The intrepid Professor William Waterman Sherman, the narrator-adventurer of the story, sets off alone to encircle the globe in his hot-air balloon. He is a retired arithmetic teacher, who is tired of forty years of spitballs and gum on his chair. He has not, however, lost either his sense of humor or his intellectual curiosity. The Professor is an eccentric individual, although a totally likeable one. His desire to maintain solitude aboard his balloon is an eccentric urge that he never loses—at the end of the book he is ready to try once more. With quiet irony the author places the Professor in a society filled with eccentrics, among whom he seems comparatively ordinary. His own curiosity and flair for experimentation are reciprocated by the inventive islanders and their fabulous creations.

In a balloon you con decide only when to start, and usually when to stop. The rest is left up to nature.
When Professor Sherman lands on Krakatoa, he finds himself in the midst of a peculiar Utopian society. The twenty families that live on this island have agreed that their mutual survival depends on two things—keeping their fabulous wealth a secret from the rest of the world, and cooperating totally with one another. They have, therefore, devised an unusual kind of democracy. Under their constitutional Gourmet Government, each of the families operates a restaurant where everyone else eats on one day of each twenty-day month. In this way everyone makes a good living, and no one has to work more than one day out of twenty.

In their impeccably democratic way, each of the families goes by an alphabetical name. The "A" family owns the "A" restaurant, which specializes in American food; the "F" family manages the French restaurant, and so on. All have learned to enjoy their communal life without competing for wealth. Once a year one islander sells a diamond on the mainland to obtain enough money to pay for the necessities of the community without betraying the island's secret wealth.

Not only have the islanders developed an original form of government, but they also put their ample leisure time to enormously inventive uses. Some of their devices are wildly comical and absurd, while others are wistfully impractical. In addition to the bed-making machine, a wish fulfillment fantasy appealing to every reader, they have also invented electrified furniture that dashes about on wheels with outrageous, if not downright dangerous, results. The Twenty-One Balloons stresses the themes of creativity, individuality, eccentricity, and cooperation as the Professor learns the ins and outs of Krakatoan society.