Turning and turning in the widening gyre The falcon cannot hear the falconer; (lines 1-2)
The relationship between falcon and falconer is like that between servant and master. Yeats believed that a strong aristocracy was necessary to keep uncontrollable social forces in line. Without the direction of the falconer, the falcon is both aimless and dangerous.
"but now I know That twenty centuries of stony sleep Were vexed to nightmare by a rocking cradle." (lines 18-20)
This powerful image works in two ways. First, the "rough beast" is being disturbed from its "stony" or indifferent sleep. It is portrayed as an infant in a rocking cradle. But human society is what suffers from the "nightmare." The speaker is saying: you thought you’ve seen violence and bad stuff in the past, but that was like a baby sleeping compared to what you’re about to see.