​​‘Anumeric’ people: What happens when a language has no words for numbers?

“无数字”人群:当语言里没有表示数字的单词时会怎样?

a Piraha family

Numbers do not exist in all cultures. There are numberless hunter-gatherers embedded deep in Amazonia, living along branches of the world’s largest river tree. Instead of using words for precise quantities, these people rely exclusively on terms analogous to “a few” or “some.”

不是所有文化中都存在数字。亚马逊流域深处就有一群“无数字”的狩猎-采集者,他们与世界上最大的河流树木为伍。他们没有描述精确数量的词,而是仅仅依赖类似于“少量”或者“一些”这样的表达。

In contrast, our own lives are governed by numbers. As you read this, you are likely aware of what time it is, how old you are, your checking account balance, your weight and so on. The exact (and exacting) numbers we think with impact everything from our schedules to our self-esteem.

相比之下,我们自己的生活里则充满了数字。当你阅读这篇文章时,你可能很清楚现在几点了,你多大年纪了,你的支票账户余额是多少,你的体重多少等等。我们所记起的这些精确(甚至精确到严苛的)数字影响着一切,涵盖我们的日常计划和自尊。

But, in a historical sense, numerically fixated people like us are the unusual ones. For the bulk of our species’ approximately 200,000-year lifespan, we had no means of precisely representing quantities. What’s more, the 7,000 or so languages that exist today vary dramatically in how they utilize numbers.

然而,纵观历史,像我们这样时刻念着数字的人才是不寻常的。在大约20万年的时间里,我们这个物种的绝大多数人并没有精确表示数量的方法。此外,目前存在的7000多种语言在使用数字方面也有着巨大差异。

Speakers of anumeric, or numberless, languages offer a window into how the invention of numbers reshaped the human experience. In a new book, I explore the ways in which humans invented numbers, and how numbers subsequently played a critical role in other milestones, from the advent of agriculture to the genesis of writing.

研究“无数字”的语言可以让我们看到数字的形成究竟如何重塑了人类的经验。在一本新书中,我探寻了人们是如何发明数字,而数字又是如何在人类重大事件中扮演关键角色的,这些事件可以从农业的出现一直延续到写作的诞生。

Numberless cultures

“无数字”文化

Cultures without numbers, or with only one or two precise numbers, include the Munduruku and Pirahã in Amazonia. Researchers have also studied some adults in Nicaragua who were never taught number words.

有些文化中没有数字或者只有一两种精确数字,比如亚马逊流域的蒙杜鲁库人和毗拉哈人。研究者也研究了一些从未学过数字用词的尼加拉瓜成年人。

Without numbers, healthy human adults struggle to precisely differentiate and recall quantities as low as four. In an experiment, a researcher will place nuts into a can one at a time, then remove them one by one. The person watching is asked to signal when all the nuts have been removed. Responses suggest that anumeric people have some trouble keeping track of how many nuts remain in the can, even if there are only four or five in total.

在没有数字的情况下,健全的成年人很难准确区分和回忆起四这样小的数量。在一个实验中,研究者一次性往罐子里放了一把坚果,然后再一颗一颗拿出来,观察者则被要求判断坚果在何时被全部拿走。他们的反应表明,“无数字”人群很难记住还有多少坚果留在罐子里,就算里边儿只剩下四五颗。

This and many other experiments have converged upon a simple conclusion: When people do not have number words, they struggle to make quantitative distinctions that probably seem natural to someone like you or me. While only a small portion of the world’s languages are anumeric or nearly anumeric, they demonstrate that number words are not a human universal.

这一个和大量其他实验都在向一个简单结论靠拢:当人们没有数字用词时,他们很难辨别数量上的差异,哪怕这些差异对你我而言都很显然。虽然世界上只有一小部分语言是“无数字”或者近乎此的,但这也证明了数字用词并非人类通用。

It is worth stressing that these anumeric people are cognitively normal, well-adapted to the environs they have dominated for centuries. As the child of missionaries, I spent some of my youth living with anumeric indigenous people, the aforementioned Pirahã who live along the sinuous banks of the black Maici River. Like other outsiders, I was continually impressed by their superior understanding of the riverine ecology we shared.

值得强调的是,这些“无数字”人群的认知完全正常,并且已很好地适应了他们占据了几个世纪的领地。作为传教士的后代,我曾在年轻时和一些“无数字”土著人一同生活,他们是上文提到的居住在蜿蜒的Maici河岸的毗拉哈人。和其他外来者一样,我不断震惊于他们对河流生态的卓越见解。

Yet numberless people struggle with tasks that require precise discrimination between quantities. Perhaps this should be unsurprising. After all, without counting, how can someone tell whether there are, say, seven or eight coconuts in a tree? Such seemingly straightforward distinctions become blurry through numberless eyes.

然而“无数字”人群依旧挣扎于那些需要准确辨别数量的事中。或许这也不该让人吃惊,毕竟如果不会数数的话,谁能看出一颗树上到底有七个还是八个椰子呢?这种看起来显白的差别在“无数字”人群眼里却相当费解。

Children and animals

儿童与动物

This conclusion is echoed by work with anumeric children in industrialized societies.

上述结论也能在工业化社会里那些没有数字概念的儿童身上找到印证。

Prior to being spoon-fed number words, children can only approximately discriminate quantities beyond three. We must be handed the cognitive tools of numbers before we can consistently and easily recognize higher quantities.

在系统学习数字用词之前,孩子只能大致分辨三以上的数量。如果要更好地分辨更大数量,我们需要先掌握一些数字的认知工具。

In fact, acquiring the exact meaning of number words is a painstaking process that takes children years. Initially, kids learn numbers much like they learn letters. They recognize that numbers are organized sequentially, but have little awareness of what each individual number means. With time, they start to understand that a given number represents a quantity greater by one than the preceding number. This “successor principle” is part of the foundation of our numerical cognition, but requires extensive practice to understand.

事实上,掌握数字单词的准确含义是个艰难的过程,小孩子要花费很多年。一开始,孩子像学字母一样学习数字。他们能认出数字是按一定顺序排列的,但对单个数字的含义没什么意识。慢慢地,他们开始明白一个特定数字代表的是比前一个数字更大的数量,这种“序数原则”构成了我们数字认知基础的一部分,但要真正理解还需要更多练习。

None of us, then, is really a “numbers person.” We are not predisposed to handle quantitative distinctions adroitly. In the absence of the cultural traditions that infuse our lives with numbers from infancy, we would all struggle with even basic quantitative distinctions.

因此,没有谁是真正的“数字化个体”,没有人天生就有熟练分辨数量的能力。如果没有幼年时期就开始被灌输数字概念的文化传统,我们也都会对最简单的数量分辨束手无策。

Number words and written numerals transform our quantitative reasoning as they are coaxed into our cognitive experience by our parents, peers and school teachers. The process seems 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 instincts that are refined with age, but these instincts are very limited. For instance, even at birth we are capable of distinguishing between two markedly different quantities – for instance, eight from 16 things.

在父母、同龄人和学校老师的引导下,数字单词和手写数字逐渐将我们的定量推理行为转变成了认知经验。这个过程看起来十分平常,以至于我们都把它当做是成长过程中很自然的一部分,然而并非如此。人类大脑确实具备对数量的直觉,这随着年龄会逐步完善,但很有限。比如说,刚出生的孩子也能够区别较大的数量,像8和16。

Alex, an African gray parrot, was trained by ethologist Irene Pepperberg to count objects
Alex是一只非洲灰鹦鹉,动物行为学家Irene Pepperberg教会它数数

But we are not the only species capable of such abstractions. Compared to chimps and other primates, our numerical instincts are not as remarkable as many presume. We even share some basic instinctual quantitative reasoning with distant nonmammalian relatives like birds. Indeed, work with some other species, including parrots, suggests they too can refine their quantitative thought if they are introduced to the cognitive power tools we call numbers.

但是我们并非唯一拥有这种抽象能力的物种。和黑猩猩以及其他灵长类动物相比,我们对数量的直觉可没许多人以为的那么好。一些人类的非哺乳类亲戚——鸟类也有类似的数量推理直觉。对包括鹦鹉在内的其他物种的研究表明,如果教给它们我们称之为数字的认知工具,它们也能完善自己的定量能力。

The birth of numbers

数字的诞生

So, how did we ever invent “unnatural” numbers in the first place?

那么,一开始我们到底是如何发明出“非自然的”数字呢?

The answer is, literally, at your fingertips. The bulk of the world’s languages use base-10, base-20 or base-5 number systems. That is, these smaller numbers are the basis of larger numbers. English is a base-10 or decimal language, as evidenced by words like 14 (“four” + “10”) and 31 (“three” x “10” + “one”).

最直接的答案就在你的指尖。世界上大多数语言使用以10为基础、以20位基础或者以5位基础的数字系统,意味着这些小的数字是更大数字的基础。英语就是一个以10位基础(或者说十进制)的语言,比方说14(10+4,fourteen是four+ten的变形)和31(3个10 + 1,thirty是three × ten +one的变形)就可以证明。

We speak a decimal language because an ancestral tongue, proto-Indo-European, was decimally based. Proto-Indo-European was decimally oriented because, as in so many cultures, our linguistic ancestors’ hands served as the gateway to realizations like “five fingers on this hand is the same as five fingers on that hand.” Such transient thoughts were manifested into words and passed down across generations. This is why the word “five” in many languages is derived from the word for “hand.”

我们使用十进制语言是因为祖先的原始印欧语系就是十进制的。和很多文化一样,双手首先打开了祖先的认知——这只手的五根手指和另外一只的五根手指是一样的,这是语言采用十进制的源头。这些瞬时的想法逐渐在言语中体现出来,并一代代流传下去。这也是为什么在许多语言中“五”这个词都是由“手”这个词演变而来。

Most number systems, then, are the by-product of two key factors: the human capacity for language and our transient for focusing on our hands and fingers. This manual fixation – an indirect by-product of walking upright on two legs – has helped yield numbers in most cultures, but not all.

因此,许多数字系统都是人类的语言能力和对手及手指的关注,这两个重要因素的副产品。这种动手习性是双腿直立带来的副产品,却让大部分(不是所有)文化诞生了数字。

Cultures without numbers also offer insight into the cognitive influence of particular numeric traditions. 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 to numberless people. Minutes and seconds are the verbal and written vestiges of an uncommon base-60 number system used in Mesopotamia millennia ago. They reside in our minds, numerical artifacts that not all humans inherit conceptually.

“无数字”文化也帮助我们深入了解一些特定数字传统带来的认知影响。想想现在几点了。你的一天是由分和秒计算,而它们却并非实体的存在,对“无数字”人群来说更是不存在的。分和秒只不过是几千年前美索不达米亚使用的60进制数字系统遗留下来的口语和书面表达。它存在于我们的思想里,但并非所有人都继承了这种数字工艺品的概念。

Research on the language of numbers shows, more and more, that one of our species’ key characteristics is tremendous linguistic and cognitive diversity. While there are undoubtedly cognitive commonalities across all human populations, our radically varied cultures foster profoundly different cognitive experiences. If we are to truly understand how much our cognitive lives differ cross-culturally, we must continually sound the depths of our species’ linguistic diversity.

数字语言的研究愈发表明,人类这个物种的关键特征之一就是极大的语言与认知多元化。不可否认,人类有许多认知共性,但截然不同的文化孕育出的认知经验也有天壤之别。如果我们真的想理解生活在不同文化中的差异,就需要不断探索人类语言多元化的深度。


翻译:Kimagreggs
校对:Drunkplane
编辑:辉格@whigzhou

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