In 1984, how does "IGNORANCE IS STRENGTH" apply to the matrix?
It does not take much delving into history to become aware of the truth of the 1984 maxim of "Ignorance is Strength." Research into the history of Communism and the U.S.S.R. reveals that in all the countries that had more than 11% of the population that was illiterate, a Communist government was able to take over these countries. Likewise, when there is an uniformed public, or an uninterested public, governments can perform covert activities, cover up actions, make false statements, etc.
If the dissemination of information induces this ignorance, there is, indeed, tremendous strength for a government. In contemporary America, for instance, there are certain news agencies which place their own "slant" upon the news, or they simply neglect to report incidents, etc. The shooting at Ft. Hood is a case in point. When one news agency merely gave a cursory report, people turned to another which had more details. Only then, did the first news agency, then, report the true incident. Likewise, in 1984, people are selectively shown only certain things. For example, they are herded together in their Two Minute Hate program during which the face of the dissident Emmanuel Goldstein appears. Then, Big Brother comes on with a few words of encouragement.
People are so uninformed about reality that they do not even know what year it is. For example, when Winston makes his first entry into his secret diary, he is not sure of the date in which he writes. People's thoughts are enslaved, as well, in their ignorance of words. For, Newspeak has done away with adjectives and such descriptors. When Syme describes to Winston the changes in the language he excitedly tells him,
"We're getting the language into its final shape--the shape it's going to have when nobody speaks anything else....We're destroying words--scores of them, hundreds of them, every day....It's a beautiful thing, the destruction of words."
With the destruction of words goes the destruction of thought since language determines thought. Thus, the people remain ignorant in thought as well as knowledge.
In The Matrix you have a society controlled by the machine. Very similar to the concept of Big Brother. All "citizens" are watched for signs of difference. And when they show signs of difference then the machine goes after them, like they did with the main character Neil.
Like in 1984 the concept of Ignorance is Strength is shown when we find out that the "real" world is just a projection. In 1984 the thought police monitor and make sure its citizens remain unaware. This is similar to the way the machine monitors its citizens in The Matrix. As long as the citizens are unaware or ignorant then the design is working to the benefit of those in charge.