What is the significance of the following quote from Fahrenheit 451?
"If you don't want a man unhappy politically, don't give him two sides to a question to worry him; give him one. Better yet, give him none."
This quote is from Captain Beatty, when he is explaining some of the history of the future society to Montag. His explanations are entirely from the perspective that the changes in society have been good, and so he is perfectly fine with the idea of an ignorant populace and a massively controlling government.
"If you don't want a man unhappy politically, don't give him two sides to a question to worry him; give him one. Better yet, give him none. Let him forget there is such a thing as war. If the Government is inefficient, top-heavy, and tax-mad, better it be all those than that people worry over it."
(Bradbury, Fahrenheit 451, Google Books)
Beatty's statement explains how to control the populace through selective information and education; make sure that the people don't understand that there could be other positions or solutions, and they will come to depend on the government for all their needs. "Give one side, or none," so that only the government's side is seen as correct, and all others are seen as deviant or criminal. Through these policies, the populace evolves from seeking out diversity of opinion to accepting and promoting a single view of society and legality; no one thinks to question the system partially because they are punished (by the firemen), and partially because they now view the system as deified, above all reproach.