社会是如何学会数到10的
How societies learn to count to 10
In some traditional cultures, counting is as easy as one, two, three—because it stops there: Their languages have no words for higher numerals, and instead simply use varieties of words like “many.” But over time some societies acquired higher numbers, as the major languages spoken on the planet today must have done long ago.
在一些传统文化中，计数这件事就像数1，2，3这么简单——因为在这些文化中，计数到3就到头了。他们的语言中没有相应的词语来表示更大的数字，而只是简单地使用各种类似“很多”这样的词语。但随着时间的推移，一些社会获得了使用更大数字的能力，就像今天世界上的主要语言必然在很早之前就已经做到的一样。
Now, a new study of an Australian language family reveals how languages add, and sometimes lose, higher numbers—and how some languages lasted for thousands of years without them.
日前，一项关于澳洲语系的最新研究揭示了语言是如何获得（在某些时候也会丢失）更大数字的，以及一些语言是如何在没有这些更大数字的状态下延续了数千年的。
For some cultures, big numbers just don’t make sense. Take the shepherd who knows that he has the right number of sheep not by counting them one by one but by grasping the gestalt of his flock. That may sound strange to people from other cultures, says Patience Epps, a linguist at the University of Texas, Austin.
对于某些文化而言，大数字并没有什么意义。例如，牧羊人并不是通过逐一数羊来判断羊群数目是否是正确的，而是通过掌握其羊群的完型（gestalt）来做到这一点。对于来自其他文化的人们而言，这听起来可能很奇怪，来自德克萨斯大学奥斯汀分校的语言学家Patience Epps说。
Indeed, she says she’s often asked by incredulous Americans how people with few numerals know, for instance, how many children they have. When she asks this of the Amazonian tribe she works with, “they look at me like it’s a weird question. They list the names, they count on their fingers, but they don’t go around with a quantity in their heads,” she says.
她还表示，自己的确经常被充满怀疑精神的美国人问起诸如此类的问题：那些只能使用有限几个数字的人是怎么知道他们有几个孩子的？当她向和她一起工作的亚马逊部落民问起这个问题时，“他们盯着我看，似乎这对他们来说是个很奇怪的问题。他们会列举孩子们的名字，用手指数孩子的个数，但在他们脑海里并不存在一个具体的数字，”她说道。
But once a society becomes complex enough to require more abstract counting, higher numerals are needed. Amazonian languages add numerals when groups that don’t know or trust each other begin trading goods and need to track exchanges more closely, Epps says. Something like this must have happened in familiar languages many millennia ago.
可一旦某个社会变得足够复杂，要求更多的抽象计数时，就需要更大数字了。当并不互相了解或信任的群体开始交易物品，并且需要更加密切地跟踪这些交易时，亚马逊原住民的语言中就加入了新的数字，Epps表示。在我们所熟悉的语言中，数千年前也一定发生过类似的事情。
Looking at how languages with only a few numerals add or lose them could provide insight into how humans build numeral systems. But uncovering these patterns of cultural evolution required data from many related languages with small numeral systems over a long period of time.
通过研究那些只有有限几个数字的语言是如何添加或者丢失数字的，我们可以洞悉人类是如何构建数字系统的。但想要揭示这些文化演化的模式，我们还需要来自多种互相关联的具有小型数字体系的语言的长期数据。
Enter the Pama-Nyungan language family, which once extended across most of Australia. It contains about 300 languages that are currently spoken by about 25,000 people, though in the past they may have numbered as many as 2 million. Most of these languages have numeral systems that stop at five.
现在让我们走进Pama-Nyungan语系，该语系曾一度扩张到了澳洲的大部分地区。它包含了大约300种不同的语言，当前大约还有25000人在使用这些语言，而在过去，使用这些语言的人数或许曾达到200万之多。这个语系中大部分语言的计数系统都没有比5更大的数字。
Yale University historical linguist Claire Bowern collected current and historical data about these languages, many of which are no longer spoken. Together with undergraduate researcher Kevin Zhou, she reconstructed how numerals in the language family evolved over about 6500 years, borrowing a method from evolutionary biology to explore how the Pama-Nyungan languages were related to each other and also how they changed over time.
耶鲁大学历史语言学家Claire Bowern收集了有关这些语言的当前和历史数据，而其中的大部分语言在今天已不再有人使用了。她和本科生研究者Kevin Zhou一起，还原了过去大约6500年里数字在该语系中的演化过程，借用一种进化生物学的方法探索了Pama-Nyungan语系中的各种语言是如何关联在一起的，以及如何随时间演变的。
The researchers plugged their data into a computer model, which then generated the most likely family tree for all the languages’ numeral systems. Then they tracked how those systems added or lost numerals within the tree.
两位研究者将他们获得的数据导入一个计算机模型中，该模型为所有这些语言的计数系统生成一棵可能性最大的“家族树”。之后，研究者们会追踪在这棵“家族树”中的这些计数系统是如何加入或是丢失数字的。
The upper limits of these Australian numeral systems most often varied between three, four, and five, the team reports this month in the Proceedings of the Royal Society B. Over time, even small numeral systems sometimes lost a numeral or two, but they mainly gained numerals—yet not by plodding up the number line, one numeral after another.
该研究团队在本月的《英国皇家学会学报B刊》上发表的研究结果显示，在这些澳洲计数系统中，数字的上界通常在3，4和5之间变化。随着时间的推移，即使是很小的计数系统有时也会丢失一个或者两个数字，但大多数情况下它们都会获得更多的数字——而这并不是通过沿着数轴缓慢地一个个增加数字来完成的。
Surprisingly, they tended to acquire numerals in bunches, leaping from five numerals to 10 or 20, for example. The numeral five was often the tipping point—once a system reached five, it was likely to add more numerals, up to 20. As a result, numeral systems with five as an upper limit are rare in Pama-Nyungan languages.
令人吃惊的是，这些系统倾向于一次性获得多个数字，例如从5个数字直接跳跃到10个或20个。数字5通常会成为引爆点——一旦一个计数系统达到了5，它就很有可能会加入更多的数字，直到20。而结果就是在Pama-Nyungan语系的语言中，很少有语言的计数系统的上界是5。
“This is surprising, given the predominance of fingers and toes as things to count,” Bowern notes. Adding or losing the numeral four was the most frequent change. (The words for “four” were most often composed out of words for “two,” not by creating or borrowing a new word that means “four,” showing how the numeral systems evolved.)
“这个现象让人感到意外，尤其是考虑到手指和脚趾作为计数工具的主导地位，”Bowern评论道。而加入或是丢失数字4则是这些系统中最频繁发生的变化。（在这些语言中，表示“4”的词通常都是由表示“2”的词合成的，而不是来自创造或借用一个意为“4”的新词语，这也展现了这些数字系统的演化方式。）
Bowern thinks that numerals were added in clusters for practical reasons: If you need to count above five, you probably need to go higher than seven or eight as well. And she speculates that perhaps a cognitive shift occurs at about five. “Once you generalize beyond five or so, it becomes easier to generalize to an infinite system.”
Bowern认为数字以集群的方式被加入语言中是出于一些实际的原因：如果你需要数到5以上，那么你很可能也同样需要数到7或者8以上。同时她推测，一个认知上的变化会在5这个数值附近发生。“一旦你形成了超过5左右的数字概念，那么形成一个无限计数系统就变得更容易了。”
“This is the kind of historical linguistics using computational methods that gives me a lot of confidence,” said Brian Joseph, a historical linguist at Ohio State University, Columbus, adding that “there are a lot of nonlinguists who apply this methodology to data that they don’t seem to control or understand.”
“这些采用计算分析方法的历史语言学研究给了我很多信心，”来自位于哥伦布市的俄亥俄州立大学历史语言学家Brian Joseph说道。他还表示“有很多并非语言学家的研究者将这种方法应用在了一些看起来超出他们的掌控或理解的数据上。”
“These conclusions seem sound to me,” agrees Russell Gray of the University of Auckland in New Zealand and director of the Max Planck Institute for the Science of Human History in Jena, Germany, “and remind us that cultural evolution doesn’t always proceed incrementally.”
“这些结论在我看来很合理，”新西兰奥克兰大学的Russell Gray对这项研究结果表示赞同，他同时还担任位于德国耶拿的马克斯·普朗克人类历史科学研究所的主任，“这也提醒我们，文化的演化并不总是以逐一递增的方式进行的。”
翻译：Veidt（@Veidt)
校对：混乱阈值（@混乱阈值）
编辑：辉格@whigzhou