Absence can be as strongly felt as presence, and soon Ben, too, became obsessed with family math. He would stare at the snapshots I’d taken of his half sister holding him as a newborn: he in a tie-dye onesie, she in a matching tie-dye T-shirt. He would stare at the pictures of the two of them at his cousins’ country house taken a few summers later.

He didn’t want to be an only child. He wanted to have a sibling and be a sibling. He wanted to be part of a big family. He was also confused: At school when they made family trees, he never knew what to do, how many leaves to draw or cut out of paper and hang on the branches. More than once over the years he has said, “When someone asks me if I have any siblings, am I lying if I say I have a sister?”

“Of course you have a sister,” I would tell him. “Even if you rarely see her, and even if you feel like sometimes she doesn’t exist.”

I was telling him to count her. I was telling myself to count her, too.

By the time he was 8, the hole left in him from her absence defined him — almost all of his friends who had been only children were now older brothers to younger siblings and he was desperately lonely. Having another baby was a biological impossibility for me by then, so we took the advice of the friends and therapists and got a dog.

Lady, a deeply human Sheltie, changed our family equation from three to four. As our new plus 1, she sat in the back seat with Ben, required breakfast and dinner, and, as a puppy, needed to occasionally be picked up from day care. When first my mother, and then my father, got sick, each with a swift, lethal cancer, she kept me company during my darkest days. Now, more than ten years since she came to live with us, when I’m asked how many people are in our family, I say that my husband and I have a son and a Sheltie.

Which I guess means that there are three and we are five, even if one is someone we rarely see and another is a dog, though I don’t think in terms of numbers anymore. I’ve gotten tired of counting, of trying to do the math when it comes to the complex calculus of death and estrangement — whether you stop counting someone once they’re gone or keep counting them forever.