//------------------------------// // A New Reset Point // Story: A Mathematical Theory of ‬Hard Reset // by furrypony //------------------------------// 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...‭”