Our attention was called to the movie Triangle last year, but it vanished from store shelves before we obtained a copy, thus delaying our consideration of it.  It is a horror picture, a slasher film of the genre in which a small group of people are trapped in an isolated location and some unknown person is killing them.  As the horror unfolds, we learn that it is one of their own--but that she has somehow been duplicated.  They are not merely trapped on an abandoned ocean liner in the middle of the ocean, they are caught in a temporal loop that keeps repeating each time the killer manages to kill everyone else aboard.  That's complicated and messy, and fraught with problems.

The first problem is that there must have been a first time, that is, a moment when the passengers of The Triangle boarded an ocean liner that actually was empty.  Those passengers received no distress call, because no one sent it.  There was no killer remaining from the previous histories to begin attacking them.  We thus face the complication of how the horror begins.

It must be noted that this is not a fixed time theory story.  Fixed time theorists would argue that it is entirely possible for everything to happen because it causes itself, and it always has happened and always will happen exactly the same way.  At one point main character Jess notes that something changed, that it happened in a different way this time, and indeed several things change between the first iteration we see and the second.  Further, the accumulation of some objects (necklaces in the drain, bodies on the upper deck) suggests that we are looking at a peculiar type of sawtooth snap, something like Groundhog Day or 12:01, but that not only are memories preserved, some objects from each iteration are found in the next.  Typical parallel dimension theory is similarly excluded--if she dropped the necklace in universe 3 and then traveled to universe 4, her necklace would not be there (nor would her other selves).  The question of whether this is divergent dimension theory is more complicated, but a good part of the analysis in this case would be the same as for replacement theory, so we will address that question later.

The telling of the tale begins at home with Jess and her special needs son Tommy.  Several things happen which are eerie, but which are later explained by the actions of a temporal duplicate.  We are also later given the impression that events of major significance are omitted from the telling at the beginning, as the Jess who arrives at the pier proves to be a temporal duplicate.  This makes the construction of an original history considerably more difficult, but that will be the place to start.

We noted that there has to be an original history in which there are no temporal duplicates.

Jess was invited to sail on the yacht Triangle by its owner, Greg, who knows her as a waitress in a local restaurant and likes her, despite the fact that Sally, wife of his friend Downy, thinks she is trouble, and has brought Heather along in an attempt at alternative matchmaking.  Heather, meanwhile, is attracted to the younger Victor, who lives with Greg on the yacht and works as his assistant when they sail.  Having no reason not to go, Jess arrives possibly late due to having to clean up the paint mess and change her clothes.

In the version we see, Victor asks where Tommy is, and she says he is at school.  It is true that some special needs schools operate every day, because particularly autistic children need consistency and do not do well with changes in the daily routine.  Jess might have brought Tommy along the first time, but that would have created a tremendous additional complication--Jess could not escape until Tommy was dead, and she would never have killed Tommy.  There are ways around this--perhaps Tommy is lost when the Triangle capsizes--but the simplest is that he was at school.  This is made the more likely by the relationship she has with him, not uncommon among single parents particularly of difficult children, in that she loves him dearly but he frustrates her such that she is frequently angry.  The opportunity to get out away from him for a day would be a welcome break.

It proves otherwise, as the Triangle is abruptly becalmed then hit by a freak storm which capsizes it.  The situation is different, though.  There is no reason for Jess to be exhausted (it is the beginning of the day for her, not the end of her ordeal on the liner).  We do not know with certainty which of the passengers survive.  We must assume that Jess does, though, because if she is not one of those who makes it to the liner she has no chance of reaching the end of the loop ever.  Heather might be alive; any of the others might be dead.  What matters is that Jess and at least one other passenger who is not Tommy reaches the ship.

The ship is named The Aeolus, for the father of Sisyphus whose punishment of rolling a stone up a mountain repeatedly to see it roll down again was popularized by Albert Camus, The Myth of Sisyphus, in which the repetition of futile effort never achieves its goal.  This thus sets the tone for Jess' trap, as she struggles to find a way to get off the ship and save some group of the yacht's passengers.

No one is aboard the ship this first time.  This means that no one is killing the visitors, but also that no one knows about the time loop or that the boat will reappear the moment there is only one left alive.  They will radio for help fairly early, but will make no mention of being killed, and will not (we presume) receive a response even though the Triangle will hear them.  Food and water will be their first problem.  There is water on the ship which is probably potable, but there is a hint of the food problem--initially there is fresh food on the table in the ballroom, and it is still safe to eat when Downy and Sally head to the theater, but shortly thereafter Jess finds that it is all rotting and moldy.  Thus in the first history the stranded passengers will slowly starve to death.

They will almost certainly delay their starvation by cannibalism; once the first person dies, at least one of the survivors will insist that their only hope lies in consuming the body and hoping help arrives before the rest of them die.  Help will not arrive, and it is likely that as their numbers dwindle each will realize that he is more valuable to the others--and they to him--as food.  They will begin killing and eating each other in an effort to survive.

When one remains, the Triangle comes within earshot, and its passengers board the Aeolus.  The crazed survivor of the previous group now has the added fear that these people have not been starved and thus are stronger and healthier; thus the killing continues, in part for food, and in part because the survivor knows what will happen once the others start dying.  She--for it has to be Jess--will start killing everyone but herself.

Why it has to be Jess will be the next subject.

Jess had to board the Aeolus, and had to be the last person alive.  The logic of this lies in what we mistakenly think we know about the loop.  We are told that the Triangle will return the moment there is only one person alive on the ship; however, we never see a timeline which ends with only one person alive, technically--in every timeline we see, there are already two versions of Jess on the ship when the third boards, and the first Jess is different from the second Jess because of what she has done and experienced, just as the second Jess is different from the third.  Yet there are only two possiblities, the first that the Triangle arrives at a set time but because of the coincidence that the penultimate passenger is killed at that moment causes Jess to reach the wrong conclusion--repeatedly--and the second that she is correct, that the boat arrives when she is the only survivor, but with the caveat that it does not matter how many temporal duplicates of her there are on the boat, as long as they are all of her.

The possibility that she is wrong is belied by the reconstruction of the original history:  if the Triangle arrives on schedule before 11:30 in the morning (the time on Greg's watch when they reach the ballroom), and the temporal jump has taken them back to perhaps 8:00 (Jess' watch and the clock in the ballroom both say 8:17, but they have already explored part of the ship by then) then they only have to survive three hours before the next boat arrives; and in three hours more it will arrive again, and by then they will realize that the clock in the ballroom resets to eight when the boat arrives and the boat arrives again at eleven, and will be able to organize some way of using the gear aboard the ship to get them all safely aboard the righted and repaired boat.  The entire horror story is prevented.  Thus to have the story we see, we must begin with the assumption that the Triangle reaches the Aeolus at the moment that the penultimate passenger dies.

It might be suggested that someone else could have been the last man standing the first time through, and that Jess managed to defeat him (or her).  The odds are very much against this.  Whoever survives the first time is the only person who knows that the boat will return, or that it returns when everyone is dead; Jess has no reason to kill anyone, and no reason to suspect the doppelganger of one of the party if she does not see them together.  The doppelganger also already knows more about the ship, having been here for weeks.  He certainly has a gun and ammunition.  More fundamentally, though, both copies of him would have to die and Jess survive before the boat returned, and she has neither reason to kill them nor knowledge that there are two.  Thus the logical conclusion is that in the end of the first history, Jess happens to be the survival winner, and so faces the fact that there are two of her in the next round.

That second round is also complicated, because there are only two of her; but the first one is trying to figure out what's happening and manages to wound Victor and warn him about the second one, and when he attacks the second one she manages to survive, killing him and starting the bloodbath.  But there are still problems--until there are three, there is no sniper in the theater, no message on the mirror, no one sending people there to be fish in a barrel.  That makes it more dangerous--she might be trying to explain to people what she knows, but she has not yet deduced that the boat arrives when everyone is dead; on the other hand, she's a lot less stable, having watched some of her original companions starve, having eaten their bodies, and having killed the last of them for food.  That's a very different Jess, and it is almost impossible to imagine how that history goes; but once it is down to two Jessies, and the boat returns bringing the third, things begin to stabilize.  The first Jess will be tossed off the ship, and will wash ashore early that morning to finish out the anomalies.

That creates the situation aboard the Aeolus as we see it, but it leaves many unanswered questions.  Next we look at the keys.

Although we have provided a way to get from the original horror to the version we see, as the main character is caught in a sawtooth snap and faces her own temporal doppelganger who is trying to kill everyone, including her, there are a number of problems which remain, and the first concerns her keys.

When the party from the Triangle boards the Aeolus a second time, the surviving Jess from the first party attempts to observe them surreptitiously.  She drops her keys, and realizes that she has been heard, so she flees, leaving them behind.  Victor recovers the keys, and Jess--the new Jess--recognizes them as her own.  She then retains possession of the keys until she in her turn drops them while trying to observe the third party that boards.  At issue is whether Jess already has her keys, and why she does not realize that.  After all, if someone handed a set of keys to you that looked exactly like yours, you would probably put them wherever it is that you usually keep your keys--pocket, purse, wherever--at which point you would discover that your keys were already there.  This is a marked inconsistency as compared against the dropped locket, because there were dozens of duplicate lockets but no duplicate keys.  If Jess brought her keys aboard, she must now have two sets; if she lost them before she boarded, she cannot have any.

(There is a separate problem with the keys, which will be addressed later.)

The solution perhaps lies in the first run--the run we do not see, as we see the experience of the Jess who boards when two duplicates are already aboard.  As we mentioned, in the first history she did not take a nap and therefore the situation on the Triangle was changed somewhat when the storm hit.  We do not know who survived to reach the Aeolus--but if we assume that in that first capsizing Jess somehow kept her keys, and that in the subsequent ones she did not, that puts a single set of keys on the ship being passed from one to another.

It will not save us ultimately, though.  We have an anomaly within an anomaly, one loop that runs from 8:00 to 11:00 while they are on the ship, and a second that runs from when Jess washes up on the beach to when she falls into the ocean.  The first time she boards the Triangle she does not take that nap, for any of the times she boards the ship on that encompassing anomaly; every other time she boards the triangle she takes the nap.  The only thing that changes aboard the Triangle is that they receive a distress call, just before the storm, probably on the second and certainly on the third iteration, which they are unable to answer.  It is certainly a butterfly effect change, but apparently because they received the distress call, Jess lost her keys, so that the first Jess to board the Aeolus had hers (still after everyone else starved to death) but her subsequent counterparts lost theirs when the ship swamped.

That, though, is only one of many problems here.

One of the more difficult problems is the issue of the clocks.  When they reach the ballroom, perhaps fifteen minutes or so after boarding the ship, Greg says that according to his watch it is 11:30; that the ballroom wall clock says 8:17 is not really significant in itself--it is certainly permitted to be wrong--but that Jess is also wearing a watch and its time matches that on the clock is more challenging.

The obvious significance is that at some point, most likely upon boarding the Aeolus, the group was shifted back to eight in the morning.  There would be no reason to expect their watches to change, and Greg's does not; similarly, the clock aboard the ship ought to show what time it really is aboard the ship, and the ballroom clock does.  That, though, gives us two problems, both of which come down to stating that something is involved which knows the future.  It knows that Jess will be the one who survives, and so resets her watch to show the correct time; more significantly, it knows exactly how long it will take for her to be the last one alive, because the only sense we can make of the time resetting to eight in the morning is that minute by minute this is how long it will be before the boat arrives, and the boat only arrives when everyone but one person is dead.

Further, we have already deduced that it takes different amounts of time to reach that point with each iteration.  The first history takes weeks, as most of them starve and the remainder battle for survival against each other.  In the second history, the shooter is not yet part of the story, and so the deaths will be different and probably take longer.  It even appears that the third time through is far from the last time through--one of the second-time-through Jesses disrupts the shooter's shot because she anticipates it, having already been the first-time-through Jess and so knowing what happens, but that means that the third-time-through Jess must have been there (although why she did not anticipate her previous self making the save is yet another mystery).

Logically, then, both the clock and the watch must have different times with each iteration, to allow enough time for everything to happen before we reach the late morning arrival of the Triangle.  However, that also means one of two things.  Either, as we see in Minority Report and Next, someone or something is able to calculate with extreme accuracy exactly what will happen and how long it will take, or else somehow, as with Frequency, information is traveling from the future, a separate trip through time, simply to fix the clock.  That is a different and distinct anomaly, too, because even though its end points are identical to the endpoints of the history Jess is experiencing, it must be that only the clock is different and she has no recollection of having lived through this history before, while the other anomaly is experienced as if time continued uninterrupted.

The only way to save the movie at this point is to assume that something "intelligent" is involved in this malicious stunt, and that it is intelligent enough to know exactly how long it will take before Jess is the only person alive, so that it can set the clocks accordingly.  That moves the anomaly from an unexplained random natural event to the malicious act of a supernatural intelligence; Jess is not merely the victim, she is the target.

There is a peculiarity that catches our attention.  In each iteration of the loop, the Jess on her second time through takes a shotgun and some shells, and the Jess on her third time through also takes a shotgun, shells, two ammo bags, and a jacket.  Since the third time through Jess arrives first, there is a gun missing (and fewer jackets) when the second time through Jess arrives, which makes sense.  What does not makes sense, though, is why there are still guns if the loop has repeated so many times and where the guns go when the loop resets.

This is made the more complicated by three objects that are accumulating:  notes from Jess, pendants in the drain, and bodies on the upper deck.  That is, we might suppose that the ship resets to the way it was before anyone boarded, but it does not do so if it retains these objects.

We get closer if we assume that anything which was on the ship when the crew of Triangle boarded resets to its original condition, but anything which came aboard the ship duplicates itself.  Thus supplies in the weapons locker are restored and vanish from their places elsewhere (when Jess washes ashore, she does not have the jacket), but the lockets and the bodies accumulate.

That, though, fails to resolve the issue of the note; and it is made the more glaring by the writing on the mirror.

There are at least sixteen lockets in the drain, and at least sixteen bodies of Sally on the top deck, so they must have been through this at least that many times.  (There is a further complication with the locket, by which this must be at least the eighteenth time through.)  There are about twenty-five copies of the note, and when she finds them she picks up the pencil and paper, which are already there, and copies the note so as to compare the handwriting to her own.  However, the paper and pencil were both aboard the ship, and they ought, like the ammo and guns and food, to reset to their original condition--the notes ought to erase themselves and return to the pad.

It is difficult to argue that this is different from the ammo; after all, she changed the state and location of the shells as much as she did of the paper, perhaps more.  But when we consider the message on the mirror it is the more difficult.  She saw that message on her first and second times through the loop, but she wrote it at the beginning of the third time through, using Downy's blood.  Downy's blood counts as something brought aboard, and just as Sally's body it ought to remain where it is when the loop resets; but that would mean that the Jess passing through for the third time who already saw the message would find it already written by some previous Jess.  If the mirror erases and resets, the notes have all the more reason to do so; if the notes do not, the mirror cannot.

One little mistake, we might say; but it seems that there are more mistakes.

We noted that there was a further complication with the locket; there are a few other little problems that are very difficult to resolve.

The locket catches her eye because it is caught on the grate, dangling where it will dance in the light; she recognizes it as a duplicate of the one still around her neck, but then drops it.  Because she drops it she sees all the others; because she is looking at all the others, she hooks the locket around her neck on the grate, and loses it as the chain breaks.  That, though, means that the locket she just dropped is not caught on the grate, and neither is the locket she first saw.  The next time through the loop, the "second time through" Jess will not see the lockets at all, and will not lose hers; and since she will neither see them nor lose hers, no subsequent Jess will do so.  Yet if that is the case, we have no way for the lockets to be there at all.

The answer must be that there is a way in which she loses the locket when she does not see them, by which it falls from her neck and gets caught on the grate.  It seems improbable; there is no obvious way for this to happen.  However, it sets up a sequence in which she sees nothing, drops her necklace and does not realize it, and it gets caught in the grate; the next iteration of her sees the locket, drops it, loses the one she is wearing also, and leaves nothing for the next iteration to see, who, seeing nothing, accidentally drops her necklace to get it caught in the grate.  It is another way in which the timelines must differ for anything to work at all.

There is also the problem of the first note.  Second-time-through Jess finds a note in what she recognizes as her handwriting; she copies the note to confirm this, and now there are two; eventually there are about twenty-five, and presumably they continue to accumulate.  Yet why, and when, did she write the original?  Second-time-through Jess does not understand the idea that once they are all dead the loop will repeat; the original note would have to have been written by third-time-through Jess.  Yet that means that third-time-through Jess is trying to communicate to herself, and she has no reason to do that until she is faced with the challenge that her duplicate self is about to kill her.  In order for any of the notes to exist the first one must exist; but we cannot imagine any scenario in which the first one would have been created.  Something very different must have happened on the earliest repetitions of history.

There is also a body problem.  Sally's bodies are piling up on the top deck, and Jess tosses Downy's overboard; it seems that Victor is hard to kill, but eventually falls overboard unseen.  However, nothing is ever done to remove Greg's body from the theater--and thus every time Sally and Downy reach the theater, there should already be a dead Greg waiting, and another dead Greg should be added, and these bodies should accumulate just as Sally's do on the top deck.

The body problem is further complicated by the changes in history--we know that the third group to board is attacked in the theater, and Downy and Sally are both killed by the sniper there; but the second time through, their bodies are not there when they arrive, even though when they are killed elsewhere their bodies remain for the next iteration.  Did someone move the bodies?  Jess did not do it then, because the Jess for whom this was the first time through was fleeing and the third time through Jess was pursuing, and the second time through jess was in the hold reading papers and looking at lockets.

In a similar way, the blood trails also should be accumulating--the fresh blood left by wounded characters should be dripped atop residue of old blood from the previous run, because blood and bodies remain (they did in the bathroom, and on the top deck).  Yet the blood is always fresh, as if someone removed the old blood on the reset.

But compared to some of the problems that remain, these are relatively minor; they are more like continuity errors, points the filmmakers missed.  There are still several very large ones awaiting our attention.

We counted about eighteen lockets, about twenty-five copies of the note, and at least sixteen bodies of Sally on the upper deck, and thus we conclude that the loop has been repeating at least twenty-some times.  However, it seems to be a loop within a loop, and we see that the outer loop is happening when she tosses the body of the bird over the edge of the retaining wall, and sees that there is already a small pile of bird bodies there.  The problem is, there are not enough bird bodies--we can count about half a dozen, far short of the twenty-five copies of the note.

We might think that this is because bird bodies have washed away; but that would mean that the tide rose high enough to catch them while she was on the ship, and in that case there would be no bird bodies here:  if it rose that high one time, it would rise that high every time.  We are probably supposed to think that the outer loop does not repeat itself as often as the inner loop; that is, she goes through the loop on the ship three times and then escapes it into the other loop once, and then returns to the loop on the ship thrice more, and escapes it for one iteration of the outer loop.  Thus there ought to be about three times as many duplicates of each object on the ship as there are of the birds on the shore.  That, though, will not wash.

The problem arises because Jess escapes the inner loop by falling into the ocean and washing ashore, which puts her in the outer loop.  However, every version of Jess that boards Aeolus falls into the ocean, and thus every version that boards Aeolus ultimately washes ashore.  The count on the birds should not be more than one or two fewer than that of the lockets, or the notes, or the bodies, because every Jess who loses a locket, writes a note, or stands beside a dying Sally ultimately falls off the ship, and thus washes ashore, kills a bird, and finds the accumulating pile of birds.

Perhaps Jess tossed some of the birds farther from the ledge than others, so that most of them washed away but only some remained; or perhaps other factors interfered, such as scavenger carnivores or the gradual pull of gravity sliding bodies toward the water.  These ideas are inadequate; Jess is gone for only a few hours before another Jess falls in the water, and the bodies will accumulate, even if a few are lost to the ocean.

(There is another complication here.  Jess returns to Triangle because Tommy is killed in the car accident; she has the car accident because she was dealing with Tommy's screaming while speeding to escape the time loop, which she knew was happening because of the bodies of the birds.  The first time she hits a bird, there will not be a pile of birds, and she will not suspect that she is caught in the time loop, will not be speeding, and being in a different place doing something different will not get in the accident--as we discussed in Butterfly Effect II.  Thus she will not have the accident, Tommy will not be killed, and she will not board Triangle and so travel to Aeolus, and everything ends before it starts.  But the film obscures this by showing us the middle of a loop that cannot have a beginning.)

The other possibility for the inconsistent number of birds is that Jess does not escape every time.  We see Jess send herself into the ocean, and then see herself fall into the ocean, and then we see the Jess who pushed herself, and saw herself, fall into the ocean herself, and if they all wash ashore there are as many birds ashore as there are pendants, notes, and bodies aboard the ship.  However, the ocean is precarious and unpredictable.  It might be that two out of three, or three out of four, Jessies drown and are consumed by ocean scavengers, never reaching the shore.  That, though, forces us to wonder why.  The timing seems to have stabilized, the position of the ship is fixed, and Jess' condition is not significantly different.  We must assume that events and conditions the time traveler cannot affect are unaltered, and thus she should fall into the same currents, and ought to wash up onto the same beach in the same condition.

Ultimately, then, there are not enough birds, because Jess has to reach the shore every time she leaves the ship, in order to return and try again.

It is not clear exactly how many times Jess has boarded Triangle.  We counted at least sixteen bodies of Sally, as many lockets, and perhaps twenty-five notes.  What is clear as she boards Triangle again at the end of the film is that before she leaves Aeolus there will be at least three more of each of those.  It also appears clear that she will be no closer to undoing the loop and saving Tommy, and so will once again board Triangle for Aeolus.  There will be more lockets, more bodies--nineteen, twenty-two, twenty-five.  Roughly every three hours the count increases by one, which is eight more bodies per day, fifty-six in a week, and soon the total moves from hundreds to thousands.  Probably before it reaches millions, though, the ship will flounder from the weight.

The notes are a separate problem.  The pad and pencil are already aboard, and with each repetition she writes another note and tears a page from the pad.  We have already recognized that the pages are a problem; the pad and pencil are also problems.  We can suppose that the pencil replenishes itself to its condition before she used it, but if the pad is replacing its pages, why are the ones on the deck still there?  Eventually the number of notes will exceed the original number of pages of the pad; we do not know whether the pad will be depleted or replenished.

Yet it hardly matters; even the accumulation of lockets hardly matters, although eventually they will stack to the level of the grate and Jess will no longer be able to drop yet another through it.  It is Sally's body that becomes the problem.  Even before there are enough to sink the ship, they will pile above the rail and be visible from the boat on approach, or spill down the deck, down the steps to the decks below to be discovered sooner.

Eventually the survivors from Triangle will be unable to board Aeolus, whether because bodies of Sally block the deck or the ship sinks or the stench of death is so strong they do not proceed.  At that point, the loop breaks--and we do not have an adequate resolution for what happens after that.  All we know is that the loop continues forever, and the loop cannot continue forever, because as the repetitions approach infinity so do the numbers of notes, lockets, and bodies aboard the ship.

Infinity has another problem.

Before the movie is over, Jess kills herself.  However, she does not kill her self, in the usual sense.  Rather, her older self kills her younger self.

This immediately and directly creates a grandfather paradox, without the intervention of the grandfather:  if you kill your former self, your former self can never reach your age to kill you, and you create an infinity loop, in one segment of which you travel to the past and kill yourself, and in the other segment of which you are not alive to do so, so you live and ultimately travel to the past to kill yourself.

The film offers a classic answer to this problem, and overlooks the flaw in the answer.  It is now impossible for the younger Jessie to board Triangle, travel to Aeolus, return to that morning, and in turn kill her younger self; but what if the older Jessie takes her place?  Thus the younger Jess is dead, her body spilled on the road by the car accident, and the older Jess makes the trip which ultimately brings her back to the house to kill her younger self.

And the infinity problem we just addressed comes back in stark relief:  from the moment she returns home and discovers that it is that morning to the moment she washes up on the beach, she ages at least twelve hours, half a day  If there are six birds, she is already three days older than she was.  Perhaps no one would notice that; but when she is three years older than she was it will start to become apparent, and at three decades it will be unmistakable.  Jessie ages with each iteration, and will not pass for her younger self forever.

Films like Groundhog Day and 12:01 escape this kind of problem by having the time traveler return to his own younger body with each iteration, but with the knowledge of the previous trips intact.  Triangle cannot do that, because it specifically makes the point that the older Jess kills the younger Jess, and thus the older Jess has already aged those twelve more hours each time she does so.

Again, the infinity problem hits a limit.  Jess cannot become infinitely old; she must eventually die of old age.  Very much sooner than that, she will not be able to pass for herself--not with Tommy, and not with Greg when she reaches Triangle.  This is quite apart from the accumulated scabs, bruises, and scars from the injuries she receives during her time aboard Aeolus.  Unless the same magic which carries her back to that morning also rejuvenates and heals her, as if she had never been through all that had happened, she is not the same person and ultimately cannot convincingly pretend to be her.  That person died; she killed herself.

This same problem of infinite aging also impacts the keys, in much the same way it does the watch in Somewhere In Time:  the same keys are being passed from the end of one loop to the beginning of the next, and they get older with each pass.  However, in this case the problems of accumulation and Jessie's own aging are going to destroy the loop long before the keys change much.

Initially it appears that the problems might be resolved by taking advantage of divergent dimension theory and of a particular problem which in this case becomes a feature.  If we assume that our time traveler who traveled from eleven to eight in the morning created a new universe in which there is a parallel version of herself, then at eleven if she makes the same trip again, she will find that not only is her "original" self arriving in this new world, she will also find that her "previous" self who already made this trip is also there.  Thus we could resolve much of this if we assume that at around eleven in the morning any version of Jess aboard the Aeolus leaps back to the pristine version of the ship that existed at eight in the morning, and creates a new universe in which everything was exactly as it was the last time she experienced this moment, with the addition of her presence.  Since at the end of the third time through she falls into the ocean, there are never more than three of her on the ship, and that's not a problem.

More problematic is the accumulation problem--the lockets, the bodies.  This is not insurmountable, though; we just have to assume that everyone and everything that boarded the ship with Jess also makes the trip to the past, and thus Sally's bodies accumulate because they are all time traveling along with her.  (This incidentally suggests that the trip is not rejuvenating Jess, as it ought to have rejuvenated Sally as well, and that's not happening.)  We might even stretch it to suppose that those notes--already a problem in their origin and their continuation--also somehow are traveling to the past each time she does, because she created them (although the message on the mirror is not).

She still faces the problems of infinity accumulation, including with her aging, but accumulation is inherent in the story and so is a flaw we cannot fix under any theory.  It does not prevent the story we see, in the sense that this could happen in one of the divergent histories created.  Since she begins the "outer" loop by killing herself, she does not have the problem of her own temporal duplicate thereafter.

More difficult, though, are the dead birds.  We can understand that Triangle travels to the past, and they board Aeolus hours earlier than they think; we can understand that everyone aboard Aeolus also travels to the past at that moment, whether alive or dead.  However, if when Jess washes ashore she is once more in a new divergent universe, she is in one in which she has not yet killed a bird, and there should be no birds on the shore even if she is going to kill one, unless dead birds are also traveling to the past with her.  It would then seem that she forged a link with the birds by killing them; but if so, why did she not forge a link with her younger self when she killed her, or with Tommy when she killed him, such that they, too, travel to the past with her, and are inexplicably lying on the highway early that morning?  Or are their bodies accumulating in a morgue somewhere, causing an increasing number of duplicate coroners to ponder the problem of an increasing number of identical corpses, and indeed, wondering why drawers and tables which yesterday were empty are now filled with bodies tagged, if at all, indicating that they came from an accident which would not occur until later that morning?

Even more difficult, if she is creating a new world that matches the one from which she just came, when she arrives home at eight she should find duplicates of herself arriving at that time--that is what happened in the world she is now copying.  The number of copies of Jess ought to be roughly equal to the number of lockets, and they could not hide from each other for long.

Divergent dimension theory may resolve a few problems; but unlike with Source Code it ultimately leaves us with more problems than it resolves.

In every direction we turn in Triangle, we find another problem.  Here are some we have not yet mentioned:

Downy's body is tossed into the ocean by one Jess, and seen there by another; but this happens after time has reset, and so it is afloat there.  The gulls congregate on it.  Then when she attempts to show the body to Victor, it vanishes as the gulls scatter.  Why does Downy's body vanish, if Sally's does not, and why at a moment when time is not resetting?  The body was in the stateroom when the new Triangle survivors boarded, and Jess at the beginning of her third time through carries it to the rail and throws it in the ocean, and Jess on her second time through sees it shortly thereafter, so we are well into this line of the loop.  The body might sink, but why would it have remained afloat so long and then vanished without a trace?  If it was never there, on the other hand, why were the gulls there?

Jess also has memory problems.  It seems that when she boards Triangle she knows exactly what is going to happen--she even apologizes to Greg for it.  Then she takes a nap, awakens from a dream, and thinks the reality is the dream.  She boards Aeolus and reports a vague feeling of déjà vu, but despite having lived through perhaps nine hours of terror aboard this ship, she remembers nothing clearly, but only has a feeling of familiarity.  This did not happen to her when the clock reset, nor does it happen later when time repeats aboard the ship; it happens when she falls asleep aboard Triangle, at which point she no longer remembers any of the horror from the ship, nor even that Tommy is dead.  What happened to her memory?

On the subject of what happened to her memory, it is passing strange that on her first time through she hides in the galley, and on her third time through she does not know that she is hiding in the galley. That would make sense if the Jess who is now pursuing did not hide there when she was fleeing; but for the Jess who is fleeing this is the first time, and she will make the choices she would make the first time. Thus it makes no sense for her not to know where she is.  She has the same problem when she fails to anticipate that her next self will save Downy and Sally, despite having done so in her turn already.

Throughout the film, we have the impression that the writers were not concerned in the least with whether any of it made sense.  They simply thought of terrible things that might happen, and tossed them together in a movie loosely threaded together by something resembling a story, borrowing tropes from other time travel movies without giving thought to whether they work or what theory of time might make this possible.  I suppose in the end we can rest relieved that the story Triangle depicts is impossible, and so it will never happen to any of us.