Chapters A Mathematical Theory of Hard Reset
“The life of every individual, viewed as a whole and in general, and when only its most significant features are emphasized, is really a tragedy; but gone through in detail it has the character of a comedy.”
The story Hard Reset is about Twilight Sparkle accidentally using a time magic while studying in the Canterlot Royal Library, and finds that every time she dies, she returns to the moment just after the completion of the aforementioned time magic. In detail, each time immediately after she dies, she would hear “Well that didn't work.” spoken by Spike, and when she opens her eyes, she would see herself standing in the library.
The reset time point is just hours before the changeling invasion of Canterlot, therefore she died a lot of times from all kinds of causes, mostly being mauled by changelings, but also including suicide by falling, hit by falling objects, mind-killed by Chrysalis.
After going through the cycle many times, Twilight managed to learn enough of the details of the events immediately after the invasion to perform the exact sequence of actions to survive, and kill Chrysalis, and save her friends, and help Celestia repel the invasion with minimal casualty. For some reason, Twilight thought this marked the end of the time-loop spell's effect.
It's been five years since the changeling invasion of Canterlot. Twilight Sparkle was still living in Ponyville with her friends. Spike was still working as her assistant. Mostly things had been the same. This followup story would work even if things had been significantly different, but it simplifies matters to discuss the situation assuming things had stayed mostly the same. There is no loss of generality.
One day, Twilight Sparkle died. The reasons are not really important, as it is inevitable, and it is crucial for this followup story to begin. Without loss of generality, we assume she died of poisoning while performing chemical experiments.
The stage is set and the story can begin.
“Well that didn't work.”
Twilight opened her eyes and see that she was in some library aisle. Spike was standing beside her, holding up some books. She blinked in confusion.
“Spike? How did... where am I?”
“Oh no! Did the spell mess with your brain?” Spike threw down the books and looked around agitated, “Should I go call a doctor?”
“Where am I?” Twilight demanded.
“The Canterlot Royal Library, Top Floor, Aisle B.”
Twilight blinked again. Her best hypothesis seemed correct, but the implication filled her with dread. “Spike?”
“Yes?”
“Don't call a doctor. The spell just 'bumped' me a bit, but now I'm fine.” she took Spike by the hoof, “Let's take a break.”
“Alright!” Spike leaped on her back, happy to get out of the stuffy library. Soon they were outside in the royal gardens. Twilight noted in dismay that the shapes of the clouds seemed awfully familiar.
They settled down in the shade of a tree. Spike quickly falls into a light nap. Twilight stared at Spike and contemplated whether she should test the hypothesis straight on or wait just a few more hours. She decided to wait a few more hours.
“Spike!”
The little dragon yawned. “Yes?”
“Come on now, let's not sleep away the afternoon. Let's go into the city.”
“But have you finished your research yet?” Spike poked Twilight's saddlebag, which was filled to the brim with scrolls, “Don't go have fun today, and tomorrow shake me up at 6 am for some 'emergency' research, again.”
“No, but... there would be time enough for that.” Twilight looked up to the piercing tops of the library tower.
Twilight waited, staring at the sky to the east. Spike was eating his second tub of ice cream.
Twilight saw black swarms gathering in the distance. She waited some more. She saw the black swarms come closer and resolve into individual changelings.
Spike dropped his ice cream and clinged onto Twilight's neck. “What's that?”
“It is true.” Twilight embraced Spike. “They are going to kill us all soon.”
“You can't just give up like that! … Go get Celestia! Luna!”
“There's no use. My friends are already dead and there's no life for me without them.”
“What? But they are on the train...?”
“The train was attacked about fifteen minutes ago by a subdivision of the changelings and they were killed.” Twilight shook her head, “I remember.”
Spike was sure Twilight has indeed gone mad, but the approaching black cloud was more concerning. “Please, we got to get Celestia. She will fix things.”
“There's nothing that needs fixing, and there's no fixing that lasts.” Twilight swinged Spike onto her back, “But since you insist, let's go anyway.”
The gallop to the throne room was stopped short by three changelings hissing at the gate. Twilight could read them like a stop-motion movie, relying on her muscle memory to knock them out in minimal time. Five years and I still remember. Good job.
On the throne sat Chrysalis, staring down at Twilight with a smirk. “Your friends are already dead, and soon you'll be too.”
“I know that, but soon you'll be too.” With that, Twilight shot several magic missiles at Chrysalis as a token of aggression. She knew that she has already entered a dead end and there's no point in playing along seriously. She was simply putting up a show for Spike to give him some false hope, so that his last moments would be less hard to swallow.
A Mathematical Theory of Hard Reset
Dealing With Potentially Endless Loops
“Well that didn't work.”
Twilight knew she needed time to think things through. Think everything through. Without Spike, without anypony. “Spike, please go to my parents' place. I really need time alone right now.”
“What? But...”
“Spike, we are going to my parents' place and I'll drop you off there for the afternoon. Please. I'll buy you ice cream.”
“Alright!” Spike hopped onto Twilight's back.
Twilight dropped Spike in front of her parents' door and galloped away before they came out. She arrived at the clear stream in the royal garden to think.
OK. I see. There is probably no end to the cycle. Friendship can't break time magic. I will be forever living in this time loop no matter what event take place.
What is certain anymore? Certainly, I remember correctly and I preserve my memories. Certainly, the changeling invasion will always happen hours after the reset point. Certainly, the clouds in the sky will always look like a tube of toothpaste slightly crusted no matter how many times I am reset.
...
The absolute linear time we have been using is completely wrong. Time is not a set of world-photos, order-isomorphic to the real number line. Time is not even an acyclic directed tree. Time allows loops, and approximate loops. Time allows me to branch off and rejoin an exact copy of a world-photo... Time is loopy and far more confusing than we thought.
...
Why me? Why is everything else a perfect copy every time I'm reset, but I am different? What makes me, me? What kind of magic would target me, excise me the moment I die, transport me, then plant me into this purple little skull right at the reset point? How does it figure out what is me and what is not me?
The buzz in the air was too loud to ignore. Twilight turned her head up to see the changelings shooting down, mostly into the central district and the royal castle. She leaped behind a bush and started shooting the changelings for fun. She scored six kills before two changelings landed in her bush and mauled her to death.
Twilight signed in relief as her friends embraced her. I don't remember the timing to be that tight. thought her.
“We thought we would never see you again!”
Twilight simply nodded in fatigue. “Please, later. I'm tired. Carry me to Luna's chamber for I want to sleep with her.”
Everypony gasped, except Celestia, who smirked and nodded, “I see. Very well then. Rest well, my faithful student. I shall arrange the victory ceremony later this week.” And she sent two guards to carry Twilight to Luna's chamber.
When Twilight entered the chamber, Princess Luna was waiting on her giant bed with rose petals, and a very unimpressed look. Twilight trotted toward Luna without so much looking up.
“Celestia told me everything. But seriously, just because you saved Equestria doesn't mean you have to be so... impatient. Can't you wait at least one measly day to go to the concert with me? It's not like I would refuse you after everything you've done.”
“I would if I felt like it, but right now I'm not in the mood at all.” Twilight kicked away some rose petals below the bed. “I'm tired of... being uncertain.”
“Fine. Come on then. You can have your existential crisis later.” Luna rolled to one side to allow enough space on the edge of the bed for Twilight.
Twilight climbed onto the bed and laid down, back towards Luna. She felt Luna's hooves cradling her from behind. “Stop. I don't want to have sex with you.”
“What?”
“I just want to sleep with you. My mind is in chaos and I can't fall asleep on my own. Make me fall asleep and meet me in my dream.”
Luna's gaze turned soft. She lit up her horn and in an instant they were both fast asleep.
Twilight's mind was indeed in chaos, not a patch of stability big enough for a stable dream to form. Luna had to make a dream herself before pulling Twilight into it.
“Twilight, what happened? Your mind is in turmoil.”
“This will sound crazy, and you will not believe me, but you must believe me. I beg you.”
“Calm down, my little pony. I will believe you.”
“Just before the invasion, I was at the library, reading books about time magic. In the Proceedings of the Fifty-third Conference on Time Magic, there was a construction that caught my attention because of its unusual generator set. I attempted that construction, and it had the effect of creating... a loop in time.”
“What do you mean?”
“I thought nothing happened at first since the construction just poofed into thin air. Spike shrugged and said, 'Well that didn't work.' And I thought I needed a break, so I walked outside and saw changelings falling out of the sky, and they killed me.”
“But you are standing here right now, talking to me. You survived!”
“I didn't. They bit me in the neck and I died a painful death. The strange thing was that, immediately after I died, I heard Spike say, 'Well that didn't work.' I opened my eyes and saw Spike standing there, in the same position. I was there too, in the same position, in the library, with the same book lying on the ground.”
“What do you mean?”
“I thought it was a bad dream, so I went outside to celebrate me being alive, but then I saw changelings coming down in the exact same way, and I knew that it was not a bad dream. I was killed again.”
Luna tried to hide her skepticism behind a concerned face.
“Then I heard the same words again. 'Well that didn't work.' I was going crazy. I knew I was stuck in a loop. You know? Like a recurring nightmare that you must dream through again and again, and die again and again, except this was not just a dream for me. I was reborn at the same place, at the same time, every time I died, and I was almost going crazy. I tried to kill as many changelings as I could. It didn't work of course, but it helped me destress and practice combat skills. I tried contacting you immediately after being reborn. It would usually result in us repel the invasion, but my friends would still be killed and I couldn't live in such a world. In the end, I managed to find out one chain of actions I must take, exactly, so that I have just enough time to save my friends, save Canterlot, and save Celestia and you.”
“OK... Suppose what you are saying is true... then I guess that does explain your extremely lucky way of saving everypony single-hoofedly...” Luna frowned, “But I still find it hard to believe.”
“Well, I'm not finished yet!” Twilight stomped the ground. “After that day, I reunited with my friends and went back to Ponyville. And I couldn't live without the cyclicity of time. Everything I did was done once and unchangeable forever. If I say something to somepony, I can never change what I said. If I go down the left road, I can never go down the right road – at least not at the same moment in time. I could go down the right road later, but I can never change my choice from left to right at that past moment.”
“Yes, yes. I see, my little pony.” Luna knelt down to face Twilight at eye level, “I understand now. You are afraid of the irrevocability of choices and the paralyzing fear that seizes you when you see the terrible power of choice you wield.”
“No! You don't understand!” Twilight screamed, “I'm not finished yet! I eventually relearned how to live through life without rehearsal, completely by improvisation, metaphorically. But five years later, I died. It was a chemical accident, I'm sure, because the last thing I remember from that time is some panicked shaking view of my lab.”
Luna wanted to say something, but stopped herself, afraid of interrupting Twilight again.
“Then I heard the words again. 'Well that didn't work.' Do you see now?” Twilight waited a bit before shaking her head, “Don't worry about interrupting. I'm finally, finished.”
Princess Luna ventured a guess. “You are still stuck in the loop. It has not ended, and you fear that it will never end.”
“Exactly! And I think I'm going mad...” Twilight dropped to her knees. Luna pulled her into a wing hug.
“Luna?”
“Yes?”
“How do you end a recurring nightmare?”
“It depends on the pony having the nightmare. The only long-term method is to find the root causes of the nightmares, but there are many different short-term methods. One is to stop dreaming by only having dreamless sleeps. Sometimes when the nightmare is truly terrifying, I will personally make sure the suffering pony to have dreamless sleeps until the root causes are found. I may also teach some dream-control techniques that decrease the intensity of nightmares to the suffering pony.”
“How would you end mine?”
“I... I don't know.” Luna stopped herself from speaking her true thoughts. The truth will be sent to Celestia, but there's no need to escalate Twilight's suffering when a little lie will sooth her. “But I believe in you. We will find a way to stop this cycle.”
Twilight's dream self dropped dead on the ground.
Luna opened her eyes. Twilight was still fast asleep in her hooves.
She sighed. The truth will be harsh, but she had to report to Celestia.
Twilight shot myriad things in anger, but they kept coming and she kept shooting.
“Twilight please. Calm down, we need to talk. Your friends are very worried about you.”
Twilight screamed, “What's the point? You won't believe me and I won't believe you anyway! So why don't you just give me more flying cubes to shoot at!”
“We are doing everything we can for your own good.” said the turquoise pony standing behind Twilight, “Princess Celestia personally commanded us to try everything we can to help you.”
“Well? The least you can do to help is to believe me and let me out of this confinement dream!”
“We understand it's difficult, but it's for your own good. The last time we let you out, you almost immediately tried to kill yourself.”
“I wanted to go back to the reset point instead of being stuck in this stupid dream with stupid ponies I hardly know about trying to stupidly help me with my supposed madness WHEN I'M THE ONLY SANE PONY HERE!!” Twilight doubled over to cough. She felt like she almost tore her throat in her impotent rage.
Several minutes later. She spoke again. “Look, can I... can I go back to my room?”
“Yes, you may. This session is over for now.” The turquoise pony entered a door and disappeared along with the door.
Twilight butted open her own door and flopped herself onto the ground inside. It was a perfect replica of the library home she had in Ponyville, down to the exact arrangement of books on the shelf. She leaped on her bed and rolled herself into the blanket. Spike's basket stared at her, empty inside.
Twilight wept, then considered her options. Suicide will have to wait, and she must never mention it again, not even think about it, perhaps.
It had been a long time, but it was worth it. Twilight Sparkle had finally regained her sanity.
The reunion at the hospital gate was short but passionate. The five friends of Twilight embraced her profusely before carrying her to a Congratulations-on-getting-out-of-hospital party in Sugar Cube Corner. Twilight smiled and waved at every attending pony at the party, and Pinkie kept piling sweets in front of Twilight “to make up for the unfulfilling dreamy food you've been eating for so long!”
After party, Twilight went back home and immediately went to sleep. Lying in the dark, she could notice the faint shine of some tiny reflective surface at some corners of her book shelves. Of course you would be monitoring me. She smirked. But I will get out of this mess.
Five months later, while helping Fluttershy caring for her animals, Twilight was mauled to death by a pack of timberwolves. Fluttershy was killed while trying to save Twilight.
Now, I know what you are thinking, is it really necessary, Twilight? Did you have to be so impatient? Even at the price of killing Fluttershy?
The answer is no, yes yes! It's not really necessary and I could theoretically have waited some more, but I was literally going to lose my mind if I kept on putting up the show for them. As for the death of Fluttershy, death is not as expensive as we thought, since we will meet again soon.
Thus thought Twilight as she rushed towards the throne room, following the flow of actions she had memorized.
Something broke her flow. A changeling was biting her hindleg.
Shit. I guess in this fight sequence there's no room for a flourish.
Changelings mauled Twilight to death.
“Well that didn't work.”
“Ha, ha, very funny, Spike. It's so funny you don't even know how terribly funny it is when viewed in the full context.” Twilight picked Spike up, “No time to explain though. Hold on tight!”
“We are gathered here to honor the perceptiveness and great heroism of one pony, Twilight Sparkle, who...”
Twilight kept smiling and waving. It's her third time listening to the exact same speech and the novelty is starting to wear off, especially since it's so long and contentless, full of big words with little meanings. I pity the audience. They must feel so bored.
So what should be the plan?
The plan would be, first and foremost, keep up the secret. If I don't, they will trap me in the hospital again and that would waste my time, harm my sanity, all for nothing.
Twilight returned to Ponyville with her friends. She thought hard about the course of action she will take.
I want to – need to – convince Princess Celestia that the loop is true. Otherwise I would really go crazy from holding the secret on my own, having nopony to talk about it with.
To truly convince her, I should perform some repeatable action that is almost impossible to perform without the loop, but relatively easy to perform with the loop.
The defeat of the changelings would be enough, if not for its nonrepeatability. I need some very difficult task to perform, and it must be repeatable, in order to convince her to arbitrary precision. Public lottery ticket number should do the trick. They are a powerful source of pseudorandomness that is very difficult to manipulate.
There are about five lotteries operating in Canterlot. I can memorize their numbers and demonstrate to Celestia that I can predict them. This will convince her, and if it doesn't, I can memorize another set and demonstrate to her twice in my next cycle.
A Mathematical Theory of Hard Reset
“44, 11, 42, 8, 28, 41, 33” Twilight chanted as she leaped out the window to her death.
“Well that didn’t work.”
Twilight executed the sequence of actions to save her friends.
“We thought we would never see you again!” cheered Pinkie Pie.
“Celestia, I want to tell you something in private.” Twilight looked at Celestia tiredly.
Celestia nodded. “Meet me in my chamber in two hours.”
Two hours later, Twilight entered Celestia's chamber, and Celestia is lying in bed with rose petals floating around the room, despite there being no wind in this indoor location.
“No, I'm not here to have sex with you.” Twilight rolled her eyes. “I mean, I didn't intend to, though...”
“Well? I'm listening.”
“I mean, this is a tempting offer.” Twilight blushed, “But I have more important issues than just having sex with you.”
“I can only spend about an hour with you in private, so make your choice quickly which to do first.”
Twilight decided to have sex first. Unfortunately it took a bit longer than expected. Oh well, thought her as she dozed off on a really soft pillow, I will tell her tomorrow. The lottery isn’t out until Friday.
On the next day, Twilight sent Celestia a letter.
Dear Princess Celestia,
Please keep the enclosed scroll unopened in a tamper-proof chest until this Saturday.
Your faithful student, Twilight Sparkle
In the scroll was the lottery number along with the explanation.
On Friday, Twilight opened the newspaper in the castle suite, but to her dismay, the Canterlot Lucky-7 for this week was 14-21-40-23-11-21-29, bearing no resemblance with her prediction. Thinking fast, Twilight wrote another letter.
Dear Princess Celestia,
Please don’t open the scroll. Burn it up instead. It’s really important for me.
Your faithful student, Twilight Sparkle
Several days passed and not a word from Celestia. Twilight sighed relief. I suppose she did do as I asked. Good. At least they won’t send me to the hospital this time.
Twilight returned to Ponyville, now that there was no point for her to stay in Canterlot. She put up a show of normality during the welcome-back-party, but in the evening she dived into her books and let her thoughts race through.
Why didn’t it work? There are mainly two possibilities. The first possibility is that the world has fundamental randomness. The second possibility is that the world is deterministic, but some events in it are chaotic. They are so sensitive to initial conditions that unless I perform the exact actions, they will be different.
The subtlety between a strike to the chin and a strike to the snout is the difference between a second of my victory, which is the difference of a few seconds for the time Celestia leaves the throne room after commending my victory. This difference changes the walking flow of ponies outside the castle, and so on. When the lottery is drawn, the initial difference changes to a completely different set of numbers.
Twilight Sparkle felt the pangs of loneliness in being the only pony knowing the cyclicity of her time.
Alright, time for plan two then. If lottery is too chaotic to be used, I could use some other proof that I have really experienced excess time than what is apparent. I can study a lot, a lot more than I could have ever done, then show my knowledge to Celestia, thus proving that I did experience excess time.
This was an electrifying thought, and Twilight eyed the books around her with hunger.
Finally enough time to read them all.
She briefly contemplated ditching her friends immediately and going back to Canterlot to study a Bachelor-PhD joint program in Meteorology, one of the subjects that she had always wanted to know more about, had no specialist knowledge in, and she knew that Celestia knew that she had no specialist knowledge in it. But she shot down the idea, because it would be very lonely, and she needed all the psychological health she needed to face the potentially infinite time ahead.
After reading through the list of Dewey Decimal classes, she settled on making deep studies in five fields: Old Alpine Language, Physical Combat, Mathematical Physics, Alchemy, and Piano.
Old Alpine Language is the language of the unicorns before the Hearth-Warming Unification. Some very ancient unicorn spells are still untranslated from Old Alpine, and even those that are translated tend to work better when cast in original Old Alpine. Twilight has taken basic courses in it, sufficient for working with the occasional encounters, but she has always wanted to take an extensive course in it, to truly cast Starswirl’s spells through Starswirl’s tongue.
After battling the changelings for hundreds of times, Twilight had reformulated many points of Physical Combat on her own. Still, serious systematic training will be useful, both to make her final demonstration more impressive, and to deal with roadblocks in the potentially infinite future.
Mathematical Physics is the rigorous study of how the world works. Magic is practical physics, but practicality cannot suffice for this situation she is in. She needed mathematical precision in getting to the bottom of the mystery. Besides, the study of mathematics has always had a cool, austere effect on her mind. It is calming to immerse herself in the contemplation of mathematical entities. And if I cannot escape, at least maybe I can find solace in such studies.
Alchemy (aka Chemistry) has never been her strong point. She could perform the experiments assigned to her in school and pass the exams with high scores, but she did not enjoy it and did not take elective classes in it. This had always left a vague guilty feeling inside her, since she felt she had a responsibility to be good in all fields of magic, and such a defect must be fixed.
And the study of Piano? That is mostly an... insurance for the future. It is said that for musicians who have suffered great amnesia, they often still retain their full musical ability, and while they are playing their music, appear almost the same as before suffering the amnesia. So if I eventually lose my mind, maybe a bit of me can hang on in music.
Life is short and the study is long, but for Twilight, life had suddenly become a lot longer.
Of the five studies, she started with Physical Combat training, since it was directly useful for fighting the changelings every time she was reset. First at the local gym, she progressed to a four-year full-time study in the Canterlot Military School. Celestia was a little bemused by Twilight’s sudden change of study direction, but was mostly convinced by her explanation that it was the experience in the changeling invasion that prompted her to study physical fighting.
In order to protect her psychological health, Twilight convinced Rainbow Dash to quit her weather control job in Ponyville to come along and study together. After graduation, Twilight and Rainbow joined the elite task force in Equestrian army, further honing their battle techniques.
Eventually, Twilight felt she had learned enough to consider herself an expert in physical fighting, and she felt it was time to go. So she took a holiday on her own to the Northern Mountains and killed herself there, making sure her corpse was unrecoverable.
“Well that didn’t work.”
Twilight grinned as she saw herself back to the familiar place. She grabbed Spike and galloped full speed downstairs, but soon stopped. She felt that her leg muscles were aching and sour.
Oh, of course. Twilight facehoofed. My strength is not transported even if my muscle memories are.
She started going at a more appropriate pace, which felt uncomfortably slow to her, after living in a strong body for so many years.
Oh well! I still have my reflexes, and can still use most of the techniques for balancing and transferring of momentum. That ought to be good enough.
Unfortunately, as it turned out, she still needed time to adjust to her new old body.
“Well that didn't work.”
“I’m sure this time it will work.”
Eventually, she found the subset of techniques she could execute in her old body, and with these, she found that it was possible to pass through several chokepoints that were previously impassible. A major rerouting followed, and in the end she managed to find a route that allowed her to consistently complete the level a bit over ten minutes faster than she could before, which translates to about 30 less dead ponies per invasion.
Satisfied with her progress, Twilight started her study of Old Alpine. Convincing Celestia to allow her to change her study focus was easy, as she has always expressed an intense interest in all things Starswirl-the-Bearded-related. However, this time it was more difficult to balance her studies and friendship, as the study does not even remotely interest any of her friends, and the local institutes does not offer good courses in Old Alpine.
After one semester of full-time study in North Royal University in Goattenberg, she felt that long-distance relationship didn’t work out, so, per Celestia’s suggestion, she obtained a private tutor in Old Alpine so that she could study in Ponyville.
Old Alpine’s sound system has been perfectly preserved, since it was carefully codified by ancient linguists who tried their best to describe their language accurately, down to the smallest detail, for the very practical reason that even the smallest change in the language affects the effect of spoken spells.
Due to their obsession with the sound of their language, the ancient unicorns didn’t use a writing system until late in history. They instead preferred to recite everything, since that is the only way to ensure perfect copying of pronunciation, intonation, and even hoof gesture that accompanies the recitation.
To ensure perfect recitation, ancient unicorns developed a system of “coded recitation”, wherein a given block of words is broken into separate syllables, then weaved together in a few different ways. By reciting the coded versions of the same block of words, and comparing them, it was easier to detect a mistake in recitation. Through this technique, they achieved almost perfect collective memory.
The Book of Seas and Mountains , an Old Alpine work of literature, remained unwritten for over one thousand years after its composition. Throughout that millennium, the existence of this book relied on the memories of each pony who recited it. And when finally the unicorns adopted writing from pegasi and earthponies, they gathered around every one of them who could recite the book and started reciting. It was immediately clear that everypony recited the same book, and on every syllable, at most one or two ponies would recite a different syllable from the others. The book was thus written down in the span of days, and it is the one and only version.
As Twilight studied deeper into Old Alpine, she kept noticing bits and pieces of it poking out from modern magic spells, like an afterimage from the past. Three years’ studies exhausted her tutor’s knowledge, and to continue her studies, Twilight got hold of the seven-volume set of Starswirl’s Collected Papers, Notes, and Related Works, in original Old Alpine.
One day she found herself able to understand memes among Old Alpine researchers. At that point she decided she has learned enough. As a last validation of her competence, she wrote an article on the reconstruction of a corner case of Old Alpine adjectivals. It was published.
Feeling her work done, she locked herself in a room and swallowed two bars of copper, the most proper method of suicide for the ancient unicorns.
As she rolled on the ground in agony, she understood why this method was so highly praised in the books: because whoever could suffer through it without rolling on the floor in agony demonstrated the highest mental fortitude.
“Well that didn’t work.”
“You tell me! Just what were they thinking! I can't even start to – ” Twilight growled at Spike, who recoiled with fear. “Oh, sorry, I was... Never mind!” She picked up Spike and gave him a little hug of reassurance before galloping out.
Twilight noted with joy that her twelve-year long foray into the dusty books did not decrease her knowledge of physical combat significantly. Memories were quickly refreshed as she fought her way again and again through the changeling crowd.
For the next subject, she chose alchemy. Thanks to her previous training, she knew enough to start studying on her own, but she also met with a mentor weekly for guidance.
There is nothing much to say about these years, other than a steady increase of experience and knowledge. She reads books in Old Alpine from time to time, just to keep the knowledge afresh.
After last time’s terrible experience, she decided that ceremonialness in death is overrated. Far better to choose a painless method. So she mixed some sleeping potion to sleep away this life.
The next life was spent on Mathematical Physics. This was basically what she had been doing all along, so there was really nothing particularly out of the ordinary for her happening in this life. There were some occasional adventures, but nothing dangerous enough to interrupt her studies with death. Well, almost nothing. She eventually died in some adventure out on the sea, but she had already learned quite enough about Mathematical Physics, such that she shrugged it off and continued on with her next project.
The next life was spent on Piano. This was the largest departure from Celestia's plan for her, and as a result, it took some effort for her to convince Celestia to allow her to have a sudden career change. It went somewhat like this:
“Princess Celestia!”
“Yes, my faithful student?”
“My traumatic experience during the changeling invasion has convinced me that life is really meaningless and there's no point in pursuing magic studies that I don't really like!”
“But... I thought you loved magic? Magic is your special talent, and your passion?”
“Yes... but I feel like I have known enough magic already. I already have studied my subfield of choice to the level of current research, and all the other subfields that I care about are also at least at graduate level. And... I feel a bit tired of magic. All I'm going to understand by going for more magic studies is polishing and refining.”
“And what is your plan?”
“I plan to have a career change. I want to learn to play the piano.”
“Dear Twilight, are you sure this is what you really want? I am not saying that it is a bad idea – I will support your decision if I think it is what you really want and is good for you, but it would be a great change in your life and you must understand the consequences.”
Twilight rolled her eyes. This is getting quite troublesome. “It is not as serious as you are understanding it to be. I just want to take a break from magic, OK? I'm not saying anything permanent, but I really want to learn the piano.”
Celestia rolled her eyes. If she actually become a piano player, I'd need a substitute for her. “Alright, I respect your choice. You are hereby allowed to suspend your magic studies and begin piano studies.”
Thus began Twilight's fantastically out-of-character foray into piano-playing. She studied under Doremi, a pianist in Ponyville. She would still read up some of the magic books in her library, to refresh her knowledge here and then, but did not extend into new studies.
Twilight thought her experience in fighting might come into use for piano-playing. It didn't. Five years of full-time piano practice later, Twilight finally learned enough to play professionally. Then she settled in Canterlot, bringing Rarity and Pinkie Pie along to make sure she had sufficient supply of friendship. With the help of a reluctant Celestia, she joined the Canterlot orchestra and eventually played alongside ponies like Octavia.
It's funny, really. How I could save Equestria twice, and yet ponies didn't really pay as much attention to me as one would otherwise expect. Sure, they respect me and random ponies on the street say hi to me all the time, but that's about it. And I don't get a lot of money either – not that I need much money, but it's funny how I don't get showered in rewards for saving the world.
Now that I'm a pianist at the orchestra, I actually get fans. Not a lot, but fans nevertheless. And money! Even by Canterlot standards, I can live and look like high society – which is kind of useful when I accompany Rarity to her very important boring parties. Ponies really pay a lot of money for good music...
Enjoying playing the piano had always required some mental fortitude for Twilight, but gradually even mental fortitude became insufficient. She could keep her skills without too much trouble, but pushing forward was too much of a bore. The only thing left to do was a melodramatic exit.
What would be the most melodramatic exit? I could... kill myself on stage, which could be preceded by a sorrowful piano solo.
In the empty hours of the music hall, Twilight choreographed her dramatic exit carefully. She had to check herself from adding too much to the performance. After the solo is finished, everything must be completed within 5 seconds.
The day came. Twilight played her solo, a piece of Nocturne in minor keys. Then she stood up in the applause and proclaimed, “The rest is silence.” She then stepped two steps back and bit hard on the cyanide capsule in her mouth.
Oh the drama... If only I can live to read the newspaper next day, to see what the ponies would say about this!
A Mathematical Theory of Hard Reset
What is required is a rethinking of the whole strategy.
What is required is more friendship. And by friendship I meant experiments and studies and thinking.
Twilight looked outside her library window. She had lived in this place for an accumulative... 63 years, and is soon going to celebrate the 64-th anniversary. She had tried to keep a complete chronology in her head, but lost interest in such a thing. Continuity of a personal history is not that important when it’s quite clear that there’s something suspicious about the whole “continuity” thing, so she settled for keeping a few numbers in her memory, just enough to provide a comforting sense of continuity, but not enough to burden her mind.
She felt tired and weary, felt not in the mood of acting her age. Actually, I am going to be the oldest pony soul, in fifty years or so. Other than the princesses, nopony has ever lived longer than 200 years.
“Twily?”
“Hello, Fluttershy.” Twilight replied, her gaze still fixed on the gray skies outside the window.
“I bought some salad and pasta for tonight, and um... You look... sad.” Fluttershy put down the shopping bag on the kitchen table and came behind Twilight, “Is there anything wrong?”
“Nothing, I’m just reminiscing. Of times long gone past.”
“What times?” Fluttershy sat beside Twilight and followed her gaze.
“Just... times. I don’t even know how they came. I guess the gray sky reminded me of the day we went to the northern mountain to talk to the sleeping dragon.” Twilight pointed at the snow-capped peak in the north, “Remember that time? It feels so long ago.”
“It’s just...” Fluttershy counted on her hoof, “Four, no, five years ago, Twilight.”
“Is it? But it feels longer for me.” And it is not just a feeling.
So they sat together and reminisced about the past times.
It was after dinner when Twilight decided to cut her nightly studies short. After she started dating Fluttershy, she had chosen Old Pegasian Language as her main study project, since pegasus culture just got a lot more interesting for her. The end of the study was not in sight, but she was making steady progress.
Instead of studying the Old Pegasian declension system, she opted to simply go out for a walk with Fluttershy.
“Consider. Fluttershy. Do you believe in reincarnation?”
“I usually don't think about such things, Twilight. If I am reincarnated, I certainly don't remember what happened last time, so it makes no difference.”
“But what if this is the first life of yours?”
“Well, nopony remembers their previous life, are they all in their first life?”
“Yes of course. I know all that. It's just making conversation.” Twilight looked upward. “But if there's a next life, would you want to stay with me again?”
“Yes, though I can't make decisions for my next life.”
Twilight tried to say something poignant, but realized that the only thought inside her was something to the line of “If we blow this up, I can just try again next life.” and that disappointed her deeply, somehow.
Is it disappointment about this nonchalance? It can't be. This nonchalance is not my fault. It's just how things work: if things fail to go my way, I can always fix it next time. Romance is no longer a scarce resource, friendship is no longer a scarce resource, nothing much is scarce for me, because life itself is no longer a scarce resource.
Maybe it's just the ghost of my long-dead desire for true understanding. No pony can truly understand the loneliness of Twilight Sparkle, the time-traveler, for they might as well live in a different world from mine.
After a pause, Twilight chose the safest response, “Well, that is true. More reason for us to cherish this life.”
And as expected, Fluttershy smiled and nodded. Twilight studied her face carefully from the corner of her eyes while pretending to look at the moon, assessing if Fluttershy had been sufficiently pleased with this dialogue, and whether new dialogue options had been unlocked.
In the story of Macbeth, a classic tragedy by Shaken Pearls, a general, goaded by her husband, murders her queen to take the throne herself. Then they become paranoid and murder more and more ponies in order to stay on the throne. Eventually the husband suicides due to guilt, and Macbeth is killed in battle by the daughter of the ex-queen.
Now, it would be hard to adopt this play for me. To begin with, Equestria has two queens, or princesses. Second, I'm not a general, but a student of one of the queens. Third, nopony would play the role of the husband. Maybe Rarity will do the role just fine, but so far, all routes that leads to marrying Rarity would end with her business running smoothly, and then she would not have sufficient ambition to play the role of my murderous spouse.
Hamlet would work even less. Celestia's sister is already a queen, there's no reason for her to usurp. and I'm not Celestia's daughter. And there's no way in Tartarus I can make it so that Luna marry my father. Yup, doesn't work.
Romeo and Juliet... No. There's no family feud I can think of among ponies I know.
Doctor Faust... Well, I am a scholar who has a lot of disillusionment and desire for drama as opposed to powerless knowledge, but where am I going to find Mephistopheles? I can... just make my own take on the play.
Twilight sat on her bed in the dank cell, replaying scenes from her life in her head. She left the plain-boiled broccoli and cauliflower untouched on the bench. It tasted alright, but she knew hunger let her thoughts wander more lightly. With measured words, she was whispering toward an imaginary panel of literary critics.
“And I do believe that the part where I escaped from the guards was good, but I probably over-highlighted my recklessness when I sacrificed Spike to keep them off my trail. Now that I think about it, I might have overplayed the entire concept of 'sacrificing everything in pursuit of knowledge'. Studying the nature of the elements through lethal medical experiments might be understandable, given that the protagonist genuinely believes that it is fundamental to the survival of Equestria, but to do so without any attempt at ensuring her subjects are subjected to the minimal possible pain just seems unmotivated. Although in light of the fact that I am trying to be dramatic, the lack of realism should be at least excusable.
However, overdramatization is not the main problem that plagued my play. Rather, it was the reverse. At quite a few scenes did I fail to emote properly, the most gratuitous instance of which is the first experiment scene. I was supposed to be doing the experiment for the first time, and as such, I ought to have been nervous, amateurish, and make a gory mess, followed by a hasty cleanup and weeks of forced composure and guilt-ridden soliloquies. Instead, I was too calm, too smooth. Nopony suspected a thing – which made the rest of the play easier to perform, but it still blemishes the realism.”
She paused to hear a question raised by the critics.
“My conjecture is that I'm emotionally oversaturated after preparing and rehearsing this play for an extended time. Writing the script was easy, but rehearsing took me at least six, seven lives before I cut out all the impractical parts and finalize the script, and after rehearsing for about thirty years, I might be excused if my emotive ability failed me from time to time.”
She paused and bowed.
“Thank you, and for my next production, instead of another epic tragedy, I will consider one that is more light-hearted. I could do a rerun of the Lady and the Trump , or maybe try developing a new play with Pinkie Pie – ”
Twilight was broken out of her thoughts by a harsh yank on her chained collar.
“Sorry, it's the cue for the final scene. We'll continue later?”
Twilight was walked out of the dungeon to an elevated platform in the castle courtyard. The executioner was waiting. Tradition held that the executioner must have dark red coat, so that the blood does not stain their coat visibly. Beside the executioner stood the executioner's scribe.
“Does the condemned wish to speak any last words?”
“All the world's a stage, and all the mares and colts merely players. I see how a conversation ends before it starts, and the only function of it would be ritualistic enactment, like performing a play...” Twilight laid her head on the block, “I saw it would end this way before it began. I regret nothing.”
The executioner's scribe wrote down the words as Twilight spoke, then she wrote down the reaction of the crowd as Twilight's head bounced out of the basket and rolled around its horntip, like a cone rolling around its apex.
A Mathematical Theory of Hard Reset
I'm terribly bored. The world is not enough. I have tried saving everyone and killing everyone, and it's not enough. There are still more books to read but they are kind of the same anyway. I mean, there's no need to read yet another book on algebraic geometry when you have already learned it three times, and even novels start feeling the same after having read maybe a few thousand ones.
I'm afraid of falling into a fixed point, an infinite loop where I repeat the same actions, the same thoughts, like a record on repeat.
Maybe bringing some others along with me will be the key to breaking the monotony. What if I cast the spell on somepony else? Would they come along with me?
Twilight's thoughts drifted to Lyra. She has always been so energetic and adventurous, with a big heart... if anypony would be happy with joining the adventure of time loop, it would be her. She has always wanted to break free from the normal, “boring” world that we live in... I should at least give her a chance.
Twilight thus became Lyra's friend, which was easy, as she was extroverted and excitable.
Several months into their friendship, Twilight finally decided it was the right time to talk to Lyra about her plan. “Lyra? We need to talk.”
“Gasp! I know it!” Lyra pressed against Twilight's chest, “You stole the cheese from the fridge didn't you?”
“Yes, but that's not what I'm getting at.” Twilight rolled her eyes and gave Lyra a new piece of cheese, “Here you go. Now could you sit down a while? I need to say something important!”
Lyra tossed the cheese in the fridge before sitting down. “Well?”
“Have you ever wondered how I came to know so many things?”
“Because you are really smart and hard-working?”
“That's necessary, but not enough. Nopony could ever learn ten languages, play three instruments, know practically the entire spectrum of mathematics, physics, and magic, know the entire history of Equestria, and many other skills I don't ever care to recall, all in thirty years!” Twilight grinned a little in conceit. Listing her achievements was one of the few things that consistently brought her joy.
“Wow... I didn't know you know ten languages.” Lyra looked on with wide eyes.
“Do you know how I came to know so much?”
“Because... Princess Celestia broke open your skull and poured all the knowledge into your brain?” Lyra poked at Twilight's forehead.
“... No. Nice imagery though.” Twilight stood up for dramatic effect, “I'm an immortal time-traveler.”
“What.”
“The details will come later, but for now, here's the summary... Remember the changeling invasion of Canterlot?”
“Yes, what is it?”
“Hours before the invasion, I was in the library studying a book. I tried a spell in it, and it gave me the ability to live in a time loop. Basically, if I die, then the next thing I know, I was back to the moment after I cast the spell, in the library. I would retain all my memories, but everyone else wouldn't.”
The night continued on as Twilight told Lyra of curious stories of her travels through the time loops, but making sure only telling the presentable bits. The gory details must wait until later, if they would be spoken about at all.
A Mathematical Theory of Hard Reset
Several days later at Lyra's home, Twilight was teaching Lyra the basics of time-traveling, drawing diagrams on a board while doing so.
“Let's call 'soul' that which is preserved every time I die, and not be concerned about what exactly it's made of. It could be simply be a part of my brain made of physical material, or some special nonphysical thing that interacts with my brain in some way, or just a special mathematical pattern of my brain.
Now, when I'm still alive in a world, my soul is connected to the world, experiencing it through a body. But every time I die, my soul is disconnected from this world, and immediately connected with a world that, other than my soul, is exactly the same as the world that I was first connected to, up to the reset point.
Just how many worlds are there? Possibility one: every time I disconnect from a world, that world stops existing. This way, there is no simultaneous existence of worlds. There is always at most one world existing at any moment.”
Twilight drew a diagram on the board.
“But there's a problem with saying 'two worlds exist at the same time', since it seems to require a way to measure time outside of the worlds. We have to imagine all the worlds as floating around in some hyper-world, and that there is a hyper-world time, with which we can meaningfully say something like 'This 4 o'clock happened before that 4 o'clock.' That sentence would mean, 'In hyper-world, this world's 4'clock happened at the hyper-world's 14 o'clock, and that world's 4 o'clock happened at the hyper-world's 19 o'clock.'”
Twilight ran her hoof along the “Time” arrow on the top of the diagram, “Here, we are showing the time in hyper-world as a straight line, along which the many worlds are arranged. And we see that in this model, no two worlds exist at the same time.
Now, consider the following question. When I die in world A, does the magic create a world B that is an exact copy of the world at reset point, and put my soul into that world? If that is so, what happens to world A? Does it get immediately destroyed, so that when seen in the hyper-world, there is no world A beyond that time? Or it just goes on without me, and my friends mourn my death in world A while I keep on living in world B?”
“Either way, what about the other souls? They have no continuity, unlike my soul. Anypony other than me does not remember anything from the previous worlds. They always begin exactly as the ponies in the first world I was in, and no change in one world would carry over to the next world.
Suppose other souls exist and are made in the same way as my soul. My soul might be unique – or copied, but there's no way for me to tell unless I could see it in hyper-world – but their souls must be copied.”
Lyra asked, “How did you know that?”
Twilight replied, “I have made experiments to systematically probe the extent of soul-copying, in the following manner: I took a map of Equestria and chose by random twenty cities. I then traveled to these cities and made friends and acquaintances in these cities, of all species – pony, griffin, and others – then I revisited them in the next lives to see whether there is any recollection from their past life. There was no retention of events beyond the reset point. I also checked if they would have memories and personalities that are different with their previous life, for example, I would ask them if they went to a certain school when they were 6 years old, or ask about the details of some pivotal event in their life that occurred before the reset point. There were almost no inconsistencies. The inconsistencies that did occur were minor and could be attributed to memory errors.
Thus, I determined that the soul-copying applies to all souls everywhere, and the copying is practically perfect, and they are always copied from the original at the reset point.
This seems extremely unlikely, for such a spell I made to always copy all the souls in the world repeatedly. It would be far more likely for the spell to affect only me personally.”
Lyra asked, “'Unlikely'... Why is that?”
Twilight replied, “It's a principle of magic theory, that is hard to experimentally verify, but makes intuitive sense, and explains a lot of phenomena. It's called 'The Locality-Energy Correspondence', and it states that the 'extent' affected by a spell is proportional to the 'effort' required to cast it. For a spell to affect a large area, such as all of Equestria, requires the power of at least a thousand ponies. I performed the spell alone, so I have reason to believe it only affected me specifically.
So let's assume that the spell does not affect any souls except my own. Then where did all the extra worlds come from? Maybe in the hyper-world, all possible worlds already exist. Like in a giant garden, all the worlds are trees that grow higher and higher as their history unfolds. The spell simply transports my soul across them.”
Twilight drew another diagram on the board.
“But then, suppose upon the death in world A, my soul is transported to world B, at the reset point, then what happened to world-B-Twilight's soul? Did her soul get destroyed? Lost in the hyper-vacuum between the worlds? And if that were the case I must have killed hundreds of alternative-Twilight's souls by now, that means the spell can kill a very large number of souls across the hyper-world. Thus the spell has an extremely powerful and non-local effect, which as I said, is very unlikely... Or maybe not. Metaphorically speaking, maybe this spell has made my soul a kind of mobile parasite.”
Twilight dragged her hoof along the arrows on the diagram.
“After I experience death in world A, I split free, swim across the hyper-vacuum to an uninfected world B. Then I find the reset point in world B, kill the oblivious world-B-Twilight, then attach myself. This is certainly too much metaphor, but at least it makes it at least possible to think of this as a model of how the spell works while also assuming that the spell can affect only my soul, and maybe a little bit of space and time around me.
But this can't be true either, for, suppose I died in world A at 2 years after reset time, then I must swim to world B, then crawl backwards in time for 2 years before injecting myself into world B at reset point. Now, what would happen to the 2-year-long chuck of world B's history after the reset point? Did it just get chopped off, since, after my injection, world B's history after reset point will unfold in a different way?”
“Maybe there is only one world-tree in the hyper-world that has branches everywhere, each branch starts a different way the future can unfold. Yesterday, I bet a coin throw with a pony, and at that place, the world-tree branched into many branches. In some branches, I win the coin, in others, they win the coin, and in yet others, the coin rolls away.”
Twilight drew another diagram.
“In this case, the world-tree must have the ability to constantly generate new branches. A simple coin throw makes many branches, and the tree must branch out enough to allow them all to happen in some branch. The world is copied all the time, the souls are copied all the time. It's now a thing that the tree does, not my spell.
Every time I experience death, I detach from the branch I'm one and attach myself at the reset point. The tree then grows a new branch at the reset point, and I would kill the alternative-Twilight, which was just copied in that branch, and inject myself.”
“This is where I have gotten so far. It stands better than all the other hypotheses. It involves only local effects, and explains copying as an inherent ability of the world itself.”
After Twilight gave Lyra a rough sketch of the theory and practice of time-loop traveling, to Twilight's satisfaction, Lyra enthusiastically agreed to become a time loop traveler, so she took her under her tutorship.
One day, a few months into the tutelage, Twilight was lecturing to Lyra about implications of the spell on Lyra.
“Suppose Twilight and Lyra are currently in world K, at time '+5 years after reset point', and Lyra casts the spell on herself. Then what will happen? Lyra will live on for a while, then she would die, and her soul would go back to world K, at her reset point here, and get a branch of the world, leap onto the newly-copied Lyra's soul, kill her, and inject herself into there.
What would Twilight observe? Well, the moment after Lyra's reset point, the world splits into many branches, and it would depend on luck what future branch this Twilight would go down. Assume that there is equal probability that Twilight end up on a certain branch, then the probability that she end up in a branch that contains 'time-traveler Lyra' is N1/(N1 + N2), where N1 equals number of new branches of the universe created by Lyra's time-traveling, and N2 equals number of universes that would have branched at that moment if Lyra doesn't time-travel.”
Lyra asked, “Aren't N1, N2 both infinite?”
Twilight replied, “Let's ignore time-traveling for a moment, and just consider how the world should branch. From each state of the world, shouldn't there are an uncountably infinite number of possible worlds that could follow? For, if a coin can land 1 mm to the right or 2 mm to the right, shouldn't it also be that it can also land with any distance in between? Thus, the number of possible worlds should be at least the number of real numbers, so N2 is uncountably infinite. But Lyra, since she can only travel back in time for a countably many number of times, N1 is countably infinite. So...
N1/(N1 + N2) = 0
In other words, Twilight almost certainly will not meet a time-traveler Lyra. She will find herself going into a universe where Lyra has time-traveled exactly 0 times.”
Lyra asked, “So... you think that, just after I cast the spell, you will find yourself meeting a Lyra that is quite clueless and unsure if the spell had worked?”
Twilight nodded, “Exactly.”
Lyra looked at her suspiciously, “But I thought you said you wanted to teach me because you wanted to find somepony that can truly understand you.”
Twilight replied, “Yes, but I also want to help you find your adventure. Besides, maybe my calculations were wrong and I could meet you with positive probability. We have to give it a try to know.”
A Mathematical Theory of Hard Reset
The day had come when Lyra would cast the spell.
They stood in Twilight's library. There was no light except the faint light from a table lamp. They embraced in expectation of what is to come, then Lyra started casting. Mist of spacetime distortion surrounds Lyra, reforming her soul to give her the ability to travel through the time loop.
“Did it work?” Twilight blurted out as soon as the reformation was over. Despite experiencing the event thousands of times, this was the first time she saw it being completed on somepony else.
Lyra blinked and stared at Twilight with ice-cold stares. “Look, I have been through this for... hundreds of times, and it's always the same, the same tremble.”
Twilight trembled under the gaze. Thinking fast, she opened her mouth, “So, does that –”
“Yes, you are meeting the time-traveler Lyra, or should I say, a time-traveler Lyra.”
“A?”
“Remember the nights we spent discussing the probability you would meet the time-traveler Lyra? Remember the N1 N2 formula? Of course you do. It was recent for you, unlike for me...”
“Which was more like two millenniums ago?”
“Exactly. We thought the probability is zero, but we were wrong. N1 is also an uncountable infinity. In fact, it's an infinity at least the same cardinality as N2, and N1/(N1 + N2) is substantially nonzero. In fact, it's quite likely to be exactly 1.”
“What cardinality is it?”
Lyra shrugged, “It might be the cardinality of the real numbers, or 2 to its power, or to its power 100 times, whatever. It's independent of ZFC, ZF plus GCH, ZF plus AD, ZFC plus V equals L, and a whole other bunch of set theories we have tried throwing at it, at least without assuming a few more untestable hypotheses. All we have managed to show, and all that matters, is that N1 is at least as big as N2.”
“But why?”
“Because I also branch. Immediately after you cast the spell, the one and only time-traveler Lyra started to be copied with the rest of the world, and immediately there were many time-traveler Lyras, all able to travel back to the Lyra-reset-point and jump into new own branches from that point. Since Lyra's world continues to branch into about N2 copies every moment after Lyra cast the spell, there will be at least N2 time-traveling Lyras, all jumping towards the Lyra-reset-point. And that's why N1 is at least as big as N2.”
Twilight's mouth dropped wide open. “That's so obvious! Why didn't we realize that earlier?”
“Oh, that was just a hoof-wavy proof, I'll teach you the details later... Mostly, how to renormalize all the infinities so that you can calculate meaningfully with them.”
“But, if that's so...”
“Yes, there are also uncountably many time-traveling Twilights, all leaping towards the Twilight-reset point.” Lyra poked Twilight hard on her chest, “I'm not special. You are not special. Nopony is. You think you are a little god in your loop, but from my point of view you are as helplessly trapped in a loopless world as everypony else, unable to retain any memory from loop to loop. That's the real reason why you didn't realize that: you didn't want to realize that, afraid of the implications.”
Twilight laughed so hard she was sobbing on the floor.
Lyra picked Twilight up into her forelegs and and gave her a good scratching on her ear. “Aww, little Twily is so happy that she'd never ever be lonely again?”
“Stop it, I'm older than you.” Twilight blushed.
Lyra stopped scratching, but kept embracing, “Beyond a certain point, our psychological age barely increases anymore, Twi. Living two thousand years is little different from living four thousand.”
“I'm still older than you.”
“It doesn't matter. What matters is that I know more about time than you, because unlike you, I have rarely been alone... In most my past lives you have been with me. And so will this one.”
“What do you mean 'rarely'?”
“Ahh, sometimes I would live without you. I might have killed you once or twice just to feel it...” Lyra winked mischievously, “But yes, mostly we have stayed together through my past lives.”
Twilight spoke in Old Alpine, “How have these... ended?”
Lyra replied in Erdish, “One of us eventually die, usually I die first, because for me, death is cheap, but for you, it's expensive. So I've been often... 'careless'.” she air-quoted.
“Why?”
“After you die, you will go back to your reset point and lose contact with me forever. After I die, I will go back to my reset point and see a fresh copy of you immediately.”
“Oh...” Twilight looked down, “Please stay with me for a bit longer. Don't die off randomly. I...”
“There is no way out of this, Twily.” Lyra petted her on the back, “Think about your friends, like Fluttershy. You still care about her, yes, but it would hardly be a great loss to you if you died and left her, or if you killed her just because. But for that Fluttershy, in that world, it's the only world for her. The same is true for us. I'm the only time-traveler Lyra you have ever met and the only one you will ever meet, but I have met you, is meeting you, and will meet you again...”
“But, but...”
“You care about your friends, but how good have you been treating your friends in your past hundred lives? Not good enough? I would care about you, but not enough, and there's no way out of this.” Lyra nuzzled on Twilight's cheek to calm her down a bit, “But I do care about you.”
“Thank you...”
“Hey, cheer up. I'm feeling charitable this round, and I probably will stay with you a bit longer than last round. What do you say we go for a dinner date?”
“Dinner... date?” Twilight blushed.
“I know everything about you, but you not me, so there's still some use in dating.” Lyra took Twilight by the hoof. “Let's go.”
At the restaurant, Lyra told the waiter what they would like to order, without looking at the menu or asking Twilight, before they could even sit down. “Trust me, out of the two hundred dishes you could have ordered tonight in Ponyville, this is one of your favorite.”
During the dinner, their conversation focused on the topic of death and reset.
“As I said, when you finally die and get reset, you will go back to the Canterlot library, and when you go to Ponyville again, you will find Lyra just a friendly stranger to you. But if you really miss me, you can always make friends with alternative-me in that world, and even help her become another time-traveler Lyra. Or... if you really want to stay with me, this me,” Lyra pointed at herself for emphasis, “then there is another possibility.”
“What is it?”
“It is possible to cast the spell again on yourself. This creates a new reset point for you. If you do that, after you die, you will go to the new reset point instead. This applies to all copies of you that are branched after the spell, but not to other copies of you that were branched before the spell.” Lyra drew a branched tree on the paper to illustrate the point, “In this way, you – all copies of you after the new reset point – will meet me again and again.”
“Would I? I would like to...” Twilight leaped with joy, “I'll cast this spell on all my friends and then on me again! Then...”
“But there's something problematic... Twilight, what would happen if you were to make a reset point when you are very old? Then you will stay old forever. A fate worse than permanent death.” Lyra looked straight into Twilight, “This is why we shouldn't ever cast this spell twice. Never, ever. Every time we cast the spell we give up a bit of our eternal youth.”
“I'm willing to be stupid for you.” Twilight stood up from her chair and stared urgently into Lyra.
“Trust me, you don't want to. I know you won't want to.” Lyra looked at Twilight with warning in her frown, “About three hundred lives ago, I was married to you. It was the happiest I've ever seen you, honestly. Usually you seem to be in a permanent state of not-caring, weariness, and boredom, but you were actually happy. So happy, in fact, you made a terrible mistake.”
“What was it? I... she... I mean, the Twilight in that cycle tried to do the thing, right?”
Lyra nodded, “She cast the spell a second time. I tried to stop her, but she said, with heated sincerity, 'I'm willing to be young and stupid for you, my love.' I refuted her, telling her it's too stupid to do that, even for all the love in the world. If she really loved me, she should find the alternative-Lyra after she die, and stay with her for a while. Then if she still isn't tired of it, she could do that for some more cycles, before she gets tired of me eventually, and do something else with her lives.”
“What happened?”
“Eventually I yielded, and I stood there with her when she cast the spell. And, just like you, I was greeted with the sight of a time-traveler Twilight, version two. And she was not happy.”
“Because she was bored about living with you?”
“Much worse than that. She blamed me. She said that I was the reason that she will forever have ten years of youth taken away from her life. I was the reason, yeah, because she loved me too much and became stupid? Heh.” Lyra sighed, “Some lessons seem to remain unlearned even after you live for a thousand lives.”
“What happened then?”
Lyra looked away, “She did... nasty things. Tortured me, to express her anger. Don't ask. 80 out of 100 alternative-yous puked their dinners after I told them the details.”
“What? But I wouldn't... I mean, I have read some books about torturing, but I...”
Lyra smiled warily, “I know you didn't practice torture techniques in your past lives, but she did. A lot.”
“I-I see...”
“So, listen to me. Don't make a new reset point, ever. It's the only way to ensure your youth does not get taken away forever.”
“I will not.”
“Besides,” Lyra winked, “It's more fun when the stakes are higher, right? I don't care, but you have every reason to care about being with me!”
“I-I do?” Twilight raised her eyebrows.
“Yup! I'm the only pony in this world that truly understands your loopy way of life. Nopony else truly understands you.”
“... You got me.” Twilight rolled her eyes, “Of course. I guess I have myself told you that way too many times.”
“And after you die, you will lose contact with this me forever! The stacks are much higher for you now, you see.”
“I-I could always find the alternative-Lyra and do this again!”
“Yes, though that would take another several years, wouldn't that be a little tiring? Several years without somepony that understands you as much as I do...”
“I see. I will cherish our days together.” Twilight felt her heart stir, “Cherish it like never before...”
Author's Note
If the universe continuously branches, and the loop is unbreakable, then Twilight's struggle during her first hundreds of lives is both unimportant – since there is no “main storyline” of the universe, and she merely made one branch of the universe a happy ending while many of the others are still sad endings – and wrong-headed – since the loop is not broken.
There is a simple explanation why this followup story has made the world of Hard Reset both logically consistent and morally irrelevant. The author is a mathematician, and as Einstein said, mathematicians prefer rigor in their systems, even at the price of detaching them from reality.
Would the author want to live in Twilight Sparkle's situation? Yes.
A Mathematical Theory of Hard Reset
Another Attempt at Breaking the Loop
This is it, then, the moment of truth.
The weight of fifty years of studies carried in her head. The length of five lives lived and gone. For one moment of conviction and understanding.
Well, not completely. All these studies are very important and useful on their own, even without any consideration of your intention of demonstrating to Celestia that you are a time-traveler. Besides, if I were only intent on convincing her, I simply needed to bring along a long list of descriptions of new species found in places that haven't been explored yet... I did the studies because now I can learn whatever I want, without consequences.
She approached Celestia’s chamber, a hoof over her saddlebag, full of precious knowledge that she carried from the future, which was the past for her.
“My faithful student, what important matter is it that you wish to tell me about?”
“My dear teacher, I bring to you incontrovertible evidence that our understanding of time is wrong. Time travel is not only possible, it is repeatable, and I stand in front of you as an example of a pony who has lived through hundreds of time travels involuntarily.”
“Explain your concept of ‘time travel’.”
“I created a magical construction accidentally, and afterwards I found that, every time I die, I become transported back to an exact location in space-time, so that the moment after death, I find myself standing in the Canterlot library, at time several hours before the changeling invasion. This happens every time after death. My memories, personality, and other mental facilities are transported seamlessly, but my physical body is not transported at all.”
“Present your evidence.”
“You know very well that I should have lived through only twenty-seven years of age, and as such, despite my extraordinary talent, I could not have known all that there is to know in this wide world. Indeed, you also know very well the exact fields of studies I am familiar with, them being the five magics, history, and astronomy. However, with the help of time travel, I can study many years in one life, then die, and go back many years to start the process again. Thus, In my past five lives, I have been studying diligently, acquiring a vast knowledge that is impossible to acquire without time traveling. All this knowledge is examinable, and I will stand before any examining expert to validate myself.
Further, I have brought discoveries from the future: new potions, new spells, new species. I detailed them in my scrolls in my saddle bag. The new potions are all synthesizable using existing material and techniques. The spells are rather specialist, but should be understandable by any professor after reading it through a few times. The new species are recorded along with a drawing, a list of traits, and places to find them.
This is all that I wish to report, your highness.” Twilight groveled, awaiting Celestia’s understanding.
“Demonstrate your learning.”
“I can demonstrate here and now my learning in Old Alpine Language and Piano-playing.”
Princess Celestia nodded and asked a question in Old Alpine. Twilight replied, gave some commentary on the locative case of the noun, and then asked Celestia back, all in Old Alpine.
“Have I demonstrated to your satisfaction?”
“Will you play a piano song for me?”
“What song would you like?”
“‘Little Belle’.”
Twilight played at the piano in the room. She didn’t play perfectly, but her performance was remarkably good for a first attempt.
“I shall arrange these scrolls to be verified. Despite the wildness of your claims, the evidences you presented are very solid, and as such I will take your claims seriously.” Celestia nodded, “You may go now. I will tell you my judgment by the end of the week.”
Twilight waited until the end of the week, and heard back from Celestia.
My faithful student, Twilight Sparkle,
I have deemed your claims to be believable. Please come immediately so that we might discuss the matter further.
Your teacher, Princess Celestia
Twilight’s heart fluttered in wild joy as she read the short letter. She galloped to the throne room where Celestia was waiting.
“My dear student, I...”
Twilight knelt down and started laughing and sobbing, “Sixty years of solitude...”
“Twilight, I -- ”
“Sixty years of loneliness, sixty years struggling inside this loop, nopony understood me, on the edge of madness and emptiness...”
Celestia came down from her high seat to embrace Twilight. “I am sorry that I didn’t believe you in your past lives.”
“Dying again and again, reborn again and again, nopony ever saw what it was like, nopony to confess to without fearing psychiatric confinement...” Twilight kept raving on and on, pouring out all the frustrations and loneliness, bottled up inside her for six decades.
“But we can fix this. We will find a way to break this cycle.”
Celestia appointed Twilight, now one of the most capable pony in both magic and physics, as the head of a research team on time magic. The research began by a thorough examination of the spell Twilight used to create the time loop, and proceeded to a detailed recreation of the exact method Twilight used when she attempted the spell.
This completed the first stage of the research. Very small scale experiments confirmed that the magical construction was capable of creating many kinds of strange distortions in time, the exact quantity and quality of the distortion depending sensitively on the details of the construction.
Twenty years of research later, the progress was discouraging. Only very few constructions could be reliable made, and even them were studied only on very small systems -- usually on cubes smaller than 1 millimeter in length, as scaling the experiments up always risked affecting the researcher ponies themselves.
It was a Friday night, after work. Twilight pranced around the empty lab agitatedly. She had planned a meeting with her friends, who had moved to Canterlot to keep close with her, but she did not feel like going for now.
What is needed is subjective studies. All these objective observations can only bring us so far. Unless we can make the cubes talk, we will never understand what effects these constructions have on these cubes. And the more important problem is that these cubes have no soul. They cannot tell us what effect the spells would have on souls... I'm the only soul that's subjected to such a spell.
I will have some patience, but I don’t want to wait so much longer. The research drags on and on without a goal and I miss my younger times. And even if it were to succeed? Even if the research actually does stop me from getting reset every time I die, what good would it do?
Suppose that it is possible for suicide to be rational – which is a reasonable enough assumption, in some unusual but not impossible circumstances – and suppose that at some future time, I can calculate that it is better for me to die forever than to continue existing – which is also a reasonable enough assumption, if we trust the many arguments against immortality – so I activate the loop-breaking spell, then suicide?
There is a problem here when expected life length is infinite. The proof for the rationality of suicide assumes that the domain of integration for the utility function is compact, which is not true when the domain extends to positive infinity. In fact, it’s easy to construct utility functions that are ∞-differentiable, bounded, uniformly continuous, integrable, have infinitely many dips below zero for increasingly long periods, and at any point, the tail of the integral diverges to +∞. Any simple-minded suicide-decision program, when fed with this function, will mistakenly decide to suicide after reading the function for some finite time, thus throwing away the +∞ utility.
Five more years was all that convinced Twilight that the research was going in a dead end. Small-scale experiments on nonliving things yielded no more data, and experiments on living non-talking things did not appear any more different than experiments on nonliving things. Large-scale experiments were strictly forbidden, not only for the safety of the world, but also for a selfish reason: Twilight was afraid that large-scale experiments might break her cycle, which she was not yet willing to do.
But still she stayed in this world, in order to conduct one more experiment: see if dying from an old-age induced heart-attack would result in a different reset.
“Well that didn’t work.”
Apparently, there’s no difference. Any kind of death results in the same reset. Should have appeared obvious in hindsight.
