The Doctor and the TARDIS team land at an abandoned lighthouse, and they find out it was abandoned for good reason. Cultists purchased the island the lighthouse was on and apparently trapped a... thing inside. They believed that God is an impossibly large number, since the Bible said that God is in everything. What else is in everything? Mathematics. The Cultists began disappearing, as well as their associate, a university graduate who was interning with them. Her friend visits the lighthouse, along with the local constabulary, to discover what really happened at the mysterious lighthouse on the island. What invisible force resides on the island? Can a number really be alive?
Tropes found in Iterations of I...I...I...I
- Arc Villain: The Predator of I & Robert DeValley.
- The Bus Came Back: Adric is back! Now played by Matthew Waterhouse!
- Call-Back: The Doctor takes some time prior to the events of the story to catch up on reading the copy of "Black Orchid" that Lord Cranleigh gave him.
- The Doctor also laments having no sonic screwdriver.
- The time spent in Logopolis is also mentioned.
- Captain Obvious: While Robert runs off with the I for his villainous purposes...The Doctor: We can't let the I get into the wrong hands!
- Chekhov's Gun: Or, in this case, Chekhov's Calculator!
- Contrived Coincidence: Of all the places on the island the TARDIS could have landed, of course it would land on a cliff that would break immediately after the occupants leave! It's a defense mechanism of the I to ensure that people cannot leave and accidentally take the I Predator with them.
- Death by Materialism: Robert DeValley stole the I in the hopes of using it to steal loads of money while on the mainland. As he finds out, The I's enemy is nicknamed by the Doctor as the I Predator for good reason, and it kills him.
- Dirty Cop: Robert DeValley.
- Disposable Intern: Poor Imogen.
- Face–Heel Turn: Robert DeValley goes from another somewhat confused ally to a greedy antagonist once the Doctor and Adric list "abusing the stock market for your benefit" as a possible side-effect of carrying the I to the mainland.
- Foregone Conclusion: The ending features Adric storming off, complaining about how nobody in the TARDIS respects him. A few minutes later, the Doctor chases after him to calm him down as the TARDIS heads towards Adric's final adventure.
- Haunted House: The Fleming's Island Manor has a reputation of being one.
- Heroic Sacrifice/ I Choose to Stay: Jerome realises that Imogen is alive as one of the I, so he elects to stay behind briefly on Flemings Island instead of escaping with the Doctor. He asks her to turn him into another member of the I, so they can both distract the I Predator and allow the Doctor and friends to escape.
- Insufferable Genius: At several points, a character will announce a brilliant discovery, only for The Doctor to smugly point out that he figured it out some time before, and was surprised that nobody else had. Tegan threatens to slap him.
- Locked Room Mystery: So how did Sinead Fleming die in the library if it was locked from the inside? Her husband did it by entering the room via a removable window disguised with fake bars, killing her, then escaping the same way.
- Madness Mantra: Some of the more psychically sensitive characters have a tendency of stuttering "I....I....I" while having a fit.
-
Spiritual Successor: The basic premise is one to ...ish! (which features sentient words) but also features strong story elements from Whispers of Terror and Horror of Fang Rock. - Spooky Silent Library: To their displeasure, Tegan and Nyssa are locked in one... where they find out one of the previous owners died in the same room.
- This Looks Like a Job for Aquaman: Befitting his return to the Doctor Who series via Big Finish, Adric gets a chance to put his (rarely used and usually useless) skill in mathematics to good use to save the day.
