//------------------------------// // Another Attempt at Breaking the Loop // Story: A Mathematical Theory of ‬Hard Reset // by furrypony //------------------------------// 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.