I totally and completely understand the power of The Baby. I don't seem to have a Biological Clock tick-tick-tickin' away, but put me in the presence of a cute little baby, and I am toast. I rarely fall into baby talk, but I will make faces and generally act like a love sick puppy. But I draw the line when I start hearing the "S/He is so smart!".
My take, is that we, as adults, have a hard time believing that kids are probably more advanced than we assume. We think that because they are little, they couldn't possibly know anything. But kids are insanely intuitive and observant. I am sure it is inherent survival skill as they don't have the social skills or the physical strength that we as adults rely on.
Children are sponges, right? We all know you just have to say 'fuck' once in front of one for them to run with it - much to the embarrassment of their parents. So there is definitely the 'teaching' factor to contend with. Kids with parents who engage and stimulate their kids will have more precocious babies on their hands, and maybe they seem smarter because they have been challenged. But I think that we, in general, tend to underestimate the smaller ones among us. And that is why I cringe every time someone coos, "S/He's so smart!"