How do children learn to count? Part 3

Two posts ago, I presented some rather odd data about the developmental trajectory of counting. It turns out children learn the meanings of number words in a rather odd fashion. In my last post, I described the "number" systems that are in place in animals and in infants before they learn to count. Today, I'll try to piece all this together to explain how children come to learn to be able to count.

Children first learn to map number words onto a more basic numerical system. They learn that "one" maps on to keeping track of a single object. After a while, they learn "two" maps onto keeping track of one object plus another object. Then they learn that "three" maps onto keeping track of one object plus another object plus another object. All this follows from the Wynn experiments I discussed two posts ago.

Up to this point, they've been learning the meanings of these words independently, but around this time they notice a pattern. They know a list of words ("one, two, three, four") and that this list always goes in the same order. They also notice that "two" means one more object than "one," and that "three" means one more object than "two." They put two and two together and figure out that "four" must mean one more object than "three," even though their memory systems at that age don't necessarily allow them to pay attention to four objects simultaneously. Having made this connection, figuring out "five," "six," etc., comes naturally.

So what is that more basic number system? One possibility is that children to learn to map the early number words onto the analog number system I also described in the last post (the system adults use to estimate number when we don't have time to count)?

Something like this claim has been made by a number of well-known researchers (Dehaene, Gallistel, Gelman and Wynn, to name a few). There are a number of a priori reasons Susan Carey of Harvard thinks this won't work, but even more important is the data.

As I described two posts ago, very young children can hand you one marble when asked, but hand you random numbers of marbles if asked for "two," "three" or any larger number. They always give you more than one, but they can't distinguish between the other numbers. Following Wynn, these are called "one-knowers." Slightly older children are "two-knowers," who can give you one or two marbles, but give you random amounts greater than 2 if asked for another other number. At the next stage, the child becomes a "three-knower." Usually, the next stage is being able to succeed on any number. I'll call those "counters."

Recently, LeCorre and Carey replicated this trajectory using cards with circles on them. They presented the children a card with some number of circles (1 to 8) and asked the kid, "How many?" One-knowers tended to reply "one" to a card with one circle, and then guessed incorrectly for just about everything else. Two-knowers could count one or two circles, but guessed incorrectly for all the other cards. Three-knowers could count up to three, but just guessed beyond that. Counters answered correctly on essentially all cards.

So far this doesn't tell us whether children learn to count by bootstrapping off of analog magnitudes or some other system. Carey and Mathieu LeCorre published a paper this year that seems to settle the question. The setup was exactly the same as in the last paper (now with cards with anywhere from 1 to 10 circles), except that this time the children were only briefly shown the card. They didn't have enough time to actually count "one, two, three..." The data for one-, two- and three-knowers didn't change, which isn't surprising. Both the "3-object" and the analog magnitude systems are very fast and shouldn't require explicit counting.

However, counters fell into two groups. One group, about 4.5 years old on average, answered just as adults. When they saw six circles, their answers averaged around "six." When they saw ten circles, their answers averaged around "ten." This is what you'd expect if they have mapped number words onto the analog magnitude system.

However, the other group, which was slightly younger (average age of 4 years, 1 month), guessed randomly for cards with 5 or more circles, just as if they didn't know how to count. However, these kids can count. If given time to look at the cards, they would have said the right number. So despite the fact that they can count, they do not seem to have their analog magnitude system mapped onto number words.

This means that the analog magnitude system isn't fundamental in learning how to count, and it actually takes some time for children to learn that mapping even after they've learned to count. Carey takes this as meaning that the analog magnitude system doesn't play a fundamental role in learning to count, either, and there are other reasons as well that this is probably the case.

One remaining possibility is that children use the "3-object system" to understanding the meanings of 1, 2 and 3. This seems to work nicely, given that the limits of the system (3 objects in children, 4 in adults) seem to explain why children can learn "one," "two," and "three" without really learning to count. Carey actually has a somewhat more nuanced explanation where children learn the meanings of "one," "two," and "three" the same may that quantifiers (like "a" in English) are learned. However, to the best of my knowledge, she doesn't have an account of how such quantifiers are learned, and if she had an account, I suspect it would itself hinge off of the 3-object system, anyway.

That's it for how children learn to count, unless I get enough comments asking for more details on any point. For those who want to read more, there are many papers on this subject at Carey's web page.

How do children learn to count? Part 2

In my last post, I showed that children learn the meaning of number words in a peculiar but systematic fashion. Today, I'll continue trying to explain this odd behavior.

Important to this story is that children (and non-human primates) are born with several primitive but useful numerical systems that are quite different from the natural number system (1, 2, 3, ...). They can't use these systems to count, but they may be useful in learning to count. In this post, I'll try to give a quick summary of how they work.

One is a basic system that can track about 3-4 objects at a time. This isn't a number system per se, just an ability to pay attention to a limited and discrete number of things, and it may or may not be related to similar limits in visual short-term memory.

You can see this in action by playing the following game with a baby under the age of 2. Show the baby two small boxes. Put a single graham cracker into one of the boxes. Then put, one at a time, two graham crackers into the other box. Assuming your baby likes graham crackers, she'll crawl to the box with two graham crackers. Interestingly, this won't work if you put two graham crackers in one box and four in the other. Then, the baby chooses between the boxes randomly. This is understood to happen because the need to represent 6 different objects all in memory simultaneously overloads the poor baby's brain, and she just loses track. (If you want to experience something similar, try to find a "multiple object tracking" demo with 5 or more objects. I wasn't able to find one, but you can try this series of demos to get a similar experience.)

On the other hand, there is the analog magnitude system. Infants and non-human animals have an ability to tell when there are "more" objects. This isn't exact. They can't tell 11 objects from 12. But they can handle ratios like 1:2. (The exact ratio depends on the animal and also where it is in maturity. We can distinguish smaller ratios than infants can.)

You can see this by using something similar to the graham cracker experiment. Infants like novelty. If you show them 2 balls, then 2 balls again, then 2 balls again, they will get bored. Then show them 4 balls. They suddenly get more interested and look longer. However, this won't happen if you show them 4 balls over and over, then show them 5. That ratio is too similar. (I'm not sure if you get this effect in the graham cracker experiment. I suspect you do, but I couldn't find a reference off-hand. The graham cracker experiment is more challenging for infants, so it's possible the results might be somewhat different.)

You can also try this with adults. Show them a picture with 20 balls, and ask them how many there are. Don't give them time to count. The answer will average around 20, but with a good deal of variation. They may say 18, 19, 21, 22, etc. If you give the adult enough time to count, they will almost certainly say "20."

Those are the two important prelinguistic "number" systems. In my next post, I'll try to piece all this information together.

How do children learn to count? Part 1

How do children learn to count? You could imagine that numbers are words, and children learn them like any other word. (Actually, this wouldn't help much, since we still don't really understand how children learn words, but it would neatly deflect the question.) However, it turns out that children learn to count in a bizarre fashion quite unlike how they learn about other words.

If you have a baby and a few years to spend, you can try this experiment at home. Every day, show you baby a bowl of marbles and ask her to give you one. Wait until your baby can do this. This actually takes some time, during which you'll either get nothing or maybe a handful of marbles.

Then, one day, between 24 and 30 months of age, your toddler will hand you a single marble. But ask for 2 marbles or 3 marbles, etc., your toddler will give you a handful. The number of marbles won't be systematically larger if you ask for 10 than if you ask for 2. This is particularly odd, because because by this age the child typically can recite the count list ("one, two, three, four...").

Keep trying this, and within 6-9 months, the child will start giving you 2 marbles when asked for, but still give a random handful when asked for 3 or 4 or 5, etc. Wait a bit longer, and the child will manage to give you 1, 2 or 3 when asked, but still fail for numbers greater than 3.

This doesn't continue forever, though. At around 3 years old, children suddenly are able to succeed when asked for any set of numbers. They can truly count. (This is work done by Karen Wynn some years ago, who is now a professor of psychology at Yale University.)


Of course, this is just a description of what children do. What causes this strange pattern of behavior? We seem to be, as a field, homing in on the answer, and in my next post I'll describe some new research that sheds light onto the question.

SNPs and genes for language

Modern genetic analyses have told us a great deal about many aspects of the human body and mind. However, genetics has been relatively slow in breaking into the study of language. As I have mentioned before, a few years ago resarchers reported that a damaged version of the gene FOXP2 was responsible for the language impairments in the KE family. This sounds more helpful than it really was, since it turns out that even some reptiles have versions of the FOXP2 gene. In humans, FOXP2 isn't just expressed in the brain -- it's expressed in the gut as well. This means that there is a lot more going on than just having FOXP2 or not.

Over the weekend, researchers presented new data at the Boston University Conference on Language Development that hones in on what, just exactly, FOXP2 does.

It turns out that there is a certain amount of variation in genes. One type of variation is a Single Nucleotide Polymorphism (SNP), which is a single base pair in a string of DNA that varies from animal to animal within a species. Some SNPs may have little or no effect. Others can have disastrous effects. Others are intermediate. The Human Genome Project simply cataloged genes. Scientists are still working on cataloging these variations. (This is the extent of my knowledge. If any geneticists are reading this and want to add more, please do.)

The paper at BUCLD, written by J. Bruce Tomblin and Jonathan Bjork of the University of Iowa and Morten H. Christiansen of Cornell University, looked at SNPs in FOXP2. They selected 6 for study in a population of normally developing adolescents and a population of language-impaired adolescents.

Two of the six SNPs under study correlated well with a test of procedural memory (strictly speaking, one correlation was only marginally statistically significant). One of these SNPs predicted better procedural memory function and was more common in language-normal adolescents; the other predicted worse procedural memory function and was more common in language-impaired adolescents.

At a mechanistic level, the next step will be understanding how the proteins created by these different versions of FOXP2 do. From my perspective, I'm excited to have further confirmation of the theory that procedural memory is important in language. More importantly, though, I think this study heralds a new, exciting line of research in the study of human language.

(You can read the abstract of the study here.)

Finding guinea pigs

One problem that confronts nearly every cognitive science researcher is attracting participants. This is less true perhaps for vision researchers, who can sometimes get away with testing only themselves and their coauthors, but it is definitely a problem for people who conduct Web-based research, which often needs hundreds or even thousands of participants.

Many researchers when they start conducting experiments on the Internet are tempted to offer rewards for participation. It's too difficult to pay everybody, so this is often done in the context of a lottery (1 person will win $100). This seems like an intuitive strategy, since we usually attract participants to our labs by offering money or making it a requirement for passing an introductory psychology course.

If you've been reading the Scienceblog.com top stories lately, you might have noticed a recent study by University of Florida researchers, which suggested that people -- well, UF undergrads -- are less likely to give accurate information to websites which offered rewards.

Although these data are in largely in the context of marketing, this suggests that using lotteries to attract research participants on the Web may actually be backfiring.

Are babies prejudiced?

In 1994, in discussing how children come to learn about inheritance, Susan Carey and Elizabeth Spelke wrote: "There are many ways children may come to resemble their parents: Curly-haired parents may have curly-haired children because they give them permanents; prejudiced parents may have prejudiced children because they taught them to be so. Such mechanisms are not part of a biological process of inheritance..."

It's not clear that Carey & Spelke thought prejudice is taught to children rather than inherited through genes, but it's interesting that in picking only two examples of non-biological inheritance, Carey & Spelke chose prejudice as one. What makes this quotation remarkable is how unremarkable it is. It seems quite natural to assume that prejudice is learned. Recently, however, a number of researchers -- including Spelke -- have been suggesting that although the specifics of a prejudice may come through experience, being prejudiced is innate.

(Just to be clear, nobody I know is saying that prejudice is natural, good, or something that cannot be overcome. The specific claim is that it isn't something you have to learn.)

It's actually been known for a few years that infants prefer to look at familiar-race faces. Very recently, Katherine Kinzler in the Spelke lab at Harvard has started looking at language prejudice. People can get very fired up about language. Think about the fights over bilingualism or ebonics in the US. Governments have actively pursued the extinction of various non-favored, minority languages.

In a long series of studies, Kinzler has found evidence that this prejudice against other languages and against speakers of other languages is innate. Young infants prefer to look at a person who previously spoke their language than somebody who spoke a foreign language. Infants show the same preference to somebody who speaks with their accent rather than with a foreign accent. Older infants (who can crawl), will crawl towards a toy offered by someone who speaks their language rather than towards a toy offered by a foreign-language speaker. Keep in mind that these infants probably do not understand what is being said. Also, the speakers are bilingual (the infants don't know this), which allows the experimenters to control for things like what the speakers look like. For instance, for some babies, one speaker speaks English and the other French, and for the other babies, they reverse. Also, French babies prefer French-speakers to English-speakers, while English babies prefer English-speakers to French-speakers.

Preschool children would rather be friends with somebody who speaks their own language, which is not surprising. They also prefer to be friends with somebody who uses their own accent rather than a foreign accent, even when they are able to understand what the foreign-accented child says.

Of course, none of this says that babies are born knowing which languages and accents to prefer. However, they seem to quickly work out which languages and accents are "in-group" and which are "out-group." This also doesn't say that linguistic prejudice cannot be overcome. For one thing, simply exposing children to many accents and language would presumably do much all by itself. Although it's not possible yet to rule out alternative explanations, what it does suggest is that prejudice -- at least, linguistic prejudice -- can't be overcome by simply not teaching it to children. They must be actively taught not to be prejudiced.

The paper, which is pretty easy to understand, is not available on the authors' website, but if you have a decent library:

Kinzler, Dupoux, Spelke. (2007). The native language of social cognition. Proceedings of the National Academy of Sciences, 104(30), 12577-12580.

Quantum Vision

Can quantum physics explain consciousness? The fact that the mind is instantiated in the physical brain has made it difficult for people to imagine how a physical object like the brain leads to conscious experience in similar ways that it becomes difficult to believe in free will. A number of people have hoped to find the solution in the indeterminacy of quantum physics.

There is a new hypothesis out from Efstratios Manousakis of Florida State University. The phenomenon that he is interested in understanding is binocular rivalry. In binocular rivalry, a different image is displayed to each of your eyes. Instead of seeing a mishmash of the two images, you tend to see one, then the other, then the first one again, ad infinitum. It's not possible to do a demonstration over the internet, but the experience is similar to looking at a Necker Cube, where you first see it popping out of the page, then receding from the page, then popping out, and so on. Notice that what your "eye" sees doesn't change. But your conscious experience does.

Manousakis has found that quantum waveform formulas describe this reasonably well. The question is whether they describe it well because the phenomenon is a quantum phenomenon or because there are two different phenomena for which the same formulas work. Keep in mind that binocular rivalry is something that can actually be seen with neuroimaging. That is, you can see the patterns in the brain change as the person first sees one image, then the other, etc. So if this is really a quantum effect, it is operating at a macro scale. New Scientist has an interesting article on this story this last week. It's not clear from the article if this is a problem Manousakis has thought about or not, and unfortunately his actual journal article isn't available on his website.

The neuroscience of theory of mind

The study of social cognition ("people thinking about people") and social neuroscience has exploded in the last few years. Much of energy -- but by no means all of it -- has focused on Theory of Mind.

"Theory of Mind" is something we are all assumed to have -- that is, we all have a theory that other people's actions are best explained by the fact that they have minds which contain wants, beliefs and desires. (One good reason for calling this a "theory" is that while we have evidence that other people have minds and that this governs their behavior, none of us actually has proof. And, in fact, some researchers have been claiming that, although we all have minds, those minds do not necessarily govern our behavior.)

Non-human animals and children under the age of 4 do not appear to have theory of mind, except in perhaps a very limited sense. This leads to the obvious question: what is different about human brains over the age of 4 that allows us to think about other people's thoughts, beliefs and desires?

It might seem like Theory of Mind is such a complex concept that it would be represented diffusely throughout the brain. However, in the last half-decade or so, neuroimaging studies have locked in on two different areas of the brain. One, explored by Jason Mitchell of Harvard, among others, is the medial prefrontal cortex (the prefrontal cortex is, essentially, in the front of your brain. "medial" means it is on the interior surface, where the two hemispheres face each other, rather than on the exterior surface, facing your skull). The other is the temporoparietal junction (where your parietal and temporal lobes meet), described first in neuroimaging by Rebecca Saxe of MIT and colleagues.

Not surprisingly, there is some debate about which of these brain areas is more important (this breaks down in the rather obvious way) and also what the two areas do. Mitchell and colleagues tend to favor some version of "simulation theory" -- the idea that people (at least in some situations) guess what somebody else might be thinking by implicitly putting themselves in the other person's shoes. Saxe does not.

Modulo that controversy, theory of mind has been tied to a couple fairly small and distinct brain regions. These results have been replicated a number of times now and seem to be robust. This opens up the possibility, among other things, of studying the cross-species variation in theory of mind, as well as the development of theory of mind as children reach their fourth birthdays.

Having solved the question of monkeys & humans, I move on to children and adults

Newborns are incredibly smart. They appear to either be born into the world knowing many different things (the difference between Dutch and Japanese, for instance), or they learn them in a blink of an eye. On the other hand, toddlers are blindingly stupid. Unlike infants, toddlers don't know that a ball can't roll through a solid wall. What is going on?

First, the evidence. Construct a ramp. Let a ball roll down the ramp until it hits a barrier (like a small wall). The ball will probably bounce a little and rest in front of the wall. Now let an infant watch this demonstration, but with a screen blocking the infant's view of the area around the barrier. That is, the infant sees the ball roll down a ramp and go behind a screen but not come out the other side. The infant can also see that there is barrier behind the screen. If you then lift the screen and show the ball resting beyond the barrier -- implying that the ball went through the solid barrier, the infant acts startled (specifically, the infant will look longer than if the ball was resting in front of the barrier as it should be).

Now, do a similar experiment with a toddler. The main difference is there are doors in the screen, one before the barrier and one after. The toddler watches the ball roll down the ramp, and their task is to open the correct door to pull out the ball. Toddlers cannot do this. They seem to guess randomly.

Here is another odd example. It's been known for many decades that three-year-olds do not understand false beliefs. One version of the task looks something like this. There are two boxes, one red and one green. They watch Elmo hide some candy in the red box and then leave. Cookie Monster comes by and takes the candy and moves it from the red box to the green box. Then Elmo returns. "Where," you ask the child, "is Elmo going to look for his candy?"

"In the green box," the child will reply. This has been taken as evidence that young children don't yet understand that other people have beliefs that can contradict reality. (Here's a related, more recent finding.)

However, Kristine Onishi and Renee Baillargeon showed in 2005 that 15-month-old infants can predict where Elmo will look, but instead of a verbal or pointing task, they just measured infant surprise (again, in terms of looking time). (Strictly speaking, they did not use "Elmo," but this isn't a major point.)

So why do infants succeed at these tasks -- and many others -- when you measure where they look, while toddlers are unable to perform verbal and pointing tasks that rely on the very same information?

One possibility is that toddlers lose an ability that they had as infants, though this seems bizarre and unlikely.

Another possibility I've heard is that the verbal and pointing tasks put greater demands on memory, executive functioning and other "difficult" processes that aren't required in the infant tasks. One piece of evidence is that the toddlers fail on the ball task described above even if you let them watch the ball go down the ramp, hit the wall and stop and then lower the curtain with two doors and make them "guess" which door the ball is behind.

A third possibility is something very similar to Marc Hauser's proposal for non-human primate thought. Children are born with many different cognitive systems, but only during development do they begin to link up, allowing the child to use information from one system in another system. This makes some intuitive sense, since we all know that even as adults, we can't always use all the information we have available. For instance, you may know perfectly well that if you don't put your keys in the same place every day, you won't be able to find them, put you still lose your keys anyway. Or you may know how to act at that fancy reception, but still goof up and make a fool of yourself.

Of course, as you can see from my examples, this last hypothesis may be hard to distinguish from the memory hypothesis. Thoughts?

How are monkeys and humans different (I mean, besides the tail)

Marc Hauser, one of a handful of professors to be tenured by Harvard University (most senior faculty come from other universities), has spent much of his career showing that non-human primates are smart. It is very dangerous to say "Only humans can do X," because Hauser will come along and prove that the cotton-top tamarin can do X as well. Newborn babies can tell Dutch from Japanese? Well, so can the tamarins.

For this reason, I have wondered what Hauser thinks really separates human cognition from that of other animals. He is well-known for a hypothesis that recursion is the crucial adaptation for language, but I'm never sure how wedded he is to that hypothesis, and certainly he can't think the ability to think recursively is all that separates human thought from tamarin thought.

Luckily for me, he gave a speech on just that topic at one of the weekly departmental lunches. Hopefully, he'll write a theory paper on this subject in the near future, if he hasn't already. In the meantime, I'll try to sketch the main point as best I understood it.

Hauser is interested in a paradox. In many ways, non-human primates look quite smart -- even the lowly tamarin. Cotton-top tamarins have been able to recognize fairly complex grammatical structures, yet they do not seem to use those abilities in the same ways we do -- for instance, they certainly don't use grammar.

In some situations, non-human primates seem to have a theory of mind (an understanding of the contents of another's mind). For instance, if a low-ranking primate (I forget the species, but I think this was with Chimpanzeees) sees two pieces of good food hidden and also sees that a high-ranking member of the troop can see where one piece was hidden but not the other, the low-ranking primate will high-tail it to the piece of food only he can see. That might seem reasonable. But contrast it with this situation: these primates also know how to beg for food from the researchers. What if primate is confronted with two researchers, one who has a cloth over her eyes and one who has a cloth over her ears. Does the primate know to beg only from the one who can see? No.

Similarly, certain birds can use deception to lure a predator away from their nest, but they never use that deceptive behavior in other contexts where it might seem very useful.

These are just three examples where various primates seem to be able to perform certain tasks, but only in certain contexts or modalities. Hauser proposes that part of what makes humans so smart are the interfaces between different parts of our brains. We can not only recognize statistical and rule-based regularities in our environment -- just like tamarins -- but we can also use that information to produce behavior with these same statistical and rule-based regularities. That is, we can learn and produce grammatical language. We can take something we learn in one context and use it in another. To use an analogy he didn't, our brains are an office full of computers after they have been efficiently networked. Monkey computer networks barely even have modems.

This same theory may also explain great deal of strange human infant behavior. More about that in the future.

Do ballplayers really hit in the clutch?

If you've been watching the playoffs on FOX, you'll notice that rather than present a given player's regular-season statistics, they've been mostly showing us their statistics either for all playoff games in their career, or just for the 2007 post-season. Is that trivia, or is it an actual statistic? For instance, David Ortiz hits better in the post-season than during the regular season. OK, one number is higher than the other, but that could just be random variation. Does he really hit better during the playoffs?

Why does this even matter? There is conventional wisdom in baseball that certain players hit better in clutch situations -- for instance, when men on base. This is why RBIs (runs-batted-in) are treated as a statistic, rather than as trivia. Some young Turks (i.e., Billy Beane of the Oakland A's) have argued vigorously that RBIs don't tell you anything about the batter -- they tell you about the people who bat in front of him (that is, they are good at getting on base). Statistically, it is said, few to no ballplayers hit better with men on and 2 outs.

So what about in the post-season?

I couldn't find Ortiz's lifetime post-season stats, so I compared this post-season, during which he's been phenomenally hot (.773 on-base percentage through the weekend -- I did this math last night during the game, so I didn't include last night's game), compared with the 2007 regular season, during which he was just hot (.445 on-base percentage).

There are probably several ways to do the math. I used a formula to compare two independent proportions (see the math below). I found that his OBP is significantly better this post-season than during the regular season. So that's at least one example...

Here's the math.

You need to calculate a t statistic, which is the difference between the two means (.773 and .445) divided by the standard deviation of the difference between those two means. The first part is easy, but the latter part is complicated by the fact that we're dealing with ratios. That formula is:

square root of: (P1*(1-P1)/N1 + P2*(1-P2)/N2)
where P1 = .773, P2 = .445, N1 = 659 (regular season at-bats - 1), N2 = 22 (post-season at-bats - 1).

t = 2.99, which gives a p value of less than .01.

I was also considering checking just how unusual Colorado's winning streak is, but that's where my knowledge of statistics broke down (maybe we'll learn how to do that next semester). If anybody has comments or corrections on the stats above or can produce other MBL-related math, please post it in the comments.

New Harvard president to be installed today

Drew Faust will be installed today as Harvard's 28th president. That's right -- Harvard has only had 28 presidents since Henry Dunster was named in 1640. That's not counting some acting presidents, like Samuel Willard (1701-1707) or Nathaniel Eaton, who was "schoolmaster" from 1637 to 1639.

Faust is of course the first female president of Harvard. She is also the first since Charles Chauncy (1654-1672) to have neither an undergraduate nor graduate degree from Harvard (From 1672 to 1971, all Harvard presidents had done their undergraduate work at Harvard. The last three -- Derek Bok, Neil Rudenstine and Larry Summers -- had graduate degrees from Harvard).

The ceremony will be outdoors on Harvard Yard at 2pm. It rained heavily overnight, but it seems to be clearing up now. If the weather is decent, I'll check it out and report back. I hear tell that Harvard ceremonies have all the pomp and splendor you would expect, but I have yet to see one.

People who can't count

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.)

Brazil issues warrant for scientist's arrest

The government of Brazil recently ordered the arrest of the well-known linguist and anthropologist, Dan Everett.

Everett has been both famous and infamous for his study of the Piraha people, a small tribe in Brazil. He has made a number of extraordinary claims about their culture and language, such as that they do not have number words or myths.

These claims are important because they undermine a great deal of current linguistic and psychological theory, and so they have been hotly debated. Some of these debates, however, have spilled over from arguments about data and method to personal attacks.

Just before Everett spoke at MIT last fall, a local linguist sent out an email to what amounted to much of Boston's scientific community involved in language and thought. It looked like the sort of email that one means to send to a close friend and accidentally broadcasts. Language Log describes it better than I can, but the gist was that Everett is a liar who exploits the poor Piraha for his own fame and glory.

This was just one instance in a series of ad hominem attacks on Everett over the last few years. I am not going to weigh in on whether Everett is exploiting anybody, because I simply don't feel I know enough. I've never met a Piraha -- not that any of Everett's detractors have either, to my knowledge. If this means anything, I am told by friends who have visited the Piraha that they really like Everett.

A couple weeks ago, I heard from a friend who has collaborated with Everett that all further research on Piraha language and has been essentially banned. A warrant is out for Everett's arrest on charges of, essentially, exploiting the Piraha. I have no idea how much this has to do with the controversy the aforementioned linguist has been raising, but I suspect that it is not unrelated.

On the topic of language, my Web-based study of how people interpret sentences is still ongoing, and I could use more participants. Not to exploit this post to further my own academic fame and glory...

Scientists create mice with human language gene

Scientists at the Max Plank institute in Germany recently announced that they had successfully knocked the human variant of the FOXP2 "language" gene into mice.

The FOXP2 gene, discovered in 2001, is the most famous gene known to be associated with human language. There has been some debate about what exactly it does, but a point mutation in the gene is known to cause speech and language disorders.

Part of the interest in FOXP2 stems from the fact that it is found in a wide range of species, including songbirds, fish and reptiles with only slight variations. Also, FOXP2 is expressed in many parts of the body, not just the brain. Previous research had found that removing the gene from mice decreased their vocalizations...and ultimately killed the mice.

In the new study, scientists created a new mouse "chimera" with the human variant of the FOXP2 gene. This time, the only differences they could find between the transgenic mice and typical mice was in their vocalizations.

Read more about FOXP2.

(Disclosure: This research does not appear to have been published yet. I heard about it from Marc Hauser of Harvard University, who heard about it this summer from a conference talk by Svante Paabo of Max Plank, one of the researchers involved in the project.)