While humans explored outer space and reached as far as the edge of the galaxy, they are still amazed by the discovery of the rock that they believe to be left behind by aliens. The reaction of those who discovered the rock can be seen as being ironic and even exaggerated considering how far they have managed to travel and how much they explored the universe.
First man to Saturn
The phrase "First man to Saturn’’ is the name given to one of the chapters in the novel and is ironic because of the event unfolding in the chapter. In the chapter, Frank Poole gets outside the ship to fix a technical error but is crushed by the pod coming towards him. The pod then gets further away from the ship, dragging Frank with it as well towards Saturn.
Pull the plug
When Hal tries to kill every human on the spaceship, Bowman tries to fight against him and save himself. Despite being more intelligent that Bowman and having more power, Hall is eventually defeated by the last human left alive. The way in which Bowman defeated Hall is ironical because while Hall tried to kill the humans by throwing them into space, making them die because of the lack of oxygen or crushing them while they were outside the spaceship, all Bowman had to do was pull a plug. This event shows that while humans are more fragile, they will always be smarter than a robot.
Humankind imagined the aliens to have extraordinary bodies, something that will match their power. This is however not true; the narrator reveals that the aliens are in fact shapeless and are just bursts of energy traveling from one place to another at an extraordinary speed. When the truth is revealed about their exterior, it seems almost ironic to see that everything the humans imagined them to be is actually untrue.
What they feared
Bowman and the other men are sent to Saturn to investigate possible alien life and stop it should they want to harm the life on Earth. Ironically, Bowman becomes what he was sent to stop. Bowman is transformed by the aliens he encounters and given immensurable power and then sent back to earth where he is thrown into the middle of a nuclear war. Weather he is the one starting the nuclear war or the one stopping it is unclear but what is certain is that he became what he was sent to fight against. In this sense, the whole situation seems ironical.