Laputa

Laputa is a flying island described in the 1726 book "Gulliver's Travels" by Jonathan Swift. It is about in diameter, with an adamantine base, which its inhabitants can maneuver in any direction using magnetic levitation. It has a cave in the very centre which is precisely there to gather all the rainwater. It is also used by the king to enforce his supremacy.
Location.
Laputa was located above the realm of Balnibarbi, which was ruled by its king from the flying island. Gulliver states the island flew by the “magnetic virtue” of certain minerals in the grounds of Balnibarbi which did not extend to more than above, and beyond the extent of the kingdom, showing the limit of its range. The position of the island, and the realm below, is some five days' journey south-south-east of Gulliver's last known position, 46N, 183E (i.e. east of Japan, south of the Aleutian Islands) down a chain of small rocky islands.
Description.
The island of Laputa is described as being exactly circular and about in diameter, giving an area of roughly . The island was thick, and comprised a bottom plate of adamant thick, above which lay "the several minerals in their usual order", topped with "a coat of rich mould deep". 
In shape the upper surface sloped down from circumference to centre, causing all rain to form rivulets into the centre where four large basins in circuit lie from the absolute centre. In the centre of the island itself was a chasm 50 yards in diameter continuing down into a dome extending into the adamantine surface. This dome served as an astronomical observatory, and also contained the lodestone which enabled the island to fly and move above the realm.
Inhabitants.
Laputa's population consists mainly of an educated elite, who are fond of mathematics, astronomy, music and technology, but fail to make practical use of their knowledge. Servants make up the rest of the population.
The Laputans have mastered magnetic levitation. They also are very fond of astronomy, and discovered two moons of Mars. (This is 151 years earlier than the recognized discovery of the two moons of Mars by Asaph Hall in 1877.) However, they are unable to construct well-designed clothing or buildings, as they despise practical geometry as "vulgar and mechanick". The houses are ill-built, lacking any right angles, and the clothes of Laputans, which are decorated with astrological symbols and musical figures, do not fit, as they take measurements with instruments such as quadrants and a compass rather than with tape measures. They spend their time listening to the music of the spheres. They believe in astrology and worry constantly that the sun will go out.
Many of them have heads angled to one side, and they often suffer from strabismus: one eye turns inward and the other looks up "to the zenith", conditions that Swift uses to mock the microscope and the telescope. Laputans are described as becoming so lost in thought that they cannot focus their attention on a conversation or avoid running into a tree or falling into a ditch unless periodically struck by a bladder full of pebbles or dry peas carried by one or two "flappers" or, in their native language, "climenoles", hired for the purpose. 
Laputa is a male-dominated society. Wives often request to leave the island to visit the land below; however, these requests are almost never granted because the women who leave Laputa never want to return.
The Laputan women are highly sexed (having "an abundance of vivacity") and adulterous, and, whenever possible, take on lovers out of visitors from the lands below. The Laputan husbands, who are so abstracted in mathematical and musical calculations, might assume their wives are adulterous, but so long as they have no flapper around, they won't notice the adultery even should it occur right before their eyes.
Nearby lands.
The land beneath the floating island, within the region the Laputa can travel, is known as Balnibarbi. Balnibarbi is controlled by the king of Laputa; its ground capital is the city of Lagado.
Laputa's king is able to control the mainland mostly by threatening to cover rebel regions with the island's shadow, thus blocking sunlight and rain, or by throwing rocks at rebellious surface cities. In extreme cases, the island is lowered onto the cities below to crush them, although this is not successful every time, notably in the case of Lindalino.
The Balnibarbian language, spoken on both Laputa and Balnibarbi, is described by Gulliver as sounding similar to Italian.
Symbolism.
Lindalino's rebellion against Laputa is an allegory of Ireland's revolt against Great Britain, and Great Britain's (meaning the Whig government's) violent foreign and internal politics (see Jonathan Swift for his political career). The Laputans' absurd inventions mock the Royal Society.
As "la puta" means "the whore" in Spanish, some Spanish editions of "Gulliver's Travels" use "Lapuntu", "Laput", "Lapuda" and "Lupata" as bowdlerisations. It is likely, given Swift's education and satirical style, that he was aware of the Spanish meaning. (Gulliver claimed Spanish among the many languages in which he was fluent.)
Legacy.
On Mars's largest moon, Phobos, there is one named regio, "Laputa Regio", which is named after Swift's Laputa because of his 'prediction' of the two then undiscovered Martian moons, which his Laputan astronomers had discovered.
The 1986 Japanese anime film "Laputa: Castle in the Sky", directed by Hayao Miyazaki, also derives its name from Swift's novel.
In the video game "Deus Ex", agent Gunther Hermann's killswitch phrase is "Laputan Machine", an allusion to the fact that despite being enhanced with numerous bio-mechanical and neurological implants, agent Hermann is still highly flawed and impractical.