What is the meaning of the following quote from Fahrenheit 451? "We're going to build a mirror factory first and put out nothing but mirrors for the next year and take a long look in them."
Granger, telling Montag about his group's idea for the future of books and society, uses this quote as a metaphor for examining society with a critical eye.
"But even when we had the books on hand, a long time ago, we didn't use what we got out of them.
Come on now, we're going to go build a mirror-factory first and put out nothing but mirrors for the next year and take a long look in them."
(Bradbury, Fahrenheit 451, Google Books)
Granger's point is that society has become so shallow and contemptible, people are incapable of looking at it from the outside. Instead, they ignored their own follies in the past, and ignore them even more in the present. Even with books and free thought available, people didn't learn from their mistakes. Granger hopes that his group will act as a "mirror" for society, allowing people to recognize their mistakes and learn from them. Granger intends to foster the ability of free thought and objective criticism, instead of the blind acceptance of social norms.
Granger says this to Montag at the end of the novel, after their civilization has been destroyed in a war and the survivors are camping by the river. Granger is speaking about civilization rising anew from the ashes, like the Phoenix, and he says that the survivors need to think about all the mistakes their civilization has made and how to improve it. He believes that remembering the past and the mistakes of the past is the key to improving the future. He says that they are going to "build the biggest goddam steam-shovel in history and dig the biggest grave of all time and shove war in and cover it up." He realizes that war must become a thing of the past if civilization is to have a rebirth.
When he says that they are going to build a mirror factory, he is speaking metaphorically. He means that in order to rebuild their society, the survivors must take a long, hard look at themselves and think about their faults and mistakes. They must first reflect on what society has been before they can attempt to rebuild it along better lines in the future.
This is in reference to Montag describing Clarisse as a mirror in "The Hearth and the Salamander." The idea is that mirrors are symbols of being able to see oneself clearly, to understand oneself.