Two goodbyes.

Cooper has agreed to fly. He goes to tell Murph. She has worked out what he is doing and she will not have it: she stays in her room, turns away, refuses the goodbye, and when he leaves she runs out too late, shouting after a truck that is already dust. That scene is the film's emotional peak, and it is a father and daughter scene. Nothing else in the story reaches that temperature.

Tom's goodbye is the other kind. He walks his father to the truck. They speak briefly about the farm. Two men, sad, and decided to carry out what has been decided. There is no scene, no tearing, and an emotional distance between them that is remarkable and exactly right. Nobody watching thinks Tom loves his father less. It is the same love in a different register.

That contrast is the pattern's first claim in a single image. The bond across sex is the intense one. The bond along sex is the steady one. Neither is better. They are different instruments, and a family plays both.

Cooper is an engineer who was made to farm. Murph is the child who takes apart the official story, who reads the dust on her floor as a message, who keeps his watch and decodes it, who ends up solving the problem he flew off to solve. None of that was taught. He was gone for the years in which she became it. She has his mind the way a daughter in this project's catalogue has her father's temperament: not by instruction, by inheritance, and the bond between them is the one that can survive a black hole because it is the one built to that strength.

Tom is the character the film does not know what to do with, and this reading says why. His line does not run to Cooper. It runs through his mother, who is dead before the story starts, to her father, Donald, who is in the house every day. Tom becomes the farmer Donald was. He keeps the land when it is killing his family, he keeps the house, and in the end he holds Donald's fatalism about the world as it is. Cooper looks at his son and sees nothing of himself, and the film agrees with him. Someone else's nature is in the boy, and that someone is at the kitchen table.

The project's longer argument says that the bond between a man and his wife's father is the hinge a family turns on. When it is at war, the grandchild's line to that grandfather is blocked, and the damage is done quietly, in childhood, surfacing later. Cooper and Donald are the other case. Two men who lost the same woman, running a household together without a quarrel, one raising the children the other cannot stay for. Because that line is open, Tom's inheritance from Donald flows. This is what the working shape looks like, and it is why the same story on the Gladiator page, with the hinge broken, ends in murder.

Murph's own grandparent step, on the same rule, would land on her father's mother. The film never mentions her. It has no need to; the story is Murph's and Cooper's. But the absence is worth marking, because it means the film shows three positions of the shape and leaves the fourth blank, which is the same thing Shakespeare does on the Shakespeare page: every piece that is present falls where the pattern says, and the composite is never quite assembled. That is what evidence from stories usually looks like.

Before Hans Zimmer knew the film had anything to do with space, Nolan gave him a single page, typed on his father's typewriter: a short fable about a father and his son, with two lines of dialogue in it. Nolan wrote it as a son on purpose: Zimmer's own son, then fourteen, wanted to be a scientist, and the page was aimed at that.

"I'll come back." "When?" The whole of the dialogue on the page Nolan sent Zimmer, by Zimmer's account

Zimmer wrote the theme that night, for his son. The daughter came later and for the director's own reasons: in Jonathan Nolan's first draft Murph was a boy, and Christopher Nolan made her a girl when he took the film over because his oldest child, Flora, was Murph's age at the time. Zimmer's account is that Nolan "switched it on me".

Two things follow, and only two. The bond came before the plot: before there was space there was a parent, a child, and those two lines. And a theme written for a father and a son carries a father and a daughter without a seam, which is a caution worth keeping. The intensity of a parent losing a child belongs to both lines. What differs is the register, and that is what the two goodbyes show. The family around the bond fell into the pattern's shape on its own, which is more persuasive than a story that set out to illustrate it.