Bradbury illustrates in his novel that ignorance is dangerous and destructive. He does this by depicting a dystopian society in which people are forbidden to own or read books.

As Beatty explains, everything in the society has been dumbed down to the least common denominator. He asserts that this is what people wanted. They didn't read informative books or good literature when they had it freely available, even then preferring comic books or mindless magazines. Beatty also states that it makes people unhappy to be intelligent, because then they stand out from the crowd and end up isolated and unhappy.

Montag's society promotes a numbing—and ignorant—conformity that involves people sitting in their homes every night watching inane programs, such as clown shows, on giant television screens. Nobody talks in a deep way to anyone anymore, and people have lost touch with the natural world. Montag's encounter with Clarisse, who actually focuses her attention on him and reminds him of the beauties of nature all around him, is a mind-altering experience for him.

Orthodox supporters of the current system, such as Beatty, believe it makes people happy not to think. However, characters such as Mildred show that people are actually leading lives of quiet desperation. In the end, this society full of ignorant people is destroyed in a nuclear war. Those who have broken the law and read and memorized books, gaining knowledge, are the people who will be relied on to rebuild a new and better world. Ignorance is not bliss in the novel, but the road to annihilation. Knowledge, on the other hand, brings fulfillment, wisdom, and power.

One of the most prevalent themes in Bradbury's Fahrenheit 451 is that of knowledge vs. ignorance. It is with through the lack of knowledge that the government controls society, keeping people locked in the ignorance brought on by careful and precise manipulation.

We see Millie's ignorance in plugging herself into the Seashell radio each night. Millie is so unaware, that she takes an overdose of pills and does not remember doing so, or even having her stomach pumped. She watches the wall-sized TVs in the living room and finds the programming fascinating, even though she learns nothing and is not even afforded the opportunity for original thought. The government controls what the actors say, and viewers can participate, but only in that they read the script provided by the government. 

Society is not allowed to read—the government is once more controlling thought, as well as curiosity and questions. Books are burned. Beatty has a great deal of knowledge from books, and while he quotes it, he never uses it for self-enlightenment: he is almost disgusted with knowing so much information that he believes is useless—he has knowledge, but lives in ignorance...also controlled by the government's rhetoric.

Montag is ignorant of the effect his actions create. He burns books and enjoys it. He loves to watch things burn.

It was a pleasure to burn.

It was a special pleasure to see things eaten, to see things blackened and changed.

However, when he answers a call that takes him to 11 No. Elm, the owner is still there. Here he is confronted by knowledge: the desire to keep books and the loss when they are burned. This information makes it impossible for him to live (and work) in ignorance any longer. At this point, destroying homes and books becomes personal. Confronting the homeowner and seeing what she is willing to sacrifice for books, changes everything for Montag.

Always before it had been like snuffing a candle. The police went first...so when you arrived you found an empty house [...] You weren't hurting anyone, you were hurting things!

After this, Montag does not think he'll ever be able to burn a house again.

Something else that changes Montag is the knowledge he receives from Clarisse McClellan. The first thing she does (that is so foreign to him) is asking questions. She asks him if he has ever read any of the books he has burned. His first response is that it is illegal: this is a programmed response. He does not really know why they burn books. Clarisse notices things, too.

"There's dew on the grass in the morning."

He suddenly couldn't remember if had known this or not...

Then Clarisse asks Montag if he is happy. His first unthinking response is yes. And he laughs because it seems such a silly question. But this is just another example of how he lives in ignorance, never questioning anything. For when Montag stops to ponder the question, he is shocked to realize that he is not happy at all.

Everything changes for Montag when he starts to ask questions. He starts to read books. He starts to wonder why the government requires the burning of books. He seeks out Faber, a former professor, in order to understand the world and his place in it, something he never did before. Knowledge of how he has been controlled and a desire to learn more are what drive Montag to rebel against the government and to join others like him who want to remember the information in books, and to rebuild society.