WEDNESDAY One evening when he had just turned 2, C proclaimed “half moon up!” at the half moon rising in the dusk sky. By their second birthdays children may have vocabularies of hundreds of words. Impressed? Recently Chaser, a border collie, was trained to retrieve, nose or paw 1,022 objects by name. Still, Chaser, like all dogs, utters nary a word. C, like many 2-year-olds, speaks a blue streak. It might be that D has told me about the half moon; I just don’t understand his dialect.

In the mornings, C not only speaks, he also babbles — a fantastical, meaningless stream of sounds that plays with his burgeoning language. When C toddles off down the hall in search of breakfast, D gives me a look. I know the look: I get it when C is playing too roughly with him or taking all of my attention. I imbue C’s babble and D’s look with great meaning, based more on my familiarity with them than any evidence of their signifying anything at all.

THURSDAY Until six months ago, C and D were identical in one respect: they both used their mouths as exploratory organs — a habit that C has happily relinquished. Now, on finding a ladybug in the house, D sniffs at it, then grabs it with his mouth. C does not: he points at it, then turns to me. Who got more information from his exploration? It’s hard to gauge: I doubt that any of us knows what the taste of ladybug can tell us about it.

What this difference reveals is the divergence, growing more profound by the day, in how the dog and the child see the world. And this reflects the fact that the dog’s olfactory ability dwarfs ours; just what this means for how they see (smell) the world is only now beginning to be understood. D has located the places that his friends — human and dog — live in the neighborhood entirely by smell. More than once on a walk I have found myself standing at the entrance to a strange building, waiting for my dog to finish sniffing the doorjamb, when someone I know from the dog park walks out.

C, by contrast, is all about vision, and vision leads to visual attention, which leads to communication we can understand. In infants, this burgeoning interest in where people have (visually) gone is what makes peekaboo fun: when I disappear behind a scarf, maybe it really is the case that I am long gone! But then pop! there we both are.

For his part, D is bemused by peekaboo.

FRIDAY My son has taken to kissing the scar left by my back surgery. My dog licks my tears when I cry. Neither wants to see me angry. In all cases they are not exhibiting a fully developed, adult understanding of injury, sadness or anger — but something recognizable.

This sure feels empathetic. Do D and C see others as having qualities like sadness or anger — or selfishness? The research suggests they do. Two recent canine studies showed that dogs who eavesdropped on experimenters who were generous or selfish in sharing food with other people chose to interact with the generous ones.