How does the narrator realize how the doll danced in Chapter 21 of The Invisible Man?
The narrator experiments with the offensive doll, trying to figure out what makes it move. He notices that it is nothing more than "a construction of tissue, cardboard and glue," and that its faces, drawn on both sides of a disk of cardboard, are grinning. He holds the doll by its feet and stretches its neck, but it only crumples and falls forward. He tries a second time, this time turning its other face around, but once again it only falls in a heap.
Finally, the narrator turns the doll around and around in his hands, and this time notices that there is a fine black thread attached to it. There is a loop tied in the end of the thread, and when the narrator slips this loop over his finger and stands stretching it taut, the doll dances. Out on the street, it had been Clifton who had been manipulating the string to make the doll dance. The thin black thread had been invisible to the eyes of the crowd (Chapter 21).
The doll is a caricature, a ludicrous "Sambo" which is totally offensive to the black race. For reasons which the narrator does not understand, his friend Clifton had been exploiting the offensive toys in hopes of selling them to the laughing people in the crowd. The narrator is aghast and ashamed that his friend would repudiate everything the Brotherhood had been trying to achieve concerning the building up of pride of black brothers and sisters in their race. By profitting from the sale of the demeaning toys after his friends had tried so hard to "make (them)selves known, and (to) avoid being empty Sambo dolls" in the eyes of the world, Clifton has in effect negated everything for which they had been fighting (Chapter 20).
Clifton is not the only one who has failed, however. The narrator berates himself for having "blown up and acted personally," expressing his rage at his friend, instead of having taken the opportunity to educate the crowd and denounce "the significance of the dolls (and) the obscene idea" (Chapter 21).