The narrator's first job is in a highly patriotic paint company most famous for its Optic White paint color. In order to create this pure white, the narrator is instructed to add ten black drops of toner into each bucket. Could this possibly have anything to do with black/white relations in America? Great question. We think that this paint business demonstrates the necessity of the black contribution to white America – although America is often thought of as a white man's country, America would not be America without the contributions of black people. Taking another angle, the name "Liberty Paints" is ironic since it implies freedom for all, which is clearly not the experience of the narrator throughout this entire story.
Vision and Sight
When there's a lot of talk about eyeballs in a book called Invisible Man, you know something's up with sight. Reverend Barbee gives a crowd-pleasing speech praising the Founder of the college only to later reveal that he is a blind man. Then Brother Jack turns out to have a false left eye. This shows the flawed nature of their visions – Barbee gave a great speech praising an institution and man that are basically shams, and Jack espouses a horribly cold ideology.
As for the narrator, he comes to believe himself an invisible man because no one actually sees him for who he is – but as someone of whom they can take advantage. Realizing this social invisibility, the narrator decides to pair it with actual invisibility, and drops out of sight for an indeterminate amount of time.
When the narrator further examines the paper doll that Clifton was selling, he realizes that Clifton controlled the doll with a thin black string that was invisible to the audience. Clifton puppeteers the flimsy black doll in much the same way that the Brotherhood manipulated both Clifton and the narrator, or the way the narrator has been manipulated his entire life, or the way blacks have been manipulated for whites' entertainment (think of the battle royal, for example).
The Battle Royal Briefcase
We think it's symbolic that the narrator receives the briefcase as a naïve kid, and then hangs onto it for the rest of the novel. Emblematic of his past vulnerability, eagerness to please, and youthful ambitions, his final loss of the briefcase suggests a complete severance of ties to his youthful past and a true rebirth.