In the show’s hierarchy of nerddom, Sheldon, played by Jim Parsons, is the king, socially clueless and irritatingly, rigidly rational (his former roommate left the words “Die Sheldon, Die” painted on the walls of his room), while Leonard, played by Johnny Galecki, is more of an everyman, trying to break out of his shell. “Leonard is in the most discomfort, he wants to move through the world,” said Mr. Lorre; Sheldon doesn’t care. Leonard’s efforts to establish and then maintain a romantic relationship with Penny have constituted a major part of the narrative arc of the first three seasons.

How does it feel to be such a freak? During a break from rehearsals recently, Mr. Parsons and Mr. Galecki both said they did not understand any of the scientific dialogue in the show. Mr. Parsons said his last interaction with academic science had been when he flunked a course in meteorology at the University of Houston.

But then again, he added, they did not understand all the pop culture references to comic books and “Star Trek” any better. “What am I trying to say by saying this is the most important thing,” he said.

Mr. Galecki said: “A lot of people thought it would be a show that poked fun at smart people, but it has become a show that defends smart people much more often than that. These guys, as socially inept as they might be, are the type of people that are molding our future as a society.”

Mr. Parsons memorizes his lines by writing them out longhand and says he is astonished when people ask if the actors on the show ever improvise. “To veer away from the scripted dialog is a one-way trip to sudden death,” he said.

Still, problems and questions arise, which is where David Saltzberg, a particle physicist at the University of California, Los Angeles, and the show’s scientific consultant, comes in. Besides supplying the equations that appear on whiteboards in Sheldon and Leonard’s living room, he sometimes advises on the plotting and characters’ scientific predilections.

Dr. Saltzberg, who blogs about his activities on the show, said that many of the people who grouse to him about the show have not seen very much of it. His comments were echoed by Mr. Prady, one of the producers, who rejected the notion that the show stereotypes women. “Far from being a dumb blonde, Penny has demonstrated time and again that she possesses above average intelligence and practical knowledge that often far exceeds that of the guys,” he wrote in an e-mail message.