The second evening they were there, a man in the hotel bar came out to the lobby to talk to them — he was a twin himself, he said, and had to meet them. He and his colleague smiled at the girls, asked them some questions, pronounced them adorable and returned to their waiting drinks inside the bar. But when the girls ran by the bar again an hour later, the same man came out with tears in his eyes. He had obviously been thinking about them and their family and his own. The year before, he said, he had lost his adult son to suicide. “So tell the mother they are blessed,” he said.

The message, relayed to Simms in the hotel restaurant, where the family was dining, did not particularly faze her: people often share their family tragedies with her. Simms understands the impulse, but feels they are trying to empathize with someone whose feelings they do not actually understand. “They feel sorry for us,” Doug McKay, the girls’ step-grandfather, said. “But we feel like we got chosen out of millions of people to be their parents. That’s better than the lottery.”

As I watched the girls negotiate their occasionally conflicting impulses at dinner, I thought of how my friend Peter Freed, a neuroimager and assistant professor of clinical psychiatry at Columbia, explained their possible experience of each other: “It’s as though the secretaries of Goldman Sachs and Lazard Frères have decided, without their bosses’ permission, to share certain visitors and executive memos with each other.” The executives in charge — the parts of the brain more directly involved in decision-making — would inevitably become frustrated. Every time that executive next door makes a decision, the results are “subtly influencing or altering the information the other has to work with,” says Freed, who also writes a blog called Neuroself about the construction of the self in the brain.

The frustration of one executive was on full display as the evening wore on. The girls were tired. It was late for them. Someone ordered them chicken fingers, and Krista took a bite. Suddenly, Tatiana made a face. “It’s too yucky,” she said, starting to cry. The mayhem level went up a notch, and Tatiana crawled under the table, wailing, as Krista was trying to pull her back up by the force of her neck. Krista tried to put the chicken finger directly into Tatiana’s mouth. “Krista likes it!” she said. “It’s yummy!” Tatiana spit the food out, crying: “Let me hide! Let me hide!” She covered her mouth with her hand. “Don’t make her eat it, sweetie,” said their grandmother, as Doug sighed in frustration. “Sissy eat it!” Krista said again, trying to push it in Tatiana’s mouth. Krista started pulling her sister’s hair, and then both girls were crying. Tatiana’s futile declaration rose above the sounds of the restaurant. “I am getting out of here!” Tatiana sobbed. “Let me alone.”

As would be true of any other two sisters, the girls’ relationship to each other and to their unusual connection is unpredictable. Their union could prove, as their grandmother predicts, a model of boundless, blissful empathy. The girls will show the world “true love,” she once said, tearing up. But their lives could also entail a barrage of confused impressions, with each girl having just enough of a sense of self to resent the intrusions of the other’s. Over time, would the girls increasingly tune out each other’s perceptions, with some kind of neural pruning doing the work that surgery could not? Or would some complicated, constant interplay of sensory input and response further fuse their personalities, rendering them ever more like one? Would they have any say in the matter?

Only one set of conjoined twins has ever made the adult choice to be separated, according to “One of Us,” a book by Alice Dreger that traces the history of cultural responses to conjoined twins. Ladan and Laleh Bijani were craniopagus twins who grew up in Iran. When they were 29, they were so desperate to live apart that they decided to take the 50-50 odds that they were given of surviving a separation. In 2003, in the hands of highly regarded surgeons in Singapore, they died after surgery. Despite the countless high-tech brain images they had produced, the surgeons were caught unaware by a major vein the women shared. They thought they had seen inside; but what they learned, tragically, was how little they knew about the union after all.

Tatiana and Krista will start kindergarten in the fall, their first major foray into the outside world. And their lives may soon change even more significantly if Chuck Harris, a talent manager who also manages the Schappells, has his way. Harris has been helping the family pursue a reality television show, not just about the girls (a detail upon which he insists) but also about the range of strong personalities living together in their small home. The decision to expose the girls to the gawkery of the American public is less fraught for the family than you might think — partly for financial reasons, but also because the girls are unlikely to have a normal childhood under any circumstances. The constant exposure, in some ways, would actually normalize them for the public, show them as they are, not as the people who pass them in malls perceive them.