This seems appropriate for the first posting of the new year. It is observed that new born babies can distinguish between two objects and three objects.
The observations are made as follows:
1. New born babies are shown pictures of two objects. It does not matter what the objects are. When the baby stops looking at the picture, becomes bored with it, a second picture replaces the first with TWO different objects. This is repeated over and over again with different objects and it is observed that the attention span remains more or less the same.
2. Then the picture is replaced with THREE objects and the baby's attention span increases significantly, indicating that the baby notices that there is more than two objects.
3. Same results going from 3 to 2 objects.
4. Same results using two or three real objects behind a screen. In this case however, we can allow the baby to see us changing the number of objects. Then the baby has expectation, and if the number is changed and the screen put in place and then removed, the attention span of the baby is small.
5. But if the baby sees us, say placing 3 objects and covering them with the screen. And then before we remove the screen we remove one object, then when the screen is removed, the baby has the longer attention span, presumably because the baby's expectation was confounded.
So what does it mean that new born babies have inherent mathematical ability? Perhaps math is genetic. It seems to be more than just the invention of humans since it is not an entirely learned behavior. To some extent math cognition comes from nature rather than nurture.
There seems to be a connection here with dolphin's pattern recognition. Any comments? There must be more meaning to those observations than the little meaning I can attach to them.