How we cite our quotes: (Chapter.Paragraph)
Quote #7
He had thought that a hibernating man showed no sign of life, but now he knew that this was wrong. Though it was impossible to define it, there was a difference between hibernation and death. (26.22)
Even with all their technology, humans can't bridge that gap between death and life. Yet.
Quote #8
Bowman could bear no more. He jerked out the last unit, and Hal was silent forever. (29.59)
Bowman kills Hal—a sort of echo of the novel's other murder, when Moon-Watcher killed One-Ear. Both are part of humans' evolutionary push out to the stars. Transcendence requires a bunch of dead bodies (flesh or metal), apparently.
Quote #9
They would replace their natural bodies as they wore out—or perhaps even before that—by constructions of metal and plastic and would thus achieve immortality. (32.15)
Humans speculate how aliens might become immortal. Of course, this could be Clarke himself speculating, since it's exactly how he makes his aliens immortal. Mortal humans like to think about immortality, in gods or aliens.