In Interstellar, how can the small girl solve codes? She even decoded correctly and accurately the "STAY" word but how?
In The Imitation Game, the boy learnt codes from his school days, that's why he became a codebreaker, it makes sense.
But in Interstellar Nolan didn't show it like that, a girl studying a coding book. It doesn't make any sense.
Cooper is an experienced Engineer and Pilot who used to fly for Nasa, and Murph has picked up on his interest in science and engineering. This is shown by her interest in the moon landing book, which she defends even to the point of fighting at school where she is ridiculed for believing they really happened.
You compare the encoding schemes of Morse Code to the Enigma Cypher. While they are both ways of encoding data, they are of course totally different in their intention. Morse code is a very simple scheme of substituting patterns of dots and dashes for letters and to be easily learned and understood, the Enigma cypher is designed to completely obscure the meaning of the message by imposing on it an apparently random pattern. The skills required to 'break' the codes are totally different.
I don't remember (or its not said) how the 'STAY' message was encoded, whether it was Morse or the binary code that was used to communicate the coordinates of the facility. However if it was the binary code, by the time Murph works it out she'd already seen the example of the encoding of the coordinates when Cooper decodes it. So she was able to apply the same technique to the pattern of books pushed off the shelves. Yes binary encodes numbers, but in various ways numbers can be mapped to letters, such as A=1, B=2 etc. An intelligent girl puzzling over the meaning of the books would be motivated to try to work this out.
In short, it was extremely easy for her to work it out because
Coop (in the future)
wanted it to be easily decodable and because Morse Code is about the most accessible form of encryption known to man:
“Nothing special about which books,” Murph said, moving into the room from behind him. “Been working on it, like you said.” She held up the notebook in which she’d been drawing. The page was covered by a pattern that looked something like a barcode.
“I counted the spaces,” she said, as if that explained it all. “Why?” Cooper asked.
“In case the ghost is trying to say something,” she explained. “I’m trying Morse.”
“Morse?” he said.
“Yeah, dots and dashes, used for—”
“Murph,” he said, trying to be gentle. “I know what Morse code is. I just don’t think your bookshelf’s trying to talk to you.”
She looked at him with a mixture of hurt and embarrassment. But she didn’t even try to reply.
later
“I figured out the message,” she said. She opened her notebook. “It was Morse code.”
“Murph…” Cooper said, gently.
She ignored him.
“One word,” she continued. “You know what it is?”
He shook his head. She held out her notebook so he could see it.
STAY - Interstellar Novelisation
I guess the word 'STAY' was communicated by Cooper to his daughter in morse as she seemed more informed about decoding that method. (Remember the scene when she tried to decode the signals of dust separated via gravity near the window she forgot to close. She tried to decode it with morse, got no success but later on Cooper learnt it was rather binary and the decoded message gave him the coordinates to the NASA site they visited in their truck.
Take a look at this page of her notebook, it could elaborate more. Below that is the set of morse codes (taken from wikipedia)
Honestly, I haven't understood it completely, but when got the same curiosity that you got, researched a bit and it looked to me related.
