Dr. Fletcher uses deductive reasoning to ascertain which of the twenty three identities of "Dennis" she speaks with. She uses her observations of the character's behavior to draw a conclusion.
Ed's penpal sends him memorabilia from his home country. Rolf sees this memorabilia, and it reminds him of some trauma he experienced as a child. Rolf hurts the Eds in response, and they are confused as to what is wrong with Rolf.
Leo asks Josh about his day with Stanley, a psychotherapist. He uses a metaphor to describe Josh's PTSD situation and states that he'd like to help him. After Josh leaves the office, the carolers trigger Josh's PTSD.
This clip illustrates the effects of schizophrenia on an individual. John Nash sees and interacts with people (who are hallucinations) that do not exist to other people. These hallucinations can seem so real that one would think that they actually exist.