Gulliver feels neglected on Laputa, since the inhabitants seem interested only in mathematics and music and are far superior to him in their knowledge. He is bored by their conversation and wants to leave. There is one lord of the court whom Gulliver finds to be intelligent and curious, but who is regarded by the other inhabitants of Laputa as stupid because he has no ear for music. Gulliver asks this lord to petition the king to let him leave the island. The petition succeeds, and he is let down on the mountains above Lagado. He visits another lord, named Munodi, and is invited to stay at his home.
Gulliver and Munodi visit a nearby town, which Gulliver finds to be populated by poorly-dressed inhabitants living in shabby houses. The soil is badly cultivated and the people appear miserable. They then travel to Munodi’s country house, first passing many barren fields but then arriving in a lush green area that Munodi says belongs to his estate. He says that the other lords criticize him heavily for the “mismanagement” of his land.
Munodi explains that forty years ago some people went to Laputa and returned with new ideas about mathematics and art. They decided to establish an academy in Lagado to develop new theories on agriculture and construction and to initiate projects to improve the lives of the city’s inhabitants. However, the theories have never produced any results and the new techniques have left the country in ruin. He encourages Gulliver to visit the academy, which Gulliver is glad to do since he was once intrigued by projects of this sort himself.
Gulliver visits the academy, where he meets a man engaged in a project to extract sunbeams from cucumbers. He also meets a scientist trying to turn excrement back into food. Another is attempting to turn ice into gunpowder and is writing a treatise about the malleability of fire, hoping to have it published. An architect is designing a way to build houses from the roof down, and a blind master is teaching his blind apprentices to mix colors for painters according to smell and touch. An agronomist is designing a method of plowing fields with hogs by first burying food in the ground and then letting the hogs loose to dig it out. A doctor in another room tries to cure patients by blowing air through them. Gulliver leaves him trying to revive a dog that he has killed by supposedly curing it in this way.
On the other side of the academy there are people engaged in speculative learning. One professor has a class full of boys working from a machine that produces random sets of words. Using this machine, the teacher claims, anyone can write a book on philosophy or politics. A linguist in another room is attempting to remove all the elements of language except nouns. Such pruning, he claims, would make language more concise and prolong lives, since every word spoken is detrimental to the human body. Since nouns are only things, furthermore, it would be even easier to carry things and never speak at all. Another professor tries to teach mathematics by having his students eat wafers that have mathematical proofs written on them.
Gulliver then visits professors who are studying issues of government. One claims that women should be taxed according to their beauty and skill at dressing, and another claims that conspiracies against the government could be discovered by studying the excrement of subjects. Gulliver grows tired of the academy and begins to yearn for a return to England.