The realisation that I might have discovered the solution didn’t dawn on me until a day after I had begun experimenting with this particular approach.

  At that point, I had already experimented with a dozen different formulations of stochastic dynamical systems that could satisfy maybe a few of the conditions outlined in the mathematical document, but not all. Oftentimes, they would meet the required criteria only on an approximate basis, or under strong regularity assumptions. Frustrating, but the process was educational. Even if only incrementally. The conditions that were always the most elusive were the ones that demanded a strong, unfamiliar notion of consistency. Almost as if they were asking for some kind of predictability criterion.

  “Glad to see you’ve cleaned up my office,” Mariam said as she walked in.

  I chuckled as I continued to pen symbols onto paper. “Sorry about that. I’m trying to see if a tidier office is conducive to better research.”

  “Fair enough,” Mariam said. “It’s all a part of the process I suppose.” She sat down on the chair on the other side of my desk and subtly peered at my writing. “And is it working?”

  “Maybe.”

  Eventually, I decided to try something radically different. Like introducing a new species into a terrarium and seeing how it tips the equilibrium of all other living things inside it, I defined a new object into the dynamical system. An experimental process such that its current state depended on its successive state, and that state depended on its successive state, and so forth. My thought was that this mathematical recursion—backechoing, as I called it—would be an expedient way to meet the slippery consistency conditions I had been struggling to satisfy. It was, admittedly, a nihilistic and nonsensical technical convenience that made no theoretical sense. Kind of like a mathematical fake it ‘til you make it. But I just wanted to see if it could be done. What a home run might look like. And it looked too easy. Almost suspiciously so. Not to imply that the elusive conditions were trivially met, but with a bit of work, they seemed to snap right into place.

  “That’s strange,” Irene said. “You look content.”

  “Bad strange?”

  “Good strange,” she said with a smile. “But are you going to tell me why?”

  I grinned. “Well. I am in bed right now with a beautiful woman who’s way out of my league that we’re not even from the same layer of earth.”

  “Three things,” Irene said. “First, ‘woman’ makes me sound old. Second, you could say that about every person here. And third, is it really me, or is it maths?”

  “What? How could you accuse me of—”

  “Do you think of trig identities when we fuck?” Irene asked.

  I laughed. “Absolutely not. I mean, they’re kinda sexy, but they don’t even come close to you.”

  “They better not,” Irene teased, before smiling knowingly and saying, “But research is going well, then?”

  “We’ll see.”

  But even then, it was still like being a poor kid looking through the windows of a jewellery store. That was what it would look like if I could do it, but the approach was theoretically absurd. The mathematical object I dreamt up vaguely resembled a stochastic process, but every stochastic process needed to be defined over some kind of filtration—the theoretical structure that modelled the information space the process lived on. But for an object that depended on its successive state, the conventional theory of filtrations needed to be thrown out the window. And so to justify the existence of this object that would solve my problems, I began fleshing out an exotic theory that would complete the solution.

  The new manuscript that sat atop my desk was my response to the original mathematical documents that had appeared in front of my apartment door a lifetime ago. The first act began by describing a new theory of nonlinear filtrations. It then shifts into the second act on closed-curve filtrations. Its final act ends with an example of an application; the formulation of a stochastic dynamical system that implies the existence of a solution that satisfies the conditions provided by the Receiverist Particle Physics research group. I had gone over the document half a dozen times at this point. With each review, my certainty grew. It had been a while since I felt like a real mathematician. I closed the manuscript and stretched. As I reached for my cup, I was taken off guard by how light it was. I suppose another trip to the cafe wouldn’t hurt, I thought.

  Just as I stood, the tones from my handheld played. I reached for it.

  Script alert: Job completed. 23/23 tests passed.

  Despite knowing what the notification would say before I had seen it, I still had a moment. I raised a clenched fist to my mouth and bit on it. Not hard enough to draw blood, but enough to stop me from having a euphoria attack in my office. It took half a dozen paces around the room to calm my ragged breathing.

  I haven’t told anyone that I had made a substantial breakthrough yet. I didn’t want to claim progress only for it to come crashing down on me later. I was certain that Irene knew I was onto something, and that illustrated just how well she could read me. But I hadn’t explicitly told her. But now that I had both the theory and simulation results backing my solution, there was no uncertainty. I had done it.

  I tapped away at my handheld.

  Alex: Hey, can we meet?

  A moment later, Irene responded.

  Irene: Right now?

  I had only realised how absurd my request was after receiving her message. Irene was at work. It wasn’t reasonable to ask your girlfriend—not that we talked about labels yet—to abruptly abandon work for you.

  Alex: Sorry, not if you’re busy

  Irene: Ok, your place in 30 min?

  Alex: See you soon

  I’m still her work, I realised. The thought was slightly demoralising. But then again, once I hand off my research, I would no longer be her assignment. Irene would get that promotion she wanted. I would stay. Mariam and Lennox seemed to suggest that I could, and this work was irrefutable evidence of not only my current contribution, but also potential future value of my continued presence here. I would speak to Lennox about this after turning in my results.

  I grabbed my laptop and the manuscripts with me as I left my office. I figured I would do some final polishing in my apartment before heading for Mariam’s office tomorrow. When the elevator opened, there were already a few people in it, and I joined them. Seeing that the group got off at a street, I left as well, deciding to take a detour in this building-level combination that I hadn’t been on before. There was no rush. Irene would get there in about over half the time it would take me. And the newfound freedom that came with accomplishment was intoxicating.

  I would become a Receiverist. A resident of Sanctuary. I was walking among fellow Receiverists on the streets. This would be my home. I would be rid of the white stripe above my heart that was the single tangible discriminant between me and everyone else in this city. Perhaps it would be replaced by a green stripe, of which Mariam had three. I wondered where Irene lived. Whether she might be opposed to moving in together. Is it too soon for that? I wondered. Yeah. It probably is. Definitely. I don’t want to come off too strong. I don’t want to rush anything—

  The Backecho

  A pub. The brick facade was quaint, but the grey colours made it entirely unassuming as it blended into the space between the barber and the gym that were on either side of it. Through the windows it looked almost empty, which was entirely reasonable for this hour—except for one bloke having a late lunch with a pint. None of those details about this pub was at all noteworthy. This was an entirely unexceptional establishment. All with the exception of the name of the pub that hung above its front door.

  I froze in my tracks. It didn’t make sense. It shouldn’t. “Backecho” wasn’t a word in the dictionary. I was sure of it. But it appeared only in one place I knew of. The manuscript that was in my hands. The one that didn’t exist until a few days ago. The one that no one else had seen. Backecho, to my knowledge, was a term that I had very recently invented to describe a backward recursion in a very technical context. So why was it the name of some dingy pub in Sanctuary? The name gnawed at my mind. As I entered the pub, the bartender looked up from his book and nodded at me.

  “Hey,” he said indifferently. “What can I get—”

  “What does it mean?” I interjected.

  “Excuse me?” the bartender asked in bemusement.

  “The name of the pub,” I clarified. “What does it mean?”

  “Oh, it’s—” the bartender’s gaze flicked down at my little white stripe. “You know what? Now that you mention it, I haven’t a clue.”

  This story has been stolen from Royal Road. If you read it on Amazon, please report it

  “I don’t believe you,” I said indignantly. “You clearly know. So why don’t you just tell me?”

  The bartender looked past me at the other patron, before fixing his gaze back on me. “Hey, keep it down—”

  “Just tell me what it means!” I demanded. It surprised me how frantic I sounded. “I need to know.”

  “I’m going to ask you to leave,” the bartender said in a low voice. I felt chills down my spine. “I won’t ask twice.”

  I stared him down for a moment, before I stormed out of the pub. The interaction had left me feeling even more uneasy than before. There was a reason why the pub was called The Backecho, but it was a guarded secret. At least to me. Somewhere, someone had decided that I didn’t deserve the privilege to be privy to that knowledge. As much as I wanted to pin the blame on the bartender, it was clear that he was merely abiding by some directive. So now the question wasn’t just why that name exists, but also why I couldn’t know. I chewed on the question angrily as I traversed the streets. I deserved to know.

  Something ate away at the back of my mind. It was just outside the peripheral of my consciousness. Something important. Relevant. But I struggled to pin it down. I wasn’t sure why I was invaded by this sudden, overwhelming sensation. It displaced the frustration. This feeling was not unfamiliar; it was a feeling I got when I worked on a maths problem, when the solution to a particular permutation of symbols was at the tip of my tongue, but ever so slightly out of reach. It would always come to me in the end. What is it, what is it, I rummaged through my mind. Something to do with backechoes? Something to do with work? Something to do with Irene—

  The future is set in stone.

  My breaths became shallow. Irene had said those exact words. A hypothetical for me to think about. To help me take meaning from things that were otherwise too meaningless and horrible. And yet, I now couldn’t help but relate it to the idea of backechoes. The mathematical objects where each state depends on the next. Like dominoes, they fell. But from a certain frame of reference, when indexed over a temporal variable, they fell backwards in time. In which case, the future really was set in stone for these objects.

  The edges of my vision pulsated in sync with my pounding chest. Does my work describe a time travelling phenomenon? I thought frantically. Is that what I’ve been working on this whole time? But that couldn’t be. Time travel didn’t exist. It couldn’t. It would violate the laws of physics. It simply wouldn’t make sense. But sense from an academic perspective was really just another way of describing theories and models. And indeed I had been told that I had been working on a mathematical model that would describe a new theory of particle physics. So could it be that time travel didn’t make sense in the current understanding of physics, but the phenomenon could exist in my new model?

  Without waiting to find a bench, I sat myself outside of a grocery store, wiped my sweaty palms on my pants and began scanning through the pages of my work. Passers-by looked at me curiously, but otherwise reciprocated my indifference. I flipped back and forth between pages, tracing the occurrences of mathematical expressions. Substitutions were mentally made and I checked whether contradictions arose. They didn’t. The results resolved themselves, almost like snapping a new part perfectly into place, like it was always meant for it. Like it was the singular purpose of the entire design. Time travel was consistent in this new theory. And it was I who uncovered it.

  I creased the documents that I had so carefully tried not to before. I didn’t care. I needed answers. And I was certain that Irene had been holding them back from me. I stood and began walking at a brisk pace. Other people on the street moved to avoid me.

  The maths that I had written only proved that time travel could theoretically exist, not how it could be done. This was the one occasion that I wished my maths was wrong. But I knew it wasn’t. The simulations showed that it was valid, and the theoretical foundations were all there. But I was still hopeful that time travel was still practically impossible. My rather rudimentary understanding of contemporary physics told me that to achieve actual time travel—if it was even possible—would require tremendous amounts of energy. More than would be feasible. But that was just the old theory.

  When I reached my apartment I was breathless. I fumbled with my handheld until the door opened.

  “Irene?” I yelled. “Irene?”

  No response. She wasn’t here yet.

  My thoughts swam like a school of slippery eels. It was difficult to focus on one without jumping to another. To properly process them would require me to calm down and think it over a substantial amount of time. But I couldn’t do either. Not when Irene was going to be here any second now.

  The existence of time travel would mean that time itself wasn’t as linear as anyone had believed it to be; the fundamental assumption that grounded the way we think. It would mean that time wrapped back on itself in convoluted, dizzying ways that had implications for quite literally everything. It would recontextualise the very origin of all things; if time travel really did exist, then it would mean that the future already happened. Things would exist because they were always meant to exist, not because of the result of some causal chain of events.

  If time travel existed, it would be a divine secret that humans should never discover. All technologies inevitably converge to military applications and warfare. New advancements only ever lead to weapons of devastation against fellow humans on a scale beyond what came before. And so if time travel really exists, then eventually so will weapons of time. Perhaps they had already been deployed without anyone ever knowing. Entire civilisations wiped out, turned into not ruins and rubble, but into inexistence itself. The very thought shook me to my core. I felt sick. I had always chosen to take research projects from financial mathematics to avoid this kind of responsibility; I would rather have my research amount to meaninglessness than something terrible.

  I felt the onset of a deep panic. Am I the creator of the final weapon? I thought frantically. Am I the destroyer of everything? It seemed that I couldn’t do anything right. I couldn’t save my parents. I couldn’t save my brother. And I couldn’t save humanity. No. When I finally thought I was doing the right thing, it turned out I was doing the very opposite. Humanity wouldn’t be saved by my hand. It would be destroyed. Because that was all I was able to do. I should have known.

  When the door opened, I stopped mid-pace.

  “Alex, so what is it that you’re so excited—” Irene saw how I looked and froze. Standing by the door, she took a moment to study me. I hated that. At that moment, I hated how penetrating she always was with me. “What’s wrong?”

  “Irene,” I began slowly, sternly, “what is my research for, really?”

  “We’ve been over this already,” Irene said. “I’m not a physicist. I’m sure you’ve asked Mariam already.”

  “Tell me the truth!” I demanded angrily. A part of me felt bad for raising my voice, but Irene didn’t look scared at all. She only tensed ever so imperceptibly. “I know you know more than you’re letting on. Just tell me. Please.”

  A pregnant silence. Irene’s eyes were unreadable as ever, but I knew that behind them was a calculus taking place to determine whether she should lie or not.

  “I can’t,” Irene said. “I don’t want to lie to you, but I can’t give you any answers. It’s not my place.”

  “What do you mean ‘it’s not your place’?” I asked. “I deserve to know! I’ve been strung along on some ambiguous story about what I’m doing, and I ate it up because I wanted to believe. That the world isn’t as shitty as it is. That I don’t have to live in hopelessness. That I can do something truly good. But I’m not sure I believe any of that anymore. I’m not sure I believe in anything you people have told me.”

  “Alex, please,” Irene placated. “It’s not like that. Not like that at all. We haven’t lied to you about the importance of your work, nor what we’re trying to do here.”

  “I don’t believe you,” I said.

  It happened for a split second. There was a flash of hurt on Irene’s features, before it dissipated as if it was never there. “Okay,” she said. “Then what is it that you think we’re doing here?”

  I looked at her for a moment. I thought about the things I could say, about how I could play this conversation out so I could get as much information I could without giving away the knowledge I had that she didn’t know I had. But I was tired. Tired of half truths and reading between the lines. Amorphous meanings and devious whispers.

  “Time travel,” I said. “I think you’re working on time travel.”

  She didn’t seem too surprised. “You’re not serious. You can’t believe that.”

  “I know you’re lying,” I said. “The only thing that has been honest with me this whole time is the maths. It’s the only thing that hasn't manipulated me since I’ve been here.”

  Irene regarded me for a moment. I couldn’t tell what the silence meant. She sighed. “Don’t do this to me, Alex,” she said. “Not right now.”

  “I’m not doing anything,” I said. “I just want the truth.”

  Irene smiled. It looked a little sad, a little pitying, but I didn’t know for whom. In a flash, she turned and ran. The door slammed shut behind her. By the time I had opened it and entered the corridor, she was nowhere to be seen, no doubt having turned into a different corridor. And another one after that. It was impossible to find her now.

  But Irene did run. Which had to indicate that I was onto something. That I wasn’t delusional in seeing the implication in my model for the existence of time travel. But what did it mean? That the Receiverists had been after time travel this whole time, and that they needed someone like me to complete the theory? Or could it be that they were already aware of time travel because it had already happened?

  As impossible as it was, I needed to rid myself of those questions for now. Time wasn’t on my side. With Irene out of sight, she could have called security already. Whatever I was going to do, it needed to be done fast. And I had to do something. I couldn’t just wait for the Receiverists to apprehend me and throw me into yet another prison cell. And this time, it would be for the rest of my life, which could be very short if they decided to just off me to save resources. Now that I was thinking about it, that seemed like the Receiverist thing to do. Fuck, I really am screwed, aren’t I? I thought, before, Maybe not yet. I needed leverage if I was going to have any chance of finding out the truth and surviving this. And it occurred to me that I had one.

  I switched on my laptop. I needed to erase my simulations. Unfortunately, all computing systems in this city were distributed, meaning that I couldn’t just smash this laptop to get the job done. Fortunately, I was provided enough privileges to access the cluster history. The justification had been that it would come in handy if I ever lose my copy of the script somehow. Now, it was infinitely more useful. I logged onto the cluster and opened the history. Since this particular cluster session was created just to run my simulations, all of it was my scripts. I erased it all. I then fitted the laptop into the microwave oven, set the heat to the highest possible and turned it on.

  The real leverage was the theory. Without the mathematical machinery, even if they somehow recover the simulations wouldn’t mean much. It would amount to little more than gibberish to the uninitiated, which was everyone who wasn’t me. So my manuscript was worth something. I turned the ventilation on and held the papers to the stove. It took a while, but eventually they caught on fire. I was in a trance as I watched the sheets of paper turn into black ashes. Once, I had believed that writing this paper would save me. Now, I knew that burning it was my only chance.

  With the leverage I had in my head, I needed to figure out what to do next. In Sanctuary, there was nowhere to hide. Nowhere to run. My survival depended entirely on how generous the Receiverists were feeling. But answers? I might be able to do something about that. A plan formed in my head. An insane one, but when your back is against the wall, sanity and insanity were entirely arbitrary.

  I walked into my room and opened a drawer that I had only ever opened once. It was still there. The dark metal shined against the ceiling light. I took the gun and left my apartment for the last time.