What connects us to each other? What creates a sense of obligation? Why is it that we somehow find ourselves alone when we don’t want to be and with others when we don’t want to be? Are there secrets that completely change the way we think about people we thought we knew?

And is it possible to be fair to the other people in our lives when we tell stories about them?

Writer Alan Bennett (“The History Boys,” “The Madness of King George”) got an urgent appeal from a disheveled woman in a kerchief. You know the kind of person I am talking about, the ones we ignore or pretend to ignore. She is not exactly homeless. She has a dilapidated, broken-down van parked on the street near his new home. His neighbors are not unkind. One even tries to bring her food. But for some reason, Miss Shepherd (Maggie Smith) likes Bennett. And for some equally inexplicable reason, he kind of doesn’t dislike her. And for another equally inexplicable reason, as frustrating and annoying and inconvenient and often infuriating as Miss Shepherd (as he always calls her) is, he finds it easier to deal with her than with his own mother, who is beset with her own cognitive challenges.

“A writer is doubled,” Bennett tells us, “the one who writes, the one who lives.” He is clearly most comfortable as the one who writes. And we get to see them both. Alex Jennings plays two slightly different variations on Bennett, the subtle variations of clothing and attitude showing us the tension as he wavers between being involved and observing. Part of him recoils from Miss Shepherd’s “multi-flavored aroma” with a thin layer of talcum powder. Part of him knows that she could lead to exactly what we are watching — a book, a radio play, a theatrical production, a movie with an Oscar-winning Dame in the title role. Yes, she asks if she can park temporarily in his driveway and stays for 15 years. But given the money he made from the story, who was sponging on who?

A writer will inevitably be drawn to the peculiar mix of sense and nonsense, sometimes called a word salad, coming from someone like Miss Shepherd. There’s something about the way she ends her mildly preposterous statements with equivocation. “I’m in an incognito position, possibly,” she tells Bennett. He will learn more about her past, but Bennett has enough respect for us and for Miss Shepherd that there is no attempt to try to explain her. It is just to help us do what he did instinctively, though perhaps reluctantly — to see the person inside the weirdness.

“A proper writer might welcome such an encounter.” Yes, he might. Yet, he thinks, “You won’t catch Harold Pinter pushing a van down the street.” Shouldn’t a writer get to pick his subject? “I don’t want to write about her,” he says. “I want to write about spies.” He knows that “you don’t put yourself into what you write; you find yourself.” And his two selves seem to come closer together as Miss Shepherd disintegrates further. If, as Arthur Miller wrote in “Death of a Salesman,” attention must be paid to people we would prefer to overlook, Bennett has done that for Miss Shepherd, with grace and humanity.

Parents should know that this film includes themes of mental and physical illness, fatal car accident, blackmail, and non-explicit sexual situations and bodily functions.

Family discussion: Why did Alan treat his mother and Miss Shepherd differently? Why does he let her stay? Why are there two Alans and what can we tell from the way they dress and speak?

If you like this, try: “The Madness of King George” by the same author and his early work in “Beyond the Fringe”