He is often shown "stimming". "Stimming" is basically self-stimulation, a repetitive sound or motion made by people who have difficulty integrating all the sensory input around them as a buffer between themselves and the sensory stimulus.
Charlie has sensory integration issues. This means he has difficulty integrating sensory input around him into a cohesive whole, something that most of us do automatically but is sometimes an exhausting task for individuals in the autism spectrum. Charlie wears enormous headphones with no music playing while figuring out a math problem.
Charlie fails to see the big picture at almost every turn and has extreme difficulty anticipating spontaneous behavior. Charlie is most comfortable with inductive reasoning, and despite his high intelligence levels, finds deductive reasoning difficult at best.
Charlie struggles to interpret social cues from others, when he picks up on them at all. Charlie rarely intuits when he annoys everyone around him, either with his single-minded preoccupation with mathematics or his inability to accurately read the nuances of social situations. He is very literal minded, often rambles past the point where anyone is listening, and in fact, sometimes DOES NOT NOTICE everyone has stopped listening.
Charlie fails to connect his concrete theorizing to abstract human reality, and in fact, doing so is deeply disturbing to him.
Charlie displays an extremely limiting and persistent social naivete that also can translate as extreme social immaturity. He is 27, doesn't date, doesn't notice that his very pretty friend is probably interested in him.
There is the compulsive and completely preoccupying nature of Charlie's obsession with discrete mathematics.
( This entry is a summary of this article on "tv makes you stupid". )
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