Image Natasha Paremski at 12, rehearsing Ravel. Credit... Natalie Paremski

At their home in California, I asked Marc what he thought of a normal childhood. “I already have a normal childhood,” he said. “Do you want to see my room? It’s messy, but you can come anyway.” Upstairs, he showed me a yellow remote-controlled helicopter that his father had sent from China. The bookshelves were crammed with Dr. Seuss, “Jumanji” and “The Wind in the Willows” but also “Moby-Dick”; with “Sesame Street” videos and also a series of DVDs on the music of Prague, Vienna and so on. We sat on the floor, and he showed me his favorite Gary Larson cartoons, and then we played the board game Mouse Trap.

Then we went downstairs, and Marc sat on a phone book on the piano bench so his hands would be high enough to play comfortably and launched into Chopin’s “Fantasie-Impromptu,” which he imbued with a quality of nuanced yearning that seemed almost inconceivable in someone with a shelf of Cookie Monster videos. “You see?” Chloe said to me. “He’s not a normal child. Why should he have a normal childhood?”

A parent is the progenitor of much of a child’s behavior, telling that child repeatedly who he has been, is and could be, reconciling accomplishment and naïveté. In constructing this narrative, parents often confuse the anomaly of developing fast with the objective of developing profoundly. There is no clear delineation between supporting and pressuring a child, between believing in your child and forcing your child to conform to what you imagine for him. If society’s expectations for most children with profound differences are too low, expectations for prodigies are often perilously high. “When you have a child whose gift is so overshadowing, it is possible for parents to be distracted and lose track of the child himself,” says Karen Monroe, a psychiatrist at Boston’s McLean Hospital who works with prodigious children.

If you dream of having a genius for a child, you will spot brilliance in your child, sometimes even when it isn’t there. Such children, despite being the subjects of obsessive attention, can suffer from not being seen; their sorrow is organized not so much around the rigor of practicing as around invisibility. And yet, accomplishment entails giving up the pleasures of the present moment in favor of anticipated triumphs, and that is an impulse that must be learned. Left to their own devices, children do not become world-class instrumentalists before they turn 10.

When I spoke to the mother of one musical prodigy on the telephone to set up an interview, I invited her and her daughter to dinner, but she said, “We have a family of fussy eaters, so we’ll eat before we come.” The girl and her parents, whom I’ve granted anonymity for their own protection, arrived wearing coats, and I offered to hang them up. “That won’t be necessary,” the mother said, and they sat holding them through the interview. I offered them something to drink, but the woman said, “We are so used to our schedule, and it’s not time for a drink right now.” In three hours, none of them had a sip of water. I had put out homemade cookies, and the daughter kept glancing at them; every time she did, the mother shot her a look. Whenever I asked the daughter a question, her mother jumped in to answer on her behalf; when the daughter did reply, she did so with an anxious glance at her mother, as if worried that she delivered the wrong response.

The daughter was holding her instrument case, so I invited her to play. “I think I’ll play the Bach Chaconne,” she said. Her mother said, “How about the Rimsky-Korsakov?” She replied, “No, no, no, the Chaconne is better.” The daughter had told me that she chose her instrument for its resemblance to her voice; now it provided her only chance to be heard over her mother. She played the Chaconne. When she finished, her mother said, “Now you can play the Rimsky-Korsakov.” The daughter dutifully launched into “Flight of the Bumblebee,” the proof of every virtuoso. “Vivaldi?” her mother said, and she played “Summer” from “The Four Seasons.” She played with a clear, bright tone, although not with such brilliance as to resolve the question of why a childhood had been sacrificed for this art. I had hoped this child would light up when her bow met the strings, but instead she brought out her instrument’s searing melancholy.