The Rift

by Colors

#33 ◈ 2

I

“Discord is gone!” Celestia exclaimed, in a voice which Fluttershy had never heard from her before. “When I tried to reach for Twilight, I sensed emptiness, now I see you carry her dead body with you. When I reached for Rarity, I found her hundreds of yards above us, at the entrance to this chasm. Others were still with her. Rainbow Dash. Fluttershy. Tell me, what did you do?”

Silence. Flutershy’s heart pounded. This was too much. She had already lost two friends, she couldn’t bear Celestia’s anger. She could feel herself crying again, and she was infinitely far away from forming a response...

“She is the one who made us go down there!” Rainbow exclaimed, pointing at Sigma. “She’s responsible! Ask her!”

Celestia’s gaze fixated the purple unicorn. “Is this true?”

“Um,” Sigma said. “Yes, I suggested this trip. Um, there has been a rift in the sphere around the universe, princess.”

“If that were true, everyone standing here, as well as every other creature alive today, would face certain death.”

“It’s closed!” Gold Star exclaimed. Fluttershy gave a silent sob that nopony noticed. “Sigma closed it! That’s why we’re here! That’s how Twilight died!”

“Nopony is strong enough to affect the sphere, neither you nor me. The only creature-”

Suddenly, Celestia fell silent. Through her swollen eyes, Fluttershy could see her whispering something to Luna, and Luna responding something.

“Explain what you claim to have done and how you did it.”

“Um. Um ... I used the hall at the end of the tunnel we just came out of to reprogram the sphere’s software. Um. I made it absorb Discord’s magical energy and, um, use it to repair itself. Um, it worked, and that is how Discord died. Um, Twilight and Featherfall died when we were attacked on the, um, flight down here.”

“You claim to have saved the universe.”

Sigma didn’t respond to that.

“What is this hall?”

“Um, it is a coded control panel for the sphere’s software. It is possible to order it to do things, but mistakes are likely to have catastrophic consequences. Um, the sphere’s software is based on group theory. It would probably be very bad if anyone who isn’t very good at group theory and has good intentions and good reasons tried to do anything with it. Um, I suggest you prevent anyone except me from accessing it in the future.”

Once again, Celestia whispered something to Luna, and Luna gave a longer reply.

“If I went there now to see it for myself, I would find proof of your words?”

“... um, you would find a large hall with a lot of flowing symbols on the floor. I don’t know how much about it you would understand. Um, it would be very bad if you stepped onto the symbols without understanding what effect it has, but staying on the edge would be harmless. Um, I suggest you read my mind if you want evidence that what I’ve told you is true.”

“You volunteer to let your mind be invaded?”

“Yes.”

“Invading anyone’s mind against their will is breaking an ancient law, one that is still in effect. I have to abide by this law, just like everyone else. Will you confirm that you give me explicit permission to do this, and that I did not force it upon you?”

“Um, yes.”

“Sigma!” Gold Petals interrupted, rushing towards her to whisper something in her ear. After a few moments, Sigma replied something. She walked over to Gold Star, saying something to her. Celestia watched the scene calmly.

“Princess,” Gold Star said cautiously. “Princess, may I ask you for a favor? It, um, it won’t hurt anyone if you do this. You might find it strange, but it won’t hurt anyone and it needs to happen soon. Then we can go back to discussing, um, what... um, what we were just talking about...”

“Speak.”

“Can you please freeze Featherfall’s body down enough so that she doesn’t... um, doesn’t... decay?”

Cyclone heaved the body in question from her back, laying it onto the ground.

“Why would you ask this of me?”

“Please! Just do it! I beg you! It won’t do permanent damage, right?”

“I cannot do something like this to a dead one without her family’s permission.”

“Her old family is thousands of miles away,” Gold Petals said. “We are her real family. All of us with silver wings. We want this for her.”

“Thousands of miles,” Celestia repeated. “You claim she is from outside Equestria.”

“She is,” Gold Petals said firmly, “out of a nameless region only referred to as the land of mountains.”

Once more, Celestia had a silent exchange with Luna.

“I have been to this land,” Luna then said, “two thousand years ago. How would a pony travel this far?”

“Please!” Gold Star plead, “please, it doesn’t matter how she got here! Just cool her down! Or she’ll decay while we stand here talking!”

This was followed by another exchange between Celestia and Luna, this one going back and forth a number of times.

“Luna will do what you ask,” Celestia declared. “You. Is Sigma your name?”

“Um, yes.”

“Sigma. You gave me permission to enter your mind. Are you still certain?”

“Yes.”

“Then stand still and do not resist.”

II

It took over ten minutes for Celestia to read in Sigma’s thoughts, her horn brightly lit, and Sigma standing before her, tiny in comparison, her eyes set onto the ground. Ten minutes, during which the only thing Gold Star had been able to do was hope that everything would turn out well.

“It appears I must thank you,” Celestia said eventually, and Gold Star’s heart made a leap. Then Celestia shook her head. “Or perhaps not, as merely thanking you seems like a laughable response to what you have done. Everyone I will ever know, and everyone I will never know, ponies and other species alike, and even the plane itself, all of it will continue to exist because of you. Without you, we would drown in chaos, worse chaos than any of us could imagine, until all lights go out, all life is spent, and the plane itself dissolves into dust. For as long as we may live, we will be in your debt.”

Then Celestia’s legs gave away beneath her, and she kneeled onto the ground, bowing her head. Moments later, Luna followed her. Without questioning it, so did Gold Star, and then everyone else, until the only pony left standing was Rainbow Dash, and then no-one as even she followed.

And, of course, Gold Star knew what the response Sigma was going to have would inevitably start with.

“... um. Um. Um. You’re, um, welcome. Um, princess, it would be good if you did a number of things I will suggest.”

Celestia stood back up. “There are few things I shall not grant,” she said, “as long as they don’t harm my subjects. Name them.”

“Um. I have not shown you how I can do the things I did. It would be bad if you knew, and it would be worse if others knew. Um, I ask you to permanently prohibit all research into the theory of magic, and if they consent, I ask that you remove the knowledge of what I found out from everyone standing here or on the top. Um, I also ask you to hide this place as best as you can and remove the knowledge of where to find it from everyone standing here or at the top, including yourself and Luna.”

“No-one should know of this place,” Celestia agreed. “But why do you not want us to progress our understanding of magic?”

“Um, if I devoted myself to it, I think I could destroy Equestria in a few decades, using what I found out. It would be bad if others could do similar things.”

“You fear power being misused.”

“Yes.”

“This is an enormous decision. Dozens of bright minds will be thrown off their work and passion, and knowledge that might help us grow together will forever remain hidden. But I meant what I said. If you tell me what you found out and demonstrate the risk it brings, I will do what you ask.”

“Aren’t you forgetting something?” Lynn suddenly threw in. “Maybe I don’t get this right. There is this large sphere that surrounds everything. There was a rift in it. The rift would have destroyed literally everything if it remained open for too much longer. The only way to close it was to use Discord, ‘cause Discord is crazy strong. So you did that, and now Discord is dead and the rift closed. Right?”

“Um, yes.”

“... in other words, the next time there is a rift, everyone dies guaranteed.”

Gold Star wondered whether the sinking feeling that was in her breast right now was something the others shared.

III

“Another rift would surely cause the world to end,” Celestia said. “Unless it comes at a time when our understanding and abilities are far, far beyond our current point. A time which will never come if I do what you ask.”

“Um. If we are knowledgable enough to close a rift by ourselves, I think it is much more likely that we will destroy ourselves than that a new rift forms.”

Celestia bowed her head. “I cannot disagree.”

“So we just sit around waiting,” Rainbow said, “at some point there’s another and then swoosh, we’re done?”

“Luna and I always believed the sphere to be infallible. That it can malfunction in this way, I will not deny, is tragic news. We all depend on it. If it ceases to work, I fear there is nothing we can do.”

“Did it just malfunction?” Cyclone asked. “Did nothing cause the rift?”

“We know of no cause,” Luna said. “What about you?”

“Um. I think that, um, whatever caused Discord to exist also caused the rift. But, um, I don’t know what that was.”

Silence spread after those words. If this was supposed to be victory, Gold Star thought, then she had imagined it differently.

“Let us not forget that there has been no rift before since the beginning of time,” Celestia said at last. “Yellow one. Why did you wish for the pegasus to be frozen?”

“Uhm. S-Sigma thinks she can bring her back.”

For a moment, Celestia seemed lost for words.

“You are one of a kind, Sigma. I do not think I have ever known a smarter pony than you, not in my nine thousand years of existence. Not even I know how to reach beyond the realm of darkness. If you think you are capable, then I do not have the confidence to tell you otherwise. But it is forbidden.”

“Um, I ask you make an exception,” Sigma said. “For Twilight and Featherfall.”

“Perhaps I should say no,” Celestia mused. “It is a misuse of my power, an authority I should not have. But after all...” She sighed. “The law is not there because I want the dead to stay dead. The law is there to prevent fools from hurting themselves in pursuit of a goal they will never reach. Who am I to tell a pony so much smarter than myself what to do? If you want to, go ahead and try. Two ponies?”

“Yes.”

“You will not attempt to revive a third one without my permission.”

“Um. I swear it.”

“We will make up a story,” Celestia murmured. “Equestria cannot know that you have this power, if you do have it. Twilight is on a journey, far away. If you succeed, she returns safely; if you fail... well...” She shook her head. “Here we are, like fools standing at the bottom of a giant hole. Let’s all return home. We still have a lot do discuss.”

Comments

[Cloud Hop]

This has been a very interesting story to read both in terms of how the plot progressed and how it explores the implications of a machine so complex it literally simulates an entire universe.

From a purely mathematical point of view, however, I'm slightly baffled by this story's fixation on Group Theory. If one were to build a system this wildly complex, it seems like it would actually be based on Calculus of Constructions or Homotopy type theory, since both theories can act as both a foundation for mathematics and for creating a mathematically consistent programming language. Calculus of Constructions was notably used to prove several theories in Group Theory itself. It is possible that Group Theory only forms the interface to the device, but that also doesn't really seem to make much sense. If the system does not expose itself using its foundations, it seems like it would expose a highly abstracted interface based on Type Theory. In contrast, Group Theory is designed primarily for the analysis of mathematical structures, and is not conducive to actually writing a meaningful program.

It's possible that Group Theory here is a gross simplification of an interface that is actually built in a highly abstract language like Haskell that simply re-derives Group Theory inside the language to then construct even higher level abstractions. In this case, the machine is built on top of something like high-level lambda calculus, but builds it's interface on top of Group Theory, perhaps resulting in something so high-level we have no accepted name for it, like Inter-universal Teichmüller theory. This, however, makes the choice of Group Theory rather arbitrary, since whatever mathematical language the machine is using is so high level it can only be expressed in terms of some random theory somewhere in the middle of the ladder of abstraction.

Since readers are unlikely to know what Group Theory even is, I'm wondering why the story simply doesn't invent it's own name for whatever ridiculously high level mathematical language is being used here instead, as it would convey pretty much the same amount of information as "Group Theory". In the context of governing an entire universe, the result would either be a computational approximation, or a chaotic function with an effectively infinite Lyapunov exponent that could only be analyzed using tools from Chaos Theory and Bifurcation theory, both of which sound suitably exotic and could be used in place of Group Theory in a pure literary sense, but also hold up under mathematical scrutiny better.

I'm not entirely sure if the author had a mental model of what the interface actually looked like in terms of Group Theory, or if it was just something that was supposed to be "really complicated" and intended to be glossed over as "really advanced technology" and i'm just over-analyzing the fuck out of it because it had the words "Group Theory" in it. Then again I'm pretty sure this entire story is about how over-analyzing things saves the universe, so perhaps I'm intended to over-analyze it...?

I dunno, man.

[Colors]

8384231
This... this comment! It’s so beautiful!

My response, in contrast, will be disappointing. I’m sorry! Ahm, yeah, there is no deep reason why I chose group theory over type theory. It just jumped into my head when I wrote the second Sigma chapter and then I rolled with it. Uhm, I expected almost everyone to have no idea what it is, making it simply a weird name for something mathy...

On the other hand

It's possible that Group Theory here is a gross simplification of an interface that is actually built in a highly abstract language like Haskell that simply re-derives Group Theory inside the language to then construct even higher level abstractions. In this case, the machine is built on top of something like high-level lambda calculus, but builds it's interface on top of Group Theory, perhaps resulting in something so high-level we have no accepted name for it, like Inter-universal Teichmüller theory.

If I have that authority, I hereby declare this canon. The idea that divine machinery runs on functional programming (or something even more abstract) is (Even though I honestly doubt group theory would have any useful role to play there.)

I hope you stick around for the epilogue. Story isn’t fully completed yet. Oh, and for honesty’s sake I should add that you also know more about maths than I do. I had certainly never heard of chaos theory before. That would have been pretty cool as well.

[Cloud Hop]

8385003

My college refused to let me into the Computer Science major so I majored in Applied Mathematics instead, and one of the classes I took was all about analyzing chaotic functions that are impossible to derive solutions for, which seemed applicable here

You were doing such a good job of being consistent with all the math terms being thrown around that I honestly couldn't tell if you actually knew Group Theory or you were simply using a particularly fancy math word for effect (which was apparently the case). Regardless of the mathematical implications, this is an extremely good characterization of a highly intelligent character.

I look forward to the epilogue!

[Colors]

8385016

You were doing such a good job of being consistent with all the math terms being thrown around that I honestly couldn't tell if you actually knew Group Theory or you were simply using a particularly fancy math word for effect (which was apparently the case).

Hm... I must have been too modest in my comment for you to reach that conclusion. I for one certainly hope I do know group theory, because I have to write an exam (partially) about it in 12 days I just didn’t think too much about how it actually fits. I might have just liked the idea that it’s actually important, because it seems so awfully theoretical. Particularly finite groups, which we focused on primarily.

Regardless of the mathematical implications, this is an extremely good characterization of a highly intelligent character.

Thank you! Yeah, as you can probably guess, I strongly disagree with most portrayals of what highly intelligent characters would be like.

Ahm – I now feel compelled to recommend you this. It’s pretty much the greatest thing on earth, and based on our brief conversation I have a sense that you might appreciate it.

[Cloud Hop]

8385037

Aha, so you do know group theory, but you didn't actually contextualize it, you simply used it as technobabble. That explains how you were able to write such consistent mathematics. When you said you simply used it as "a weird name for something mathy" I got the impression you weren't actually familiar with it. In that case, good luck on that exam

I have read several chapters worth of HPMOR, but it's awfully long and I generally prefer Friendship Is Optimal over it. If I get an abundance of free time in the future I might attempt to finish it.

I have to point out that Group Theory would be applicable at a very low level when constructing a mathematical interface in Haskell, because Haskell doesn't have dependent types, so you only get to write one definition of a function inside your module. Hence if you need an element with just an addition operator, and another with addition and multiplication that itself can be passed into a function that only requires addition, you have to define both operators separately, and you wind up with what is essentially a monoid and a semiring, depending on which restrictions are used. When I was constructing a type system, I ended up with what is essentially a semilattice construct, and lattices are commonly employed when constructing type systems using type theory. However, this would be at a very low level and probably not meaningfully related to whatever the high level interface would be.