In Chapter 6 we learn that Richard, who sailed ships when he was a kid, loves to tie sailing knots. He teaches Miranda how to do the same and even buys her a set of ropes for Christmas one year.
Richard unties knots when he's trying to solve a problem at work – he says it gets him "in the right frame of mind" (6.3). We often see Miranda doing the same thing – like when she's trying to figure out all the stuff about the Laughing Man's death, for example, in Chapter 46.
So knots, and untying knots, are symbols of critical thinking, puzzle solving, and answering tough questions. They are also a link between Richard and Miranda, as when Miranda gives Richard a key tied onto a sailor's knot at the end of Chapter 52.