NAN languages according to their genetic classification, beginning with the phylum. For each phylum we will consider what the current distribution of counting and tally types is and, in particular, which types appear to predominate and have a general spread throughout the various stocks of the phylum and which types appear to be restricted to a relatively small class of languages. From such an analysis we will attempt to infer which types may have been present in the languages that existed in the early history of the phylum and which types may have arisen in the later history of the phylum as a result of invention or external influence. This analysis will provide the basis for reconstructing the prehistory of counting and tallying in the NAN languages.
With regard to the AN languages, we provided in Chapter 1 a summary of the results of a recent study by Ross in which he uses the methods of historical linguistics to unravel the complexities of the early history of the Oceanic AN languages in PNG.[1] Using Ross's reconstruction, we will trace the fate of the counting systems of the various clusters and groups of the daughter languages of Proto Oceanic (POC) as they dispersed in PNG and throughout Island Melanesia and the Pacific. Developments in the archaeology of this region, in particular the discovery of the remains of a distinctive style of pottery in 1952 at Lapita in New Caledonia, have resulted in a large number of studies which trace the spread of the culture with which the Lapita style of pottery is associated, from Melanesia into the Pacific. Various scholars have identified the Lapita cultural complex as belonging to the speakers of the Oceanic AN languages: this means, essentially, that the estimated dates from various archaeological sites provides a means of establishing a chronological sequence of the post-POC migrations and, thus, the linguistic prehistory of the region and, by inference, the prehistory of the post-POC counting systems.[2]
8.2 COUNTING SYSTEMS AND TALLIES OF THE NAN LANGUAGES
In the previous chapters it has been established that the counting systems and tallies which are found among the NAN languages of New Guinea, the islands lying to the east of the mainland, and the Solomon Islands, comprise mainly the various 2-cycle variants, the body-part tallies, the (5, 20) digit tally, several 4-cycle systems, and a small number of 6-cycle systems. There is also a number of languages which have counting systems possessing either a primary or secondary 10-cycle. In discussing each of these types individually we have indicated in previous chapters how they are distributed among the various phyla of the NAN languages. We will now put this information together in order to obtain an overview of how the counting systems and tallies are distributed among the NAN languages according to this broad linguistic classification. It seems likely that certain systems may have been present in the languages of a given phylum from an early date while other systems may have been introduced or have developed as localized innovations. We will then attempt to infer, for each phylum, which systems fall into each category and, in particular, which may have been present as "proto" systems in languages which existed in the early history of the phylum.
In order to infer which among the counting systems or tallies that are now found in a given phylum, may be possible candidates for such proto systems, it will be assumed that as the original languages of the phylum differentiated they nevertheless retained the basic cyclic structure of their proto systems even though the numerical lexis of each daughter language would have diverged from another. We would therefore expect to find the descendants of a proto system to have a reasonably wide distribution throughout the major stocks or subphyla of the phylum. On the other hand, those systems which are found today to exist in only one or two families in a circumscribed geographical area can probably be rejected as candidates for proto systems and indeed it seems likely that such systems have developed in those languages as localized innovations. We also need to consider which systems in a given phylum may have resulted from influence external to that phylum. Each of these considerations will be taken into account as we discuss below the distribution of the major counting and tally types throughout the main phyla and their constituents.
8.2.1 Distribution according to phyla
According to Laycock "number systems, at least in the New Guinea area, afford few indications of genetic relationship of languages; closely related languages may show widely-differing systems".[3] While this is to some extent true, it is nevertheless possible to discern that certain types of systems are characteristic of broad linguistic groupings. The broadest level of linguistic grouping used to classify the NAN languages is the phylum. As discussed in Chapter 1, there are five major phyla: the West Papuan, East Papuan, Torricelli, Sepik-Ramu, and Trans-New Guinea. There are also six minor phyla together with a total of seven phylum-level isolates.[4] The distribution of the various counting system and tally types among the phyla is shown in Table 63 on the following page. In this Table the minor phyla and isolates have been combined. The distributions in each phylum will be discussed below.
8.2.2 The West Papuan Phylum
There are 24 languages belonging to the West Papuan Phylum, however 11 of these are located in North Halmahera which lies outside the New Guinea region and are not considered here. Of the remaining 13 languages, data have been acquired for 10.[5] All of these are located in the Bird's Head or Vogelkop of western Irian Jaya. Referring to Table 63 it can be seen that the counting systems of these languages are such that their cyclic structures contain either a primary or secondary 10-cycle and that there is no trace of a 2-cycle. It has been indicated earlier, in Chapter 4, that several of these systems show traces of AN influence in that AN numerals have been borrowed into their numerical lexis.[6] The islands peripheral to the Bird's Head are inhabited by speakers of non-Oceanic AN languages and it is from these that the considerable AN influence on the NAN languages of this region, which has been noted by Wurm,[7] emanates. This influence is apparent in the counting systems of all the West Papuan Phylum languages, if not in the direct borrowing of numerals then in the presence of a 10-cycle. The inference that may be drawn from this is that, at some time in the past, the West Papuan Phylum languages possessed digit tally systems with a (5, 20) cyclic structure and that as a result of AN influence the present situation is such that two languages now have (5, 10) systems, five have (5, 10, 20) systems, and two have lost the original 5-cycle and have (10, 20) systems instead.
Table 63
Showing the Distribution of
Counting System and Tally Types Among the Phyla of the NAN Languages
_____________________________________________________________________
Types West East Torricelli Sepik- Trans- Minor Total
Papuan Papuan Ramu N. G. Phyla
______________________________________________________________
(2) 0 0 0 3 39 0 42
(2, 5) 0 1 16 5 86 1 109
(2', 5) 0 1 3 5 17 1 27
(2'', 5) 0 0 5 3 31 1 40
(5, 20) 0 1 2 17 52 7 79
(4) 0 0 0 1 6 2 9
(6) 0 0 0 0 5 0 5
Body-Parts 0 0 0 8 58 4? 70?
(5, 10) 2 12 0 3 4 0 22
(5, 10, 20) 5 0 0 0 4 3 13
(10) 1 8 0 1 2 0 13
(10, 20) 2 0 0 0 1 0 3
_____________________________________________________________________
8.2.3 The East Papuan Phylum
The East Papuan Phylum consists of 23 languages located in New Ireland (1), New Britain (6), the North Solomons Province (8), the Milne Bay Province (1), all in PNG, and in the Solomon Islands (7).[8] A further language for which data exist, Kazukuru, was spoken in the Solomon Islands but is now extinct.[9] At least 18, possibly 20, of these languages have counting systems with either a primary or secondary 10-cycle. One, Taulil, has a (5, 20) digit tally system while two, Sulka and Kol-Sui, have 2-cycle variants with a secondary 5-cycle: these three are located in the East New Britain Province (PNG). At least four languages, Nasioi, Nagovisi, Siwai, and Buin, all situated in the North Solomons Province (PNG), display numeral classification as discussed in Chapter 6.
All the languages of this phylum are located in regions which are inhabited predominantly by speakers of AN languages. Wurm has noted that virtually all these NAN languages show some degree of AN influence, this being particularly so of the Reefs-Santa Cruz Family in the eastern Solomon Islands: "the languages of the family show evidence of overwhelming Austronesian influence on all levels ... As much as half of the vocabularies of the languages may be Austronesian in origin".[10] It has been indicated earlier, in Chapter 7, that Yele, a member of this phylum in the Milne Bay Province (PNG), has borrowed several AN numerals as has Mbilua in the Solomon Islands.[11] While several other languages also have counting systems which have incorporated AN loanwords, the majority have not. However, the AN influence may be detected by the presence of a 10-cycle in the NAN counting systems and this has been achieved without direct borrowing.
The remaining three languages of the phylum which show no trace of a 10-cycle in their counting systems may perhaps provide an indication of the type of counting systems which existed in this phylum prior to the advent of the AN immigrants. The data suggest that candidates for such proto systems are the 2-cycle system and the digit tally with a (5, 20) cyclic pattern: while no pure 2-cycle systems are found, Sulka nevertheless has a 2-cycle system augmented by a digit tally system. There are, in addition, 12 languages which have systems with a secondary 10-cycle which also have a primary 5-cycle and it seems likely that these may have developed from (5, 20) systems. Whether these hypothesised proto systems were also associated with numeral classification is uncertain. While noun classification is not uncommon among the East Papuan Phylum languages, it is only among the languages of southern Bougainville that a well developed type of numeral classification occurs.
8.2.4 The Torricelli Phylum
The languages of the Torricelli Phylum are located mainly in northwestern PNG in the Torricelli Mountains and in areas between these and the coast in the West and East Sepik Provinces. The Marienberg Family, comprising six languages, is situated in the coastal and inland region extending from the east of Wewak to the Murik Lakes in the East Sepik Province. Two languages of the Monumbo Family are situated near Bogia in the northern coast of the Madang Province. There is a total of 48 languages in the phylum of which data were obtained for 26.[12]
Several of the Torricelli Phylum languages situated near the coast are adjacent to small AN enclaves. None of these, however, show any detectable signs of AN influence in their counting systems. Indeed, in some instances, there appears to be instead NAN influence on the systems of the AN languages: Sissano, for example, in the West Sepik Province, is an AN language spoken in a region adjacent to the NAN Olo language, a member of the Torricelli Phylum. As shown previously, in Table 4, Sissano now possesses a counting system with a (2, 5) cyclic pattern and with numerals which are no longer AN in character.
As can be seen from Table 63, 24 of the languages for which data exist possess a 2-cycle variant system. In most of these there is a secondary 5-cycle and we have essentially 2-cycle systems augmented by digit tally systems. Wurm notes that the morphological features of the Torricelli Phylum languages include the use of subject prefixes which "show number, gender, and (class) concordance. The concordance extends to numerals ...".[13] This is true, for example, of the Southern, Mountain, and Bumbita Arapesh languages.[14] In addition to possessing a complex system of noun classification, these three languages also have counting systems with unusual features. Mountain Arapesh, for example, has a main system with a (2', 4, 24) cyclic pattern and a further system which shows some features of a rare 3-cycle. These systems appear to be unique to the Arapesh languages and may well be localized innovations. In addition to these, two languages of the Torricelli Phylum appear to have primary 5-cycles and may be digit tallies. There is no evidence that body-part tallies are found in this phylum. Thus, in attempting to determine likely candidates for the proto counting systems which existed in the languages ancestral to the current day languages of the Torricelli Phylum, we have either a single type with a (2, 5, 20) cyclic pattern or, perhaps, two types, one with a pure 2-cycle structure together with a digit tally having a (5, 20) cyclic structure.
8.2.5 The Sepik-Ramu Phylum
Larger in composition than the other three phyla just discussed, the Sepik-Ramu Phylum comprises 98 languages situated in northern PNG, mainly in the West Sepik, East Sepik, and Madang Provinces. Being larger, this phylum also displays a greater degree of heterogeneity in its counting system types than do the other three. The possibility of major AN influence on the languages of the Sepik-Ramu Phylum appears to be slight: their geographical distribution is such that the majority are located inland and away from the few areas of AN incursion. Only two languages, Boiken and Murik, are presently located in regions adjacent to AN languages and indeed it is possible that both of these may have interacted with their AN neighbours.
By reference to Table 63, there are 16 languages which have 2-cycle variant counting systems; 13 of these are augmented by a digit tally while three are pure 2-cycle systems that are associated with body-part tallies. There are 17 languages which have (5, 20) digit tallies with no trace of a 2-cycle; one of these, Boiken, has a dialect which is spoken in the islands lying off the north coast near Wewak and possesses a 4-cycle system.[15] At least eight language groups employ body-part tallies and the cycles of several of these range from 26 to 29. Although the cycles differ, five of these tallies have the first ten tally points in common with the tenth point being the shoulder. In addition, there are three languages which appear to have counting systems with (5, 10) cyclic patterns and another one, Wapi, which also has a system showing evidence of a 10-cycle. The latter has adopted the numerals of the neighbouring Enga language and it was indicated in Chapter 4 that the modern Enga system has probably been affected by the tok pisin or English 10-cycle systems and now differs from its traditional and unusual 4-cycle system.[16] Of those systems which appear to display a (5, 10) cyclic pattern, Murik, Kapriman, and Kopar, we have insufficient data for the latter two. Murik, however, may have originally possessed a (5, 20) digit tally system and, possibly through AN influence, now has a system with a secondary 10-cycle.[17]
Except for the body-part tallies, the common element which is found in the counting systems of this phylum is the (5, 20) digit tally either in its pure form or with a primary 2-cycle. Thus, in attempting to identify those counting systems which may have been present in the languages ancestral to the contemporary Sepik-Ramu Phylum languages, we have at least two candidates, the 2-cycle system and the (5, 20) digit tally. The question as to whether body-part tallies were also present in these ancestral languages, possibly with those having pure 2-cycle numeral systems, is debatable. Several languages, such as Hewa, Abau, and Alamblak, which have such tallies, are located in regions which are adjacent to languages belonging to the Trans-New Guinea Phylum and which also possess body-part tallies. Wurm notes that "the southernmost languages of the Sepik Hill Stock, especially Hewa, appear to have been subject to strong influence from the East New Guinea Highlands Stock languages and other Trans-New Guinea Phylum languages".[18] I suggest, therefore, that there is a possibility that body-part tallies may have been introduced into the Sepik-Ramu Phylum languages by such influence and that the tallies were not present as an original feature.
8.2.6 The Trans-New Guinea Phylum
The languages of the Trans-New Guinea (TNG) Phylum comprise about 70% of the total number of NAN languages spoken in the region under consideration. Wurm provides details of the complex classification of the phylum into its constituents.[19] Rather than considering an analysis of the counting system situation by these constituents, we will proceed by considering the main counting and tally types and whether these have a general or specific distribution throughout the phylum. We will also consider the degree to which members of this phylum appear to have had their counting systems affected by AN influence.
With reference to Table 63 it can be seen that, taken as a group, the 2-cycle variants are the predominant type of system found in the TNG Phylum: as noted in Chapter 2, a total of 173 such systems occur. Of these, 39 appear to be pure 2-cycle systems although it is possible that some of these may have secondary 5-cycles: in a few cases insufficient data were available to determine whether this was the case. About 25 of these 2-cycle systems are found in language groups which also possess body-part tally systems. The most common of the 2-cycle variants is the (2, 5) or (2, 5, 20) system which is found in 86 languages; the other two variants, the (2', 5) and the (2'', 5), are together found in 48 languages. The distribution of the 2-cycle variants in the TNG Phylum is such that they are found in all the major stocks. In the Finisterre-Huon Stock, for example, of the 53 languages for which data exist, 30 possess a 2-cycle variant. Similarly, in the East New Guinea Highlands Stock, of the 49 languages and dialects for which we have data, 33 possess a 2-cycle variant.
The digit tally system in its pure form, that is without any trace of a 2-cycle, is found in 52 languages of the TNG Phylum, which is about 17% of these languages for which data exist. This type does not have a widespread distribution throughout the phylum and is most commonly found in the Finisterre-Huon Stock, in which there are 20 examples, and in the Madang-Adelbert Range Sub-Phylum which accounts for a further 17. Isolated examples are found in several other stocks. The geographical distribution of the (5, 20) digit tally is such that the majority are located in the north-eastern sector of PNG, inland from the coastal region which stretches from Finschhafen in the Morobe Province to Bogia in the Madang Province.
More than 80% of all the documented body-part tally systems which are found in New Guinea occur in languages belonging to the TNG Pylum. Their distribution throughout the main stocks, however, is not uniform. There is no evidence, for example, of the existence of body-part tallies in the Finisterre-Huon Stock nor in the Angan, Gogodala-Suki, Marind, Sentani, and various other smaller stocks. There appears to be only one example in the Madang-Adelbert Range Sub-Phylum. On the other hand, in the Central and South New Guinea Stock, there are 15, in the East New Guinea Highlands Stock there are 11, in the Teberan-Pawaian Sub-Phylum level Super-Stock there are 10, in the Trans-Fly Stock there are 8, and in the Border Stock, 4. The geographical distribution of the body-part tallies was given in Map 7 in Chapter 2 and is such that the large majority are located in the central and southern part of the New Guinea mainland.
Throughout the whole of the TNG Phylum there is evidence of only six languages which exhibit examples of 4-cycle systems. Five of these belong to the East New Guinea Highlands Stock and are situated in the Western Highlands, Southern Highlands, and Enga, Provinces (PNG). In the Kewa and Wiru languages, the 4-cycle systems are a digit tally variant in which the four fingers but not the thumb comprise "one hand" as discussed previously in Chapter 5. Both of these languages have, in addition to these systems, body-part tallies. The Melpa dialect of Hagen has a counting system with a (2', 4, 8) or (2', 4, 8, 10) cyclic pattern and this too is essentially a variant digit tally in which 4 is "one hand". In addition to these, there is also the very unusual 4-cycle system which employs "cycle units", as described in Chapter 5, and which is found in the Mae dialect of Enga, the Gawigl or Kaugel dialect of Hagen, and the Angal-Heneng dialect of Mendi. The five languages of this region which possess 4-cycle systems all belong to the Central or West-Central Families.[20] I have suggested in Chapter 7 that the occurrence of 4-cycle systems among these languages appears to be a localized innovation and an adaptation and extension of the standard digit tally.
Apart from these highlands languages, there is evidence of only one other member of the TNG Phylum possessing a 4-cycle system. This is Nafri which is located on the north coast of Irian Jaya near the border with PNG.[21] Several of the languages spoken in the coastal to the east and west of the Irian Jaya/PNG border have counting systems which show traces of a 4-cycle: Wutung and Vanimo, for example, both of which are NAN languages belonging to the Sko Phylum-level Stock, and Ormu and Yotafa which are both Oceanic AN languages. Nafri is spoken in a region adjacent to the Yotafa area which surrounds Jayapura.[22] The inference which may be drawn is that Nafri has probably acquired its 4-cycle system from its AN neighbour.
There are five languages of the TNG Phylum which possess 6-cycle systems, as discussed in Chapter 5. Three of these, Kimaghama, Riantana, and Ndom, belong to the Kolopom Subphylum-level Family and are located on Kolopom Island in southern Irian Jaya.[23] The other two, Kanum and Tonda, belong to the Trans-Fly Stock and are located to the east of Kolopom Island on the PNG side of the border. Map 15 shows the location of these 6-cycle systems.[24] There is no evidence of the existence of 6-cycle systems outside this region and I have suggested in Chapter 7 that these systems appear to be a localized innovation.
The only remaining counting systems of the TNG Phylum to be considered are those possessing a 10-cycle. There is evidence of four languages which have systems with a (5, 10) cyclic pattern and a further four which have systems with a (5, 10, 20) cyclic pattern. Three of these, Baham, Iha, and Semimi, all of which belong to the Mairasi-Tanah Merah Stock, are located in western Irian Jaya in coastal regions which are also inhabited by non-Oceanic AN neighbours.[25] A further three, Ulingan, Pay, and Tani, which are members of the Madang-Adelbert Range Sub-Phylum, are located on the coast north of Madang near Malala Harbour in a region in which the AN language Medebur is situated.[26] There is, in addition, Kovai , which belongs to the Finisterre-Huon Stock, whose speakers live on Umboi Island in the Morobe Province (PNG) and whose neighbours are all AN.[27] The remaining members of this group having counting systems with a secondary 10-cycle are Kwale and Magi, both belonging to the Central and South New Guinea Stock and which are situated in the Central Province (PNG). Kwale is located in a region adjacent to that of the AN Sinagoro while Magi is spoken along the south coast which is also inhabited by the speakers of the AN Magori, Ouma, and Yoba languages.[28] Finally, there are three languages not included in this group of eight, Koita, Koiari, and Domu, which have counting systems that are 2-cycle variants with secondary 5-cycles but with tertiary 10-cycles. These are also members of the Central and South New Guinea Stock and are located in the Central Province. The first two are situated outside the Port Moresby region which is dominated by the AN Motu speakers while Domu is situated on the south coast near Cape Rodney and is adjacent to the region inhabited by the AN Keapara speakers.[29] We thus have, for all of these TNG Phylum languages, circumstantial evidence that the presence of 10-cycles in their counting systems is due to the influence of proximate AN languages.
The remaining three languages which are shown in Table 63 as having counting systems with a primary 10-cycle are Enga, Lembena, and Ekagi. The last has been discussed several times previously: Table 35 in Chapter 4 and Table 60 in Chapter 7 shows the numerals of the Ekagi language which indicate clear evidence of borrowing from an AN source. Both Enga and Lembena have also been referred to in Chapter 4 where it was suggested that the original Enga 4-cycle system has undergone change relatively recently to a 10-cycle one, probably as a result of the influence of English or tok pisin, and that the neighbouring Lembena speakers appear to have adopted the modern Enga system.
The foregoing survey of the counting system and tally situation in the TNG Phylum languages provides a means of inferring which counting systems and tally types may have been present in those TNG Phylum languages which are ancestral to the present-day languages. Of the various types discussed above, several may be eliminated as candidates for such proto systems on the basis that they appear to be innovations which have occurred in a relatively restricted group of languages and at a time when the TNG Phylum languages were already established in the New Guinea region. The 4-cycle and 6-cycle systems fall into this category. In addition, I have suggested that all systems which show evidence of a 10-cycle have acquired this feature as a result of the influence of language groups external to the TNG Phylum, that is mainly AN language groups or the relatively recently introduced English or tok pisin languages.
The most obvious candidates which may be considered as possible proto systems of the TNG Phylum are the 2-cycle variants and the (5, 20) digit tally. In addition, it seems likely that some form of body-part tally was present in the languages ancestral to the present day ones. An interpretation of the data available suggests that there may have been at least two separate developments which have led to the distribution of counting and tally types that we now see in the TNG Phylum. First, it seems possible that the proto systems of the phylum were the 2-cycle numeral system and the body-part tally and that, second, the digit tally was introduced into the phylum subsequently, probably as a result of interaction with members of other phyla. Other aspects of this interpretation will be developed further in 8.3 below.
8.2.7 The Minor Phyla and Isolates
The six minor phyla account for some 29 languages of which data have been obtained for 21.[30] The distribution of these among the phyla is as follows: the Sko phylum-level Stock (6), the Kwomtari phylum-level Stock (4), the Arai phylum-level Family (4), The Amto-Musian phylum-level Family (2), The East Bird's Head phylum-level Stock (2), and the Geelvink Bay Phylum (3). In addition to these there are seven phylum-level isolates and data have been obtained for six of them.[31]
In the Sko Stock, one language, Warapu, has a (2, 5) system; three languages, Vanimo, Wutung, and Rawo, have digit tally systems which show evidence of a 4-cycle and in which "four" is one "hand". Only the first language has a pure 4-cycle system, the latter two showing evidence of a 5-cycle as well.[32] The Sko languages are situated on or near the north coast of the New Guinea mainland near the border of Irian Jaya and PNG. In this region there are several languages, both AN and NAN, which show evidence of a 4-cycle in their counting systems, as discussed in Chapter 5, and this appears to be a localized development peculiar to this northern coastline. Whether the innovation occurred with the NAN languages and was adopted by the AN languages, or vice versa, is uncertain. We have, in addition, two other languages, Sko and Sangke, which appear to have the standard (5, 20) digit tally.[33] The common feature of all the languages is a form of digit tally either in this standard form, in its modified 4-cycle form, or as a 2-cycle system augmented by a digit tally.
In the Kwomtari Stock, two languages, Fas and Baibai, possess 2-cycle variant systems. The speakers of the Kwomtari language appear to possess a body-part tally while the Biaka-speakers appear to have a digit tally.[34] Kwomtari is spoken in a region adjacent to that of the TNG Phylum language Amanab. This and other languages of the TNG Phylum found in this general area all possess body-part tallies and there is a possibility that Kwomtari may have been influenced in this respect as this is the only member of the Kwomtari Stock to have such a tally. Apart from this, the common factor among the Stock appears to be the digit tally which, in two cases, augments a 2-cycle variant.
The data for the Arai Family is such that there is somewhat incomplete information for four languages.[35] None of these appears to possess any indication of a 2-cycle system nor, probably, a digit tally. It is possible, though not certain, that body-part tallies are used: these have not been counted as definite in Table 63. That such tallies may exist in these languages is also suggested by the prevalence of body-part tallies in the other neighbouring languages of this region, particularly Mianmin, a member of the TNG Phylum.[36] Similarly, the data for Amto and Musian, the two constituents of the Amto-Musian Family, do not provide conclusive evidence regarding their counting or tally types except to indicate that there is no trace of a 2-cycle.[37]
Data exist for two languages of the East Bird's Head phylum-level Stock, Meax and Mantion, both of which have systems with a (5, 10, 20) cyclic pattern.[38] As is the case with the languages of the West Papuan Phylum, which are located largely in the western half of the Bird's Head in western Irian Jaya, there is evidence of marked AN influence on certain structural features of both Meax and Mantion.[39] This influence is also apparent on their counting systems and is detectable by the presence of a 10-cycle which appears to have been incorporated into what was originally a (5, 20) digit tally.
For the Geelvink Bay Phylum, data are available on three languages, Yava, Tarunggare, and Bauzi.[40] The last has a (5, 20) digit tally while the Tarunggare system may have a primary 5-cycle. The Yava system, however, has a (5, 10, 20) cyclic pattern. The presence of a 10-cycle can most likely be attributed to AN influence as Yava is the only NAN language spoken on Yapen Island which is otherwise inhabited by the speakers of 12 different AN languages. The current system can be interpreted as being originally a (5, 20) digit tally which has subsequently incorporated a 10-cycle. The common feature shared by the counting systems of the members of the phylum is a primary 5-cycle and it seems likely that, at some time in the past, each possessed a digit tally.
Of the six isolates for which we have data, three are located in the West Sepik Province (PNG) and three are located in Irian Jaya. The first three, Yuri, Nagatman, and Busa, each appear to possess a body-part tally. Yuri is spoken in a region adjacent to several TNG Phylum languages, including Anggor and Dera, both of which have body-part tallies. There is a possibility that that the Yuri-speakers may have acquired their tally from these neighbours, and indeed the same may be true of Nagatman and Busa as well: both of these are located to the east of the Anggor region and are surrounded by languages groups which have body-part tallies.
The other three isolates, Warenbori, Taurap, and Pauwi, are such that the first two have systems which show traces of a 5-cycle while the last appears to have five distinct numerals although there is insufficient data to determine the full nature of the system. It seems likely, however, that at least the first two languages may have irregular digit tallies. No trace of a 2-cycle is apparent in any of the systems.
The foregoing analysis of the counting system and tally situation as it pertains in each phylum and its constituents has attempted to identify which types are possible candidates for the proto system(s) which may have existed in the early history of the phylum. In addition, an attempt has been made to identify which types may have originated in the later history of the phylum either as a result of influence external to the phylum or as a result of innovations. The results of this analysis will now be used in an attempt to reconstruct the prehistory of number and counting in the NAN languages.
8.3 RECONSTRUCTING THE PREHISTORY OF NUMBER IN THE NAN LANGUAGES
The archaeological evidence by which we may judge the minimum timespan of human habitation in the New Guinea region indicates that people were living in the Huon Peninsula, in the Morobe Province (PNG), at least 40,000 years ago and in New Ireland at least 30,000 years ago. Similar dates from archaeological sites in Australia such as those at Keilor in Victoria (40,000 B.P.) and at Lake Mungo in New South Wales (38,000 B.P.), provide additional evidence in that it is assumed that the migratory routes into Australia passed through New Guinea.[41] The dating of materials from the highlands region of New Guinea indicate the presence of a pre-agricultural people at least 25,000 years ago.[42] Given this vast time-scale, it is impossible with current methods to reconstruct the nature of the languages spoken by the various early immigrants into the New Guinea region: while the methods of historical linguistics have been used to reconstruct features of such "proto" languages as Proto Oceanic and Proto Austronesian, the time-scale for these is of the order of 5000 to 7000 years. It is, therefore, out of the question to reconstruct, say, the numerical lexis of a language spoken in New Guinea 10,000 years or more ago and thus know the precise nature of its counting system.
A counting system, however, can be thought of as having both surface and deep features. The surface feature is the numerical lexis: this is subject to the normal and inevitable linguistic change over time. The deep feature is the counting system's cyclic structure and the evidence suggests that this is the one single feature of a system which is likely to remain relatively stable as the daughter languages of some proto language differentiate and diverge. The history of the counting systems of the AN languages, for example, indicates the remarkable stability of the systems' 10-cycle structure over thousands of years despite the divergence in the numerical lexis of one language from another. However, it is also abundantly clear from the evidence, as given in Chapter 7, that the cyclic structure of the counting systems of certain of the AN languages, particularly those in the PNG region, has undergone change. Such change, I suggest, is not the norm but occurs only under certain special circumstances. As discussed in Chapter 6, it is largely in those AN groups which moved into regions occupied and dominated by NAN groups and were influenced by these to the extent that changes occurred to their traditional cultures and economies, that a significant and concomitant change also occurred to the cyclic structure of their counting systems. The act of counting is embedded in the culture of a society and is an integral part of ceremonial occasions and economic transactions: to change the nature of a society's counting system requires changes to its institutions.
As discussed towards the end of Chapter 1, Wurm and his co-workers have attempted a reconstruction of the possible prehistoric linguistic migrations into New Guinea using evidence from both linguistics and other disciplines.[43] Those aspects of the reconstruction which concern us here are that, first, the Australoid migrations into the single New-Guinea continent occurred 50,000 B.P. or earlier and, second, that at a much later date, perhaps around 15,000 B.P., the first migrations of the speakers of the ancient NAN languages occurred. Wurm suggests that these languages may still have direct descendants today in the West Papuan Phylum and East Papuan Phylum languages, as well as in some of the minor phyla and isolates, all of which he believes to be archaic. The members of the Torricelli Phylum are also thought to be archaic and pre-date the spread of the Sepik-Ramu Phylum languages. Third, Wurm indicates that the main NAN migration was that of the TNG Phylum languages which entered the New Guinea mainland in the southern Bird's Head-Bomberai Peninsula area of Irian Jaya, subsequently spreading west to east. Wurm gives the date of the beginning of this west-to-east migration as about 5000 B.P. The argument for this date is based on the presence of AN loanwords in TNG Phylum languages which, Wurm suggests, occurred as a result of the interaction of speakers of ancestral forms of TNG Phylum languages with AN groups in western Irian Jaya prior to the main migrations to the east. Given this postulated late date of entry into New Guinea, the timescale does not allow for the degree of linguistic diversity now apparent in the TNG Phylum languages and thus Wurm believes that their ancestral form started to split up 9000 years or more ago, considerably earlier than their entry into New Guinea. While this brief summary of the NAN migrations into New Guinea omits further details, given by Wurm, of subsequent migrations of the language groups of various phyla within the New Guinea area, it is sufficient for our purposes here.
In considering the results of the analysis given in section 8.2, the distribution of the suggested proto systems and tallies in the major and minor phyla is remarkably restricted: in all phyla the candidates comprise only 2-cycle variants and/or the (5, 20) digit tally. In the large majority of cases, where such systems occur in the languages spoken today, they take the combined form of a 2-cycle variant augmented by a digit tally. While it is possible that this combined form is itself a proto system, however, in most phyla, there is evidence of the two types existing independently and in the West Papuan Phylum languages there is no trace of a 2-cycle. We may recall, in addition, that the 2-cycle variant systems and the digit tally are both present in the Australian languages. The joint existence of both types in New Guinea and Australia does not provide any compelling evidence that one type of system has historical priority over the other. On the other hand, their joint existence in Australia suggests the possibility that they were present prior to the separation of New Guinea and Australia 8000 years or more ago. If this were the case, did the two types of system enter with the original Australoid populations or were they introduced subsequently as a result of NAN migrations into New Guinea and the diffusion of the systems southwards into Australia? Furthermore, did such diffusion necessarily occur prior to the separation of New Guinea and Australia or did it occur after separation with the diffusion occurring via the Torres Strait islands?
With the current evidence available, it seems likely that none of these questions can definitely be resolved satisfactorily. As Wurm indicates, "it has long been believed that Torres Strait constituted a clear linguistic boundary between the Australian and Papuan language areas".[44] Subsequent work, however, has revealed a degree of interaction between the two; Wurm notes that "connections between Papuan and Australian languages across Torres Strait can be attributed to mutual linguistic influence and the adoption of loanwords. It seems the influences have gone in both directions, with northward Australian linguistic influence antedating a scattered southward Papuan influence".[45] Thorne and Raymond indicate that cross-Torres Strait interaction was not just linguistic: "there was considerable contact across this narrow water gap ... and many elements of Melanesian culture were taken up by people across the north of Australia: outrigger canoes, skin drums, smoking pipes, funeral posts, and certain initiation ceremonies and hero cults".[46]
It seems that with considerations such as these we cannot eliminate the possibility of the cross-Torres Strait diffusion - in either direction - of counting systems and tally methods. However, while such presumed trading contact between southern New Guinea and northern Australia is probably a necessary condition for such diffusion to occur, the question of whether it is also a sufficient condition is debatable. The circumstances in which, for example, the AN groups on the east coast of PNG have had substantial changes induced in their traditional counting systems have involved more than just the establishment of trading relations with their NAN neighbours. The changes to numerical institutions are outcomes of more fundamental changes which occurred to the traditional politico-economic institutions of the AN societies as they established sustained and geographically proximate contact with dominant NAN groups. The Australian-New Guinea connection, on the other hand, appears to be more tenuous than this and probably does not satisfy the rather more stringent conditions necessary to induce such basic change. If this is the case, then it seems likely that proto counting systems were present in Australia prior to the separation of New Guinea and Australia and, moreover, that these were already present in the languages of the Australians or were introduced by the early NAN migrations that began prior to separation.
The picture that we have of the distribution of proto systems in the various NAN phyla does not strongly suggest that the languages of one phylum rather than another may have been the carriers of each of the two proto systems into New Guinea. The most economical interpretation of events, rather, suggests that the 2-cycle numeral system and the digit tally were present from an early date in the ancient languages ancestral to each of the major and minor phyla. It may be that the digit tally entered New Guinea independently of the 2-cycle numeral system and that they were brought by different language groups, however subsequent interactions between the NAN groups over many millennia have resulted in both types being present, either separately or in hybridized form, in each of the phylic groups. In addition, other developments within New Guinea due to localized innovations and the introduction of AN influence have introduced a degree of complexity into a situation which, I suggest, was not originally there.
There is an important exception to the idea that it is difficult to associate the proto counting and tally types with a particular phylum, given the present-day distribution of languages. I have suggested above that the body-part tally appears to be associated specifically with members of the TNG Phylum and that, where this is found sporadically in other New Guinea languages, this may probably be attributed to influence by neighbouring TNG Phylum languages. However, we need to recall that, as indicated earlier, body-part tallies very similar to those found in New Guinea are also found in southern Australia and in the islands of Torres Strait. In attempting to interpret this situation we may consider, first, the possibility that the body-part tally was not present in New Guinea prior to the advent of the languages ancestral to the TNG Phylum and that it was the speakers of these who introduced it. If this was the case, then the presence of the tally in Australia suggests that it was diffused from New Guinea southwards into Australia.
We have the same difficulty here as was discussed above regarding whether the diffusion took place before or after the separation of New Guinea and Australia. If the body-part tally was introduced to Australia prior to separation then this requires the TNG Phylum languages to have been established in the region 8000 to 10,000 years ago. This date conflicts with Wurm's suggestion that these languages began their west to east migration into New Guinea about 5000 B.P. However, this date is based on the observation that AN loanwords are found in certain of the TNG Phylum languages and that the contact with AN groups probably occurred in the western part of New Guinea when the AN-speakers arrived in that region perhaps about 5500 years ago. If the TNG Phylum languages were, on the other hand, already established in New Guinea long before this date then it seems likely that the AN contact occurred not in the west but in the east, perhaps in the Markham Valley of the Morobe Province (PNG), after the establishment of POC and the migration of AN-speakers onto the mainland.[47]
An alternative scenario, which we might note, for explaining the joint presence of the body-part tally in New Guinea and Australia is that this tally was already present in Australia prior to the advent of the NAN languages in New Guinea. Sometime after the establishment of the TNG Phylum languages in the region there was a northward diffusion of the tally as a result of Australian influence on these NAN groups, as noted by Wurm,[48] with subsequent further diffusion into the New Guinea highlands regions. Interesting though this conjecture is, I suggest that, on balance, it seems less likely than the alternative southwards diffusion in that, while the body-part tally has only a sporadic appearance in Australia, it has a substantial occurrence in New Guinea suggesting that the latter was its original homeland.
It was observed earlier that the body-part tally is not uniformly distributed throughout the TNG Phylum languages and that it tends to occur in certain stocks located in the central and southern highlands, in the Sepik Provinces (PNG), and in parts of Irian Jaya. One possible explanation of this is that the ancestors of the TNG Pylum languages may have comprised at least two different strands, one strand bringing with it the 2-cycle numeral system and the body-part tally, and another strand bringing a 2-cycle numeral system and a digit tally. Alternatively, if the ancestors of the TNG Phylum entered New Guinea bringing only the 2-cycle numeral system and the body-part tally then we must assume that those language groups which have lost the body-part tally have done so within New Guinea as a result of contact with languages from other phyla. Generally speaking, according to this interpretation, the change has been such that the body-part tally was displaced by the digit tally. In certain cases, particularly for languages in the Southern Highlands Province, a modified 4-cycle digit tally was adopted and used for counting while the body-part tally was retained for calendrical purposes. For a number of languages in the Finisterre-Huon Stock and the Madang-Adelbert Range Subphylum, both the 2-cycle system and the body-part tally have been displaced by the digit tally.
If Seidenberg's view of the diffusion of counting practices, as dealt with in the previous chapter, were applied to the situation in New Guinea and Australia, the events that we have discussed above would have developed in the following way. The ancestors of the Australian languages and those of all the major and minor phyla of the NAN languages would all have been established in the region well before the time suggested by Seidenberg for the genesis of the 2-cycle system, that is about 5000 to 6000 B.P., which is just prior to the time that the first AN immigrants moved into the POC homeland in eastern New Guinea. Thus, none of these speakers of these languages, according to this view, would have possessed a means of enumeration and they would remain in this state until the 2-cycle system had diffused across the world from the Middle East, with the diffusion of other systems following subsequently. On the other hand, the view of the prehistory of counting and number which has been developed above presents a different picture in which the possession of numerals and a means of tallying is seen as an archaic feature of human societies. In this view, the 2-cycle numeral system, the digit tally, and the body-part tally, were brought into Australia and New Guinea as part of the cultural baggage of the ancient immigrants whose descendants now speak the languages which exist today. Similarly, as discussed further below, the 10-cycle system entered the New Guinea region with the original AN immigrants. We therefore have that the essential features of the counting and tallying situation which we see in New Guinea and Australia today had already been laid down by the time that the city-states of the Middle East were being established and that, therefore, the origins of counting cannot be sought in these but in the pre-agricultural and neolithic societies of a much earlier historical period.
8.4 RECONSTRUCTING THE PREHISTORY OF NUMBER IN THE AN LANGUAGES
The current situation regarding the nature of the counting systems distributed throughout the AN languages of New Guinea and Oceania has been delineated in the previous chapters. In Chapter 1 we discussed Ross's recent classification of the AN languages of PNG and the northwest Solomon Islands into two first-order subgroups, namely the Admiralties Cluster and Western Oceanic, the latter comprising three clusters termed the North New Guinea, the Papuan Tip, and the Meso-Melanesian.[49] The remainder of the Oceanic AN languages of Island Melanesia and the Pacific comprise a further subgroup, Central/Eastern Oceanic, delineated by Lynch and Tryon.[50] In Chapters 2 to 5, the distribution of the various counting system types among the PNG clusters and the subdivisions of Central/Eastern Oceanic were discussed. In Chapter 6, a number of brief case studies of a several AN societies were given and these dealt with certain matters relating to the place of counting and number in those societies. Other matters relating to the existence and nature of numeral classification were dealt with, as was the extent to which large numbers are found in the AN languages. Finally, in Chapter 7, the changes which appear to have occurred to the cyclic structure of certain of the AN counting systems were summarized together with some discussion of how these changes may have come about.
In this section we will begin by summarizing the material given in Chapters 2 to 5 as it relates to the AN languages. In Table 64, the distribution of the various counting system types now apparent among the AN languages of New Guinea is given. The subdivisions of the languages are Ross's four clusters together with a group of five Oceanic AN languages which are located in Irian Jaya. In Table 65 we summarize how the counting system types are distributed among the remaining AN languages of Island Melanesia, Polynesia, and Micronesia. The discussion which follows uses the language subdivisions employed in each table and for each subdivision an attempt is made to reconstruct the prehistory of the counting systems of its constituent languages. This task is approached in a somewhat different manner from that used in the previous discussion of the prehistory of the NAN languages. Instead of attempting to infer the nature of the proto system of the AN languages we assume that this is known. The methods of historical linguistics have enabled linguists to reconstruct the numerals of POC, given previously in Table 36, and the ten distinct reconstructed numerals indicate that the POC system was a 10-cycle one. The reconstruction of the prehistory of the AN counting systems involves, essentially, tracing the fate of this system as the daughter languages of POC developed and dispersed throughout New Guinea and Oceania and, where possible, placing this dispersal in a chronological framework.
Table 64
Showing the Distribution of
Counting System Types Among the Four Clusters of the PNG Languages and the AN
Languages of Irian Jaya
_____________________________________________________________________
Admiralties/ North New Papuan Meso- Irian Total
St Matthias Guinea Tip Melanesian Jaya
____________________________________________________________
(2) 0 2 0 0 0 2
(2, 5) 0 15 2 1 0 18
(2'', 5) 0 7 5 0 0 12
(5, 20) 1 19 11 1 2 34
(5, 10) 1 20 7 17 0 45
(5, 10, 20) 0 13 5 0 1 19
(10, 100) 23 0 9 41 0 73
(10, 20) 0 0 0 3 0 3
(4) 0 2 0 0 2 4
___________________________________________________________
Totals 25 78 39 63 5 210
_____________________________________________________________________
Table 65
Showing the Distribution of
Counting System Types Among the Languages of Island Melanesia, Polynesia and
Micronesia
_____________________________________________________________________
S.E. Vanuatu New Fiji/ Polynesia/ Total
Solomonic Caledonia Rotuma Micronesia
_____________________________________________________________
(5, 20) 0 15 8 0 1 24
(5, 10) 0 68 0 0 0 68
(5, 10, 20) 0 0 19 0 0 19
(10) 28 19 0 3 39 89
(10, 20) 0 0 0 0 6 6
_____________________________________________________________
Totals 28 102 27 3 46 206
_____________________________________________________________________
8.4.1 The POC Language Community and the Lapita Cultural Complex
The reconstruction of the nature of the POC language community, the dating of its establishment and of its breakup and dispersal into Island Melanesia and the remainder of the Pacific, has been a joint enterprise between linguists and archaeologists. The lexical reconstruction of POC now extends to about 2000 items. Pawley and Green note that these "represent only a fraction of the total vocabulary of the language community, but tell us a good deal about the culture". They add that "these reconstructions indicate that POC speakers had an economy based jointly on gardening and fishing. The major root and tree crops of contemporary Oceanic societies, other than the sweet potato and cassava, are represented: yam, taro, breadfruit, coconut, etc. A variety of fishing techniques were exploited, including nets, lines, basketry traps, and plant poisons."[51] The reconstruction of certain kinship terms suggests the possibility "that POC society had descent groups in which land rights were invested" and a further set of terms suggests that the society also had hereditary chiefs.[52]
It was indicated at the end of Chapter 1 that the locus of the POC community is thought to be New Britain, in or near the Willaumez Peninsula.[53] Ross notes that if "it remains the case that the earliest settlement date from the Admiralties lies around 1850 B.C., then the latest possible date of arrival in New Britain for the ancestors of the Proto Oceanic speech community will be around 2100 B.C."[54] There are two points to note regarding these dates. The first is that they are based on work by Kennedy in the Admiralties, the results of which were published in 1981.[55] Subsequent studies, also by Kennedy, have however resulted in the establishment of earlier dates for settlement of the Admiralties at about 4500-5000 B.P. and this implies that the POC community must have been in place at some time prior to this period.[56] The second point to note is that the dating of these events is based on archaeological evidence and on an assumption that there is a connection between the POC community and the cultural complex associated with the Lapita-style ceramic tradition found throughout Island Melanesia and western Polynesia.[57] This connection provides a means of establishing a chronological sequence for the spread of the descendants of the POC community from their putative homeland onto the PNG coastal areas and southwards into the remainder of Melanesia.
8.4.2 Tracing the Fate of the POC Counting System in PNG
According to Ross, "at least two groups of people - some of whose descendants spoke Proto Admiralty and Proto South-East Solomonic respectively - departed from the (POC) homeland area before the occurrence of the innovations which characterise Western Oceanic languages".[58] The most probable migratory route of the first group from the POC homeland to the Admiralties is, as also noted by Ross, through New Ireland and Mussau in the St Matthias group.[59] While these travellers have left no trace on the languages spoken in New Ireland, Ross indicates that the language spoken on Mussau, Emira-Mussau, may be related to those in the Admiralties Cluster. Once the separation from the New Britain-New Ireland occurred, it seems likely that "Proto Admiralty and its descendants would have developed without much external linguistic influence."[60] As indicated above, the earliest date established for the settlement of the AN immigrants in the Admiralties is the period 4500-5000 B.P.
From Table 64 we can see that 23 languages in the Admiralties/St Matthias group have 10-cycle systems while one, Nauna, has a (5, 10) system and a further one, Seimat, has a (5, 20) system. Of those languages possessing 10-cycle systems, only one, the Mussau dialect of Emira-Mussau, has a pure 10-cycle system with a completely intact second pentad.[61] The remainder are such that 21 systems belong to the subtractive "Manus" type and one, Wuvulu-Aua, has features of the "Motu" type. We should also note that with regard to Emira-Mussau, there is some evidence, published by Friederici in 1913, that the Emira dialect had at one time a (5, 10) system but this no longer appears to be in use. Thus, all the members of the Admiralties Cluster now have counting systems which deviate in some way from the system of their POC ancestor and the changes are such that they occur in the numerals of the second pentad. As discussed in Chapter 7, there are two ways of viewing these changes. The first is that the changes in the second pentad are innovations which were not induced by external influence but occurred spontaneously. The second view is that the second pentad instability may have resulted from the interaction of the original 10-cycle system with the (5, 20) digit tally system perhaps by means of the AN migrants coming in contact with NAN groups, conceivably in New Ireland, for a sufficiently sustained period for changes to be induced in the AN numerical institutions. Whatever the mechanism, the subtractive construction used in most of the counting systems of the Admiralties Cluster appears to be a post-POC innovation that, with one exception, is not shared with other AN languages.[62]
One further aspect of number in the Admiralties languages, discussed in Chapter 6, is the occurrence of numeral classification and, in particular, the use of classifier constructions in which numeral roots, the "quantifiers", are suffixed by "classifiers", that is a QC order is used in noun phrases, as indeed we also find in the Micronesian languages. While Ross has indicated that classifiers are reconstructible for POC, he has suggested that this QC sequence, rather than the reverse, is an innovation.[63] On the basis that the QC sequence is commonly found in the non-Oceanic AN languages of South-East Asia, I have suggested in Chapter 6 this was perhaps the more archaic form. Be that as it may, the phenomenon of numeral classification does not now generally appear in the majority of the Oceanic AN languages with the exception of some of the Papuan Tip Cluster and a number of the Polynesian languages. It may be the case that the ancestors of the Admiralties Cluster, having left the POC homeland relatively early, retained this original feature of POC.
After the departure of the ancestors of the speakers of Proto Admiralty and Proto South-East Solomonic from their homeland, the innovations unique to the Western Oceanic group occurred.[64] This group, according to Ross, comprised the remaining three clusters of the AN languages located in PNG and the north-west Solomon Islands. We now consider the fate of the POC counting system in each of the clusters
Referring to Table 64, of the 78 languages of the North New Guinea Cluster for which we have data, none now possesses a counting system with a primary 10-cycle. In reconstructing the history of the cluster, Ross argues that the current languages are descended from an early Oceanic communalect which developed in the POC homeland.[65] Two groups subsequently separated from the homeland: the first, the ancestors of the Proto Schouten group, moved onto the PNG mainland and moved along the north-west coast and adjacent islands, occupying Manam Island and dispersing from there to the islands of Wogeo and Bam, and also along the north coast to the Sepik Provinces. Ross notes that in Proto Schouten the POC numeral 10, *sangapulu, has been replaced by *kulemwa.[66] Other notable changes which occurred in this group are the adoption, by the Wogeo and Bam language groups, of a 4-cycle system (see Chapter 5) and the adoption of a 2-cycle system by the Sera and Sissano language groups, most likely as a result of the influence of NAN languages. With these exceptions, all the other languages of this group now have systems with a primary 5-cycle.
The second group of the North New Guinea Cluster to depart from the POC homeland were the speakers of Proto Huon Gulf who settled first on the coast of the Huon Gulf in the Morobe Province with subsequent migrations inland. One such group which moved inland was the ancestors of the Markham Family, discussed in Chapters 6 and 7, and whose member languages now mainly possess 2-cycle counting systems. The exception to this is Labu which has a (5, 10, 20) system and which shows evidence of having possessed numeral classification such that the classifier preceded the numeral, that is it had a CQ sequence.[67] The other group that migrated inland gave rise to the languages now found in the Mumeng region of the Morobe Province, most of which now possess 2-cycle variant systems.[68]
The North New Guinea Cluster group remaining in the vicinity of the POC homeland and who spoke, according to Ross, Proto Ngero/Vitiaz, now has descendants located in the East and West New Britain Provinces as well as in the Madang and Morobe Provinces. With the three exceptions of Matukar, Roinji, and Nenaya, which have 2-cycle variant systems, the remaining descendants of Proto Ngero/Vitiaz all possess systems with a primary 5-cycle.
The inference that can be drawn from this analysis is that very early in the history of the North New Guinea Cluster, the ancestral communalect spoken in the region of the POC homeland had its counting system affected in such a way that it ceased to have a primary 10-cycle and by loss of the numerals 6 to 9 became instead either a (5, 10) or (5, 10, 20) system. This may have occurred as a result of interaction with NAN groups located in the West New Britain area and who possessed (5, 20) digit tally systems. The migrants who departed from the homeland and moved onto the PNG coastal regions carried their 5-cycle system with them. Further interaction with NAN groups on the mainland resulted in some of the AN languages losing more of their numeral lexis, thus acquiring 2-cycle variant systems. In the case of Wogeo and Bam, the adoption of a 4-cycle system may have been a localized innovation although, as noted in Chapters 5 and 7, 4-cycle systems have a sporadic appearance along the northern seaboard of PNG and Irian Jaya which suggests the possibility of diffusion having occurred. There are no firm archaeological dates resulting from Lapita sites on the PNG coast which might give an indication of when the North New Guinea Cluster languages may have entered this area; however this must have occurred after the departure of the ancestors of the Admiralties Cluster who were settled in the Manus region by 4500 B.P.
Ross says that "Proto Papuan Tip seems to have separated from an early Oceanic dialect chain ... and, to judge from the exclusively shared innovations of most member languages, to have remained separate from it".[69] Ross also indicates that a subsequent split in the original group that migrated away from the POC homeland gave rise to two daughter networks which he terms the Nuclear Papuan Tip and the Peripheral Papuan Tip.[70] The languages of the first network are now largely located in the Milne Bay and Oro Provinces on the mainland and the D'Entrecasteaux Islands adjacent to it. None of the languages for which we have data now possesses a 10-cycle system: 7 have a 2-cycle variant and the remaining 18 have systems with a primary 5-cycle. The languages of the Peripheral Papuan Tip network are located in two main areas: the eastern islands of the Milne Bay Province, and along the southern coastal and inland region of the Central Province.[71] At least two languages situated in the the Milne Bay Province, Nimowa and Sudest, have 10-cycle systems with numerals very similar to those of their POC ancestor. The other four languages of this network and which are situated in this Province each has a system with a (5, 10) cyclic pattern. This Milne Bay group is also distinguished by the possession of numeral classification which is such that the classifier precedes the numeral, that is a CQ sequence operates. The remaining 10 languages of this network and which are situated in the Central Province are such that three have (5, 10) systems and the remainder have the "Motu" type, discussed in Chapter 4.
The foregoing discussion suggests the following interpretation. The speakers of Proto Papuan Tip left the POC homeland with an intact 10-cycle counting system. After the split into the Nuclear and Peripheral Papuan Tip networks, the languages of the former network lost at least the numerals 6 to 9 thus changing the primary cycle of their counting system from 10 to 5. Some of these languages had a further loss of their numeral lexis in the first pentad giving rise to systems which are 2-cycle variants. These changes to the counting systems of the Nuclear group may be most likely attributed to the influence of NAN groups which have a strong presence in the Milne Bay and Oro Provinces. With regard to the Peripheral Papuan Tip languages, only those situated in the easternmost islands of the Louisiade Archipelago retained a 10-cycle system while Kilivila, Muyuw, and Budibud developed systems with a (5, 10, 20) cyclic pattern. The remaining part of this network migrated to the south coast of the Central Province, possibly settling inland where the Sinagoro language is now spoken.[72] The development of the "Motu" type of system may have developed here. Several languages of this group have systems with a primary 5-cycle and this may have occurred prior to migrating from the Milne Bay Province. Kirk notes that the archaeological evidence indicates that the migration of AN groups along the southern coastline of the Central Province appears to have happened at about 2000 B.P.[73]
The 64 languages of the Meso-Melanesian Cluster for which we have data are now located in West New Britain, New Ireland, parts of East New Britain, the North Solomons Province, and the north-western half of the Solomon Islands. Ross indicates that "the linguistic evidence is ambiguous as to whether there were one or several migrations (that is by speakers of different dialects at different times) from the Meso-Melanesian homeland to New Ireland and its offshore islands, but it is clear that the portion of New Ireland from the present day township of Namatanai southwards became a centre of dispersal, from which Proto Northwest Solomonic originated".[74] In addition to this southward migration, some groups also migrated back across St George's Channel and into East New Britain.
Two languages in West New Britain, descended from the stay-at-home group of the Meso-Melanesian Cluster, possess 10-cycle systems and a further four have systems with a (5, 10) cyclic pattern.[75] The languages of southern New Ireland, which formerly served as the centre of dispersal, uniformly have 10-cycle systems, however as we proceed north the majority of languages have systems with a (5, 10) cyclic pattern. Lihir, spoken on an island off the east coast, has a (5, 20) digit tally system while Tomoip, located in East New Britain, has a system with a (2, 5, 20) cyclic pattern. Proceeding south to Nissan Island and Buka, the languages have 10-cycle systems while, on Bougainville, several languages have 10-cycle systems and a number have (5, 10) systems instead. South of Bougainville, in the northwest Solomon Islands, the 23 Meso-Melanesian languages of this region uniformly possess 10-cycle systems, three of these having secondary 20-cycles.
This discussion of the current distribution of counting systems in the Meso-Melanesian Cluster enables the following interpretation to be made. The speakers of Proto Meso-Melanesian had a 10-cycle system which they carried with them to New Ireland. While the date of their first arrival in New Ireland is unknown, the earliest Lapita site, at Ambitle Island in the Feni Group to the east of southern New Ireland, has yielded an estimate of 3200 B.P. and this suggests that New Ireland proper would have been settled sometime prior to this time.[76] After this settlement, the 10-cycle system was carried southwards into Nissan and Buka. On Bougainville, certain languages lost part of their numeral lexis and acquired (5, 10) systems, probably as a result of the strong presence of East Papuan Phylum languages which influenced the immigrant AN groups. In New Ireland, as the AN migrants moved northwards they may have also come into contact with established NAN groups (although today only one such group, the Kuot-speakers, still survives) and as a result acquired (5, 10) systems with a loss of their numeral lexis in the second pentad. A subsequent migration brought the ancestors of the Tolai-speakers to East New Britain, carrying their (5, 10) system with them.
The foregoing discussion deals with the vicissitudes of the POC 10-cycle system as the descendants of POC dispersed from their homeland and into the coastal and island regions of PNG. We consider, finally, the fate of the POC system as the AN migrants moved southwards into Island Melanesia and beyond.
8.4.3 Tracing the Fate of the POC Counting System in Island Melanesia, Polynesia, and Micronesia
The two groups which left the POC homeland early before the innovations unique to Western Oceanic occurred were the ancestors of the speakers of Proto Admiralty, discussed above, and of Proto South-East Solomonic. This latter group moved southwards into the Solomon Islands, and possibly further, and may be the source of the Central/Eastern Oceanic group of languages which, as noted in Chapter 1, comprises "all the languages of north and central Vanuatu, Fiji, Polynesia, and Micronesia ... together with the southeast Solomon Islands, Utupua and Vanikoro, the south Vanuatu, and possibly the Loyalties and New Caledonia groups".[77]
Referring to Table 65, there are 28 languages comprising the South-East Solomonic group and the Eastern Outer Islands group and all of these have systems with a primary 10-cycle. Ross indicates that various features of the South-East Solomonic languages imply that they have been little disturbed by external linguistic influence, including NAN influence, since their separation from POC.[78] The counting systems of this group, therefore, are probably direct descendants from the POC 10-cycle system and they have retained the original 10-cycle nature unlike the systems of many of the Western Oceanic languages. If the migration away from the POC homeland occurred relatively early, as Ross suggests, then we might expect that the arrival in the Solomon Islands may have happened at a time not too different from that when the other early immigrants from the homeland arrived in the Admiralties, i.e sometime before 4500 B.P. The earliest date available from archaeological evidence, however, is that from an excavation in Santa Ana which yields an estimate of 3000 B.P.[79]
In Vanuatu, the linguistic situation is now such that there are 105 AN languages spoken, three of which are Polynesian Outliers. No NAN languages are present. Referring to Table 65, of the 102 non-Polynesian languages, 19 have systems with a primary 10-cycle, 68 have (5, 10) systems, and 15 have systems with a (5, 20) cyclic pattern. The distribution of these is not uniform throughout the islands of Vanuatu as can be seen by reference to Maps 10 and 14. The northern Torres and Banks Islands account for 13 languages, all of which have (5, 10) systems. The remainder of the (5, 10) systems are located on the central islands of Espiritu Santo (19), Maewo (3), Pentecost (4), Malekula (21), Ambryn (4), and Efate (3). The 10-cycle systems are mainly found in parts of these central islands, including Malo Island to the south of Espiritu Santo. It is on Malo that the earliest Lapita sites in Vanuatu are located and these have yielded dates that indicate occupation at about 3000 B.P.[80] The languages with (5, 20) systems are located in the central and southern islands, particularly Tanna and Aneityum. Archaeological sites on each of these islands have yielded dates indicating occupation by 2370 B.P. and 2900 B.P. respectively.[81]
The existence of 5-cycle systems in Vanuatu has been discussed previously in section 7.5.3. In that discussion, three possibilities for their existence were suggested: (1) that the 5-cycle systems were introduced by long distance diffusion from PNG, by-passing the Solomon Islands; (2) interaction of the ancestors of the Vanuatu languages in situ with now-extinct NAN languages; and (3) uninfluenced, spontaneous change. There is no compelling evidence, archaeological or linguistic, for (2). With regard to (1), the internal linguistic evidence of the Vanuatu languages does not appear to suggest that there was an original AN settlement followed later by one or more other intrusive AN migrations which may have brought a (5, 10) cycle system, as well as other innovations, with them. On the other hand, archaeological evidence from central and northern Vanuatu does suggest that several unrelated pottery traditions, only one of which is Lapita, overlap.[82] This may indicate that there were several different movements of AN groups into the islands over a period of two or three thousand years.
With regard to (3), it has not been generally necessary to invoke the mechanism of spontaneous change in the counting systems of PNG because of the strong and ubiquitous presence of the NAN languages and the likelihood of their influence on AN groups. In Vanuatu, however, if as seems likely we cannot attribute counting system change to NAN influence in situ and if, for the moment, we discount long-distance diffusion, then uninfluenced and spontaneous change seems to be the default mechanism. The circumstances which may bring about such change need to be considered.
First, we have suggested above that counting system change is an outcome of changes to a society's politico-economic institutions. In Vanuatu, such changes might conceivably have occurred as groups settled on some of the larger islands and moved into the interior regions of these, thus abandoning their traditional maritime economies. Second, the counting system change is in the direction of the introduction of a primary 5-cycle. It may be that finger tallying, and probably toe tallying as well, may have been an accompaniment to the POC method of counting: this is suggested by the use of POC *lima, that is "hand", for the numeral 5. Thus, in serial counting to 10, two alternative methods may have customarily been used: either all ten numerals were enunciated or, on reaching 5, the units were repeated until 10 was reached; this essentially introduces a primary 5-cycle. This is a somewhat radical proposal because it suggests that, while the reconstructed POC system is a 10-cycle one, nevertheless the exigencies of everyday counting mean that the system has an inherent instability which, under certain circumstances, may cause it to become a 5-cycle one and that this may occur without external influence, for example by NAN languages. With certain groups, this method of enumeration could become the norm, resulting in the atrophy of the original 10-cycle system in favour of a (5, 10), (5, 20), or (5, 10, 20) system.
The situation in Vanuatu, then, may have developed as follows. An AN migration from the north brought settlers - who were probably the initial settlers of the region - carrying with them a 10-cycle counting system. These occupied the northern/central region of the islands. Over a period of time there was probably a further filtering through the islands southwards to Tanna and Aneityum and then to New Caledonia. Tryon notes that an early migration from Vanuatu appears to have reached Fiji by 3500 B.P.[83] He adds that "at about this time, a set of migrations apparently began in the north/central Vanuatu region, one moving north, spreading the Austronesian languages through Micronesia (for which there is evidence of an east to west spread), another moving southeast to the Fiji group. From there, after a period of consolidation, the Polynesian languages evolved, moving out from the Tonga-Niue area sometime around 1000 B.C.".[84]
The counting system situation in Fiji, Rotuma, Polynesia, and Micronesia, as given in Table 65, is such that all the languages, with one exception, have 10-cycle systems. The exception, Faga-Uvea, is a Polynesian Outlier in the Loyalty Islands: it has a (5, 20) system and is situated in a region where 5-cycle systems are universal.[85] The inference which can be drawn is that the AN migrants to Fiji and Micronesia carried 10-cycle systems with them and that this system was retained in Proto Polynesian and was subsequently carried with the Polynesian dispersal throughout Triangle Polynesia which was largely complete with their arrival in New Zealand by 900 A.D. The situation in Micronesia is distinguished by the marked presence of numeral classification which, like the Admiralties group, has a QC order. In the Polynesian languages which still exhibit numeral classification, a CQ order is the norm. Even though the two sequences differ, the presence of numeral classification in both the Micronesian and Polynesian languages suggests that it may have been present in the languages ancestral to those groups and which were spoken in the north/central Vanuatu region.
Referring to Table 65, the counting system situation in New Caledonia, including the Loyalty Islands, discussed in Chapter 3, is such that 19 languages have systems with a (5, 10, 20) cyclic pattern and 8 have (5, 20) digit tally systems. The geographical distribution of these is given in Map 11. The uniform occurrence of systems with a primary 5-cycle present similar problems of interpretation as in the case of Vanuatu, discussed above. Pawley and Green have cited archaeological evidence of an aceramic tradition in New Caledonia dated at 5000 B.P.[86] They do not accept, however, a suggestion by Shutler that there may have been a NAN occupation of the region prior to the arrival of the AN immigrants.[87] It seems therefore unlikely that the change to the AN counting systems can be attributed to the influence of NAN groups in situ. One possibility is that once the 5-cycle system was established in Vanuatu, AN migrants moved south into New Caledonia carrying the system with them.
8.4.4 Summary
Of the 420 Oceanic AN languages for which we have data, only 171 or 41% have counting systems with a primary 10-cycle while 209 or 50% have systems with a primary 5-cycle. The original AN immigrants who settled in the POC homeland, probably about 5000 years ago, brought a 10-cycle system with them, as judged from the reconstructed Proto Austronesian numerals.[88] The essential features of this system have survived in certain of the daughter languages of POC which are now found in PNG, Island Melanesia, Micronesia, and Polynesia, and thereby displaying remarkable stability over thousands of years. And yet, as the discussion above has indicated, various changes have occurred over time to the way in which these early AN immigrants enumerated their world. If, as seems likely, the inhabitants of the POC homeland used numeral classification, this survives today in only a relatively small number of languages. Also, the majority of the Oceanic AN languages now have counting systems with a primary 5-cycle, although many of these still have a secondary 10-cycle. For many of these languages in PNG, the change to a 5-cycle system and, in some cases, 2-cycle variants, can be attributed to the influence of NAN languages. However, for some languages, this attribution can be somewhat tenuous and I have suggested the possibility that, under certain conditions, the 5-cycle systems may have developed from the original POC system through the practice of accompanying serial counting with finger tallying, a mechanism which induces change without the requirement of an external stimulus such as the sort of diffusion suggested by Seidenberg. New Guinea and Oceania, once the NAN and AN languages were in place, may be regarded as a virtually closed system: the initial conditions having been set, the situation evolved over time under its own internal dynamics to produce the complex picture that we see today. Within this system we may trace the genealogy of the counting systems and tally methods that exist in the contemporary indigenous societies of the region and this reconstruction may provide an indication of how enumeration developed in human societies generally.
8.5 GENEALOGIES OF ENUMERATION IN NEW GUINEA AND OCEANIA
The prehistoric epoch which begins with the introduction of various means of enumeration into New Guinea and Oceania may be divided into two periods. First, that in which the NAN languages arrived and then subsequently spread throughout New Guinea, undergoing speciation over a period of 10,000 years or more. This occurred after the much earlier Australoid migrations through New Guinea and into Australia: the NAN migrations which followed overlaid the remnants of whatever Australoid groups remained in New Guinea. The second and later period begins at about 5500 B.P. when AN immigrants reached the western part of Irian Jaya. A further migration to the east brought AN settlers to the POC homeland by about 5000 B.P. after which a series of movements out of the homeland resulted in the occupation of the coastal and island regions of PNG and eventually the remainder of Oceania. In PNG, this brought about a degree of interaction between AN and NAN language groups. The two figures given below summarize the results of the analyses given in 8.2 to 8.4 above and they respectively provide outlines of the genealogical development of enumeration during each of these two periods.
NAN LANGUAGES
(From 15,000 to 5000 B.P.)
(TNG Phylum)
body-part tally pure 2-cycle (5, 20) digit tally
Ù Ù Ù
Ù Ù Ù
Ù Ù Ù
````````````|`````````````````|```````|``````|``````|
hybridized
body-part (2,5) (2',5) (2'',5) Ù
Ù
|````````````````|
4-cycle 6-cycle
Figure 2: Genealogy of the NAN Counting Systems
and Tally Methods Prior to the AN Migrations
AN LANGUAGES
10-cycle
Ù
Proto Austronesian (~7000 B.P.)
Ù
Proto Oceanic (~5000 B.P.)
Ù
NAN influence 2-cycle Ù NAN influence 5-cycle
Ù Ù Ù
````````|```````|```````````````|```````|`````````|``````
(2,5) (2,10) Ù (5,10) (5,20) (5,10,20)
Ù
Ù
|````````````````````|
Motu Manus
type type
(post-2000 B.P.) (post-4500 B.P.)
Figure 3: Genealogy of the AN Counting Systems
The date of 15,000 B.P. given for the entry of the NAN languages into New Guinea is not meant to indicate the date of origin of the 2-cycle system or the tallies. Similarly, the date of 7000 B.P. assigned to the existence of the 10-cycle system in Proto Austronesian is not meant to indicate the date of origin of that system. In both cases the dates provide the minimum time spans for their existence: it is likely that their origins can be extended much further back in time than these dates suggest.
[2] See, for example, Pawley & Green (1973, 1985), Green (1973, 1979, 1981), Spriggs (1984), Allen (1984), Blust (1976), Kennedy (1983), Kirch (1982), Tryon (1984).
[5] The 10 languages are: Tehit, Kalabra, Moi, Moraid, Karon Pantai, Madik, Brat, Hattam, Borai, and Amberbaken.
[10] Wurm (1982, p. 240).
[11] See Chapter 4 and Chapter 7 (p. 181).
[12] The information of the general features of the Torricelli Phylum is taken from Wurm (1982, pp. 226-230).
[13] Wurm (1982, p. 229).
[14] See the Southern Arapesh data in (CV14, pp. 9-12) and the Mountain Arapesh data in (CV14, pp. 37-44).
[15] The Boiken data are given in (CV14, pp. 44-47).
[16] The Wapi data are given in (BV9, pp. 18-19).
[17] The Murik data are given in (CV14, pp. 74-75), the Kapriman data in (CV14, pp. 65-66), and the Kopar data in (CV14, pp. 76-77).
[18] Wurm (1982, p. 218).
[19] Wurm (1982, pp. 97-99).
[20] The data for these 5 languages may be found as follows: Kewa (BV10, pp. 25-38), Wiru (BV10, pp. 39-40), Hagen (BV9, pp. 25-35), Enga (BV9, pp. 10-17), and Mendi (BV10, pp. 20-25).
[21] The data for Nafri are found in DV5T86.
[22] The data for Ormu and Yotafa are found respectively in DV5T85 and DV5T84.
[23] The data for the members of the Kolopom Family are found in DV5T118-T121.
[24] The data for Kanum and Tonda are found in DV5T132 and BV12T22 respectively.
[25] The data for Baham and Iha may be found, respectively, in DV5T33 and DV5T29.
[26] The data for Pay, Tani, and Ulingan may be found, respectively, in CV15T14,15, CV15T16, and CV15T17.
[27] The Kovai data are given in CV16T1. Its AN neighbours are Mangap, Mutu, and Barim.
[28] The Kwale data are given in BV7T17 and the Magi data in BV7T30.
[29] The data for Koita, Koiari, and Domu are found, respectively, in BV7T12, BV7T13, and BV7T26.
[30] The minor phyla and their constituent languages are discussed in Wurm (1982, pp. 247-251).
[31] The isolates are discussed in Wurm (1982, pp. 252-254). The six languages for which some data exist are: Warenbori (DV5T61), Taurap (DV5T64), Busa (CV13T22), Yuri (CV13T20), Nagatman (CV13T21), and Pauwi (DV5T62). Wurm includes Maisin in his list of isolates: this is found in AV5T12 where it has been taken to be an AN language which has been extensively influenced by NAN languages.
[32] The data for these three languages may be found as follows: Vanimo (CV13T2), Wutung (CV13T1), and Rawo (CV13T3).
[33] The Sko data are given in DV5T87 and the Sangke data in DV5T88.
[34] The data for Fas are given in CV13T16 and for Baibai in CV13T17. The Kwomtari are given in CV13T18 and the Biaka data in CV13T19.
[35] The languages of the Arai Family for which some data exist are: Rocky Peak (CV14T11), Iteri (CV14T12), Bo (CV14T13), and Nimo (CV14T26).
[36] The Mianmin data are given in (CV13, pp. 60-64).
[37] The data for Amto and Musian are given respectively in CV13T27 and CV13T26.
[38] The Meax data are given in DV5T19 and the Mantion data in DV5T22.
[39] Wurm (1982, p. 249).
[40] The data for Yava are given in DV5T46, for Tarunggare in DV5T46, and for Bauzi in DV5T63.
[41] Thorne and Raymond (1989, p. 43) give the dates for both New Guinea and Australia.
[42] Brown (1978, p. 271) quoting Bulmer (1975).
[43] The account of this migratory picture is given in several sources. The source used here is Wurm (1982, pp. 258-275).
[44] Wurm (1975, p. 915).
[45] Wurm (1975, p. 922).
[46] Thorne & Raymond (1989, p. 146).
[47] Lynch suggests this possibility and also notes that Wurm and his colleagues indicate that this may have been the case.
[48] Wurm (1975, p. 922) as quoted earlier.
[49] See page 13 above and also Ross (1988).
[50] See page 13 above and also Lynch and Tryon (1985).
[51] Pawley & Green (1984, pp. 129-130).
[52] Pawley & Green (1984, p. 132).
[53] Ross (1989, p. 143).
[54] Ross (1989, p. 149).
[55] As quoted in Ross (1989, p. 149).
[56] Kennedy (1983, p. 118).
[57] See, for example, Spriggs (1984), Allen (1984), Pawley & Green (1984), and Green (1979).
[58] Ross (1988, pp. 382-383).
[59] Ross (1989, p. 383).
[60] Ross (1988, p. 383).
[61] The data for Emira-Mussau are given in AV1T1,2.
[62] The exception is the Mioko dialect of Duke of York as given in AV4T4.
[63] Ross (1988, p. 328).
[64] Ross (1988, p. 351).
[65] Ross (1988, p. 188).
[66] Ross (1988, p. 124).
[67] The Labu data are give in CV16T70.
[68] These languages are: Vehes, Mapos Buang, Mangga Buang, Mumeng, and Piu, all of which are documented in CV16.
[69] Ross (1988, p. 193).
[70] Ross (1988, p. 191).
[71] These islands are: the Trobriand, Marshall Bennett, and Woodlark Islands, and those of the Louisiade Archipelago.
[72] Ross (1989, p. 145).
[73] Kirk (1982, p. 234).
[74] Ross (1989, p. 145).
[75] The two languages with 10-cycle systems are Bola and Nakanai. The four languages with (5, 10) systems are: Bali-Vitu, Bola, Meramera, and Harua.
[76] The date for Ambitle Island is given in Allen (1984, p. 197).
[77] Ross (1989, p. 136).
[78] Ross (1988, p. 384).
[79] Pawley & Green (1973, p. 10).
[80] Green (1979, p. 33).
[81] Spriggs (1984, p. 208).
[82] Pawley & Green (1973, p. 13).
[83] Tryon (1984, p. 155).
[84] Tryon (1984, p. 155).
[85] The data for Faga-Uvea are given in DV4T15.
[86] Pawley and Green (1973, p. 11).
[87] Shutler (1978, p. 222) and Spriggs (1984, p. 209).
[88] Smith (1988, p. 45) gives the Proto Austronesian numerals 1 to 10 as reconstructed by Dahl (1976).