As Twilight makes final preparations to depart the area, Ocellus takes a final look towards the forest, then back down the road leading to Elysium, before turning back to face Coccyx. “So what now?” she asks simply.
“Tarsus and Carpus are already heading back to the Hive to inform Thorax of our developments here. We’ll be starting small-scale, but if all goes well, there should be a strong faction of changelings in all the triple-towns within just a few moons.”
“Are you sure Sunbolt will really abide by your wishes? He was so adamant about not allowing changelings for so long.”
“I’ve seen firsthoof how these ponies react when it comes to logic,” Twilight replies as she joins the others. “At the least, I doubt Zodiac would let him back down, after what Pinkie Pie did to him the last time I was here.” She turns to Coccyx. “I do wonder how your being here will affect the way the townsfolk will greet strangers in the future.”
“I’ve already had some discussions with the Society members,” Coccyx answers. “Already, they have ideas for greater logic challenges.” He turns from Twilight to Ocellus. “Remember the quiz I gave you?”
Ocellus nods.
“As the changelings begin to populate the towns, the plan will be for changelings who take pony forms to answer questions related to place of residence in a similar manner to what currently exists, but for changelings to respond in the opposite. So a changeling who takes a unicorn form and resides in Utopia would make false statements, and if that same changeling takes on a pegasus form instead, his or her statements would then be true.” He muses for a moment. “That could lead to some really complicated puzzles.”
Twilight chuckles. “I think I’m all puzzled out for a while. In any event, we really need to get back to Ponyville.”
Coccyx addresses Ocellus one final time. “None of this would be possible without your help. The Hive owes you a great deal.”
Ocellus smiles sheepishly and gives Coccyx a warm embrace before flying into the balloon.
“It was great meeting someone as well-versed in logic as yourself,” Coccyx tells Twilight. “Hopefully our paths will cross again, under friendlier circumstances.”
“I would like that very much, and I hope all goes well for you and the changelings who come to call these towns home.”
Twilight embraces Coccyx, then joins Ocellus in the balloon before undoing the ropes, allowing the balloon to rise and drift back to Ponyville.
As the balloon passes over rolling grasslands and sparse woodlands on its way back home, Ocellus turns from the scenery to observe Twilight staring at a piece of parchment. “What are you looking at,” she asks.
“I’m still trying to make manes-or-tails of your statement. I must admit, I’m still struggling to figure out why Sunbolt just gave in the way he did, especially after you told him he could answer however he chose, and didn’t even have to be truthful.
“Oh … well, I did say he could either lie or tell the truth, but he was forced to choose one. And that’s what made all the difference.”
“Huh???” Twilight shakes her head. “I’m sorry, I’m still lost.”
Ocellus flutters over and inspects the question she posed to Sunbolt:
Will you either truthfully answer ‘yes’ or falsely answer ‘no’ if and only if you allow the changelings to settle in the triple towns, or else falsely answer ‘yes’ or truthfully answer ‘no’ if and only if you continue to disallow the changelings to settle in the triple towns?
“There really is a lot going on here,” Twilight adds.
“True,” Ocellus admits, “but it’s easier if you break down the possibilities one by one. For example: what if Sunbolt answered ‘yes’?”
Twilight inspects the question. “Well … he can either answer truthfully or falsely. If his ‘yes’ is truthful, then that satisfies the first-half of the question, and so he would be forced to allow the changelings in. What if he was lying?”
“In that case,” Ocellus answers, “the second-half of the question would kick in. Now, his false ‘yes’ would be equivalent to not allowing the changelings in … but as he’s answering falsely, that means the negation must be true, so now he does have to allow the changelings in. Otherwise, his ‘yes’ wouldn’t be false!”
“That’s … I’ve never seen anything like this in the logic books I’ve read. And I’ve read a lot of logic books! But what if he answered ‘no’?”
“Well, his ‘no’ would then be true or false,” Ocellus explains. “Suppose he was being truthful: then the second-half again kicks in, and he would be truthfully stating that he would not continue to disallow the changelings in … in other words, he would again be forced to allow the changelings in.”
Twilight simply looks on, desperately attempting to process Ocellus’s explanation.
“Finally, a false ‘no’ would come back to the first-half; basically, he would be falsely denying that he would allow the changelings in, which is equivalent to truthfully acceding that he would allow the changelings in. So you see,” Ocellus says in summation, “No matter how he answers, and no matter if his response is true or false, he has to allow the changelings in.”
“That’s … just astounding,” Twilight states in all earnestness. “So for all the choices you gave Sunbolt … ‘yes’, ‘no’, true, false … you really didn’t give him any choice at all!”
“Not if he wanted to remain faithful to his own logical beliefs. I know I hadn’t been there very long, but I could tell quickly how important that was to everyone.”
“Wow … just, wow.” Twilight pauses again to take in Ocellus’s explanation. “When it comes to logic, you could be a professor.”
Ocellus smiles sheepishly. “Well, I try hard to be as good a learner as I can be. In the past, I feel like that mindset isolated me from the other changelings, even though I was always more comfortable around books. Even when I got to your school, I was apprehensive that I would slip into my old ways … maybe I still do, at times … but I hope I’m getting better.”
Twilight nudges Ocellus’s face so that they see eye-to-eye. “Ocellus … you remind me so much of what I was like back when I was still living in Canterlot as Princess Celestia’s student. Never lose that thirst for knowledge … there’s always something new to discover, as I’ve learned over these last few hours. But you’re also blossoming as a true friend, opening up your life to others in a way far beyond where I was.” Twilight chuckles. “I had to be sent away to Ponyville to learn how important friendship really was.”
“Sound familiar?” Ocellus asks, causing both to laugh.
“You know,” Twilight says, “your exploits over these last couple days could make for an incredible logic-based story. ‘Ocellus’s Logic Puzzle Adventure’ … how does that sound?”
“I don’t think I’m well-known enough. Maybe call it ‘Twilight’s Logic Puzzle Adventure’ instead.”
Twilight laughs again. “I didn’t even do anything this trip; that title would be so misleading!”
Ocellus laughs with Twilight. “I guess it would. So … what now?”
“Now we get back to Ponyville, and you get back to your regular lessons with everyone else. I’m sure they’re curious to hear firsthoof about your exploits.”
“You think Uncle Coccyx will actually be able to acclimate the other changelings to those towns.”
“I have faith that Coccyx and the others will do just fine … but we’ll see what the future has in store.”
“Um … Headmare Twilight? I’m still curious … what can you tell me about Professor Pinkie Pie? Did she really accompany you to these towns?”
“She did,” Twilight answers, “and don’t let her silly nature fool you. She is one of the most intelligent ponies I’ve ever met. Oh, and she nearly became an alicorn herself.”
“WHAAAA???”
“Oh yes … but maybe I should back up. It all started when our cutie marks first led us to the twin towns …”