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1A) Numbers do not exist in all cultures. There are numberless hunter-gatherers embedded deep in Amazonia, living along
2branches of the world's largest river tree. Instead of using words for precise quantities, these people rely exclusively
3on terms analogous to “a few” or “some.” In contrast, our own lives are governed by numbers. As you read this, you are
4likely aware of what time it is, how old you are, your checking account balance, your weight and so on. The exact (and
5exacting) numbers we think with impact everything in our lives.
6B) But, in a historical sense, number-conscious people like us are the unusual ones. For the bulk of our
7species'approximately 200,000-year lifespan, we had no means of precisely representing quantities. What's more, the
87,000 or so languages that exist today vary dramatically in how they utilize numbers.
9C) Speakers of anumeric, or numberless, languages offer a window into how the invention of numbers reshaped the human
10experience. Cultures without numbers, or with only one or two precise numbers, include the Munduruku and Pirah? in
11Amazonia. Researchers have also studied some adults in Nicaragua who were never taught number words. Without numbers,
12healthy human adults struggle to precisely distinguish and recall quantities as low as four. In an experiment, a
13researcher will place nuts into a can one at a time, and then remove them one by one. The person watching is asked to
14signal when all the nuts have been removed. Responses suggest that anumeric people have some trouble keeping track of
15how many nuts remain in the can, even if there are only four or five in total.
16D) This and many other experiments have led to a simple conclusion: When people do not have number words, they struggle
17to make quantitative distinctions that probably seem natural to someone like you or me. While only a small portion of
18the world's languages are anumeric or nearly anumeric, they demonstrate that number words are not a human universal.
19E) It is worth stressing that these anumeric people are cognitively normal, well-adapted to the surroundings they have
20dominated for centuries. As a child, I spent some time living with anumeric people, the Pirah? who live along the
21sinuous banks of the black Maici River. Like other outsiders, I was continually impressed by their superior
22understanding of the ecology we shared. Yet numberless people struggle with tasks that require precise discrimination
23between quantities. Perhaps this should be unsurprising. After all, without counting, how can someone tell whether there
24are, say, seven or eight coconuts（椰子） in a tree? Such seemingly straightforward distinctions become blurry through
25numberless eyes.
26F) This conclusion is echoed by work with anumeric children in industrialized societies. Prior to being spoon-fed number
27words, children can only approximately discriminate quantities beyond three. We must be handed the cognitive tools of
28numbers before we can consistently and easily recognize higher quantities. In fact, acquiring the exact meaning of
29number words is a painstaking process that takes children years. Initially, kids learn numbers much like they learn
30letters. They recognize that numbers are organized sequentially, but have little awareness of what each individual
31number means. With time, they start to understand that a given number represents a quantity greater by one than the
32number coming before it. This “successor principle” is part of the foundation of our numerical(数字的) cognition, but
33requires extensive practice to understand.
34G) None of us, then, is really a “numbers person.” We are not predisposed to handle quantitative distinctions
35skillfully. In the absence of the cultural traditions that fill our lives with numbers from infancy, we would all
36struggle with even basic quantitative distinctions. Number words and their written forms transform our quantitative
37reasoning as they are introduced into our cognitive experience by our parents, peers and school teachers. The process
38seems so normal that we sometimes think of it as a natural part of growing up, but it is not. Human brains come equipped
39with certain quantitative instincts that are refined with age, but these instincts are very limited.
40H) Compared with other mammals, our numerical instincts are not as remarkable as many assume. We even share some basic
41instinctual quantitative reasoning with distant non-mammalian relatives like birds. Indeed, work with some other
42species, including parrots, suggests they too can refine their quantitative thought if they are introduced to the
43cognitive power tools we call numbers.
44I) So, how did we ever invent “unnatural” numbers in the first place? The answer is, literally, at your fingertips. The
45bulk of the world's languages use base-10, base-20 or base-5 number systems. That is, these smaller numbers are the
46basis of larger numbers. English is a base-10 or decimal（十进制的） language, as evidenced by words like 14 (“four” + “10”)
47and 31 (“three” × “10” + “one”). We speak a decimal language because an ancestral tongue, proto-Indo-European, was
48decimally based. Proto-Indo-European was decimally oriented because, as in so many cultures, our linguistic ancestors'
49hands served as the gateway to realizations like “five fingers on one hand is the same as five fingers on the other.”
50Such momentary thoughts were represented in words and passed down across generations. This is why the word “five” in
51many languages is derived from the word for “hand.”Most number systems, then, are the by-product of two key factors: the
52human capacity for language and our inclination for focusing on our hands and fingers. This manual fixation — an
53indirect by-product of walking upright on two legs — has helped yield numbers in most cultures, but not all.
54J) Cultures without numbers also offer insight into the cognitive influence of particular numeric traditions. Consider
55what time it is. Your day is ruled by minutes and seconds, but these concepts are not real in any physical sense and are
56nonexistent to numberless people. Minutes and seconds are the verbal and written representations of an uncommon base-60
57number system used in ancient Mesopotamia. They reside in our minds, numerical artifacts(人工制品) that not all humans
58inherit conceptually.
59K) Research on the language of numbers shows, more and more, that one of our species' key characteristics is tremendous
60linguistic(语言的) and cognitive diversity. If we are to truly understand how much our cognitive lives differ
61cross-culturally, we must continually explore the depths of our species' linguistic diversity.
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