What’s most surprising about the second and third episodes of Foundation is how much time is spent on Trantor with the Emperor clones long after Hari Seldon (Jared Harris) and his team have left the planet. In “Preparing to Live” half the episode is devoted to the investigation into the destruction of the Starbridge and the brutal punishment of both Anacreon and Thespis when neither will confess to the crime. The remaining part of the episode offers a look-in at the Foundation team traveling slowly through space which confirms a relationship between Gaal Dornick (Lou Llobell) and Raych (Alfred Enoch), makes an odd supposition that psychohistory isn’t complete, and ends with a bizarre series of events that isn’t even referenced in the next episode which pushes forward 35 years to Terminus.
“The Mathematician’s Ghost” offers a closer look at the settlement on Terminus, while still spending a large chunk of time examining how succession works on Trantor. We get a far better sense of the Vault’s warden Salvor Hardin (Leah Harvey), and her relationships with others on Trantor, and a change in the mysterious Vault which foreshadows larger change within the empire and the arrival of the Anacreon on the planet offering the first big test of the settlement who only have science and wits to battle the brutal future which seems to have just begun.