How does Granger's comparison of humanity to the phoenix add to the novel Fahrenheit 451?
In order to truly understand this question one must understand the mythical importance of the Phoenix. The Phoenix was a mythical Greek bird-like creature that was born out of fire. Once the Phoenix reached the culmination of its life, the bird was said to burst into flame and out of its flames it would be reborn anew.
At the end of Fahrenheit 451, Montag's city is bombed. Although it is only briefly touched upon in Part 2, there has been a war going on for quite some time. Montag is already living with the Book People and he doesn't know whether anyone from his previous life in the city is even still alive. The Book People watch the bombs drop as the war begins and ends. (153)
After the bombs have dropped, the Book People continue on their way, heading back towards the ruins of the city. Granger mentions the story of the Phoenix and compares it to mankind.
There was a silly damn bird called a Phoenix back before Christ, every few hundred years he built a pyre and burned himself up. He must have been first cousin to Man. But every time he burnt himself up he sprang out of the ashes, he got himself born all over again. And it looks like we're doing the same thing, over and over, but we've got one damn thing the Phoenix never had. We know the damn silly thing we just did. We know all the damn silly things we've done for a thousand years and as long as we know that and always have it around where we can see it, some day we'll stop making the goddam funeral pyres and jumping in the middle of them. We pick up a few more people that remember, every generation. (156)
Granger is saying that Man is just like the Phoenix. Man always returns or continues to exist. The biggest difference is that Man can get a little better or keep his knowledge, allowing himself to learn from previous mistakes. Granger is suggesting that someday Man might actually learn enough to keep from destroying himself. In order to enable that to happen, Man must continue learning, documenting, and educating himself. Knowledge is what will save mankind in the end.