"Red Sector A". It's based on Geddy's mother's experience as a Holocaust survivor, and it's just as nightmarish as you'd expect.
"WE HAVE ASSUMED CONTROL. WE HAVE ASSUMED CONTROL. WE HAVE ASSUMED CONTROL."
When you think about it, the entire concept of 2112 is nightmarish. A society in which the tyrannical government controls EVERYTHING and no one is allowed to be any different from anyone else and creativity is discouraged to the point that the government crushes a prodigy's beloved guitar to pieces beneath their feet right in front of him and drives him to suicide! Ditto BU2B, which sounds like your average "God isn't real" song, but when you think about it, is scary: a population brainwashed into believing that whatever happens is what's best for them no matter what. All is for the best, indeed.
"Cygnus X-1", a song about a space explorer sacrificing himself to a black hole. His success leads to arguably the pinnacle of Geddy's screaming; considering the events, these are screams of agony and pleasure all at the same time as "every nerve is...TORN APAAAART...". And that leaves just Alex's guitar and an ominous pulse fading out.
To make it less horrifying though, the explorer turns out to be OK, and eventually becomes a god.
The tragedies that Neil Peart suffered, in addition to being tear-jerking, are nightmarish too. Losing your wife and daughter is bad enough, but he lost both within one year of each other. And then given that his daughter died an even worse death than his wife (his daughter died in a fiery car accident and his wife died of cancer- one burned to death and the other's body went "fuck you, I'm gonna create poisonous cells that will make you horribly sick and lose your will to live."), it's amazing this man didn't kill himself. Though it's heartwarming that he now hit the reset button on his personal life and has a new wife and baby daughter, the fact that he managed to survive this is just amazing.
To this day, Neil holds the belief that his first wife didn't necessarily die from cancer, but from a "slow suicide by apathy." In other words, she didn't care what happened to her after her daughter died, and as such, just gave up. And Neil could do nothing except watch her waste away.