Here it comes, Father's Day, and as a new dad I'm wondering just one thing: Um, when exactly is it again?

You might think I'd have marked the date with a big calendar star. But somehow I've never taken Father's Day seriously. When I was a kid, Mother's Day was a major event in our family. My sisters and I served our mom lavish breakfasts in bed, we did our chores without the usual groaning and stalling: it was a highly choreographed, dawn-to-dusk show of solicitude. But Father's Day barely registered. Dad opened his gifts over morning coffee (Hey, socks and a necktie!), gave us a pat on the head, then continued his day as usual — another Sunday spent doing chores and watching sports on TV. Father's Day was blatantly paltry.

So why did Moms get treated royally, while Dads got royally rooked? Maybe this discrepancy reflected the difference in parental roles back then, the strict division of labor — and, in a sense, of love. A mother's love was hands-on. Count up the diapers changed; count up the meals made, noses blown, temperatures taken in the night, rooms picked up after, faces wiped off, and on and on over the years. But a father was mostly hands off. Those generic gifts dads got mirrored a certain abstract quality in the love they gave. It was love, yes, but at a distance.

There's a concept in basketball of "getting touches:" a player can't score if he doesn't get his touches, doesn't get the ball. Dads back then didn't get a lot of touches. Much of the time they just weren't around. When my sister and I were the age Larkin is now, our father was a surgical resident, working eighty-hour weeks while our mother stayed home. That meant eighty hours, week after week, that we were with her and not with him. A snapshot from 1960 shows our father stretched out on the couch after work, dead asleep – with my sister and me riding horseback on top of him. For years we were crammed into the margins of his working life. It was a pretty typical arrangement for that era.

So much is different now. On Sundays, when Larkin and I go to the gym to play basketball and romp around the playscape, plenty of other dads are there, doing exactly the same thing. We're all putting in time with our toddlers. In my case, working at home means even more time together. I get a lot of touches, at least as many as Molly does. It all adds up to a different model of dadhood. After I wrote about a spring day with Larkin, my father emailed me. "There's so much richness to your days with Lark," he wrote. "You are enjoying an experience with her that very few fathers ever have — or are even aware of missing."

I love having Larkin at the center of my daily life, instead of in the margins. I'm able to pay attention, registering changes in her world as they occur. The other day, for instance, we drove past the sapling I wrote about some weeks back, the one Larkin decided was sad. She studied the tree, which had bloomed since last we saw it. "The little tree grow flowers," she said, "and now the tree is happy, Dada!"

I'm glad I have the time to take these things in — an unimaginable luxury for my father in 1960. Unlike him, I get to be a major player in the diapers changed, the meals cooked, books read, naptimes negotiated, trips taken to the supermarket. The intimacy that gets built up bit by bit is the kind formerly reserved for moms; that's that "richness" my father mentioned in his email. It includes all the daily games Larkin and I share. Like the cafeteria-style play table at the playground — she calls it "the restaurant" — where she sits me down and plays waitress. "Here your eggs, Dada," she says, dumping a handful of wood chips in front of me. "Would you like some coffee?" And the nonsense conversations. We'll be stuck in traffic when for some mysterious reason she bursts out with "Dada, we are all doctors!" Doctors? I ask.

"Yes. Doctor Mama, Doctor Dada, and Doctor Bertie!"

I start laughing, picturing our bulldog, Bert, in white coat and stethoscope. It's hilarious. In the rearview mirror I see Larkin grinning.

"Dada," she says, "you laughing!"

The closeness we share isn't just about laughter. One day last September I was sitting at the table in a moment of quiet sorrow — it was my late mother's birthday — when Larkin reached out, cupped my face in her hands, and said "Poor Dada, you feel better." Another morning, sitting in my lap, she shivered, and when I hugged her and rubbed her cold hands, she snuggled into me and said, "Dada keep me safe and warm."

What father can resist that?

Then there is the ritual that began one day when I hugged Molly as she left for work, and Larkin horned in, slinging one arm around each of us. What is this, I asked, a family hug? Now she initiates it herself. "Family hug!" she calls, and we huddle up, the three of us — a miniature team, calling our play for the day.

As for June 15th (I just checked the calendar), well, Larkin's a bit young to be giving gifts — and sitting here in my work outfit of tee shirt, jeans and sandals, I don't know what I'd do with socks and a necktie anyway. But that's OK. It's a different era, a different life; and gifts are hardly necessary when every day is Father's Day.