The young Murph who did not doubt the ghost
At ten, Murph is a child who calls the books falling from her shelf a 'ghost' and tries to decode them in Morse and binary. The intuition Cooper waves away with 'be scientific about it' turns out, in the end, to have pointed precisely at the future self of her father behind that bookshelf. The film, once again, places a child's unscientific intuition in the position of being right.
The first message sent only at the age her father was when he left
For 23 years Murph sends her father no video messages. Only on the birthday that makes her the same age her father was when he left does she turn the camera on for the first time, and opens with 'You son of a bitch' — closing with 'Now I would just like you to come back.' Love and rage held inside the same single sentence: the film's most accurate emotion.
Eureka — and keeping the same surname to the end
Murph eventually pairs with Getty, but to the final scene she still uses her maiden name 'Cooper.' As an adult she wears a coat that resembles the Carhartt jacket her father used to wear. A single sentence the film does not say out loud — that every choice Murph made was, in the end, oriented back toward her father — is written by her costume on the film's behalf.