The book begins as a 19th century maritime adventure. The narrator is Silas Coade, the ship's doctor. Coade attempts to conceal his own drug addiction and keep the crew healthy as they search for a mysterious object hidden in a narrow fjord. The crew includes a tough-as-nails security officer named Ramos, a mathematician named Dupin, and a countess named Ada Cossile. However, there are clues that things are not as they seem, and the same crew soon find themselves on a zeppelin and in what appears to be a pulp science fiction space opera. This allows the author the fun of imitating different writing styles and genres, but it turns out that these are essentially dreams hiding a darker reality: crew members are being held captive in a spherical alien space craft that has undergone partial eversion, so that it is no longer easy to tell the interior from the exterior.

Two major themes of the novel are the ethics of sacrificing some members of the crew to save others, and the extent to which an artificial intelligence can be thought of as being "human". But, in the portions featuring Dupin, the beauty of mathematics and the sort of fame which mathematicians desire also arise.