WARNING: The following contains spoilers for Foundation Season 1, Episode 3, "The Mathematician’s Ghost,” streaming now on AppleTV+.

“Every world has ghosts,” Gaal's voiceover says as the third episode of Foundation season 1 starts, and it is a bit ironic that the episode begins with that phrase, considering how the last one ended. But lest you think Foundation is going to give you the answers right away, the voiceover simply goes along with the story – even if that story doesn’t include the answers we want.

The ghosts Gaal is referring to are in the palace of the Empire some 400 years earlier, where we see Demerzel, looking exactly like the one who was just walking beside Brother Dawn last episode. Except now she’s casually talking to Cleon The First, who asks if he can count on her to see it through. To see everything through. She reassures him, not that we need her to. We know she’s still around.

RELATED: Foundation: Lou Llobell Teases Gaal Dornick's Journey in the Apple TV+ Series

Foundation Mathematician's Ghost

Even if, perhaps, as Cleon I says, the Empire hasn’t been as loyal to her as she has been to the Empire.

Because there’s nothing this show loves more than time jumps, we move to Demerzel looking at the preserved Body of Cleon I as Brother Dusks asks if she thinks of him often. Except, is it Brother Dusk? It certainly doesn't look like the Brother Dusk we'd seen before. This is explained by the passing of time, as it's been 19 years since the starbridge bombing. And this Brother Dusk is dying.

We see him being fitted for a final time, and later he is joined by …Brother Day and an older version of Brother Dawn. It’s a confusing scenario because it’s the same actors – except for the older Brother Dusk. In his final moments, Brother Dusk is thinking of …Hari Seldon, even if he’s a man long dead. Because men can die, but do their ideas?

Or perhaps he’s thinking about his legacy, about the legacy of Cleon I, about the starbridge. Brother Day, however, is clear. They are Cleon I’s legacy, not the bridge. I’m not quite sure Brother Dusk agrees.

RELATED: Foundation: Lee Pace Explores the Riddle of Purpose as Asimov's Brother Day

Foundation The Mathematician's Ghost

He does, however, seem to enjoy his final gift, a trip to the ruins of the starbridge. This is both beautiful and devastating, and it serves to reinforce the point that we have absolutely no idea what happened to Gaal, Raych or even Hari Seldon after the cliffhanger from Episode 2. We’re not even sure if Seldon did die by Raych’s hands, or if he survived only to perish later. All we know is that there must always be three Empire, and one of them is saying goodbye.

Well, that and that Demerzel can apparently harbor feelings.

The starbridge – or what’s left of it – is blown up. Brother Dusks sneaks in to see the new Brother Dawn in the middle of the night. The baby has still not been “born,” as he must wait for Brother Dusk to expire. Demerzel, meanwhile, is going through the same mourning she clearly goes through every few years, and as much as this dynasty might feel like living forever, it’s striking how cruel it also is, to have to say goodbye over and over and over again, with no end in sight.

RELATED: Foundation: David S. Goyer Reveals the Key to Adapting Genre Fiction

Foundation The Mathematician's Ghost

We say goodbye to Brother Dusk – Brother Darkness in his final moments before he basically walks into the light and disintegrates – and the cycle starts again, with a new Brother Dawn, a new Brother Day and a new Brother Dusk. Because babies are not very interesting, however, the storyline moves forward once again, 17 more years into the future, where Cleon the 14th is now a young adult. Thankfully, we don’t stay for his teenage angst, as it’s time to check on Terminus.

“The Empire underestimated Hari,” the voiceover says, as we see the Foundation settle on Terminus according to plan. We get no real explanation of what happened to Hari – or Raych, but as they’re not around, we can probably assume things did not go well. There’s no mention of Gaal either, but considering she is telling this story, it’s probably safe to hold out some hope for her.

One thing, however, seems to have deviated from plan – or at least the plans Hari’s followers knew of, as the Vault is waiting for them as they settle on Terminus. No one can figure out what it is, or how to get close to it, so they just ignore it as they go about settling on the planet. Or, at least, most of them do, because we soon learn that teenage Salvor Hardin wasn’t afraid of the Vault.

RELATED: Foundation: David Goyer Shares How He Brought Asimov's 'Unfilmable' Sci-Fi Classic to Life

Foundation The Mathematician's Ghost

Adult Salvor Hardin seems afraid of absolutely nothing, as we move into the later timeline this show has introduced so far. But she does seem curious, as she experiments to try to determine how close living things can get to the Vault – and if the field remains the same. Later, we learn from a conversation with her father that her job is basically security for the colony, which tracks with what we’ve seen so far from her.

She’s got to report to someone about her discovery regarding the Vault, though, and as she walks into the town these people have created on Terminus there is, ironically, a statue of Hari Seldon that looks a lot like the statue of the Empire on Trantor. Inside the main building, the conversation about what to preserve continues, even all these years later, and it’s basically the same idea from last episode, when it was Gaal sitting in on the meeting, not Salvor.

The person Salvor was reporting to turns out to be her mother, and as they head to the Vault together our earlier suspicions are confirmed, the field has indeed expanded. They discuss Salvor not being hurt by the field, and how that makes her special, but Salvor has more pressing issues in mind, her theory that the Vault, whatever it is, is waking up. She believes the crisis they’ve all been preparing for has arrived.

RELATED: Foundation: Leah Harvey Breaks Down Salvor's Badass Ways

Foundation The Mathematician's Ghost

We go back to the town, where Hugo has arrived. We don’t know much about Hugo, but it becomes clear as soon as he steps down from the ship that Hugo is someone to pay attention to. This is pretty much confirmed as the scene shifts to him in Salvor’s kitchen, where she is trying to pretend she isn’t thrilled to see him. It doesn’t last long.

But even Hugo cannot calm Salvor’s racing thoughts. Only walking the perimeter can, apparently. She soon sees a boy heading to the abandoned wreck of the ship that brought everyone to Terminus, and being as she is who she is, she follows him and runs into one of the creatures native to Terminus. But there are bigger problems than that, as Salvor spots a ship approaching. An Anacreon ship.

As Salvor informs everyone in town, we learn Hugo is actually from Thespin, and also, he’s pushing seventy. He looks pretty spry for his age; we’re not going to lie. Salvor posits the Vault was trying to warn them, but that doesn’t really go over well. These people always try to go back to the plan.

RELATED: Foundation: Jared Harris Shares What Drew Him to Asimov's Hari Seldon

Foundation The Mathematician's Ghost

“Forget the plan. Seldon’s gone. When are any of you going to start thinking for yourselves?” Salvor asks. Not that anyone pays attention, as the plan seems to be to just call the Empire and wait. Salvor isn’t the kind to wait, though. She’s the kind to take action, which is why she goes to check the armory. Sadly, there isn’t much there, which means that when the plan to contact the Empire fails, things look dire.

Salvor follows her mother to her room, where we see the same device where Seldon’s work resides that Gaal was told to check during the first episode. Salvor’s mother took it from Hari’s office after his funeral, she confirms. “If you were part of the plan, it would make it a lot easier for me to believe in all of this,” she then tells Salvor. But Salvor can’t understand the math and doesn’t think she’s special. She’s just different, she says.

Outside, in the shadow of Hari Seldon’s statue, Salvor tells Hugo to go. They might all be in danger, but he even more so, considering where he’s from. “I’m not going anywhere,” he says. Not without her, goes without saying. But she’s not going anywhere. For Salvor Hardin, this is her job. To protect everyone.

Gaal’s voiceover returns to tell us that the Empire feared Harry “because he could forecast the future, but in reality, all he was doing was re-examining the past.” Ironically, right after that line, we see Salvor in Hugo’s arms, and then lather, rinse, repeat the earlier scene where she wakes up, goes outside, and follows a boy into the ruins of the ship. Except this time, someone’s waiting. And they don’t seem to be friendly.

To see how the story of Foundation starts to take shape, the first three episodes are available on Apple TV+. New episodes are released every Friday.

KEEP READING: Foundation Won't Stick Too Close to the Books - and That's a Good Thing