As the Dalek Wars draw to a close, Earth is trying to bring its distant colonies back into the fold -- but all attempts to contact the Spinward Corporation’s colony on Arcadia have failed, and an expedition sent to investigate has vanished without trace. Captain Isabelle Defries sets off on a follow-up expedition with a team of Irregular Auxiliaries, telling them that Arcadia is suspected to be a Dalek outpost. One of the Auxies turns out to be an impostor who slipped on board for a chance to fight more Daleks, but Defries is impressed by her attitude and allows her to remain. The impostor gives her real name as Ace… Curious about the “secret weapon” which is rumoured to be held in cryogenic stasis in the medical bay, Ace gets to it and learns that it’s the body of Abslom Daak, Dalek Killer. She decides to thaw him out prematurely to speak with him, but only after doing so does she recall that she knows from the TARDIS data banks how he’s fated to die.

Arcadia is a pastoral paradise, like an idyll fairy-tale kingdom, with a population that sees nothing odd about the fact that the average life expectancy is thirty years. The courtiers are happy to accept “suggestions” from the odd Humble Counsellors, and when the scribe Francis is found to have read forbidden texts about life on other worlds, the Counsellors “suggest” that he be sent to Landfall for proper education. Francis has noticed that people who go to Landfall tend to be somewhat different when they return, and his lover, the Lady Christina, decides to intervene with the King on his behalf. But before she can do anything further she dies, and her little sister Elaine is found in her room, catatonic with fear. Her family tries everything to snap her out of her condition -- leeches, dousing her with water -- but nothing works, and they eventually decide to send her to Landfall for treatment. They are unaware that her condition was brought on when she saw a Humble Counsellor murder her sister and drill a hole in her head.

As the Admiral Raistrick nears Arcadia, Ace’s tesseract folds open through several dimensions and becomes a tunnel linking her cabin to the TARDIS. The Doctor is sitting alone and confused in his ship’s new Zero Room, and when Ace arrives he has no idea who he is or what he is doing here. Ace, however, soon restores his memories -- and he remembers that this is just what he intended to happen. For some time, the TARDIS has been infected by an impurity in the organic material the Doctor retrieved from Tir na n-Óg, and due to his symbiotic link with the TARDIS, the infection always knew when he was trying to get rid of it and was able to stop him. Over a period of months, while trying not to think about what he was doing, he has reprogrammed the tertiary console to link itself to the Zero Room; it is cut off from the outside Universe, and inside its confines the Doctor is free of the infection. He manipulated Ace into leaving him so she could return and restore his memories when he was ready to act, and now he can cleanse his ship properly. Ace is upset to realise that he’s still using her as his pawn, but eventually she calms down and makes a suggestion which will enable him to cleanse the TARDIS much more quickly. As he prepares to do so, he asks her what she’s been up to, and is surprised to learn that she’s spent the last three years in Spacefleet killing Daleks. She tells him about her current mission and the ethical problem she faces knowing Daak’s future, but he is more puzzled by her mention of Arcadia; to his knowledge, there are no Daleks there. While Ace returns to her cabin on the Admiral Raistrick, the Doctor decides to go to Arcadia himself to find out what Earth Central’s real interest in the planet is.

Britta Hoffman, a young and enthusiastic employee of the Spinward Corporation, arrives on the space station orbiting Arcadia to begin her new duties, but she slowly comes to realise that there is something odd going on. The station’s layout seems to defy logic, and in some cases the laws of physics as well, and although new sections sometimes seem to be added overnight she can never find any evidence of construction. Diaries have been forbidden on the station, but Britta begins writing one anyway to keep her thoughts in order. This is discovered, and she is brought to Lacuna, the mistress of Arcadia Station. Lacuna has been selected to provide the masters of the Spinward Corporation with the tactile sensations that they lack in their new state of being, and she has chosen Britta to help her. Over the next five days, Britta becomes initiated into a sadomasochistic relationship -- and soon becomes addicted to it.

When the Admiral Raistrick arrives in the Arcadia system, the crew are shocked to see that the asteroid belt has been reconfigured so the asteroids lump together in the shapes of distorted, screaming faces. The ghostlike head of a beautiful woman appears in space, and transforms into the head of a Medusa which crushes the ship in its tentacled hair. Ace, realising that the ship is doomed, manages to get to a lifepod with Defries, Trooper Johannsen, and Daak. They are the only survivors, and the escape pod automatically makes for the nearest planet -- Arcadia.

Benny finds the rooms and corridors of the TARDIS shifting around her as the infection rages out of control, but she manages to reach the console room safely and shelters there as the TARDIS reconfigures itself. The TARDIS then materialises, and, eager to escape, Benny emerges to find herself on Arcadia. The Counsellors have warned the Arcadians to expect a ship carrying plague victims from another world, and when Benny wanders into the nearby village of Beaufort, the panic-stricken townspeople nearly shoot her on sight. Lord Gerald Delahaye rescues her at the last moment and takes her to his castle, intending to let the Prince decide how to deal with her. At the castle, Benny meets Elaine, Gerald’s daughter, and is appalled by the horrific conditions in which she has been kept by aristocrats who don’t understand the first thing about mental illness. Simply by showing Elaine a little kindness, Benny brings the girl out of her state of shock, and Elaine tells Benny about her sister’s murder. Gerald, however, doesn’t believe her, and he turns both Elaine and Benny over to the Counsellors to be taken to Landfall.

Lacuna’s master, Pool, detects the arrival of the TARDIS, and is surprised by its vast capacity for calculation and the complexity of the mind that controls it. Pool therefore decides to send its Counsellors to bring the TARDIS and its pilot to the station. Meanwhile, the Doctor has completed his work and is searching for Benny outside when he encounters Francis on his way to Landfall. The Doctor has already noticed odd discrepancies in the planet’s weather patterns, and as he accompanies Francis they encounter strange forms of plant and animal life which Francis doesn’t recognise. The Doctor realises that Arcadia has been partially terraformed, but now the natural alien world is reasserting itself, which suggests that the purpose Arcadia was designed for is nearly complete. They are both confronted and captured by Humble Counsellors, which the Doctor recognises as androids designed using technology which should not exist in this era. It appears that what is happening on Arcadia is the Doctor’s fault.

At Landfall, the Doctor and Francis are reunited with Benny and Elaine, and they are all sent to the space station via transmat. As they try to find their way through what appears to be an endless maze of corridors, the Doctor explains to Benny that these events are linked to actions in his past. Time is fluid until observation crystallises event patterns; the future can be changed but the past is immutable. By travelling through Time, however, the Doctor has interfered in certain areas of the space-time continuum and crystallised events into history; he now finds himself in the position of keeping the causal ties bound, to prevent the Universe from collapsing into chaos. But when faced with the limitless possibilities of the inchoate future, he can only guess at the most likely of probable outcomes, and as he can’t keep track of what’s happening everywhere, he sometimes misses a vital detail. Centuries ago, in Earth time, the Doctor interfered in a project initiated by the Butler Institute, a parent company of Spinward; but this may have caused them to divert their research into more dangerous directions, which are now about to bear fruit.

The Doctor and his companions finally meet Lacuna and Britta, who introduce them to Pool -- the collective consciousness of the Spinward Corporation executive board, living in a giant brain made up of the neural material harvested from the Arcadian colonists. Pool exists in a state of sensory deprivation and requires stimulation from outside sources, which is provided to it by Lacuna. Just as the Doctor had feared, the collective consciousness that is Pool has learned the secret of Block Transfer Computation, which explains the bizarre construction of the space station; Pool has created it from pure mathematics, and once the Arcadian project is complete, Pool intends to design its own Universe in which it can exist in a realm of pure thought. But the Doctor reveals that the plan is doomed to failure. Even the destruction of the entire Arcadian system won’t provide Pool with the energy required to create a Universe, and in any case, the impossible geometry of the space station proves that the “stimulation” provided by Britta and Lacuna is not enough. Centuries of deprivation have already driven Pool quite mad.

Defries’ landing party fights through the Counsellors to Landfall, but Johannsen is killed on the way and Ace finds herself in the uncomfortable position of fighting to save the berserker Daak’s life so he can die as history intends, thus convincing Daak that Ace has a thing for him. Eventually they reach Landfall, seize a shuttle and pilot it to the station, but Pool’s defenses become even stranger as it attacks them with nightmarish creatures generated by Block Transfer Computation. In the end, they win through and dock with the station, and Pool has no choice but to reveal their arrival to the Doctor and his friends -- and when Benny sees Ace, she is somewhat upset to realise that the Doctor came to Arcadia deliberately without telling her. While the Doctor distracts Lacuna, Benny sets off, locates Ace and the others and tells them what is happening here. They decide to locate and destroy the brain that is Pool.

Pool sends Counsellors to destroy the intruders, but its sanity and concentration are rapidly deteriorating and it is unable to fight them off. Daak prepares to make a kamikaze strike on Pool’s brain, but the Doctor contacts Ace and urges her to stop him so he can die at the proper time and place. Ace reluctantly stops Daak by claiming she loves him, thus saving his life and Pool’s as well. The Counsellors capture the attackers and take them to Lacuna, who orders the Doctor to turn over the TARDIS to Pool or watch his friends die, one by one. To prove its intentions, Pool encloses Ace in a force field and begins to crush her to death, and she fires a projectile dart at the field controls just as Daak leaps forward to free her. When the smoke clears, Ace is free, but Daak is dead.

The Doctor appears to have no choice but to hand over the TARDIS, but now Pool must work out how to possess it intact. Benny suddenly recalls a conversation she once had with the Doctor, in which he told her about the TARDIS’ one weakness -- a socket on the console through which any intelligence can be uploaded into the TARDIS’ core. Pool reads her mind and orders Lacuna to connect a cable through the socket so it can pass into the TARDIS, but when it does so it becomes trapped in the tertiary console in the Zero Room. Benny realises that the conversation she just remembered never happened; the Doctor planted the memory in her head to lure Pool into his trap. Without Pool’s influence, the station becomes subject to the ordinary laws of physics and begins to fall apart, and Britta helps the confused and abandoned Lacuna to an escape pod while the others flee in the TARDIS.

The Doctor returns Francis and Elaine to Arcadia, where life is going to change dramatically as the terraforming continues to break down. He then takes Defries to a nearby Spacefleet outpost to make her report -- but to Benny’s surprise, Ace decides to remain in the TARDIS with them. Ace has worked out that “Daak” was a clone all along, and that the Doctor knew it and deliberately lied to her so she would stop his suicidal attack. Despite its madness, Pool was a unique and vastly intelligent creature, and the Doctor chose to save its life because he felt an affinity with it. Since Ace has nowhere else to go, and the Doctor obviously needs someone to keep him honest, she will resume her travels with him. The Doctor allows her on board and ejects the tertiary console room into the Vortex, unaware that Pool knows itself to be trapped and has vowed to avenge itself on him. But the Doctor has more immediate worries, for he suspects that the new Ace has another reason for returning which she hasn’t told him yet…