Having discovered that he is invisible to the white world after repeated attempts to have his own reality acknowledged, Ellison's narrator retreats beneath the streets of New York. There he notes that in being invisible he is able to "see around corners" and find an understanding of his own identity.
This identity is a result of his improvising with the basic principles of the nation and the hopelessness in which he exists. As he continues his narration, the invisible man reflects upon the various individuals that he has met, people of differing races and backgrounds, who have applied the nation's principles in a variety of ways. All of these attempts, however, have come up short because as Ellison's IM says,
They were...attempting to force his picture of reality of me....I was simply a material, a natural resource to that of Jack and the Brotherhoob, and it all came out the same--except I now recognized my invisibility.
Then, in an experimental way, much like the improvisation of jazz, the narrator arrives at an identity with the aid of Reverend Hickman who tells him, "There's no logic to it or its [the nation's founder's] ways. There is a gap between what is on paper and what exists in society. After gaining this knowledge, the narrator reaches an authentic moment and realizes that the only way to be free is to live as though he were free. Improvise. From his grandfather he learns to express himself in a way that reminds white America of the humanity of the black man, not as a race but as an individual since, afterall, the Constitution was written about the rights of the individual.
Still, as in improvisation, the narrator returns to the mode of the Prologue, which takes place inside his head. In his last chance to explain his life and choices, the narrator yet feels that he is invisible; he describes himself as being in "hibernation." Morever, he suggests that invisibility is universal.
The way that Ralph Ellison looked at improvisation was the way that Americans improvised a new way of life here. He said in part, “that they were improvising themselves into a nation, scraping together a conscious culture out of the various dialects, idioms, lingos, and methodologies of America’s diverse peoples and regions.” Different from the way we usually look at improvisation, he viewed it as combining different ways of life and different ways of speaking into one group. We see this in the Invisible Man as a black man struggles in a white community. He has to “improvise” his way, in some ways conforming to a new way of life while clinging to his known ways of life and combining them both. See link for entire quote and others.