Honoré has recently found himself thinking about his late mother, who was murdered by two serial killers when he was a boy. Even before he understood himself to be time-sensitive, he felt that he could see what had happened to her, and was frustrated by his inability to stop it; it was his grandmother who helped him to come to terms with the hard lesson that a thing once done cannot be undone. Now, he has the ability to travel through Time, but he can only do with the help of his friend Emily -- and they're thus surprised when an old man, Jonah Rankin, appears out of nowhere in an alley, all by himself. Honoré is unable to see Rankin's time-snake, as if his past and future are disconnected from the rest of the world. The agitated Rankin babbles about the world being wrong, and blue sparks shoot out of his body; however, nothing else appears to happen.

Honoré takes Rankin to a gangland acquaintance, Vic "Scarper" Styvessant, but the thuggish Styvessant has become an effete fop who nervously laughs off Honoré's offer to pay him for putting Rankin up. Confused, Honoré and Emily return to Honoré's home -- only to find that Honoré's landlady's son, Tom, is still alive, and that they themselves are already there. Their other selves are apparently living together in a flat wired up with CCTV surveillance systems from years in the future; in the few seconds it took Emily and Honoré to walk up to the door from the curb, their other selves saw them coming, leapt through Time, had a chat with Einstein, and returned understanding where their doubles must have come from. It appears that Rankin has the ability to leap between parallel timelines, and this time, he brought Honoré and Emily along with him.

Realising that Rankin is their only way back home, Honoré and Emily return to Styvessant's flat, only to find that Rankin has vanished into thin air, leaving them stranded. They have no choice but to return to Honoré's flat, and on the way, they spot airships in the sky, implying that this world's history diverged from their own some time ago. However, while speaking with Blandish and Lechasseur, they discover that airships are still in service because their doubles changed history to prevent the destruction of the Hindenburg. Their doubles are startled to learn that Emily and Honoré don't use their powers to make history better, and insist that, by doing nothing to avert tragedy, Emily and Honoré are allowing evil to prosper. Emily and Honoré remain unconvinced that they have the right to meddle, and Blandish thus places a phone call to America -- and allows Honoré to speak to his mother, who is still alive.

The next morning, after Honoré and Emily have had some time to get over the shock, Blandish and Lechasseur explain more about their ability to travel through Time and alter history, which they've learned is the result of their collapsing quantum probabilities upon their arrival. Lechasseur then collapses in pain, feeling the effects of his war injury even though the War never happened, and Blandish explains that their changes to history don't always stick. She invites Emily and Honoré to accompany them on their attempt to put things right, and Honoré agrees, wishing to see for himself. Lechasseur and Blandish use a rather poorly-done painting to leap back in time to Vienna -- where Honoré is appalled to see his counterpart casually murder an old man walking down the street. This was Professor Roche, who was about to recommend against admitting the untalented Adolf Hitler to the Vienna Academy of Fine Arts; now, Hitler will be admitted to the Academy after all instead of joining the Nazi Party. The War will never take place, which means that Lechasseur was never injured after all, and he takes to his heels when the police arrive. The sickened Honoré follows, but realises that he and his counterpart are nothing alike.

Deeply concerned by their doubles' casual attitudes towards human life and history, Emily and Honoré decide to track down Rankin and get back to their own world. However, Blandish and Lechasseur trick their doubles into splitting up by pretending to be their own counterparts. Rankin has returned to Styvessant's home, and Emily realises that she's accompanying Lechasseur instead of Honoré when Lechasseur coshes the disoriented Rankin, knocking him out before he can jump away again. Blandish has kept Honoré safely out of the way, and when they return to the flat, she and Lechasseur lock up their counterparts in a closet. Honoré and Emily realise that, since their counterparts' changes to their own history have been unravelling, the counterparts intend to leap over to Emily and Honoré's world and start again from scratch.

Tom finds and rescues Emily and Honoré from the closet, believing that his lodgers were overpowered by burglars. Emily and Honoré find Rankin and explain what has been happening to him, but he can't cope with the explanation, and in his confusion and rage he inadvertently leaps again. Unfortunately, Blandish and Lechasseur arrive at that very moment, and thus are transported to Emily and Honoré's world as well. The counterparts now intend to kill Honoré and Emily to prevent them from fixing the changes that the counterparts intend to make, but Honoré and Lechasseur find that they can see and counter the other's moves before they are made. As they hesitate in stalemate, Blandish pulls out a knife -- but Rankin has had enough of this madness, and he leaps at Blandish, impaling himself on the knife just as he jumps again. Blandish and Lechasseur are dragged away with Rankin as he dies.