Numbers

I was listening to an old broadcast of Radio Lab last night on my walk. It was a crisp, starry winter night. Perfect for walking. The broadcast was about "numbers" and started with an interesting discussion of how our number sense develops. I may be a little fuzzy on the details, but three basic experiments were described.

First, there was a study with 2-3 month old babies. They hook them up to some brain electrodes and plop them in front of a computer screen. The kids see a screen with some object, say 8 ducks. The screen flashes again, same image. The researchers note that at first there is a lot of brain activity, "cool, ducks on a screen" but, gradually the activity slows as the image repeats. Then a screen with 8 trucks appears, prompting a brain wave response in the temporal lobe..."cool, something new to look at!" The babies recognize that something has changed. If they repeat the experiment, but this time switch not the object, but the number, for instance go from 8 ducks to 16 ducks, the babies show an increase of brain activity, but this time in a different place (parietal lobe, perhaps?). Babies recognize a different kind of difference now.

Second experiment. Find a 2 year old. Give her a bunch of pennies. Sit down and say, "can you give me 1 penny?" The kid will pick up one penny and hand it over. Ask, "can you give me 2 pennies?" and the kid will just pick up a bunch of pennies and hand them over. They know that 2 is more than 1, but have no clue how much more. The idea of 2 doesn't develop until about 1/2 way through the year. Then the idea of 3 takes a little longer, then 4. I think they said it wasn't until 3.5 years old that kids can count out objects. They can count before then, that is, recite the numbers in order, but they have no meaning. Making that connection is a big leap.

In that discussion the idea was introduced that our "natural" way of thinking about numbers was closer to a logarithmic understanding than a scalar (?) way of thinking. Leading to the 3rd experiment. In this case an aboriginal group was found that had very little concept of numbers. They might count up to 4 or 5, but after that numbers had no real meaning. If given a number line with 1 on one end and 9 on the other, and asked to say what number comes in the middle, they are apt to choose not 5 (the Western answer) but 3! Since 3 is 3x 1 and 9 is 3x 3 then, 3 is in the middle...they are thinking in logarithms!