Ayangkidarrba: Counting eggs

Ayangkidarrba (Groote Eylandt), early in the twentieth century. A woman has gathered turtle eggs, and she returns to camp in the early evening, carrying them in a paper-bark basket. Others have hunted, fished, gathered. She shares out the heap, counting in fives: awilyaba, ambilyuma, abiyakarbiya, abiyarbuwa, amangbala …

Groote Eylandt lies about 50 kilometres off the Australian coast, at the western side of the vast Gulf of Carpentaria. It has been an island for 7,000 years or more, and the original inhabitants of its 2,000-odd square kilometres are the Anindilyakwa. Hills, springs, rivers and of course the coast make for a rich range of habitats from forest to sand dunes. Traditionally, it supported a few hundred people, at one of the highest population densities in aboriginal Australia.

The island was a dense network of named places: natural features and resources controlled by different clans. The human world was a similarly dense network of kinship relationships linking fourteen clans. A prodigious knowledge of the local environment enabled the Anindilyakwa to gather foods ranging from berries, roots and fruit, wild honey and drifting coconuts to wallabies, dugong, fish and turtles, in a pattern changing with the seasons. Spears, harpoons, bags and baskets, ornaments, musical instruments and even canoes were all made from local materials including wood and bark.

Sea turtle eggs, as counted on Groote Eylandt.

Sabena Jane Blackbird / Alamy Stock Photo.

An ethnographer visiting in the 1970s described a visit to the bush, by then much rarer than in earlier generations:

[the people] would awake at sunrise, boil some tea and have a bit to eat from what had been left over from the previous day. Then they would work fishing, hunting or gathering until the sun was directly overhead, eating enough to sustain themselves from what they could gather as they went along. During the heat of the day they would sleep, then begin work once again in mid-afternoon, returning to camp in the early evening with the bulk of the day’s catch, which they would then prepare and consume communally. Following this they would sometimes wander through the shallows with a light in search of fish, or rest beside their campfires four abreast with a fire between each pair telling stories. After a few hours of sleep they would again wake up, have something more to eat, wander around and perhaps tell another story, then sleep again, waking at sunrise.

The Anindilyakwa had strong relationships with their neighbours on the smaller islands surrounding Groote Eylandt, and on the mainland; they imported certain materials – flint, ochre, emu feathers, bamboo – in exchange for local products, and they intermarried. And for two hundred years or so, up to the early twentieth century, they were regularly visited each December by Makassar people from Sulawesi in Indonesia. Ranging widely on the north Australian coasts, these visitors harvested sea cucumber (boiled, dried and smoked, it made food and medicine prized in south-east Asia); they also took turtle shell and pearl shell. Employing the Australian people to work for them collecting sea cucumber, they provided such imports as tamarind and chilli, cloth and metal items. They introduced the dugout canoe, some new place names, and perhaps forty words, mostly for the items they themselves brought.

The Anindilyakwa’s own language – Amamalya Ayakwa – spoken on Groote and the smaller islands nearby, is probably related to languages spoken on the nearby coast, but long development in separation from the mainland has given it a highly distinctive character. Words are long – up to fourteen syllables – and there are thirty-two distinct consonants. The grammar is one of the most complex ever documented, with nouns divided into eight classes which require different prefixes on the corresponding verbs and adjectives. As well as singular and plural options there are also special forms of verbs, nouns, pronouns and adjectives for the dual (two items) and the trial (three items, sometimes four).

Meanwhile, the actual counting words work in fives, with words for ‘one’, ‘two’, ‘three’, ‘four’, ‘five’, ‘ten’, ‘fifteen’ and ‘twenty’. They gain prefixes to agree with the nouns they accompany, like other adjectives in the language. There are special forms for ‘once’, ‘twice’, ‘three times’ … and for ‘by ones’ ‘by twos’, ‘by threes’ … Sometimes gestures support the counting routine:

The hand is held loosely with the palm facing the person counting. The fingers are placed together one by one; index finger to thumb, middle finger to thumb, ring finger to thumb and little finger to thumb, until all fingers are bunched together. If the number is more than five the fingers are held together while counting continues with the other hand. After ten, the toes are touched one by one, first on one foot and then on the other.

Despite this, the number words show no detectable relationship with the terms for hands or feet.

What were the counting words used for? One context was hunting: counting numbers of people available to hunt or numbers of animals brought in. Similarly, the number of warriors going out to fight or returning might be counted. Another possibility was calendar calculations; yet another, the counting of food resources like eggs. In fact, the main context for counting in Amamalya Ayakwa seems to have been sharing mid-sized food items like fish, eggs or wild apples.

There is a story on Groote Eylandt about a mythical dog that could count. The story tells how the dog went hunting and returned to his family with the turtle eggs he had found. He began counting them in order to share them (though the story reveals that the dog cheated by hiding some eggs, causing a fight to develop!).

Reports from the mid-twentieth century show that turtle eggs could be gathered in quantities of over a hundred, and the counting procedure, as demonstrated to a visitor using a heap of pebbles, showed how they were counted out into heaps using the base-5 number words.

The Anindilyakwa were both typical and atypical, on a continent where change and diversity seem to have been the norm. Australia was populated – following a rapid human expansion through Indonesia – at least 55,000 years ago, perhaps more than 65,000. At that time, sea levels were much lower; large parts of island Southeast Asia were connected to the mainland as the single landmass of Sunda, while Tasmania, Australia, the Torres Straits and New Guinea were joined as Sahul. Nevertheless, some significant stretches of open ocean had to be crossed to reach Sahul: passages of 20 kilometres or more. Genetic evidence shows that there was a small degree of interbreeding with the hominids already present in Asia and Indonesia. It also shows that the peopling of Australia was essentially a single event, with no substantial new incursion into the aboriginal population after the initial period of settlement. The Australian cultures and languages were thereafter substantially isolated for tens of thousands of years.

That is an enormous depth of time: as in the African Stone Age, it is more than long enough for words, clusters of words, technologies and practices to have been invented, forgotten and invented again, perhaps many times. In an oral culture, it need take no more than a few generations for a word or an idea to be forgotten, leaving no trace that it ever existed. Of course, a degree of cultural stability is to be expected, but there is no sense in which Australia was either a static environment or an unchanging set of cultures. Shifting coastlines and gradually changing climates combined with the creativity and restlessness of human beings to make the continent a shifting mosaic of different lifeways, from the tropical north to the arid central deserts, from the temperate southern coasts to the sinking islands and land bridges of the Torres Strait.

A reliance on hunting and gathering united the continent, as did the use of a broad range of animal and plant species, from fruits, seeds and wild honey to wallabies, fish and geese. Tools ranged from harpoons and axes, fishing lines and lures, to spoons, bags and cloaks. Fire was used for warmth and cooking and to manage vegetation and species diversity, with some plant species deliberately planted and reseeded.

A tradition of painting on rock likewise spanned the continent, with a range of regional styles; beads of shell and bone were worn, and each tribe had its stories handed down across unknowable gulfs of time. And Australia was also crossed by networks of trade, each tribe interacting directly with its neighbours and indirectly with the sources and destinations of goods, stories, ideas across long distances, even as far as the Torres Strait Islands and Papua after they split from the mainland.

By the eighteenth century, there were perhaps five hundred tribes linked in the Australian network of trade and lifeways. They spoke 240 or 250 distinct languages; many people spoke two or more. It is likely, though not certain, that nearly all of those languages descend from a single ancestor: but the depth of time for which they have been changing is huge and has facilitated much mutual borrowing of words, sounds and structures as well as much evolutionary change. No languages anywhere else in the world can be shown to be related to the Australian languages.

Like any languages anywhere in the world, each of the Australian languages stands at the end of a development of tens of thousands of years whose roots lie in Stone Age Africa. Like their cultures, they are not in any sense ‘primitive’ languages; their vocabularies are as large as others and their grammars are if anything more complex than most. They tend to have many distinct consonants, but few – typically three – distinct vowels. Large or complex systems of noun classes are common, as are certain phenomena of noun case which are rare elsewhere in the world.

It is important to know that Australia’s cultures and languages are not ‘primitive’ – not ‘relics’ – in order to approach their counting systems, which are also distinctive compared with those of the rest of the world. When the languages were documented in the nineteenth and twentieth centuries, three-quarters of them possessed just three or four number words. Five per cent of them counted only as high as 2. For the remaining 20 per cent, counting limits from 5 to 100 were reported. Observer bias may have played a role in underestimating the extent of Australian counting, as may the fact that many of the languages were already badly disrupted by the time their words were written down. But still, compared with other parts of the world, Australian languages show a tendency to low limits in their sequence of counting words.

The internal structures of the lists of counting words show a striking diversity from language to language. While a proportion of the Australian languages show no evidence of any base system – in one case, a set of nineteen counting words appears to have no internal structure at all – the majority of them do extend their verbal counting routine by combining smaller counting words into larger ones. But decimal systems are rare here. A list of two, three or four numbers cannot possibly have a base-10 structure: but even those Australian languages with larger sets of counting words are remarkable for the absence of decimal systems. Most in fact use 2 as a base, but systems with bases 3, 4 or – particularly – 5 are also found.

In a final twist, some of the languages with very small sets of counting words seem sometimes to have extended them using gestures, counters or tallies: expressing, recording or calculating with numbers for which the language had no specific word. Reports from around Australia show that certain kinds of counting tasks tended to be performed using fingers in routines like the one on Groote Eylandt. In languages whose number words stopped before five, displaying a hand could perform the functions of the fifth counting number.

The Anindilyakwa were part of a complex mosaic of different ways of doing things: small number systems, large number systems, systems with or without a base structure, systems extended or not extended by the use of gestures. But even this does not exhaust the possibilities to be found in Oceania; for elsewhere in the Pacific world, counting by gestures attained even greater importance and sophistication.

Oksapmin: Body count

The central highlands of Papua New Guinea, 2012. A man walks into a small store and buys some food items using the local currency, kina and toea. Prices are written up on a board behind the counter.

He and the proprietor use coins and number words to negotiate about what must be paid and what change must be given. They also use a complex, rapid series of gestures, pointing to a conventional sequence of body parts around the hands, arms and head; the gestures are just as important as the words, perhaps more so. In fact, the words are simply the names of the body parts.

To add two numbers together or subtract one from another, it is necessary to repurpose these gestures in ways which the participants’ ancestors would not have recognised. But both men leave the transaction satisfied that the correct number of coins has been exchanged.

North of Australia, south of the equator, New Guinea is the world’s second largest island, home to a multitude of species, including human beings. It was populated by humans many thousands of years ago while it was still connected to Australia, but the central highlands remain remote to this day, with arduous trails leading in by foot and a few scattered airstrips for single-engine planes. A rugged geography of mountains, rivers and gorges, as well as internal warfare, have contributed to the isolation of the human groups living here.

One of those groups is the Oksapmin. Their territory in the mountains near the centre of the island is bordered to the west by the Victor Emanuel mountain range (cold enough to kill), to the north by the Ok Om river (a raft crossing described as ‘very risky’) and to the south and east by the Strickland Gorge, sometimes compared to the Grand Canyon and involving a cliff of nearly 500 metres which must be scaled with the help of wooden hand-and-foot holds. It is a beautiful landscape, with sparkling valleys, sandy rivers and smoke creeping from thatched roofs. A chequer of gardens fills the land; clouds garland the forested peaks. The climate is tropical, with wet and dry seasons, and temperatures characteristic of the highlands, down to ten degrees during the colder nights, up to the thirties on the warmest days.

In the traditional Oksapmin lifestyle, the days are filled with work in gardens of taro and sweet potato – repairing fences, clearing weeds, harvesting – punctuated with tending pig and hunting in the forests for birds and small animals. Tools are of wood, bone and flint, supplemented over the last half-century by imported steel knives and axes. Houses are of pandanus bark, roofed with leaves, and they scatter the valleys in groups of two or three. The total population of Oksapmin speakers was estimated in the 1960s at around 4,000 people; today, it may be more than twice that.

Trade was important to the prehistoric life of the Oksapmin and their neighbours: they obtained stone axes, shells, bows, salt and drums from their neighbours, and shell valuables were used as a kind of currency across groups in the mountains. Goods could travel hundreds of kilometres, despite the boundaries of geography and language.

The Oksapmin counting sequence consists of gestures towards twenty-seven parts of the body. It begins at ‘one’ on the thumb of one hand, and moves across that hand to the little finger (‘five’), with the index finger of the other hand being used to point. Next, it continues up the arm – wrist, forearm, elbow, upper arm, shoulder, neck, ear, eye – finally reaching the nose (‘fourteen’), the midpoint of the count. The count then continues symmetrically down to the other wrist, with a switch in the hand being used to point. The final five elements – ‘twenty-three’ to ‘twenty-seven’ – run from the thumb of the second hand to its little finger, meaning that the end of the sequence is not quite the mirror image of its beginning.

Showing the number 6 in Oksapmin.

J. Wardhaugh.

Each item in this sequence also has a spoken word – tipana, tipnarip, bumrip, hadrip, hatatah – which is identical with the name of the body part; context makes it clear whether the body part or the counting number is intended on any given occasion. A prefix (tan) is added to the names of parts on the second side of the body to distinguish them from those on the first. Some reports indicate that the words can be used on their own to count, but most descriptions of the system regard the gestures as essential.

The complete cycle ends at twenty-seven – second little finger, tan-hatatah – and may be denoted by the word fu. If it is necessary to count slightly further, the system may be extended: not by starting again at the beginning, but by looping back from the little finger to the wrist of the same hand (‘twenty-eight’), and proceeding back up the arm. To interpret the resulting – potentially ambiguous – words and gestures is again a matter of context.

A separate set of words for the numbers from one to five also exists: the so-called conversational counting words, which correspond to nothing in the body tally. They run tit, yota, yetir, yota yota, hanen; they can be combined with the body tally if it is necessary to count more than one complete cycle: tit fu (one cycle), yot fu (two cycles), and so on.

The system was well suited to the uses to which it was put in traditional Oksapmin life. It could be used in any everyday situation where the number of elements in a set needed to be indicated. It could count valuables like shells or pigs, measure string bags, indicate a set of positions along a path. In daily life, a counting system of twenty-seven elements was more than adequate to count these things in the quantities in which they existed. There is no evidence that the system was ever used in arithmetic, that anyone ever learned addition or multiplication tables in terms of the body parts or their names. Indeed, there is no evidence that in traditional Oksapmin life any arithmetical computation was done at all.