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Section B
Directions:In this section, you are going to read a passage with tenstatements attached to it. Each statement contains information given in one ofthe paragraphs. Identify the paragraph from which the information is derived.You may choose a paragraph more than once. Each paragraph is marked with aletter. Answer the questions by marking the corresponding letter on Answer Sheet 2.
What happens when a language has no words for numbers?
Numbers do not exist in allcultures. There are numberless hunter-gatherers embedded deep in Amazonia,living along branches of the world’s largest river tree. Instead of using wordsfor precise quantities, these people rely exclusively on terms analogous to “afew” or “some.”
In contrast, our own livesare governed by numbers. As you read this, you are likely aware of what time itis, how old you are, your checking account balance, your weight and so on. Theexact (and exacting) numbers we think with impact everything from our schedulesto our self-esteem.
But, in a historical sense,numerically fixated people like us are the unusual ones. For the bulk of ourspecies’ approximately 200,000-year lifespan, we had no means of preciselyrepresenting quantities. What’s more, the 7,000 or so languages thatexist today vary dramatically in how they utilize numbers.
Speakers of anumeric, ornumberless, languages offer a window into how the invention of numbers reshapedthe human experience. In a new book, I explored the ways in which humansinvented numbers, and how numbers subsequently played a critical role in othermilestones, from the advent of agriculture to the genesis of writing.
Cultures without numbers, orwith only one or two precise numbers, includethe Munduruku and Pirahã in Amazonia. Researchers have alsostudied some adults in Nicaragua who were never taught number words.
Without numbers, healthyhuman adults struggle to precisely differentiate and recall quantities as lowas four. In an experiment, a researcher will place nuts into a can one at atime, then remove them one by one. The person watching is asked to signal whenall the nuts have been removed. Responses suggest that anumericpeople have some trouble keeping track of how many nuts remain in the can,even if there are only four or five in total.
This and many otherexperiments have converged upon a simple conclusion: When people do not havenumber words, they struggle to make quantitative distinctions that probablyseem natural to someone like you or me. While only a small portion of theworld’s languages are anumeric or nearly anumeric, they demonstrate that numberwords are not a human universal.
It is worth stressing thatthese anumeric people are cognitively normal, well-adapted to the environsthey have dominated for centuries. As the child of missionaries, I spent someof my youth living with anumeric indigenous people, the aforementioned Pirahãwho live along the sinuous banks of the black Maici River. Like otheroutsiders, I was continually impressed by their superior understanding of theriverine ecology we shared.
Yet numberless peoplestruggle with tasks that require precise discrimination between quantities.Perhaps this should be unsurprising. After all, without counting, how cansomeone tell whether there are, say, seven or eight coconuts in a tree? Suchseemingly straightforward distinctions become blurry through numberless eyes.
This conclusion is echoed bywork with anumeric children in industrialized societies.
Prior to being spoon-fednumber words, children can only approximately discriminate quantities beyondthree. We must be handed the cognitive tools of numbers before we canconsistently and easily recognize higher quantities.
In fact, acquiring the exactmeaning of number words is a painstaking process that takes children years.Initially, kids learn numbers much like they learn letters. They recognize thatnumbers are organized sequentially, but have little awareness of what eachindividual number means. With time, they start to understand that a givennumber represents a quantity greater by one than the preceding number. This "successorprinciple" is part of the foundation of our numerical cognition, butrequires extensive practice to understand.
None of us, then, is reallya “numbers person.” We are not predisposed to handle quantitative distinctionsadroitly. In the absence of the cultural traditions that infuse our lives withnumbers from infancy, we would all struggle with even basic quantitativedistinctions.
Number words and writtennumerals transform our quantitative reasoning as they are coaxed into ourcognitive experience by our parents, peers and school teachers. The processseems so normal that we sometimes think of it as a natural part of growing up,but it is not. Human brains come equipped with certain quantitative instinctsthat are refined with age, but these instincts are very limited. For instance,even at birth we are capable of distinguishing between two markedly differentquantities — forinstance, eight from 16 things.
But we are not the onlyspecies capable of such abstractions. Compared to chimps and other primates,our numerical instincts are not as remarkable as many presume. We even sharesome basic instinctual quantitative reasoning with distant nonmammalianrelatives like birds. Indeed, work with some other species, including parrots,suggests they too can refine their quantitative thought if they are introducedto the cognitive power tools we call numbers.
So, how did we ever invent"unnatural" numbers in the first place?
The answer is, literally, atyour fingertips. The bulk of the world’s languages use base-10, base-20 orbase-5 number systems. That is, these smaller numbers are the basis of largernumbers. English is a base-10 or decimal language, as evidenced by words like14 (“four” + “10”) and 31 (“three” x “10” + “one”).
We speak a decimal languagebecause an ancestral tongue, proto-Indo-European, was decimally based.Proto-Indo-European was decimally oriented because, as in so many cultures, ourlinguistic ancestors’ hands served as the gateway to realizations like “fivefingers on this hand is the same as five fingers on that hand.” Such transientthoughts were manifested into words and passed down across generations. This iswhy the word “five” in many languages is derived from the word for “hand.”
Most number systems, then,are the by-product of two key factors: the human capacity for language and ourpropensity for focusing on our hands and fingers. This manual fixation — an indirectby-product of walking upright on two legs — has helped yield numbers in mostcultures, but not all.
Cultures without numbersalso offer insight into the cognitive influence of particular numerictraditions. Consider what time it is. Your day is ruled by minutes and seconds,but these entities are not real in any physical sense and are nonexistent tonumberless people. Minutes and seconds are the verbal and written vestiges ofan uncommon base-60 number system used in Mesopotamia millennia ago. Theyreside in our minds, numerical artifacts that not all humans inheritconceptually.
Research on the language of numbers shows,more and more, that one of our species’ key characteristics is tremendouslinguistic and cognitive diversity. While there are undoubtedly cognitivecommonalities across all human populations, our radically varied culturesfoster profoundly different cognitive experiences. If we are to trulyunderstand how much our cognitive lives differ cross-culturally, we mustcontinually sound the depths of our species’ linguistic diversity.
36. [E] It is worth stressingthat these anumeric people are cognitively (在认知方面)normal, well-adapted to the surroundings they havedominated for centuries.
37. [H] Compared with othermammals, our numerical instincts are not as remarkable as many assume.
38. [E] It is worth stressingthat these anumeric people are cognitively(在认知方面)normal, well-adapted to the surroundings they havedominated for centuries.
39. [B] But, in a historicalsense, number-conscious people like us are the unusual ones.
40. [K] Research on thelanguage of numbers shows, more and more, that one of our species’ keycharacteristics is tremendous linguistic(语言的) and cognitive diversity.
41. [D] This and many otherexperiments have led to a simple conclusion: When people do not have numberwords, they struggle to make quantitative distinctions that probably seem naturalto someone like you or me.
42. [G] None of us, then, isreally a “numbers person.” We are not born to handle quantitative distinctionsskillfully.
43. [A] Numbers do not existin all cultures.
44. [I] So, how did we everinvent “unnatural” numbers in the first place? The answer is, literally, atyour fingertips.
45. [F] This conclusion isechoed by work with anumeric children in industrialized societies.
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