The action of the story follows Sybil Gerard, a political courtesan and daughter of an executed Luddite leader (borrowed from Disraeli's novel Sybil); Edward "Leviathan" Mallory, a paleontologist and explorer; and Laurence Oliphant, a historical figure with a real career, as portrayed in the book, as a travel writer whose work was a cover for espionage activities "undertaken in the service of Her Majesty". Linking all their stories is the trail of a mysterious set of reportedly very powerful computer punch cards and the individuals fighting to obtain them.
During the story, many characters come to believe that the punch cards are a gambling "modus", a programme that would theoretically allow the user to place consistently winning bets. This is in line with Ada Lovelace's penchant for gambling (in both the novel and actuality). Only in the last chapter is the true importance of the punched cards revealed.