These were an adventurous people, riding the path of the winds to find tiny specks of land in a vast ocean. They farmed, traded, made the islands habitable by introducing plants such as taro, yam, sweet potato, banana, coconut, sugar cane, kava; they also brought with them some animals such as fowl, pigs and dogs. And they brought their words.

The proto-Austronesian number words, used by those who left the East Asian mainland 6,000 years ago, can be reconstructed with confidence (a-sa, dusa, telu, sempat, lima …) and it seems certain that their counting system was a regular decimal one. It is not clear how high they counted, but the first to enter Polynesia certainly had a word for ‘one hundred’, while proto-Polynesian itself had words up to ten thousand; possibly right up to a million. A decimal system with a large range is ancient in this part of the world, though the words for the very largest powers of ten seem to have developed independently on different islands according to need.

It seems certain that these large counting numbers arose in the context of resource collection and distribution at feasts and rituals: a cult of public generosity, in which the more a chief had to offer the gods and the people, the higher his status. ‘On Lamotrek and Fais in the Central Carolines, for instance, large amounts of til fish were regularly distributed among the villages according to fixed proportions, and on Woleai, an instance of redistributing more than 12,000 coconuts locally during a funeral is documented.’ In fact, it is not so much the accumulation of resources as their orderly redistribution that really requires an ability to count efficiently to high numbers.

As to the use of special counting systems to count certain items, their origin seems to be bound up with the use of classifier words in these languages. Many of the Micronesian languages and a few of the Polynesian ones, like Tongan, categorise nouns into as many as a few dozen classes. Compared with the four noun classes of Tongan, for instance, Samoan has fifteen and Trukese and Kiribati ninety, each with its own classifier word. This feature of the languages is certainly also an ancient one, present in the ancestral proto-Polynesian if not earlier.

Some of these classifier words not only specify the kind of thing being counted but also the unit in which it is counted: not bananas but bunches of bananas; not coconuts but strings of coconuts. It looks very much as though this was the origin of the special counting systems. In contexts where it was necessary to count large numbers of objects accurately, the task was simplified by adopting a classifier that specified you were counting not single items but groups of them: sometimes pairs, sometimes tens and sometimes twenties. This technique effectively extended the range of verbal counting without the need to devise any new number words.

Oceania has one of the longest and most complex and multilayered histories of human settlement of any region outside Africa. Its people’s traditional reliance on words to transmit ideas and culture makes it a showcase for what words can be and can do. The counting practices of Oceania are sophisticated, creative and perfectly suited to the purposes they served. They are the best evidence for what counting in words can achieve, and the unexpected range of ways it can achieve it. The Polynesian languages would not have run out of numbers when YouTube did. The Oksapmin have shown a remarkable inventiveness and flexibility in devising arithmetical procedures to use with their number gestures in contact with modern ideas about money and payment. And the tribes of Australia had all the number words they needed for their rich and diverse ways of life over tens of thousands of years.

Further around the globe, in the Americas, the picture is different in every respect. This pair of continents have the world’s shortest period of human occupation, and perhaps its most diverse range of ways of counting.

8

Panorama

: Counting in the Americas

Humans entered North America as the ice began to retreat: perhaps 14,000 years ago, perhaps more. They crossed on foot, likely aided by boats, over what is now the Bering Strait, from Siberia into Alaska.

They found an immense continent: a quarter of the habitable land on the planet, stretching nearly 16,000 kilometres from north to south. Over hundreds, perhaps thousands of years people spread down the coast and into the interior, populating North, Central and South America: the last major landmass to gain a permanent human population. They created a rich mosaic of cultures and languages.

By 1500 CE there were a thousand languages in the Americas. They do not group into a small number of large families, like the languages of Africa, Europe and Asia, but into a large number of small, unrelated families. It is the same with American counting practices. Almost everything to be found in the rest of the world can be found here: from simple counters and strung beads to elaborate systems of number words and number symbols, in a dense patchwork of unrelated – or only distantly related – practices.

So this chapter is something like a recapitulation. The last five chapters have followed counting around the world, from Africa and the Fertile Crescent, through Europe and India, to East Asia and the Pacific. This chapter follows it through the Americas, from Alaska to the Amazon. It follows the path of the first humans to set foot here, from north to south, and it tells not one story but many. For in this continent that is a microcosm of the cultural diversity of the planet, counting too shows just as much range, difference and surprise, as in the rest of the world put together.

Yup’ik: Counting games

Dug from the frozen soil of the Kuskokwim Bay in western Alaska, a bundle of thirty-eight matching wooden sticks: tally sticks used in a game, in all probability. Today they are stored at the museum at Quinhagak with many thousands of other finds from the same site.

Bundle of tally sticks from Nunalleq.

Richard Knecht / nunalleq.wordpress.com.

This find was made … in a very thin charred house floor under a wall. This house floor rests on natural [ground], so it represents one of the very first activities that took place on site. Close to the tally sticks were a large wooden spoon and the remains of a large clay pot. This and the evidence of burning make us think that this might be a cooking area – but what are the game pieces doing in the kitchen?

The American Arctic has long been the site of complex movements of population, driven at least in part by its ever-changing climate. It was around a thousand years ago that a group known today as the Thule culture appeared in the Bering Strait area of northern Alaska. They expanded down the western coast as far as the Kodiak archipelago and the Gulf of Alaska, and eastward across northern Canada and into Greenland, absorbing or replacing the existing populations. Their descendants live in the region today, and are known now as the Yup’ik people.

The village of Agaligmiut was occupied by the late fourteenth century; it stood in the Kuskokwim Bay, near both the ocean and the mouth of the river Arolik. At that time – the Little Ice Age – temperatures were a little colder than today, but this location was not the high Arctic: days were never shorter than five hours, and there were three months of summer when temperatures could push above 25° Celsius.

The whole Yukon–Kuskokwim region is a delta the size of a state: a wide marshy plain crossed by streams and ditches, dense with waterways. River mouths shift; the coast erodes. A single storm can change the shoreline out of recognition. It is a rich tundra landscape, and host to some of the planet’s largest populations of water birds and fish. On certain days, the geese blot out the sun.

The village’s site was chosen for its access to these natural riches: seals from the coast, salmon in the river and caribou on land. The main house was extended, remodelled and refloored on several occasions. First excavated deep into the soil, by its final phase in about the 1670s it had at least three separate entries, with long hallways and six or more side rooms.

The people’s way of life was closely adapted to the resources of the site. They used wood and antler to make tools, weapons, game pieces, masks, kayak parts and arrows. Baskets were made of grass, clothing of skin and hide, other containers of fired clay. The Yup’ik harvested the fauna of land, river and sea with bows, harpoons and nets; they focused on the coast, but perhaps also made excursions to inland hunting and trapping camps for part of the year. Dogs pulled their sledges.

This was a broad, flexible lifestyle, capable of adapting to changes in the availability of one resource by leaning more heavily on another. The cooler period from the fourteenth century saw fewer fish, and the people turned to consuming an increased proportion of caribou, dog and seal meat: there is no evidence that they went hungry even in the coldest years. On the other hand, there is clear evidence of warfare across much of Alaska during the 1700s – possibly starting much earlier – and one suggestion for its cause is resource stress and perhaps competition for the most richly endowed sites, such as the Kuskokwim Bay. Raids, ambushes, and the destruction of whole villages took place. Agaligmiut itself was burned to the ground in a raid some time in the later years of the seventeenth century.

Today, the inhabitants of the area call the deserted site ‘Nunalleq’: the old village. Agaligmiut may in fact not be what the village was originally called: some say the element ‘Agalik’ refers to the local term for ashes.

A combination of ethnography and archaeological finds – like the set of tally sticks described above – reveals that this was a world into which numbers and counting were richly woven. Games of skill are mentioned often in descriptions of the Yup’ik lifestyle, including darts games such as one observed in the 1890s. A wooden block about 15 centimetres long was cut into a cylinder, flaring at one end and pointed at the other. Planted in the ground, it formed a circular target two or three inches across, with a deep hole cut in its centre. Players gathered around it, cross-legged on the floor. They passed around a small wooden dart, with which each player tried to hit the hole in the top of the target. Nearby was ‘a small pile of short sticks, of uniform size, used as counters’. A successful player would take one of these counting sticks, and would also have a second try at hitting the target. When all the counters were gone, the game ended, ‘the players count up and the one having the most counters [was] the winner’.

‘Ordinarily this game is played by men, women, or children merely for pastime’, wrote one observer, ‘but sometimes small articles are staked upon the outcome. It is a source of much sport to the players, who banter and laugh like school children at each other’s bad play.’ Indeed, according to local tradition the burning of Agaligmiut was an act of revenge provoked by an injury during a game of darts.

Other dart-throwing games were played, including throwing at an upright stick planted in the floor: ten wooden counting sticks were used to keep score and determine which team had won. In other games, the sticks could be both counters and part of the play itself:

A bundle of from fifty to seventy-five small, squared, wooden splints, about 4 inches long and a little larger than a match, are placed in a small pile crosswise on the back of the player’s outstretched right hand. The player then removes his hand quickly and tries to grasp the falling sticks between his thumb and fingers, still keeping the palm downward. If one or more of the sticks fall to the ground it is a miss and the next player tries. Every time a player succeeds in catching all of the falling sticks, he lays aside one of them as a counter until all are gone, when each player counts up and the one holding the greatest number is the winner.

The sticks could similarly be used for a game like jackstraws; they were placed in a heap and each player challenged to remove one without disturbing the others. Once again, the sticks functioned as counters: the player with the most sticks at the game’s end was the winner. Of course, not all games were numerate in the same way: ball games involved keeping score but games of strength like wrestling or tug-of-war did not, and neither did speed trials such as foot-or kayak-racing.

Equally, not every use of counting was a game. Tallies of animals taken in the hunt were carved on ivory or whale tooth, either with simple straight marks or with incised representations of the animals in question: walrus, bear, geese. One beautiful example survives of a set of carved bird heads in a box, quite possibly another form of hunting tally.

More intimately still, some hunters were tattooed with – among many other marks and designs – tallies of the animals they had taken during their lives: caribou, or in communities where it was feasible to hunt them, whales. The hafts of harpoons were reportedly marked in the same way, to denote numbers of animals killed or, in one report from an Inuit community further north, the passage of time. In a tale about a group of Inuit lost on the ice:

‘How long was it’, I asked, ‘from the time they were swept out to sea before they reach their homeland again?’. ‘Ten summers and ten winters were the numbers of the notches that Comock cut on the handle of his harpoon’, Nanook replied.

In the same way, ivory carvings of various designs were sometimes fitted with removable arms so that one could be inserted on each day of the week, forming a tally calendar.

The Yup’ik people counted in words, too. The language of Agaligmiut was the Central Yup’ik of the Yukon and Kuskokwim area. The group of five Yup’ik languages, of which this is one, were spoken across Alaska and the Russian Far East; its Inuit sibling is spoken further north in northern Alaska, Canada and Greenland. Together, the Yup’ik and Inuit languages – with the Aleut tongues of the Aleutian archipelago – make up one of the few really large language families of the North American continent, called Eskimo-Aleut.

The number words of Yup’ik correspond closely to a practice of gesture counting on the hands and feet: from left thumb to left little finger, continuing from the right little finger to the right thumb, and then similarly across the toes from right to left. The expression for ‘five’, tallimat, derives from the word for ‘arm’, taliq. That for ten, qulit, seems to mean ‘top’: that is, the digits of the top half of the body. The word for twenty, yu-i’-nik, meant ‘a man is completed’.

Up to twenty, the count was in fives: albeit with some irregularities, so that expressions for nine and nineteen meant literally ‘almost ten’ and ‘almost twenty’. Objects for counting seem regularly to have been grouped in heaps of five. Beyond that, the system worked in twenties, with the multiple of twenty given first, followed by the extra numbers. One situation where the larger number words were particularly important was when storing and counting fish.

Early in contact with outsiders, a word for ‘thousand’ was adopted from Russian – tiisicaaq – and its half used to denote five hundred, complicating the system further for larger numbers. During the twentieth century, the word forms also gradually changed, obscuring the relationship with body parts and on the whole making the system more regular, with a base of 5 for low numbers, and a base of 20 for larger ones. Central Yup’ik has over 25,000 speakers today, and its number words in this form are likely to survive into the future.

After its loss, Agaligmiut was rediscovered. Changes in the shoreline meant that the burned and buried village began to be eroded by the sea, its artefacts deposited in a trail along the beach: ‘whittled bits of wood, sharpened stakes, and fragments of cut birch bark that were thinly distributed among more modern flotsam along the high tide line’. The site itself was emerging from the ground: ‘Protruding from the dark soils were shaft fragments, pieces of bentwood bowls, and the trimmed timber supports of collapsed sod houses.’ From 2009, it was dug by archaeologists with the consent and participation of the local people at Quinhagak. The cold, dry conditions meant that wooden, bone and antler artefacts – even woven grass – survived in staggering numbers. Some still bore traces of paint despite their centuries in the ground.

The set of thirty-eight tally sticks was excavated in July 2018. How were they used? There are many possibilities. For a game of darts, perhaps, or to report numbers of animals taken or keep track of the days. Perhaps they saw more than one type of use over the years. For they bear witness to an Arctic world in which counting was a part of everyday life; in which numbers, as at other times and places, were something to handle, grasp and manipulate.