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INTRODUCTION

What is counting?

What does it mean, to count?

A woman collects shells, pierces them, threads them one by one onto a leather strip. Ties the strip, wears it.

People creep into a sacred space deep beneath the earth bearing torches, water and pigment. At specially chosen places, they mark the walls with hand signs: one finger, two fingers, three fingers …

A scribe squats on the ground in the greatest city in the world; marks a slab of clay with symbols that, for him and his people, mean two, three, five, goats, grain sacks.

A sophisticated, literate Athenian citizen spends his day exchanging counters, voting tokens and coins, in an elaborate dance that determines the outcome of trials, gains him food to eat, reaffirms his status in the city and the world.

A weary Dutch businesswoman pores over a table of symbols in a handwritten ledger, checking, copying and correcting until the text matches up with reality.

A young Korean girl obsessively checks and rechecks her phone to see how many likes her latest vlog post has accumulated.

A Tongan woman utters a traditional, special set of counting words as she assembles hundreds of strips of pandanus ready to make a woven mat.

A Mayan king, deep in trance, presides as a new monument is dedicated in his capital city, adorned with elaborate symbols representing number, time and the gods.

The story of counting is as wide, deep and tangled as the story of human culture. It is the story of human attempts to find some order in an unruly world; or, perhaps, to impose on a reluctant world the order that humans find within themselves. Very nearly every culture documented in history has counted in one way or another, usually in several. The huge array of different ways people count, and of reasons why they do so, reflect their different preferences and preoccupations, their ways of thinking and being.

Counting underpins a vast range of activities, from census taking and food management, to assessing your popularity or tracking appointments and anniversaries. It leaves traces in the archaeological record across tens of thousands of years, starting long before cities, agriculture or writing. It stands at the root of science and technology, and it has often been suggested that if humans make contact with species on other planets, one of the first things to talk about with them – perhaps even the subject with which to learn to talk in the first place – will be counting.

But what is it?

‘Counting’ can seem like an unruly grab-bag of almost totally unrelated actions; a label covering a huge set of very different cultural practices. The range of different activities called counting seems too wide for comfort, and at least superficially, it is not clear what they all have in common; or even whether they have anything in common at all.

Almost any definition of counting is problematic, but one of the best is attributed to the seventeenth-century German philosopher Gottfried Leibniz. It says that counting is repeated attention. Counting is what happens when you think ‘this … this … this … this’, and have some way of keeping track.

The means of keeping track might be a set of words or a set of symbols; it might be a set of tally marks or a set of beads on a string. There are several other possibilities. But if you are paying repeated attention to objects or events and you have some way of keeping track of that process, then you are counting.

It is in the different ways of keeping track, in fact, that much of the enormous diversity of human counting takes place.

Counting is different from measuring, which is concerned with comparing one object with another, although symbols that record the outcome of a count have a very long history of being repurposed to record the outcome of measurements as well. Counting is different from calculation, although it turns out that nearly every method of counting has at one time or another been adapted in order to do at least simple arithmetic: to add together two counts or to take one away from another.

Counting is also different from using number words or number symbols as a handy set of labels. A phone number is not the result of anybody counting anything, and ‘prisoner two-four-six-oh-one’ does not necessarily stand at the end of a line – real or imaginary – of 24,601 people. Although he might.

Counting has a less clear boundary in the direction of machines that count: visitor counters at the doors of shops and museums, for instance. It seems eccentric to insist that those machines are not really ‘counters’, yet they break any claim that counting has to involve conscious, human attention. Perhaps not every boundary can be quite distinct, particularly at a time when counting machines are changing the world so rapidly.

Animals do not spontaneously count. They certainly pay attention to features of their environment one after another, but no wild animal has been spotted devising a way to keep track of that repeated attention. And even the brightest specimens of the most promising species struggle to use counting techniques invented by humans – words, symbols – after the first few numbers. On the other hand, animals do display some of the capabilities that underlie human counting: an ability to estimate the relative size of groups of objects, in particular. In biological terms, counting didn’t come from nowhere, although it does seem to be unique to humans – at least on this planet.

Counting does not have one single history. There are several different ways to keep track of the things you pay attention to; they have different advantages and disadvantages that become important in different situations. Counting with words, with gestures, with symbols, using machines: each has risen and fallen and risen again at different times and places. There is no way to take the world’s ways of counting and arrange them in a line, from worst to best or from most primitive to most sophisticated.

The story of counting is shaped, instead, like a tree. It has several roots, many branches, and innumerable twigs and leaves. Counting has grown and travelled with the human species, ramifying into very nearly every culture past and present. Sometimes it is possible to follow a single branch for some distance: sometimes a branch turns out to cross, to touch (or nearly touch) other branches. The number symbols that were invented in India, and now dominate the world, are like this. It is possible to follow them from their origin through their long – and ongoing – peregrination across the world, and to watch their interaction with many other traditions of counting along the way.

Elsewhere there are groups of branches – perhaps, better, the twigs within a single branch – with something definite in common. A preference for counting devices in East Asia: rods, the abacus and microchips. A preference for words and gestures in Oceania.

This book is shaped like a tree, too. First, there are two chapters about the roots of counting: the features of human cognition and anatomy, and of the Stone Age environment, that make it possible for humans to count, and that provide the most basic, pervasive and enduring ways to keep track of different objects or events. Humans have innate abilities that are relevant to counting, as well as perhaps an innate habit of spontaneously focusing on quantity. And the earliest available ways of keeping track of a count are counters, fingers, tally marks and words: technologies that will turn up again and again in the different branches of the world’s story of counting.

Then there are six chapters about different branches of counting’s story, organised as a world-wrapping journey that follows the great human spread out of Africa: to the Near East, Europe, South and East Asia, and on into Oceania and finally the Americas. These emphasise what is most characteristic in each part of the world: the invention and use of number symbols in the Fertile Crescent, for instance, or counters and counting boards in Europe. One chapter is about the Indian number symbols, and necessarily spans the world in pursuit of their story. Further east, the book emphasises counting machines in East Asia and counting words in the Pacific. Different choices could have been made; no part of the world has an exclusive preference in its ways of counting.

The stories told in each chapter emphasise the local and the personal: narratives of specific people actually counting, for specific reasons. Some illustrate novelties and turning points, but most are about the way things usually were, the kind of events so common they are seldom written about or remembered. Within each chapter, the illustrations are often arranged by their date, but they are still branches on a tree, not stops on a highway, with ‘later’ often meaning different but seldom meaning better (or worse).

The story of counting has the tree’s property that a closer look always brings more structure into view. That property comes to a head in the Americas. They were the last major landmass to be populated, and their languages and cultures are famously diverse, with dozens of different human groups across millions of square kilometres. Ways of counting in the Americas span the whole range from beads to tallies to words to symbols, with no clear, continentwide preference. So by way of an epilogue, this final chapter presents something more like a tree in its own right, a microcosm of the world’s counting in a 15,000-kilometre journey from the Alaskan Arctic to the Amazon basin.

But first, the roots.

PART 1

Roots