From “One, Two, Three . . . Infinity,” an essay in the anthology Ways of Hearing, which will be published this month by Princeton University Press.

My father wanted his own orchestra. He couldn’t read music and his tastes tended toward the beer hall, but he loved singing and had a clear bass-baritone: “Blue Skies” at morning that changed, by night, to “Many Brave Hearts Are Asleep in the Deep.” When he sang, our small house on the North Side of Chicago turned bigger on the inside than it was on the out.

A junior high school principal, my father believed in giving his children the keys to every kingdom worth entering. We each played something: clarinet, French horn, guitar, viola. My instrument was the cello. The five of us would hold forth from different corners of the house, often at the same hour of the afternoon, in a riotous Midwestern nightmare out of Ives.

I remember, at nine, grinding away for what I was sure was hours—This is, a symphony, that Schubert wrote and never finished—only to be stunned, when coming up for air, to discover that no more than fifteen minutes had passed. None of us loved practicing except my father. No matter how harsh the squeaks and clashes, he had his band.

The exhilarating monotony of practice was, for me, the paradox of childhood writ small. I lived between unbearable excitement and mind-crushing boredom. Those two states formed the twin poles of each day’s endless question: Is it tomorrow yet? Late one Sunday morning at the age of nine, I came to my father almost weeping from tedium and begged him to entertain me.

He told me to read a book. I said I’d read every book on my shelf. He went to the bookcase in his own room and picked out a small volume: One Two Three . . . Infinity, by the renowned physicist George Gamow. I opened to a table of contents dense with adult type, grim and thrilling. But the biggest thrill of all was that my father thought I might be equal to this.

I struggled. But the first part of the book was called “Playing with Numbers,” and I’ve always loved that thin edge between struggle and play. Page five had a drawing of a poor ancient Roman, taking forever to write out the number one million, which I could do in seven digits. A stunning idea formed in my head as if I myself had come up with it: however high a number anyone wrote down, I could write one higher. The thought was intoxicating. Before long the book was claiming something far wilder, something that even now, more than half a century later, I still have trouble wrapping my head around: however large an infinite set I named, someone else could name one infinitely larger.

I do not remember the rest of that day, except that it passed in no time at all. My father filled my childhood with lessons, but never one larger than this: there are books that take you to places that never end.

My sons and daughters might have read, from my own sagging shelves, books by several other writers who credit Gamow’s little book with starting their own careers. But I never had children, and my every house filled up each afternoon with an orchestra of instruments never practiced.

My father died at fifty-two, of cancer and drink, having outlived much of his life’s best music. As I write this, I’m eight years older than he ever was. Last year, I began teaching myself to play piano. No matter how much longer I live, there will be an infinite number of pieces I’ll never play or even listen to.