Helmholtz turns down a foursome with three women. That's the first thing he does. The narration explains that he's super-attractive and super-intelligent.
He reveals to Bernard that he's generally dissatisfied with his life (he writes hypnopaedic sayings and teaches others to do the same) and wants to write something "more violent" and "more intense." He just doesn't know what that might be.
When Bernard begins to feel sorry for himself, Helmholtz feels embarrassed for him (because Bernard basically has no pride).
Helmholtz doesn't respond to Bernard's story about fighting the good fight against the Director.
When Bernard calls him from the Reservation, Helmholtz tells him that the Director is planning on having him (Bernard) sent to an island.
Helmholtz reveals some of his questionable activities to Bernard. He wrote a poem, he says, about solitude. His verses discuss his inkling of a "presence," seemingly divine, which he senses only while alone. It is in isolation, he says, that he recognizes how vapid (dull or lifeless) the rest of his life is.
He continues explaining to Bernard that when he showed these verses to his students, he got in big trouble. Still, he says, he's not really concerned with the fact that he's now a marked man.
Helmholtz becomes great friends with John. The two men bond over a mutual love for powerful writing, and John introduces him to Shakespeare.
Helmholtz is enthralled with Shakespeare until he gets to the scene in Romeo and Juliet in which Juliet freaks out about having to marry Paris and offers that the bridal bed be the tomb of her dead cousin Tybalt. Helmholtz finds this to be hilarious, which offends John.
Still, after he gets over his case of the giggles, Helmholtz again expresses his desire to write something passionate and all-around awesome.
Helmholtz shows up at the hospital riot with Bernard. He makes a conscious decision to rush in and help his friend John, even though it means he'll get in a lot of trouble later. He is apprehended with the other two men and brought to the Controller, where he actually seems in good spirits, given that he's about to be exiled.
There, Helmholtz agrees with John that the feelies and even his own writings (hypnopaedia stuff) are stupid. He wants to write something that's more passionate, but about the sorts of things that people of the World State might understand.
When he is asked what island he prefers, Helmholtz asks for something with a bad climate—he thinks this will make him write better.
When Mustapha agrees to comply (and congratulates him on his spirit), Helmholtz heads off to check on "poor Bernard."
The next day, Helmholtz and Bernard find John throwing up in order to purge himself of civilization and wickedness. Helmholtz listens to him explain that he's going away to be alone.