Gulliver is immediately surrounded by a crowd of peculiar looking individuals. Many of them don’t hold their heads up straight. Some are cross-eyed. All wear clothes elaborately decorated with celestial bodies and musical instruments. Amongst these people walk servants carrying a blown bladder filled with little pebbles or peas to flap at the mouths and ears of those around them. Gulliver explains that he later learned that these servants are called “flappers” and they are responsible for striking the mouths of those who should speak and the ears of those they should speak into, for the speakers and listeners are so distracted they would often forget if left to carry on the conversation themselves. The flapper is also responsible for preventing his absent-minded master from tripping over things, bumping into walls, etc.
The designs on the floating islanders clothes suggest that their perspective values astronomy and music. Though the floating islanders’ elevation above the Earth suggests physical power, their individual appearances only indicate physical powerlessness. Their drooping heads, crossed eyes, and pathetic reliance on flappers show that they cannot even control their own bodies.
Gulliver is led to the Laputian king, who is too absorbed with solving a math problem to notice Gulliver for the first hour. (And even then he only notices Gulliver because a flapper bids him to.) The king gives orders for Gulliver to be sent away and fed. The food is cut into geometrical figures. After dinner, a tutor arrives, sent by the king to teach Gulliver the native language and, in the days that follow, Gulliver studies hard to learn to speak it.
Gulliver’s interaction with the king implies that the islanders’ lack of control over their bodies was not due to stupidity but rather to over-absorption in matters of the mind.
Gulliver learns that the floating island is called Laputa, a word whose etymology means “high governor.” Gulliver privately doesn’t “approve of this derivation,” thinking it “strained.” He thinks the etymology should actually be traced to two words meaning ‘sun dancing on the sea’ and ‘wing.’
Gulliver has his own perspective on the truth about Laputa’s etymology, though it seems a bit presumptuous to assume he knows more about the native language than the native speakers do.
At the Laputian king’s orders, Gulliver is measured for clothes using a quadrant, a ruler, and compasses, and the resultant clothes are very misshapen due to a failure in the calculation. Gulliver says such mistakes were frequently made and largely ignored.
As usual, Gulliver’s entry into a new society’s perspective comes with a new set of clothes. The tailor’s measurements exemplify an inability to apply knowledge practically.
The Laputian king orders Laputa to be steered towards Lagado, the capital of the kingdom below. Along the way, Laputa stops over certain towns and villages to hoist up “petitions” from the king’s people.
The Laputian state manages its subjects by exerting its physical power. It positions itself physically above them.
Gulliver describes life among the Laputians. Their speech relies very heavily on mathematical terms and they insist that their houses be built without any right angles because they hate practical geometry and can’t bear to live in rectangles (many of their houses are thus misshapen, as the workmen can’t manage the complex mathematics of building them). They have no grasp of common sense or practical knowledge and don’t know even have words for ‘imagination’ and ‘invention.’ However, they confidently pontificate on politics (as, Gulliver notes, do mathematicians in England). Everyone is perpetually obsessed with the health of the sun and they all worry ceaselessly about its impending death.
Laputian society suffers the inability to use knowledge to practical effect. The Laputians’ refined geometrical and astronomical theories are too complex to serve the simple tasks of daily life (like building houses). Because the Laputians’ refuse to embrace more practical forms of geometry and astronomy, their knowledge is basically useless and just causes societal dysfunction. They live in defective houses and can only discuss the day’s weather in terms of the sun’s eventual demise. All of this contributes to Swift's satire of those in English and European culture who hold the theoretical and philosophical to be higher than everything else.
The Laputian women “have abundance of vivacity,” loathe their husbands, and take Lagadans (from the kingdom below) to be their lovers on Laputa. Many women try to escape to Lagado, but it is difficult to get the Laputian king’s permission to leave Laputa because “the [Laputian] people of quality have found, by frequent experience, how hard it is to persuade their women to return from below.”
The Laputian women clearly don’t have the same problem relating to their bodies that the Laputian men do, which makes sense as women must be more in touch with their bodies given the fact of having to bear children. Their knowledge of life is visceral and practical. Still, the men that control the state use government law to restrain the women within Laputa.