Exactly. Things happen so quickly that it’s often meaningless to say “three years old” and not “3 1/2.”
Back to the original question, from the books I’ve read, it seems that once researchers discovered they could track babies’ eyes, then we got an explosion in understanding a lot about babies’ expectations. IIRC, a baby will look at an object for a certain length of time until it gets bored. If something happens which the baby don’t expect, the baby will look longer.
It’s been noticed that certain age babies, for example, are less “bothered” by objects which retain their same shape but the color changes. One research I read about, they would have object move across the screen, and occasionally go behind another object. When it came out, the baby was bored more quickly if the color of the object changed, rather than the shape. From that, researchers conclude that babies understand objects change change colors, but tend to remain in the same shape.
From the wiki entry cited above
IMHO, one problem is that when researchers attempt to put terms onto the findings, the terms can be misleading if you don’t understand the research. One example I can think of is that here is research if various animals can understand that when an object is broken up into smaller objects, if the size of the smaller objects is equal to the size of the original. If the researcher adds or subtracts smaller objects, and the animal notices that the sizes are not equal, this was reported that the animals could “count.” Well, sort of, but not in the sense laymen think of for “counting” as 1+1 = 2.
Newborns and small babies don’t have any expectations that if an object, say a ball, goes behind something, say a towel, that the ball is still going to be behind the towel. We know this by research on where the baby looks and on how long a baby will look at objects before becoming bored.
This doesn’t say squat about our knowledge or lack of knowledge if a baby believes that objects will disappear forever.
For the most part, small babies tend to love peek-a-boo not because of the wonder of the mommy or daddy disappearing and reappearing, but because of the connection with the eyes, the smiling and the interaction.