Suppose I have a bag of money with a dollar sign on it. I put it in my car alongside a few decoy bags and drive to three different warehouses, stashing a bag at each. I do this because I’m being monitored by two evil time travelers, Alice and Beth.
I left at 1 PM and returned home at 2 PM. Once there’s no chance of them running into me, the time travelers spring in to motion. Alice doesn’t have a car, but Beth does, which means Beth is able to search a warehouse and return to her time machine faster.
Let’s suppose these time mechanics implement a kind of time loop mechanic. Each has the power to mark the loop’s beginning, then reset back there, retaining their memories. Alice finishes booting up her time machine at 2:10, giving her enough time to walk to a warehouse, search, and return at 2:50. Suppose Beth boots up her time machine at 2:15 and can drive to a warehouse and back by 2:45.
What’s more, each time traveler has different expectations about where I would stash my loot. Alice starts searching at the first warehouse, and Beth at the last.
Let’s say I hid the money in the middle warehouse. Is this enough to specify what happens? Let’s walk through it.
First loop, nobody is prescient, so Alice blindly checks the first warehouse, and Beth blindly checks the last. But remember Beth resets first, so she hops in her machine. Put a pin here, there’s a few different ways to think about what happens next.
The obvious way is for the machine to do what we said it does: it resets time back to its marked beginning. 2:45 becomes 2:15, and by this point Alice is en route to the first warehouse, so she’ll blindly search the same as the first loop. She isn’t prescient, but Beth is.
Knowing the money isn’t at the third warehouse, Beth checks the second, finds the money, declares victory, and drives off into the sunset
But she isn’t the only looper. Finally Alice makes it back from the first warehouse and resets her loop. At 2:10, Beth hasn’t even activated her time machine yet. Alice is prescient, Beth isn’t. So she searches the second warehouse while Beth blindly searches the third.
She finds the money, declares victory, but before she can even make it to her time machine, Beth gives up searching the third warehouse and resets the loop.
Put another pin here. But again, the obvious way for this to work is another simple reseting of time, like loading a save slot. When this Beth had stepped in her machine, Alice only knew about W1, and planned search W2. Now Beth knows about W3 and plans to search W2, but nothing has changed for this Alice.
Now, finally, Beth arrives at W2 and this time Alice is there. Here, the two finally meet. Let’s say they each get spooked and run right back to their time machines, each planning to come back with contingencies. But Beth has a car, so she resets first.
Like earlier, only Beth should retain her memories, so she’s able to observe Alice’s behavior, realize the other woman is looking for the money too. But because of how short Beth’s loop is, she can’t reset Alice’s knowledge, nor beat her to the warehouse. There’s only one recourse for evil time travelers: Beth kills Alice.
If Alice were a regular person, this would be the end of the story. But because these are time travelers, Alice’s machine could be designed to act as a dead man’s switch. if she’s not there to climb in at the end of her loop, then the timeline resets.
It’s worth noting this is already different from most time loops. Usually the looper is the centerpiece of the time loop; there’s no machine involved.
So let’s add a few details. This time machine looks a bit like helmet or crown encrusted with crystals. You place it on your head and your senses are awash with visions of the future. Perhaps there’s a drug that must be administered, a hallucinogen that reacts to the stimulation and rapidly reconfigures your synapses to their future state in alternative timelines.
The reason I spill all this detail is to suppose something interesting. At the end of the loop, your brain is scanned and beamed back to the past. This means that when Alice’s dead man’s switch activates, there’s no brain for the machine to scan.
This time, at 2:10, Alice only knows something is wrong. Last thing she remembers, she was resetting after failing to find anything in the first warehouse. This time, she plans to check the second, except now a warning is screaming in her head. Error! Abnormal loop reset! Missing looper exception!
Alice knows this means she did exactly what she was planning to — then something killed her. Was there a trap at the second warehouse? This time, she brings her gun and stays on edge. But remember, Alice’s reset point is before Beth, so at this point Beth knows nothing.
Alice finds the money. Was there nothing at the warehouse? Does someone attack on the way home? And she’s almost right. Beth resets again, just like before, and again she goes to check W2.
But like last time, when Beth checks W2, she doesn’t know to expect another looper — but Alice does: she assumes Beth is trouble and shoots first, then resumes stealing the money. She’s less on edge walking home this time, but again, Beth was a looper, so her time machine resets again.
It’s another error, but this time Beth is one who gets it. Finally, we have arrived at a point where both loopers start off aware there’s danger at the second warehouse.
As so far described, what happens next mostly comes down to purely causal factors. Alice has more time to prepare, but Beth owning a car probably speaks to greater access to resources in general (if nothing else, she could try hitting Alice with the car). Whoever wins the first confrontation, even if it’s by chance — even if they’re staggering back home concussed and bleeding out — will be able to retain their memories and compound their advantage.
Though of course, it’d have to be a nonlethal victory. In fact, this raises a question: is the length of a loop set at the start? If it is, then Alice is fucked, because then there’s no way for her to get back and reset before Beth’s failsafe kicks in.
Perhaps when the loop begins, you must declare “If I’m not back by time T, reset without me.” But this detail ought to change the preceding section. Thirty minutes to go to a warehouse and back is a pretty tight window. What if you get stuck in traffic?
If Beth sets her dead man’s reset far enough into the future (after 3 pm), then Alice might return to her machine, declare the loop over, and then get reset back anyway.
But I’m getting a bit tired of this model. It’s a bit tedious to work out what happens, and the limitations means there must be a lot of timelines where loopers flail around unaware what’s happening. how can we improve this model?
As it stands, each time machine essentially stores the state of the universe at the time of activation, a save slot that gets loaded from later on. The next most obvious model is that when a saved state is restored, it resets everything except the state of time machines.
It’s most easy to illustrate this with a different setup. Cindy and Darlene are both playing separate games where they try to guess which box has treasure inside it. Three boxes each: Cindy’s treasure is in her third box, but Darlene’s is in her second. Cindy is sitting closer to her time machine, so she resets first.
Under the first model (call it S3, for “solipsistic save sates”) then Cindy would check each box one by one. Darlene would keep trying the first box and losing her memory each time. Cindy finds her treasure and stops looping, then Darlene gets to retain her memories, and finally guess the second box. this requires reasoning about 3+2=5 loops.
Now, under the tentative second model (call it CR, for common revision), both Darlene and Cindy should remember their first loops, meaning this only takes three loops. (Darlene finds the answer on the second loop)
First, note that this requires waiting. Cindy gets in the machine, and beams herself back, but the timeline continues until Darlene also beams herself back.
Another question is how to handle Darlene. Imagine instead of three boxes, there’s fifty. Darlene finds the right answer on her second guess, but there’s still forty-eight more loops of Cindy iterating. Does Darlene retain those memories? Since she will (want to) be doing the same thing each loop, it almost makes sense for her to voluntarily “become an NPC” and begin forgetting loops.
Here, let me sketch a narrative to illustrate what I find interesting about this. Say Cindy and Darlene are both hunting down elusive criminals — perhaps one that personally wronged them. Each loop, they try to investigate a suspect, only to find an alibi and reset. While the world around them goes through the same clockwork motions, these two remain autonomous. They chat at the start of each loop, discussing their plans, even if each ultimately works alone.
Maybe Darlene’s the outgoing one, starting up a conversation each loop. Then one day, she says the same thing she did last loop. She asks about the red herring that Cindy just wasted last loop proving to be a dead end. And thus, the horror — Darlene found the answer, and she’s part of the clockwork now.
But this presents an curious temptation. What happens if Cindy lies to Darlene? Tells her not to check the final lead, so she doesn’t lose her friend?
Importantly, this mechanic of forgetting the final loop is pretty important to any larger scale worldbuilding. Imagine someone halfway around the world also has a time machine and decided to boot it up at the same time as you.
If you remembered every loop, then you might get stuck repeating the same winning strategy over and over, not because it doesn’t work, but because someone you don’t even know is doing something much harder.
You don’t notice the loading screen until every other time machine agrees to rewind; You don’t notice that you’re repeating your final loop again and again. This is necessary so that we can compose a bunch of unrelated loop with minimal interference.
This gives me the funny mental image of a sleeping dragon looper. They are dangerous, capable of brutally ruining any looper who crosses their path, but perhaps they only want to take a nice stroll in the park and listen to the birds chirping.
If they have pleasant day, they end their loop. Now imagine a bunch of others loopers monkeying around, averting terrorists attacks and joyriding across the city. As soon as one of them intrudes on the day in the park, they get destroyed, ending the loop; now the sleeping dragon awakens and goes out of their way to dismantle the interloper.
But I digress. We’ve simplified our analysis of these “common revision” loops by assuming every looper resets to the same point. But this was not true in our first example. Beth ends her first loop at 2:45 and her machine waits five minutes for Alice to finish up (2:50). Now what? Suppose each gets beamed into the next timeline.
On the first loop, nothing happens (as usual). On the second loop, they both check the second warehouse and encounter each other. On the third loop, then, both should be aware of each other.
But consider a modified scenario where Alice’s head start is much more severe. What if Alice set up her time machine at 1:30, but still waited until after 2 PM to make her move? Now she has time to look for the second time traveler, and if she resets early enough, Beth never becomes prescient and cannot move against her.
What happens if Alice kills Beth before she can enter the time machine? Could she destroy the machine first? Would that trigger a timeline-resetting paradox?
Our early analysis supposed that the quicker, innermost loopers would be able to outmaneuver their slower opponents, so this seems like a neat way to give outer loopers an advantage.
But take the analysis a step further. Beth knows she has the machine. even if she only puts the time crown on her head at 2:15, could she check to see if the time machine will received any data from the future?
This might be getting unclear, so let me be more precise. In physics, there’s a concept of time symmetry. (I’ve made jokes about this before.) Bounce a ball off the wall, and the mechanics of that motion would be the same if the ball were going in the opposite direction, hitting the wall at the same angle to bounce back into your hand. Why time only goes one way a bit of a mystery.
Our first model of time travel, S3, was described in terms of “restoring save states”, but an equivalent way to visualize what’s happening is to imagine the whole universe pauses, and starts running in reverse — except for the time machine, which remains fixed in a certain state. This is what preserves your mind.
Thus, to get our second model, we simply imagine that when one time machine starts rewinding the universe, every time machine preserves its inner state.
But this is more than just an intuitive visual. It’s a theory, and rewinding the universe leads to different observations than if each time machine simply received — or read — information out from another timeline.
When the universe unwinds to before the reset point of a time machine, what happens to its preserved state? We’ve been imagining you have to power them on like Primer boxes, so if the machine isn’t powered on, its can’t maintain the hyperquantum confabulatrix, and so it gets reset just like ordinary matter.
But now we’re at a crossroads. On the face of it, this implies that when Alice resets her timeline, Beth stop being prescient, and will start her loops from scratch assuming Alice’s intervention doesn’t alter Beth’s plans.
But when Beth resets her loop, what happens? Whenever she emerges from her time machine at 2:15, Alice would have already emerged five minutes ago. So… first loop, A at W1, Beth at W3, and both reset. This is what we want to figure out. Beth resets to a 2:15 where Alice is already en route to W1. Beth goes to W2, finds the money, ends her loop.
What happens next? If the timeline precedes normally, then Alice finds nothing at W1, returns to her machine, and then we have a dilemma.
Remember, Alice’s machine already has a preserved state from Beth’s W3 timeline. Essentially, there’s a reset queued, which was unable to complete because Alice wasn’t in the machine when Beth reset things.
This means there are now two W1 Alices. One from a timeline where Beth found the money, and one where she didn’t. In this barebones scenario, the difference seems immaterial. but suppose Alice had seen evidence of Beth’s activity (e.g., spotted her car driving past), but didn’t recognize it as significant, because it’s just a stranger’s car. Thus, it’s meaningful to ask whether the Alice who gets out of the machine next remembers seeing Beth’s car or not. Which timeline did she come from?
One trick for dodging this dilemma here is by resetting early. When Beth resets her timeline, it also activated an fallback circuit in Alice’s machine that queues a reset. Now when Beth tries to ends her loop, it pings other time machines and triggers a reset.
Now this is a bit weird. Beth thought she was calling it a day, but unbeknownst to her, that action resets the timeline to a point where none of her loops even happened!
And there’s a deeper problem with this queuing mechanism, anyway. Consider Eve and Fortuna. Eve starts looping first, then Fortuna starts looping, then Eve ends her loop, then Fortuna ends hers.
When Fortuna ends her loops unsatisfied, she resets to a time when Eve isn’t in her machine anyway, thus a reset is queued. But Eve returns to her machine before Fortuna can trigger that queued reset. This brings us right back to the problem the queue was supposed to save us from: Eve arrives at a machine already laden with premonition, and now we have to decide which Eve takes priority.
Another feature of the Alice–Beth scenario is that it’s set up so that Beth only needs to reset once. But suppose there are more warehouses, and she needed to try out four before finding the right one. That means four slightly different Alices from W1 have been queued. Here, it seems natural for the most recent one ought to take priority.
So I guess that’s the answer. Time crowns can store memories, but that data can be overwritten. But this means that after Beth ends her loop, Alice will not only notice that there’s another looper, but she can count how many loops they lived. (Even if the machines only store one set of memories, it’s pretty trivial to increment a counter.)
But let’s specify what Eve and Fortuna were doing. Eve is abetting a criminal, Fortuna wants to catch them. Eve has two hideouts and wants to pick the one where Fortuna won’t look. She sends her client to H1, but that’s where Fortuna starts looking too, so she resets and tells them to go to H2. Fortuna finds nothing and resets.
Only before she puts on her time crown, she notices that another looper has already tried to reset the timeline. If she knows that she’s playing against Eve, then she knows the only situation where Eve would have reset is one where Fortuna had caught the criminal.
Meaning that there’s a morbid yet optimal play where Fortuna allows her machine’s dead man’s switch to trigger, resetting the timeline without her, erasing her memories and yielding to a version of herself who got a good look at the baddie.
In general, we might imagine a priority system, where whenever a looper dons the time crown to reset, they assign themselves a numeric priority, with the logic that the highest priority timeline is propagated to the next.
But if this can be exposed to the user, why stop at integers? At the end of the loop you could type out a short diary entry explaining what you discovered so that other version of you can determine if they ought to yield to you.
But this raises acute questions of self-cooperation. After all, if you discover the masterstroke to thwart all your enemies in one fell swoop, then spelling it out in your multiverse diary entry means that other version of you can just read those cliffnotes and discover it themselves. But if you say you discovered something important without disclosing what, it’s more likely you’ll be yielded to.
And if you didn’t discover anything useful, but you really don’t want to die…
The horror of discarded timelines, the inescapable conclusion that they existed by virtue of leaving this trace causality on the “real” timeline, is one the reasons I prefer so-called stable time loops. There’s only ever been one timeline, one self-consistent history. Time machines can simply pull them out of hat miraculously.
But what if it isn’t miraculous? Remember the hallucinogens loopers must ingest whenever one dons the time crown? What if that timeless period anti-between the end of one loop and the start of the next is a lot like dreaming. Synapses rewire, memories are consolidated, and one forgets all unnecessary information.
Brains are staggeringly complex, after all. For short loops, you have the advantage that source and destination are almost identical and thus you can transmit a “diff” specifying only which parts changed. But wouldn’t it be more efficient if you could specify less?
Do you need to remember every step of a long walk, if it was uneventful? Would you care to? Perhaps only the salient points are beamed back; you’re prepared, but the details are still surprising.
So far, it’s been assumed that once you decide to end the loops, the mechanics let you leave. What if they didn’t? What if, once you find a route you’re satisfied with, the universe begins optimizing. (Not quite differentiating, and yet.)
How many memories can be omitted and still get the same loop?
What makes a time loop stable is that you can’t go back and do it differently, what you did is what you went back to do. For this reason, these names strike many as deeply confusing; stable time loops are a fundamentally different thing.
And while this is true — I find it frustrating too — is it wrong at the limit? Loop long enough and you lose count, and the next loop after your million hits just like your millionth. You’ve been through this forever; it is unchanging.
Like rock at length eroding to cradle the stream that pours over it, you’ll eventually hit a fixed point and come out of one step of the eternal loop the same as you entered. And that is when it ends.
Q.E.D. We have produced a single self-consistent history from a groundhog day loop. It only required encoding a century of evolution into a brain. But this is where the optimization comes in; the more aggressively you forget between loops, the sooner you’ll happen across the fixed point.
At the furthest extreme, you can only send a few bits back in time, at most divining a couple yes-or-no questions about the future. this is the scenario I’d analyzed in my earliest rigorous explorations of time travel, because it’s most amenable to the simplest algorithms.
If two time travelers have yes/no foresight, and each asks whether her plan will work, there’s only four possibilities to check. This grows exponentially, but it’s nothing compared to the combinatorics of imagining every possible vision of the future gets its own timeline, or every possible configuration of atoms that could fall out of a time portal.
But due to the complexity of the universe around the time travel, there’s no algorithm that simulates which happens that isn’t equivalent to simulating every “discarded” timeline up to the point of provable paradox.
Ultimately, I no longer think it’s much more elegant to imagine a bunch of parallel timelines to which you need to sample randomly from, than a single, repeatedly revised, eventually consistent history.