Despite containing fewer than ten million people, New Guinea is home to around 850 languages, a sixth of the world’s total. It possesses one of the most dense and complex linguistic situations in the world, the outcome of migration and mixing over tens of thousands of years, beginning with the first population of New Guinea and Australia. The mountainous region that includes the Oksapmin area is home to several different language groups; Oksapmin itself is usually considered an isolate, with no close relatives among living languages.

The region also has probably the densest collection of counting systems documented anywhere. And body tallies like the one used in Oksapmin are typical of central New Guinea, and particularly of its highlands. About 15 per cent of the counting systems of New Guinea are of this type: several dozen separate systems of counting gestures, all slightly different. They were used for traditional purposes such as bridal payments, and for counting valuables such as shells, pigs and other goods. In some languages, they were used only in special situations such as bridal wealth negotiations or festivals (it was usual for there to be an additional set of ‘conversational numbers’, as in Oksapmin); others used them constantly, with reports of individuals even counting collections of objects for the sheer pleasure of doing so.

Each of these systems uses gestures in a trajectory around the body, beginning with the fingers of one hand, proceeding up the arm and sometimes the head, and then back down the other arm to finish with the second set of fingers. Some are symmetrical, others not. Some have a central point like the nose or sternum, making the whole count an odd number; others lack a central point and count to an even total. The lower half of the body is not normally used. All the systems use or adapt the names of body parts as counting words, although a degree of mismatch has been reported in some cases and suffixes or other modifications can be involved, in order to distinguish the counting sequence from the ordinary names of the body parts. Many systems use a special prefix or suffix to distinguish the second half of the count from the first.

The length of the sequence varies widely. At least two body-tally systems count to forty-seven, and scattered reports suggest that systems existed enabling yet higher numbers to be counted. Meanwhile, the shortest system recorded has just ten words and uses only one side of the body: possibly it has been truncated from a longer predecessor.

Where did this way of counting come from? With hindsight it seems natural, even inevitable, to extend counting on the fingers to counting on the body: but in fact, nowhere else in the world do people count using anything like the body tallies of New Guinea. Similar systems have been reported in the Torres Strait Islands and in southeastern Australia, but they are unknown further afield, and it appears they are an invention of the region, probably of the New Guinea highlands. It has been suggested that counts of this kind derive from using parts of the body – distances along the arm, for instance – to measure physical objects like strings of shells or ropes of rattan. Quite probably there was a single ancestral system at one time, subsequently transmitted and transformed around the region. An age around 9,000 years has been suggested, although other reconstructions are possible; certainly the body tallies underwent a complex pattern of changes during the centuries or millennia before written history.

The Oksapmin people were contacted in June 1938 by an Australian patrol trekking through the central New Guinea highlands, searching for minerals and for a site for a patrol station. An outpost of the Australian government was established in the area ten years later in Telefomin, about twelve days’ trek from the Oksapmin. It was not until the 1950s that contact with patrols became at all regular, and only in 1962 were a patrol post and an airstrip built actually in Oksapmin territory; a mission station opened two years later. From the 1960s, the government and the mission opened schools in the Oksapmin area; these, and the possibility of employment at the patrol post, introduced the languages of Tok Pisin and English to the inhabitants.

The resulting cultural changes were far-reaching. Specifically for the Oksapmin counting system, increasing contact with outsiders, changing systems of government and the introduction of money wrought a remarkable series of alterations. Early payments by patrols to local people were in salt or matches, and there are reports of the use of cowrie shells as money in the early period of contact. By the late 1960s, Australian shillings had replaced other means of exchange (at a rate of about one shilling to one cowrie).

By this time, Oksapmin artefacts were being exported overseas: one writer reported seeing an Oksapmin arrow for sale in Brentano’s Book Store in New York, for fifteen dollars. Employment at the airstrip, mission and patrol station became more regular, and opportunities arose for employment at plantations, and later mines, elsewhere on the island. A cash-based economy developed from the 1960s, in which labour, lumber and vegetables were sold.

The Australian currency was decimalised in 1966, with 100 cents to a dollar. Later, in the lead-up to its independence, Papua New Guinea issued a new currency with 100 toea equalling 1 kina, though the terms shilling and pound lingered in actual use long after their official withdrawal.

Meanwhile, from 1964 the mission ran a store at which it was possible to use currency to buy axes and knives, western-style clothing, matches, balls, mirrors … ‘all types of useless and unnecessary items’, in the words of one government officer. Wage labourers frequently invested their new wealth in goods such as rice and canned fish. Some opened trade stores of their own, and by 1980, there were more than a hundred such stores in the area, selling everything from food and clothing to soap and batteries.

All of these changes introduced new things to count, new structures for counting determined by the succession of currencies in use, and a new need to perform arithmetical operations in the context of – particularly – trade-store transactions. At the most basic level, this might mean counting coins in the same way other objects had traditionally been counted, matching them gesture-by-gesture with parts of the body. One pair of anthropologists report that ‘in 1960, when Australian shillings and pounds were used in the Oksapmin area, a woman might establish a one-to-one correspondence between a succession of six body parts (in a conventional order) and 6 shillings and then indicate that the value of the shillings is wrist, the sixth body part in the series’. Addition problems might be solved by including two groups of coins in the count; subtraction by physically taking away certain coins and counting the group that was left.

Individuals near the beginning of their participation in a money economy, however, struggled when the coins were not present: struggled to count imaginary coins and reach correct answers.

Some people whose participation in the money economy (in 1980) was limited had not created keeping-track functions for body parts in arithmetical compositions. In their effort to add five coins to seven coins when the coins were not present to count, they began with the forearm (7), enumerating the elbow (8), biceps (9) and were unclear where to stop.

More experienced participants, however, created new strategies. Some used a subset of the body parts to keep track of the second set of coins to be counted: in other words they counted, say, from little finger up to thumb simultaneously with counting from forearm up to ear. Others simplified this procedure by deploying the words from little finger to thumb together with the gestures from forearm to ear. Finally, particularly among trade-store clerks themselves, there arose the so-called ‘halved-body’ procedure, in which one side of the body was used to ‘hold’ one number while the other side of the body held a second. By systematically transferring units from one side of the body to the other, addition or subtraction could be carried out gesturally and the results translated into the now-required decimal form.

The most recent research on the Oksapmin counting gestures reveals a marked tendency to truncate the counting system at twenty, reflecting the importance of the 20-shilling pound and now the 20-kina note in currency transactions. The traditional ‘fu’ meaning ‘twenty-seven’ or a complete count has been repurposed to reflect this: it no longer means twenty-seven but twenty, or in a money context 2 kina (that is, twenty 10-toea coins). From meaning two kina it is being extended by some speakers to mean two of anything else, and is even starting to appear as a suffix capable of doubling each of the number words from the traditional body-tally. The possibilities for novelty and change seem to be almost endless.

The New Guinea body-tally systems are a remarkable reminder of the range of possible ways of counting: a strategy that seems perfectly natural as an extension of finger-counting, but has arisen nowhere else on Earth. And the Oksapmin and others have been quick to innovate in their ways of counting in response to the need to count new things in new situations. Unknitting the link between body parts and words, they have given old words and gestures new meanings. It is a striking illustration of how adaptable counting systems can be.

Tonga: Counting leaves

The island of Tonga, 2007. A woman collects pandanus leaves ready to weave a traditional fine mat. She collects leaves from a special kind of pandanus, the kie, and processes them to obtain a light colour.

The kie leaves are cut while still green, and the sharp parts from both edges and from the middle rib are taken away. Most people also half them along the middle rib. Rolled into big slices, the leaves are then boiled for the whole night or day, after which they are softer, but still brown. At this point, they are then tied together into bundles and taken to the sea.

The count of leaves as bundled is a traditional one:

While their methods may differ for the small numbers – some count one by one, others in pairs – they make a bundle in the literal sense at the score (tekau): 20 leaves of pandanus is the number that is tied together in a bundle to be brought to the sea. These bundles or scores of leaves are then counted up to tefuhi (‘10-scores’) and beyond if applicable.

The process of leaf preparation continues:

close to the beach, a row of sticks is dug into the ground with one end, and the other end is connected with a string. The bundles are attached to this string, hanging down into the sea at high tide and exposed to the sun at low tide. After about ten days they are taken back, rinsed and rolled up to spirals, which are dried in the sun. When perfectly dry, they are smoothed, usually with a piece of metal, and then cut into tiny strips.

Pandanus leaves drying in Tonga.

Juergen Freund / Nature Picture Library.

The strips are finally woven into mats, which have a range of uses. Smaller mats can be worn around the waist or used as bedding. The most prestigious size of mat, about 2 metres wide and 10 metres long, would be a gift for a wedding or a funeral, or perhaps made for sale. Four or five thousand leaves would be needed for a mat of this size, and it might be worked on by a cooperative association of women, each providing an equal number of strips. The best mats become heirlooms; the collection of fine mats in the palace is sometimes described as the crown jewels of Tonga, and is displayed on state occasions. When Queen Salote Tupou III of Tonga received Queen Elizabeth II of the United Kingdom in December 1953, she wore a 600-year-old mat she had also worn at her own coronation.

The kingdom of Tonga consists of over 150 islands stretching over 800 kilometres of the Pacific, in an area around a third of the way from New Zealand to Hawaii. It lies on the western edge of the great scatter of islands known as Polynesia. Its climate is tropical, with warm humid summers, cool winters and much rainfall. The soil is fertile; so is the ocean. Fish and shellfish are traditionally important, as are vegetable products grown in a dense patchwork of fields. Agriculture, fishing and forestry provide much of the island’s employment, its export earnings and its food. Few land animals, on the other hand, have ever travelled so far across the ocean, and animal food was traditionally for special occasions rather than daily consumption.

Tonga retained its political independence and its cultural heritage through the period of eighteenth- and nineteenth-century incursions, and remains a constitutional monarchy: the last remaining indigenous monarchy among the Pacific islands. The line of the Tu‘i Tonga chiefs can be traced back a thousand years.

About 100,000 people speak the Tongan language, which like many of its Polynesian siblings incorporates distinctive ways of counting. Its set of number words is a perfectly regular decimal one, with words for the numbers from 1 to 9 (taha, ua, tolu, fā, nima …) and for the powers of ten up to 100,000 (supplemented today with English words for ‘million’ and beyond). Multiplication and addition are used with near-perfect regularity to create terms for each number up to that limit.

Tongan possesses special words called noun classifiers, which accompany its number words and specify what kind of thing is being counted. Four categories of noun are distinguished: roughly people, animals, small or hand-made objects, and large or natural objects. The classifier words are also inflected to mark the grammatical distinction between dual and plural: between two things and more than two.

The system is further complicated by four separate ways of counting certain kinds of object, which involve some distinct terms for certain numbers. Sugar cane pieces are counted in pairs, with special words for ‘pair’, ‘ten pairs’ and ‘twenty pairs’. Coconuts are counted in pairs initially, but for larger numbers they are counted in twenties, then in two-hundreds: there are special words for pairs, for twenties and pairs of twenties, and for two-hundreds and pairs of two-hundreds. Pieces of yam and pandanus leaves follow the same pattern of counting groups as coconuts, but their special words are different. Fish are counted in pairs and twenties, not in two-hundreds.

All of the special systems, in fact, combine the regular decimal system with pairing of objects and with grouping them in twenties. A result is that certain words are reused in different contexts. Teau, for instance, means a hundred ordinary things, but a hundred pairs of sugar-cane thatch, or a hundred twenties of coconuts, yam or fish. Indeed, there are even separate words in Tongan for ‘counting in general’ as against ‘counting one by one’: that is, not in pairs.

At first glance, the special counting systems are baffling in their complexity, as is the decision to count certain items in an unusual way at all. The items in question are natural subsistence products; what they have in common is not their importance or their abundance but their cultural significance, particularly in the context of prestige for gift-giving or feasting. These were products that on certain traditional occasions were collected in huge quantities, presented to and redistributed by chiefs and kings. Early descriptions suggest a frequent flow of food – in particular – into the chiefs’ courts, and a corresponding regular redistribution on special occasions. Recently, birthdays, marriages and funerals have been marked in this way, with valuables exchanged. Presentation of certain foods to the king reportedly still used the traditional counting systems in the early twenty-first century.

One such presentation took place at the end of August 2004, when His Majesty, King Taufā’āhau Tupou IV, and several members of his family visited Pangai in Lifuka, Ha’apai, to preside over the Agricultural Show. The displays and presentations during this show bear a strong resemblance to the ceremony of first fruits, ‘inasi’. Such gifts usually comprise whole kava trees and sugar cane, yam, or giant taro, and senior pigs (puaka toho). Fish, turtles, octopus and giant clams can be part of the fakapangai as well, and sometimes baskets of fruits, woven mats from pandanus, and tapa mats (ngatu) are added.

While for the larger objects single pieces may suffice, … other objects have to be presented in bundles of 20. Particularly yam and giant taro are exclusively given and counted in kau (scores). Accordingly, the expected minimum is one score, and if more than that is given, it needs to be in multiples of the score.

Tongan is no outlier in these respects; similar systems are to be found in many of the nearly thirty languages of the Polynesian family, including Samoan, Tahitian, Maori and many others. Their actual number words are in many cases similar, reflecting their shared linguistic ancestry. Most use decimal number systems, and most also possess – or possessed – distinct counting systems for certain types of object, based on different counting units such as groups of two, four, ten or twenty. In general, the objects counted in special ways seem to have been those connected with traditional food production practices, with feasting or with ritual: resources that were both culturally important and abundant enough to be counted in large numbers. Fish were a frequent example; so were coconuts and tubers, and also the raw materials for making fabrics.

On Rennell, for instance, in the Solomon Islands, a Polynesian language is spoken whose counting includes special units for bananas, yam, breadfruit and taro. Bananas are counted in piles of four bunches; yam and breadfruit in pairs, with ten pairs to a basket; yam in piles of ten (or eight if they are large); topped taro in baskets usually of four pieces; taro stalks in bunches of five, twelve or twenty-two depending on type; taro tubers in bags. Coconuts in strings of ten nuts. Pandanus leaves in rolls of sixty or seventy-two. One report speaks of a collection of 7,600 piles of bananas: roughly 300,000 bananas in total when counted by these methods.

Examples could be multiplied. In Mangareva,

breadfruit, pandanus leaves, agricultural tools, and sugar cane were counted in pairs (tipau rua); ripe breadfruit and octopus were counted in fours; and the first breadfruit and first caught octopuses of the season to be given as a tribute to the owner were counted in bunches of eight. All other things (including humans, mammals, or birds) were counted singly (tipau tahi).

In Samoan, there are special units for fish, young pigs and coconuts. And so on throughout the entire family of Polynesian languages. The same is true in the more distantly related languages of the Micronesian family: a decimal system in which many of the number words reflect a common origin with those of Polynesia is supplemented by – in some cases – a system of counting in pairs or other units.

Like many of the world’s ways of counting, the Polynesian number words are under pressure. Words borrowed from other languages such as English have tended to enter the lexicon and replace terms for larger numbers. Experience with number symbols in a positional system results in number words being spoken not using the full, traditional decimal system but by naming the single digits; saying ‘two seven four three’ as the equivalent of 2,743, for instance. The more complex parts of the traditional systems are thus systematically lost: the special counting systems are no longer learned and people fluent in them become increasingly rare. Linguists report that those who know the old systems no longer agree about how they worked: ‘Some do not apply or even remember the traditional systems at all, while others over-generalize some of the counting strategies.’ Yet, like many human activities, the traditional Polynesian counting systems were well adapted to the purposes for which they were needed, and deserve to be understood and remembered, even if they may no longer be practised in the future.

The complexities of the Tongan counting systems and those of its linguistic neighbours and relatives beg the question of how things came to be this way. Archaeology bears witness to the spread of a group of seafarers out of southern China starting perhaps 6,000 years ago. The linguistic evidence – from the language family called Austronesian – tells the same story. These people spread first into Taiwan, then on to the Philippines; later to Malaysia, Indonesia, Madagascar, and east across the Pacific. They seem to have left Australia entirely alone (despite the perhaps confusing modern name ‘Austronesian’ for the language family), and to have settled only the more coastal parts of New Guinea, but they populated all the smaller islands. From perhaps 3,000 years ago they moved successively through Western and Central Polynesia and Remote Oceania. The limits of their voyaging were Easter Island, Hawaii and New Zealand. The last major archipelago was settled around seven hundred years ago. A consequence of this rapid spread across many islands is an extensive diversification of their languages: the Austronesian family accounts for about a fifth of living languages.