John's two worlds are the world state and the reservation. We see these worlds' competing demands coming to a head through the fact that Linda is dying. Her dying shows John quite clearly how the two worlds are opposed to one another.
We can see this from the very beginning of the chapter. John wants to visit Linda because she is his mother. The very fact that he has a mother and he mentions her is mortifying to the nurse. When he said "mother"
The nurse glanced at him with startled, horrified eyes; then quickly looked away. From throat to temple she was all one hot blush.
Then, we see the group of Delta children being brought to be conditioned against fear of death. They are making faces and climbing all over the place and talking about how fat Linda is. Through this, we see how the world state's demands are completely incompatible with those of the reservation. We see the emotional life of the reservation coming strongly into conflict with the world state's need to create a society with no ties between people.