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.

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.

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