Gulliver's desire to see the world and a financially lucrative offer prevails over his wife's pleas for him not to go to sea again, and he sets off on another voyage as ship's surgeon. His ship is boarded by pirates. Gulliver expects mercy from the Dutch pirate as he is a fellow Christian and Protestant, but it is the "heathen" Japanese pirate who shows more humanity, telling Gulliver that he will not die. The Dutch pirate is furious and sets Gulliver adrift in a canoe with meager rations, which the Japanese pirate augments. Gulliver sails to an island and sets up home in a cave.
The next day, Gulliver sees a large body about two miles high moving towards the island. As it draws closer, he notices that there are people moving up and down the sides of it and galleries and stairs built onto it. Gulliver shouts to them and they draw him up onto the flying island.
Gulliver reflects that these are a strange-looking people, with heads leaning to one side and one eye turned inward, while the other looks upward. Their clothes are decorated with images of planets and musical instruments. The servants carry a bladder full of dried peas, with which they strike the mouths and ears of those around them. Gulliver discovers that the people are so preoccupied with intense speculations that they cannot speak or listen without first being roused by the flapper. Indeed, they repeatedly forget about Gulliver's presence and have to be reminded by the flappers.
Gulliver is taken to see the King of the island, called Laputa. The King is surrounded by globes and mathematical instruments, and is so preoccupied that he fails to notice Gulliver and his other visitors for an hour. When the King addresses Gulliver, a servant flaps his ear. When Gulliver points out that he does not need such attention, the people think he is weak-minded.
The Laputans give Gulliver dinner. All the food is cut into geometrical shapes. Gulliver is taught their language. A tailor arrives, measures his body precisely with mathematical instruments, and later delivers a suit of ill-fitting clothes.
The King orders that the island should be floated over towns and villages on the mainland so that he can receive his subjects' petitions.
The Laputans view everything in mathematical and musical concepts, so that they describe the beauty of a woman in terms of geometrical shapes or musical terminology. However, they despise practical geometry, so that there are no right angles in their houses, which are badly built. Though they are experts in drawing diagrams, they are impractical and cannot grasp any subject other than mathematics or music. They are also fond of debating politics in minute detail. They are obsessed by the movements of the celestial bodies, and live in perpetual fear that one will destroy them. The women of the island have no patience with their husbands and exploit their absent-mindedness by having affairs right under their noses. The women are only allowed to go to the mainland by special permission of the King, since many who leave do not return. The prime minister's wife once went to the mainland and hid for months, preferring to live in rags with a deformed footman who beat her than to return to her husband.
Gulliver describes the physical characteristics of the island. The King is able to order that the island be raised above the level of clouds, so he can control how much rain the island receives. In the center of the island is a cave called the Astronomer's Cave, filled with astronomical instruments. Here too is a giant loadstone (magnet) which is manipulated in order to steer the island to different parts of the King's realm. The limitations of the technology of the loadstone means that the island cannot move beyond the extent of the realm, and neither can it rise above four miles.
The Laputans have better telescopes than are known in Europe, by which they see many more stars.
If a town rebels against the King or refuses to pay his taxes, he has two ways of reducing it to obedience. He can either float the island above the region, shutting out the sun and rain, or arrange for it to be pelted with rocks. If these methods do not work, he can drop the island on the town and crush the buildings and inhabitants. The Kings of this country have always been reluctant to do this, as the island could get damaged. Thus they drop the island on the people gently, out of a pretext of tenderness for them.
One rebellious city used their own magnet to try to force the island to descend in their midst, planning to kill the King and change the government. It took the King eight months to realize that the city was in rebellion, whereupon he ordered the island to hover above it and deprive it of rain and sun. The people had laid up provisions, so this did not work. The King then ordered them to be pelted with rocks, but they took refuge in strong towers. The King's technical advisors realized that if the island were to descend on the city, it would be trapped. The King was forced to give in to the city's demands.
By law, the King and his family are confined to the island.
Gulliver's stay in Laputa explores a different aspect of power from his stay in Lilliput or Brobdingnag. In Laputa, power is conferred not by superior size, but by technological knowledge, which becomes the instrument of oppression of the people. The Laputans have highly specialized knowledge of magnets that enables the King to dominate his realm from the relative safety of an island. He is remote from his subjects - it takes him eight months to realize that a city is in rebellion - so he does not understand their needs. Nevertheless, his control of the technology of the loadstone means that he holds the power of life or death over his subjects. The rebellious city regains some of its power by mastering the same technology that controls the King's island.
The Laputans' physical appearance reinforces the notion of their remoteness from the people living on the mainland. They have one eye turned inwards and the other heavenwards, and have to be roused with a flapper in order to speak or listen to another person. These characteristics symbolically reflect their lack of engagement with humanity and preoccupation with abstract thought. The custom of the flappers is deliberately ludicrous, emphasizing the foolishness and impracticality of the Laputans' outlook on life. It is significant that the island can only move within the limits of the King's domain and it can rise no higher than four miles: the same technology that gives the Laputans such power over the people also imprisons them within a restricted range. Mentally, emotionally, and spiritually, the Laputans are limited. They have no interests outside music (which they spend hours playing, to the exclusion of doing anything else), astronomy (which causes them only fear of cosmic accidents),
and mathematics (though they disdain the practical application of mathematics that would enable them to make clothes that fit or buildings that stand).
This section is Swift's satirical comment on the excesses of abstract thought and theoretical science that characterized the eighteenth-century Age of Enlightenment. In Laputa, humanity and practical considerations are sacrificed in pursuit of a cold intellectualism. The advanced technology that drives the island is not shared with the people to liberate them, but is used to enslave them.