William needs a new hobby and goes to a fishing shop. There he meets a strange man called the Doctor who buys fishing equipment for him and offers to take him fishing.
To William's surprise, the Doctor takes him to an alien planet with a large blue moon. The people on the planet, who look like humans, appear to be primitives but are very friendly. William is to take part in a fishing competition with the natives' champion, Little Rock.
It is a long walk to the first site of the competition. William is surprised to learn that he will be fishing for sand eels — in sand. He watches Little Rock's technique, but loses when he tries to use himself as bait and Little Rock takes advantage.
After another long trek, they reach the site of the second round. This time, William and Little Rock will be air fishing for flying fish, using kites. William happens to be very good at kite flying, and he wins this round.
In the last round, William and Little Rock fish for flame fish. They have no equipment — they must use their imagination. At first William has trouble with this, but he gets the hang of it until the Doctor tells him that his line is breaking, and it does.
The next day, William requires some explanations from the Doctor. He has noted how the natives don't get sick, they don't get eaten by wild animals, and they can regrow their limbs. He also knows that this planet is the Earth in the far future. The Doctor explains that the people are the descendants of the super rich, and that most people live in sky cities. He also admits to sabotaging William's attempt to win the third round because Little Rock had to win — his entire identity depends on his fishing prowess. The Doctor had been challenged by Little Rock but was allowed to pick William as a champion. When William wonders why the Doctor couldn't just lose to Little Rock on purpose, the Doctor is horrified at the idea.
The Doctor offers to take William anywhere he wants, and William, after verifying that the TARDIS can return him to the exact time he left home, decides to journey with the Doctor for a while.
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