People who can't count

October 10, 2007

Babies can't count. Adults can. When I say that babies don't count, I don't mean that they don't know the words "one," "two," "three," or "four." That's obvious. What I mean is that if you give an infant the choice between 5 graham crackers or 7, the baby doesn't know which to pick.

Does that mean we have to learn numbers, or does it mean that the number system simply comes online as we mature. Babies also have bad vision, but that doesn't mean the learn vision. One of the reasons we might assume that number is innate rather than learned is that all reasonably intelligent children learn to count around the same time...or do they? This is where a few cultures, such as the Piraha, become very important.

I believe that I have heard that there are some languages that only have words for "one," "two," and "many," but I'm not sure, so if you know, please make comments. I am fairly certain that the Piraha are the only known culture not to even have a word for "one."

How does one know whether they have a word for "one?" Your first impulse might be to check a bilingual dictionary, but that begs the question. How did the dictionary-maker know? The way a few people have done it (like Peter Gordon at Columbia and Ted Gibson & Mike Frank from MIT) is to show the Piraha a few objects and see what they say. According to Mike Frank's talk at our lab a couple weeks ago, they never found a word that was used consistently to describe "one" anything. Instead, there was a number that was used for small numbers of object (1, 2, etc.), another word for slightly larger numbers, and third word that seems to be used the way we use "many."

Well, maybe they just weren't using number words in this task. Did they really even understand what was being required of them? Who knows. But there are other ways to do the experiment. For instance, you can test them the same way we test babies. You show them two boxes. You put 5 pieces of candy into one box. Then you put 7 pieces of candy into the other box. Then you ask them which box they want. Remember that they never see both groups of candy at the same time, so they have to remember the groups of candy in order to compare them.

Well, Mike Frank tried this. This is an example of the responses he got:

"Can I have both boxes?"

No. You have to choose.

"Oh, is that what this game is about? I don't want to play this game. Who needs candy? Can we do spools of thread? My wife needs those. Or how about some shotgun shells?"

This experiment was a failure. Instead, they tried a matching task. You show them a row of, say, 5 spools of thread. Then you ask them to put down the same number of balloons as there are spools of thread. They can do this. Now, you change the game. You show them some number of spools of thread, then cover those spools. You then ask them to put down the same number of balloons. Since they can't see the thread, they have to do this by memory.

The Piraha fail at this and related tasks. People who can count do not.

Of course, they might not have understood the task. This is very hard to prove one way or another. I have been running a study in my lab that involves recent Chinese immigrants. I designed the study and tested it in English with Harvard undergrads. They found the task challenging, but they quickly figured out what I needed them to do. Some of my immigrant participants do so as well, but many of them find it impossibly difficulty -- literally. Some of them have to give up.

It's not that they aren't smart. Most of them are Harvard graduate students or even faculty. What seems to be going on is a culture clash. For one thing, they aren't usually familiar with psychology experiments, since very few are done in China. I suspect that some of the things I ask them to do (repeat a word out loud over and over, read as fast as possible, etc.) may seem perfectly normal requests to my American undergraduates but very odd to my Chinese participants, just as the Piraha discussed above didn't want to choose boxes of candy. So it is always possible that the Piraha act differently in these experiments because they have different cultural expectations and have trouble figuring out what exactly is required of them.

That said, it seems pretty unlikely at this point that the Piraha have number words or count. This suggests counting must be learned. In fact, it suggests counting must be taught. This contrasts with language itself, which often seems to spring up spontaneously even when the people involved have had little exposure to an existing language. (Click here for a really interesting take on why the Piraha don't seem particularly interested in learning how to count.)

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