巴西原始部族 不會數到三
2004.08.21 中國時報
看到這則報導忍不住發笑
倒不是因為這群人的數字概念僅止於「1-2-很多」
而是Dr. Paperless年久失修的類似傳說終於有了更簡易的版本
（並且獲得證實）
「很多」年前高中音樂老師所傳述的原始部落
比巴西的更進步
他們的數字系統為：「1-2-3-很多，很多…」
同學們後來也學會了如何回答老師的問題
「吳同學，期中考英文考幾分啊？」
──很多很多
「你的近視有幾度呢？」
──很多很多
當然，類似的對話還有很多很多…
（圖片引自
www.todayinsci.com/ stories/story033.htm）
【延伸閱讀二之一】巴西原始部族 不會數到三
2004.08.21 中國時報
黃建育/綜合報導
這世界上，有些人算術確實很差。不過，他們的理由卻很正當：因為他們的語言裡只有一跟二這兩個數字。
美國哥倫比亞大學戈登教授在新一期《科學》跟《自然》這份兩周刊同時撰文指出，世居巴西亞馬遜河流域一帶的「匹拉哈」部族所操的計數語言中，只有「一」跟「二」兩個數字，以及「很多」，而「一」有時還可表示「大約是一」或「很少」。
戈登指出，這個以狩獵採集為生的部落，人數只有兩百，分成十人或廿人單位居住。他們長年遺世獨居，一直拒絕融入巴西主流文化。他們沒有社會結構、沒有藝術、沒有貨幣，而是以物易物代之。
戈登說，該族語言在計數方面相當獨特，由於沒有三以上的計數語言，因而無法計數或表達稍微大點的算術觀念。
此外，他們也沒有「更多」、「幾個」、「全部」或「每個」這些字眼，甚至連「數字」這個字眼也沒有。而且，「他」跟「他們」也無所區別。
然而戈登指出，這族人智力並無問題，因為他們會狩獵，也有空間觀念及相當的語言技能。雖說成人在學習較大計數上有困難，但孩童並無問題。
戈登表示，該族語言中總共只有十個子音及母音。不過，更令人訝異的是他們也不會畫畫，甚至連畫一條簡單的直線，都得費盡九牛二虎之力，還不住嘆氣呻吟。
【延伸閱讀二之二】：
http://www.economist.com/science/displayStory.cfm? story_id=3104346
Language barriers
──Can a concept exist without words to describe it?
Aug 19th 2004
From The Economist print edition
TAKE heart, those of you who struggled with maths at school. It seems that words for exact numbers do not exist in all languages. And if someone has no word for a number, he may have no notion of what that number means.
The Pirahã, a group of hunter-gatherers who live along the banks of the Maici River in Brazil, use a system of counting called “one-two-many”. In this, the word for “one” translates to “roughly one” (similar to “one or two” in English), the word for “two” means “a slightly larger amount than one” (similar to “a few” in English), and the word for “many” means “a much larger amount”. In a paper just published in Science, Peter Gordon of Columbia University uses his study of the Pirahã and their counting system to try to answer a tricky linguistic question.
This question was posed by Benjamin Lee Whorf in the 1930s. Whorf studied Hopi, an Amerindian language very different from the Eurasian languages that had hitherto been the subject of academic linguistics. His work led him to suggest that language not only influences thought but, more strongly, that it determines thought.
Peter Gordon’s article is published in Science. Daniel Everett, who has worked with Dr Gordon, posts an abstract of an article on the absence of numerals in Pirahã language.
While there is no dispute that language influences what people think about, evidence suggesting it determines thought is inconclusive. For example, in 1972, Eleanor Rosch and Karl Heider investigated the colour-naming abilities of the Dani people of Indonesia. The Dani have words for only two colours: black and white. But Dr Rosch and Dr Heider found that, even so, Dani could distinguish and comprehend other colours. That does not support the deterministic version of the Whorf hypothesis.
While recognising that there are such things as colours for which you have no name is certainly a cognitive leap, it may not be a good test of Whorf's ideas. Colours, after all, are out there everywhere. Numbers, by contrast, are abstract, so may be a better test. Dr Gordon therefore spent a month with the Pirahã and elicited the help of seven of them to see how far their grasp of numbers extended.
Using objects with which the participants were familiar (sticks, nuts and—perhaps surprisingly—small batteries), he asked his subjects to perform a variety of tasks designed to measure their ability to count. Most of these tests involved the participant matching the number and layout of a group of objects that Dr Gordon had arranged on a table.
The tests began simply, with a row of, say, seven evenly spaced batteries. Gradually, they got more complicated. The more complicated tests included tasks such as matching numbers of unevenly spaced objects, replicating the number of objects from memory, and copying a number of straight lines from a drawing.
In the tests that involved matching the number and layout of objects they could see, participants were pretty good when faced with two or three items, but found it harder to cope as the number of items rose. Once it was beyond eight, they were getting it right only three-quarters of the time. The only exception was in those tests that used unevenly spaced objects—an arrangement that can be perceived as a group of clusters. Here, performance fell off when the number of objects was six, but shot up again when it was between seven and ten. Dr Gordon suggests that the participants used a “chunking” strategy, counting the clusters and the numbers of objects within each cluster separately.
Things were worse when the participants had to remember the number of objects in a layout and replicate it “blind”, rather than matching a layout they could see. In this case the success rate dropped to zero when the number of items became, in terms of their language, “many”. And line drawing produced the worst results of all—though that could have had as much to do with the fact that drawing is not part of Pirahã culture as it did with the difficulties of numerical abstraction. Indeed, Dr Gordon described the task of reproducing straight lines as being accomplished only with “heavy sighs and groans”.
The Pirahã are a people who have steadfastly resisted assimilation into mainstream Brazilian culture. Their commerce takes the form of barter, with no need to exchange money. Exact numbers do not exist in their language simply because there is no need for them. And in this case, what you do not need, you do not have. At least in the field of maths, it seems, Whorf was right.
