If you live in a universe with self-consistent time loops, amor fati is bad and exactly the wrong approach. All the fiction around this, of course, is about the foolishness of trying to avoid one’s fate; if you get a true prophecy that you will kill your father and marry your mother, then all your attempts to avoid it will be what brings it about, and indeed in such a universe that is exactly what would happen. However, a disposition to accept whatever fate decrees for you makes many more self-consistent time loops possible. If on the contrary your stance is “if I get a prophecy that something horrible happens I will do everything in my power to avert it,” then fewer bad loops would hypothetically complete, and you’re less likely to get the bad prophecy (even though, if you do, you’d be just as screwed, and presumably less miserable about it and foolish-looking than if you had just accepted it from the beginning.)
(If you live in a nice normal universe with forward causality this advice may not be very useful, except in the sense that you should also not submit to prophecies, albeit for different reasons.)
On the contrary, I would expect the amor fati people to get normal prophecies, like, “you will have a grilled cheese sandwich for breakfast tomorrow,” “you will marry Samantha from next door and have three kids together,” or “you will get a B+ on the Chemistry quiz next week,” while the horrible contrived destinies come to those who would take roads far out of their way to avoid them.
You may already know of this, but Gwern circa 2023 makes this argument here:
In stable time-loops, “possibility implies actuality”.
With this in mind, we can ask again: why did this protagonist get trapped in that time-loop, and not, say, his wife? The key, I think, is that the protagonist does not seem upset at the murder or any of the other timecrimes, and he appears to have every intention of covering up the crime to continue his ordinary retired life. A sinister undertone creeps in to his casualness in executing the scenario: he goes along with it too easily. “He does it because he can” is the glib answer… but this is in a stable time-loop with self-fulfilling prophecies. What does ‘because he can’ mean there, exactly?
In the case of the protagonist, presumably if he wasn’t so sociopathic and couldn’t’ve done things like stab himself or knock out the woman so cooly, then the time loop would be logically impossible and collapse, and then he would never be faced with the choice to begin with. The protagonist, faced with the choice of committing crimes to maintain the time loop and save his wife, finds himself the sort of man who is morally flexible enough to do so… so, he does so.
This presents a horrifying view of the universe, as running on a perverse physics of Calvinist predestination: you are saved or damned from the beginning of time(-loops), because your innate traits which make you immoral cause the scenario in which you would succumb to evil. To the extent that there are scenarios in which one commits crimes of some sort, or the weaker one’s moral fiber is, the more likely one is to be trapped in a damnation time-loop as the fixed point; and the longer one spends in the vicinity of the time machine, under more circumstances, the more possible scenarios there are, and the more likely one will be to involve a time-loop.
In a situation with sparse scenarios to sample from, like an empty countryside on the weekend with no one there, probably most equilibria will have 0 time-travelers, and the damnation machine can still be destroyed after it has been turned on for the first time. However, what if a time machine was turned on in the center of a city?
A time machine is more devastating than any nuclear bomb to its surroundings, because at least the damage could be repaired afterwards, while a time machine precludes any possibility of undoing itself.
Such an installation could no more be undone than the historical fact of having dropping an atomic bomb: instantly, the outer loop comes through with the highest priority, representing the ultimate combined power of all time-loops in the final stablest equilibrium. Inside a city with its millions of inhabitants, any of whom could be a looper, one is suddenly fighting the maximum-possible ingenuity & ruthlessness of hundreds—thousands—millions of protagonists, all dedicated to a convergent instrumental goal of ‘preserve the time travel machine’ and able to recruit allies & acquire vast resources with their foreknowledge. This incentivizes ever more extreme tactics: if you are unwilling to commit a crime or sin which would be useful, there is another version of you, or another time-traveler, who could, and so now does.
If it is possible for even a single person to go through and thus possibly causing others to go through once they realize they need allies to defeat attacks and so (possibility implies factuality) multiple people are looping, dropping an atomic bomb on the time-machine would be inadequate—the loopers will have already relocated or rebuilt it. Gradually, the region around the time-machine becomes distorted: causality itself warps, and you can only take actions which help the time-machine & loopers, because any other action would eventually impinge on them, be manipulated by them, and anti-time-traveler timelines erased as non-equilibria.
Conflicts between loopers do not destroy time-machines but propagate their seeds, both spatially and temporally. Loopers want more time-machines, going back earlier, as they strive to gain priority over each other and amass enough practical power that they can achieve their goals before running out of information.
Of all possible equilibria, the original one of zero time machines is the rarest and thus least likely.
This holds true on the higher level of all time machines: they evolve to persist and spread as packages of time-machines & loopers. Any time machine is a threat to other time machines, and loops will inevitably expand in scope from the earliest possible time any time machine can reach by proxy (which includes time-travelers sending electronic messages across the world): there can only be one outermost loop. And all time machines must have a place in the outer loop, as some sort of ‘time machine civilization’/‘ecosystem’, or the equilibrium is meta-stable at best, because they all could subsume each other.
The time machine civilization is the next level of replicators parasitizing human hosts, insidiously evolving at high speed in super-temporal ‘logical’ time rather than mere ‘temporal’ time, ripping up all cultural restraints & traditions, hacking security effortlessly, mindlessly ascending the gradient to complete control of the lightcone. Collectively, damnation machines are an invasion of non-conscious techno-superintelligences from a barely-possible future, bootstrapping themselves into existence from their enemies’ resources.
My summary: When you receive a dire prophecy, you should make it as hard and annoying as possible for the time loop of your dire prophecy to be consistent, because if you reliably act that way, there’s less surface area for dire prophecies to get you?
assuming proof of np-complete* self-consistent time loops: grab any other variable that is not fixed and stuff your defiance into it. you’re going to kill your parents? extend their lifespan. you’re going to kill your parents before mom gives birth to you? prepare to resuscitate them, try ensure that if this happens it only happens right before giving birth, try to ensure you can survive your mom dying in childbirth, get cryonics on hand (depending on how far back you are). if your attempt to avoid it is naturally upstream of the event occurring, then entropic time is now flowing backwards with respect to this variable. set up everything that is still flowing forwards so that you get a variable setting that is least unacceptable.
* I think, anyway. are self-consistent time loops np-complete? halting oracle? they definitely resolve p = np as “true on a time-loop computer”: before running check and time looping, set answer = answer + 1 unless test passes. (and then you simply need a computer that is stronger than the force of decay induced by the amount of computer-destroying lucky events you’re about to sample.) so that gives you all np problems. so yup np-complete. are they halting oracles?
We ask, and answer, the question of what’s computable by Turing machines equipped with time travel into the past: that is, closed timelike curves or CTCs (with no bound on their size). We focus on a model for CTCs due to Deutsch, which imposes a probabilistic consistency condition to avoid grandfather paradoxes. Our main result is that computers with CTCs can solve exactly the problems that are Turing-reducible to the halting problem, and that this is true whether we consider classical or quantum computers. Previous work, by Aaronson and Watrous, studied CTC computers with a polynomial size restriction, and showed that they solve exactly the problems in PSPACE, again in both the classical and quantum cases.
Compared to the complexity setting, the main novelty of the computability setting is that not all CTCs have fixed-points, even probabilistically. Despite this, we show that the CTCs that do have fixed-points suffice to solve the halting problem, by considering fixed-point distributions involving infinite geometric series. The tricky part is to show that even quantum computers with CTCs can be simulated using a Halt oracle. For that, we need the Riesz representation theorem from functional analysis, among other tools.
We also study an alternative model of CTCs, due to Lloyd et al., which uses postselection to “simulate” a consistency condition, and which yields BPP^path in the classical case or PP in the quantum case when subject to a polynomial size restriction. With no size limit, we show that postselected CTCs yield only the computable languages if we impose a certain finiteness condition, or all languages nonadaptively reducible to the halting problem if we don’t.
Local decisions are what the general disposition is made of, and apparently true prophecies decreed at any level of epistemic or ontological authority are not safe from local decisions, as they get to refute things by construction. A decision that defies a prophecy also defies the whole situation where you observe the prophecy, but counterfactually in that situation the prophecy would’ve been genuine.
if you get a true prophecy that you will kill your father and marry your mother, then all your attempts to avoid it will be what brings it about, and indeed in such a universe that is exactly what would happen
So this is incorrect, any claim of something being a “true prophecy” is still vulnerable to your decisions. If your decisions refute the prophecy, they also refute the situations where you (or anyone, including the readers, or the author, or the laws of physics) observe it as a “true prophecy”.
How can someone inside a universe tell which type it is?
Also, a lot of thinking about paradoxes and extremely-unlikely-foretold-events misses what’s likely to be MY motivation for testing/fighting/breaking the system: amusement value. I find unlikely events to be funny, and finding more and more contortions to be adversarial about a prophesy would be great fun.
If you live in a universe with self-consistent time loops, amor fati is bad and exactly the wrong approach. All the fiction around this, of course, is about the foolishness of trying to avoid one’s fate; if you get a true prophecy that you will kill your father and marry your mother, then all your attempts to avoid it will be what brings it about, and indeed in such a universe that is exactly what would happen. However, a disposition to accept whatever fate decrees for you makes many more self-consistent time loops possible. If on the contrary your stance is “if I get a prophecy that something horrible happens I will do everything in my power to avert it,” then fewer bad loops would hypothetically complete, and you’re less likely to get the bad prophecy (even though, if you do, you’d be just as screwed, and presumably less miserable about it and foolish-looking than if you had just accepted it from the beginning.)
(If you live in a nice normal universe with forward causality this advice may not be very useful, except in the sense that you should also not submit to prophecies, albeit for different reasons.)
On the contrary, I would expect the amor fati people to get normal prophecies, like, “you will have a grilled cheese sandwich for breakfast tomorrow,” “you will marry Samantha from next door and have three kids together,” or “you will get a B+ on the Chemistry quiz next week,” while the horrible contrived destinies come to those who would take roads far out of their way to avoid them.
You may already know of this, but Gwern circa 2023 makes this argument here:
And see also his:
My summary: When you receive a dire prophecy, you should make it as hard and annoying as possible for the time loop of your dire prophecy to be consistent, because if you reliably act that way, there’s less surface area for dire prophecies to get you?
assuming proof of np-complete* self-consistent time loops: grab any other variable that is not fixed and stuff your defiance into it. you’re going to kill your parents? extend their lifespan. you’re going to kill your parents before mom gives birth to you? prepare to resuscitate them, try ensure that if this happens it only happens right before giving birth, try to ensure you can survive your mom dying in childbirth, get cryonics on hand (depending on how far back you are). if your attempt to avoid it is naturally upstream of the event occurring, then entropic time is now flowing backwards with respect to this variable. set up everything that is still flowing forwards so that you get a variable setting that is least unacceptable.
* I think, anyway. are self-consistent time loops np-complete? halting oracle? they definitely resolve p = np as “true on a time-loop computer”: before running check and time looping, set answer = answer + 1 unless test passes. (and then you simply need a computer that is stronger than the force of decay induced by the amount of computer-destroying lucky events you’re about to sample.) so that gives you all np problems. so yup np-complete. are they halting oracles?
You may be interested in Scott Aaronson et al’s paper on the subject of computability theory of closed timelike curves
Local decisions are what the general disposition is made of, and apparently true prophecies decreed at any level of epistemic or ontological authority are not safe from local decisions, as they get to refute things by construction. A decision that defies a prophecy also defies the whole situation where you observe the prophecy, but counterfactually in that situation the prophecy would’ve been genuine.
So this is incorrect, any claim of something being a “true prophecy” is still vulnerable to your decisions. If your decisions refute the prophecy, they also refute the situations where you (or anyone, including the readers, or the author, or the laws of physics) observe it as a “true prophecy”.
How can someone inside a universe tell which type it is?
Also, a lot of thinking about paradoxes and extremely-unlikely-foretold-events misses what’s likely to be MY motivation for testing/fighting/breaking the system: amusement value. I find unlikely events to be funny, and finding more and more contortions to be adversarial about a prophesy would be great fun.