When information flow fails, when Democrats and Republicans do not talk to each other, when Israelis and Palestinians do not talk to each other, and when North Koreans and South Koreans do not talk to each other, mis-perceptions, biases and fake news arise. In this paper we present an in-depth study of political polarization and social division using Twitter data and Monte Carlo simulations. First, we study at the aggregate level people's inclination to retweet within their own ideological circle. Introducing the concept of cocoon ratio, we show that Donald Trump's followers are 2.56 more likely to retweet a fellow Trump follower than to retweet a Hillary Clinton follower. Second, going down to the individual level, we show that the tendency of retweeting exclusively within one's ideological circle is stronger for women than for men and that such tendency weakens as one's social capital grows. Third, we use a one-dimensional Ising model to simulate how a society with high cocoon ratios could end up becoming completely divided. We conclude with a discussion of our findings with respect to fake news.