Guardia Royal Line Paradox

[Zaperking]

Well, would you really trust a bunch of kids with the entire timeline of the world? Hell no.
They probably stepped on a heap of butterflys, killed many monsters that would evolve into something else in the prehistoric era.
The planet obvious has to somehow safeguard the time line, but only let Crono and co edit the main events that would lead to the planets demise. Otherwise Crono might as well never have met a bunch of people if the whole time line could be disrupted.

[maggiekarp]

But... that sorta happened anyway. CT REWARDED screwing up the timeline for their own benefit. Crono had tasty food dishes named after him and tons of buddies through time.

[alpha]

well as far as the ayla thing goes I once again state that Kino is the one brought from 65,000,000 which means that even if he would have origninally screwed ayla to start the line.. he would have found someone else. and as far as time pardoxes go.. time moves forward no matter what you are correct however.. the way the gates tied the time periods together connects all those times. think about. time would not erase the guardia line from existance becuase of the removal of ayla or kino as long as they stayed alive because their presence would still be tied to their original time by some bond or another. and Fate(not the computer) can have some influence here..

and as the chrono dania thing.. the guardia line would have continued with or without time travel
possibilities include but not limited to.
1. Lucca introduces chrono to dania someday as lucca seems to be on a walk in basis in the castle.
2. Nadia marries someone else so that she would become queen ((eventualy))
3. Even without the time travel nadia and chrono still would have met in leene;s square during the millenial fair. and who knows where that would have gone without the telepod turning into a make shift gate entrance

[Kebrel]

Fate(destiny) does not exits in the chronoverse, The whole point of the story is them making there own choices to stop lavos. In chronocross you think the whole there all so fighting a computer that is manipulating the people of El Nido that is named fate you don't think Square was trying to draw parallels.

[Thought]

Hello.

Actually, Time Error seems to be the perfect explanation as to why the Guardia Royal line doesn't vanish once Ayla leaves her own time period.

Time Error, as I understand it, is that the specific instance a gate will open up into is its original period + the time error. Or, in other words, if the gates original period is Noon, June 1st, 1000 AD and the Time Error is 3 days, (the amount of time that Crono, Lucca, and Marle were gone on their first trip), then the gate would open onto June 4th, 1000 AD, at noon.

Let us then apply that general concept to Time Travelers themselves. Any event that occurs in a time traveler’s life after they have first traveled is the period of their original departure + their own personal “time error.” Let us call the product of this equation a “Time Index.” Specifically, it is the Time Traveler’s Time Index. An event in that traveler’s life might also have its own Time Index that would match the traveler’s index when the action occurs.

Let us say that Ayla is going to have children when she is 30, as established by the timeline from Crono’s perspective in 1000 AD. When she leaves on her adventures through time, however, she is only 25 (well, her age is never given, but it doesn’t really matter). The problem posed by the Guardia Royal Line Paradox (GRL Paradox) is that the future she will travel to wouldn't have her in its past at the age of 30 in order for her to have the children that would then establish the Guardia Line. Thus those children don't exist, thus the Guardia line doesn't exist.

As a person’s actions are not predetermined, the timeline can't assume that Ayla will come back. However, neither can the timeline assume that she doesn't return. As in the original timeline Ayla wouldn’t have had a child until she was 30, that child can neither be born nor not-born until Ayla reaches 30. If her travels through time at the age of 25 made her child she bears at age 30 cease to exist, then we have a problem of fate; time is assuming that Ayla will not have children at 30, a choice that for her is still in the future!

Thus, Ayla's Time Index must be 25 + 5 before the issue of her children can even be addressed (25 being her original age when she first departed her timeline and 5 being the time that needs to pass before she would have originally had a choice in having children); as Ayla's Time Index never reaches 30 in-game, there is never a chance, in-game, for the GRL paradox to come into effect.

This, of course, leaves the question then of what time would actually look like from an outside perspective (say, for Gaspar at the End of Time). He would see the original timeline, which is all of Ayla's life played out properly, with children. Then he would see Chrono and the others arrive and leave with her, establishing a new timeline. At that point, Ayla's history up until she left would be the same but what of her history (and her effect on all of Time) after she left?

As a timeline can only change based on real actions (and not just probability), the events in her life can't change until she is old enough to be at the appropriate spot in her own personal timeline to make those "real actions" or to not make them. Her own personal Time Index (her departure point + her personal time error) must match the Time Index of the event (the specific point in the timeline when an action would have been completed) before the outcome can effect the timeline. Until such a point, the action remains unresolved and in a state of flux.

As such it would seem that the timeline proceeding from the point that an individual leaves their timeline and the point in which they would have naturally died (if they hadn't time traveled) must be in a state of flux until such a point as the specific Time Index of the time traveler matches the Time Index of the event. Only then can the event’s flux be resolved into a definite outcome. So, for every second Ayla is trekking through time, the timeline is actually being re-written with Ayla being missing from her own era for that one extra second.

One might wonder what the timeline might look like, at time index “Ayla is age 30,” when Ayla is only 29. It must, alas, remain in a state of flux. As the future must still exist, and it must be calculated based on the lives of those who lived before, I would suggest that the future would simply be based on the last valid timeline. After all, a timeline can’t be replaced until an action has occurred to change it, and no action can occur or not occur until the two Time Indexes (that of the Traveler and that of the Event) match.

As most characters aren’t gone from their timeline long enough to really miss out on any major events, the GRL Paradox doesn’t manifest. There is only one exception to this; Robo. He “travels” through time for more than 400 years. Thus, any event that the original-timeline Robo did from 2300 AD to 2700 AD would be erased. Alas, Crono and the gang never travel so far into the future in order to test this theory. As Robo is back in 2300 by the end of the game, presumably all the events in his life from 2300 to 2700 would be changed to have a new Time Index.

Nicely, this theory does get around the “The Entity Did It” argument, and really it is quite simple (which makes Ol’ Occam happy, I’m sure); the Guardia Royal Line still exists after Ayla has time traveled because time is then in flux and it defaults to the last valid timeline, which just happens to have the Guardia Royal Line existing.

[alpha]

o.o Well said. but There is a thing with Robo. Without lucca intervening he might possibly ave sat and rusted for another 400 years so not really that big a loss aye?

[dankun]

All right! A real challange to my theory... I will try to take this on, as best I can.
I'd been meaning to answer your post since a while back, but couldn't find myself to make time for it.
Oh well... here we go!

Actually, Time Error seems to be the perfect explanation as to why the Guardia Royal line doesn't vanish once Ayla leaves her own time period.

Time Error isn't exactly the answer to this problem in particular. Actually, I'd say that Time Error is the problem here.
Let me just make a quick link to it, so as to establish a reference point in my post:
http://www.chronocompendium.com/Term/Principles_of_Time_and_Dimensional_Travel.html#Time_Error

Time Error, as I understand it, is that the specific instance a gate will open up into is its original period + the time error. Or, in other words, if the  gates original period is Noon, June 1st, 1000 AD and the Time Error is 3 days, (the amount of time that Crono, Lucca, and Marle were gone on their first trip), then the gate would open onto June 4th, 1000 AD, at noon.

Time Error is, basically, another axis of time that runs perpendicularly to normal time line and its there to establish the possibility for Crono and his team to actually have a chance at making changes to the timeline, like they originally planned. Without Time Error, nothing would make any sense as they could pretty much do anything they wanted while time travelling (like going back to a same time event (only a little earlier) that they had already previously gone back to, and doing something different that could potentially disrupt the whole space-time continuum!

Let us then apply that general concept to Time Travelers themselves. Any event that occurs in a time traveler’s life after they have first traveled is the period of their original departure + their own personal “time error.” Let us call the product of this equation a “Time Index.” Specifically, it is the Time Traveler’s Time Index. An event in that traveler’s life might also have its own Time Index that would match the traveler’s index when the action occurs.

You see, what you call a 'Time Index' is actually what the Time Error concept represents. Time Error is precisely just that, a record of what a Time Traveler has done so far in his own Time Line. This record is kept, though I don't know by whom or what (probably the very fabric of time, since it is activated every single time in that someone time travels, by whatever means) so as to not allow him to go back to a previous event that he has already been to and interacted with. (Note that this also works quite well with what the concept of Time Traveler's Immunity establishes).

Let us say that Ayla is going to have children when she is 30, as established by the timeline from Crono’s perspective in 1000 AD. When she leaves on her adventures through time, however, she is only 25 (well, her age is never given, but it doesn’t really matter). The problem posed by the Guardia Royal Line Paradox (GRL Paradox) is that the future she will travel to wouldn't have her in its past at the age of 30 in order for her to have the children that would then establish the Guardia Line. Thus those children don't exist, thus the Guardia line doesn't exist.

First of all, you can't assume at which point Ayla is actually going to have children. Fate isn't a constant in the Chrono series, and as such we can't make assumptions based on such a concept. And yes, the Guardia Royal Line Paradox is the problem posed by Ayla's disappearance (and therefore that of her whole descendants) from her own time line, during the time in which she spent with Crono saving the world.

As a person’s actions are not predetermined, the timeline can't assume that Ayla will come back. However, neither can the timeline assume that she doesn't return. As in the original timeline Ayla wouldn’t have had a child until she was 30, that child can neither be born nor not-born until Ayla reaches 30. If her travels through time at the age of 25 made her child she bears at age 30 cease to exist, then we have a problem of fate; time is assuming that  Ayla will not have children at 30, a choice that for her is still in the future!

That's not the only thing that you presuppose that Time is assuming here. And yes, you are indeed correct.
The main problem here is that of fate. Time simply can't assume anything, regarding the ultimate fate of the Time Traveler. You say that the choice to have children is hers for her to make, and yet claim that she must somehow have a predetermined moment in her time line and which she must have this offrsping that will ultimately establish the Guardia Line.

Thus, Ayla's Time Index must be 25 + 5 before the issue of her children can even be addressed (25 being her original age when she first departed her timeline and 5 being the time that needs to pass before she would have originally had a choice in having children); as Ayla's Time Index never reaches 30 in-game, there is never a chance, in-game, for the GRL paradox to come into effect.

As I explained before, and to make it even clearer: A Time Index for each time traveler is actually what the Time Error stands for. We just never really see this in-game because you are always traveling in a party of three! (As stated by Gaspar, because otherwise it would cause a disrpution in the time-space continuum, which is why you ended up there in the first place)

This, of course, leaves the question then of what time would actually look like from an outside perspective (say, for Gaspar at the End of Time). He would see the original timeline, which is all of Ayla's life played out properly, with children. Then he would see Chrono and the others arrive and leave with her, establishing a new timeline. At that point, Ayla's history up until she left would be the same but what of her history (and her effect on all of Time) after she left?

Yes, he might be able to (fact is, we don't know) see what all of the main time line, for all the main charecters, looked like before they time traveled. He wouldn't be able to, however, to see what the end result of the whole journey would be... otherwise, that would actually make him the Entity. As such, he also can't see into a Time Line where Ayla never had children in the first place!

As a timeline can only change based on real actions (and not just probability), the events in her life can't change until she is old enough to be at the appropriate spot in her own personal timeline to make those "real actions" or to not make them. Her own personal Time Index (her departure point + her personal time error) must match the Time Index of the event (the specific point in the timeline when an action would have been completed) before the outcome can effect the timeline. Until such a point, the action remains unresolved and in a state of flux.

If that were truly the case here, I am more than fairly certain that it would cause a major problem to all of the space-time continuum. Just  imagine what it would be like, to keep tags at everything at every single moment in a time traveler's life, just so that a major event can be kept in existance for that peron's sake! Think of the amount of moments/events that would have to be kept in a state of 'flux' just for this to work!

As such it would seem that the timeline proceeding from the point that an individual leaves their timeline and the point in which they would have naturally died (if they hadn't time traveled) must be in a state of flux until such a point as the specific Time Index of the time traveler matches the Time Index of the event. Only then can the event’s flux be resolved into a definite outcome. So, for every second Ayla is trekking through time, the timeline is actually being re-written with Ayla being missing from her own era for that one extra second.

Again, you are presupposing the concept of 'Fate' into the whole mix. Fate doesn't exist... at least not in the Chronoverse. There is just no way/no how that a person's death (or any other event, for that matter) can be predetermined in anyone's life. This would imply the fact that, if someone time traveled to the right particular moment in time; they might be able to in fact, prevent their very own death.

One might wonder what the timeline might look like, at time index “Ayla is age 30,” when Ayla is only 29. It must, alas, remain in a state of flux. As the future must still exist, and it must be calculated based on the lives of those who lived before, I would suggest that the future would simply be based on the last valid timeline. After all, a timeline can’t be replaced until an action has occurred to change it, and no action can occur or not occur until the two Time Indexes (that of the Traveler and that of the Event) match.

Everything that you are suggesting can be equitable to one other concept that has been established by another medium, in which this theory would actually make sense: Back to the Future. You just presentend in a very organized and succinct manner, so that it could be also applied to this game.

As most characters aren’t gone from their timeline long enough to really miss out on any major events, the GRL Paradox doesn’t manifest. There is only one exception to this; Robo. He “travels” through time for more than 400 years. Thus, any event that the original-timeline Robo did from 2300 AD to 2700 AD would be erased. Alas, Crono and the gang never travel so far into the future in order to test this theory. As Robo is back in 2300 by the end of the game, presumably all the events in his life from 2300 to 2700 would be changed to have a new Time Index.

And herein lies the biggest problem of your little theory. Let's pretend your theory made sense... what of Robo's ultimate 'Fate', then? As per what your theory states, everything that he actually did from year 2300 to 2700 AD would have to be rewritten. Unfortunately this would also include all the events that took place during Chrono Cross. Meaning no 'Prometheus Circuit', and therefore no designation of Serge as 'Arbiter' of Time. Quite a big problem it poses, wouldn't you say?

Nicely, this theory does get around the “The Entity Did It” argument, and really it is quite simple (which makes Ol’ Occam happy, I’m sure); the Guardia Royal Line still exists after Ayla has time traveled because time is then in flux and it defaults to the last valid timeline, which just happens to have the Guardia Royal Line existing.

Yes, it was a nice little theory that presented quite a challange. However, I still think it only 'tries' to circumvent the problems posed by the 'Entity Did It' arguments, but that it does actually manages to at least stay somehow within Ockham's Razor Principle. Still, you also misinterpreted, in my opinion, what the concept of Time Error stands for.

[Thought]

Dankun, thank you for taking the time for such a thorough response. Before I launch into a response to your response, please let me make sure I am clear on your points (makes no sense to address an issue if no one thinks it is an issue).

1) You are claiming that my understanding of Time Error is incorrect
1a) As a sub issue, you stated that Time Error is the cause of the Guardia Paradox.
2a) You also indicate that what I call Time Index is actually Time Error.

2) You state that as fate does not exist in the series, one cannot reference a point that is in a character’s future. Specifically, this is referencing an example I used; you state that one cannot assume at what point Ayla will have children.
2a) As a sub issue to this, you also indicate that one also cannot claim that Ayla’s personal timeline has a predetermined point in which she would have children. (That is, fate in general and in specific do not exist)

3) You state that as I express Time Index (regardless of the above problems), it would create a major problem to the timeline itself since tabs must be kept on every single moment in a time traveler’s life, as my theory states that specific events that would have happened in a time-traveler’s future remain in flux once time-traveling has been introduced into that traveler’s own personal timeline.

4) You state that my theory relates to a theory established by Back to the Future and would work for that series, but that I merely ordered things in order for it to fit in with the Chronoverse.

5) Even assuming my theory is correct, you also find a problem with the theory in regards to Robo; you state that my theory would negate the originating events of Chrono Cross (the Prometheus circuit and so forth) since my theory would necessitate Robo’s future be rewritten.

6) A somewhat minor point, but you also state that my theory only tries to avoid the “Entity Did It” copout-I-mean-argument while being only marginally more inline with Occam’s Razor.

That is a lot to respond to. I will try to do so in a concise and ordered manner, but I am afraid this is a friggenly huge post.

Problem #1
I reread the article and I must maintain that my original interpretation is correct and that, indeed, your take on it does not conform to the article that you linked to.

I stated the following: “Time Error, as I understand it, is that the specific instance a gate will open up into is its original period + the time error.”

The Principles of Time and Dimensional Travel article (which you linked to) states, under the Theories Section, Sub section Time Error (1.2.2), 1st bullet point, states “time portals within the standard time axis flow through time and Time-Error at equal rates.” An example is then given: “A time portal is created at time X and Time-Error 0. At time X+T, the Time-Error of the Portal is T.”

I can find no significant divergence between my statement and the article’s in this instance. Mathematically, they are saying the same thing. You then state:

You see, what you call a 'Time Index' is actually what the Time Error concept represents. Time Error is precisely just that, a record of what a Time Traveler has done so far in his own Time Line. This record is kept, though I don't know by whom or what (probably the very fabric of time, since it is activated every single time in that someone time travels, by whatever means) so as to not allow him to go back to a previous event that he has already been to and interacted with.

This does not match up with the article on time error. Going back to the example used in the article itself, “at time X+T, the Time-Error of the Portal is T.” To represent this a little more simply, we have a basic equation: X+T=I. Time X is the exact point in time at which the portal was originally created, the article clearly states that Time-Error is T, and I am proposing that Time Index is essentially I (the result of that equation). Time Index cannot be the same as Time Error since Time Index is Time Error+X.

Furthermore, Time-Error is not a record of what a Time Traveler has done. To quote the article again, paragraph 1, sentence 2: “Time Error is the way time flows in places like the End of Time compared to the way it flows in the rest of the world.” Time Error represents time in a place, not for a person. A person can experience Time Error but only in a place that already has Time Error and only as the result of Time Error on a portal. This is confirmed in the 2nd paragraph of the article, sentence 2: “Only time portals and locations outside the axis of time (such as the End of Time, the inside of the Black Omen, or the Darkness Beyond Time) exhibit this flow.” Time Error is how time flows for portals and locations, not people. Thus, Time Error cannot be a record of what a Time Traveler has done. At best, it could be described as a record of a Time Traveler’s actions while in areas of Time Error, but not in normal time.

Before moving on to the other problems, please allow me to try to clarify Time Index a bit more.

That is really the heart of my argument; previously Time-Error was a concept that can only be applied to locations, I am proposing that a variation on that theory could also be applied to animate objects (aka, people like Chrono and Ayla). To be fair, I am not using Time Error exactly as expressed in that article either. I am using Time Error as the difference between one value and another (that is, the moment that Time Travel has been introduced into a specific section a timeline and any event that follows after). This value will always be equal to the article’s exact definition of Time Error, but I am applying it in a manner that wasn’t expressed by the article.

To try to illustrate what I am proposing Time Index is, allow me to compare it to Time Error. If Time Error flows perpendicular to normal time, then Time Index potentially flows in (essentially) a scribble to normal time. It doubles back on itself, it skips ahead, it falls behind, etc. Despite this, Time Index still flows in a straight line; it is only in comparison to normal time that it takes an odd shape. Compared to Time Error it is also a straight line.

Time Index represents the Time Traveler’s travels through time in chronological order, which do not necessarily match up with the chronological order of normal time. According to normal time, Chrono and Co enter 600 AD (Marle disappears in the teleporter accident), leave 600 AD (after rescuing her), leave 1000 AD (Marle disappears in the teleporter accident), enter 1000 AD (their successful return from saving Marle). According to Time Index, these events happen more along the lines of how the player sees them; Chrono and Co leave 1000 AD, enter 600 ad, leave 600ad, and enter 1000 ad. From the perspective of normal time, Chrono and Co arrived in 600 AD before they left in 1000 AD (specifically, they arrived 400 years before they left). From the perspective of Time Index, just before Marle steps onto the teleporter, 600 AD is actually in the future. Just after Chrono goes through and enters 600 AD, 1000 AD is then in the past.

Problem #2
I actually quite agree that fate does not exist in the series and that one cannot determine the point in Ayla’s future that she will have children. However, my argument is actually drawing from the past in order to determine a hypothetical “when” for Ayla to have children. The specific “when” that I used (30) is just for the ease of discussion. Really, if we assume that Ayla is the ancestor of the Guardia line, and the Guardia line exists, then we know that Ayla must have had a child at time X. I merely assigned an arbitrary value to that variable, but we can leave it as a variable if you prefer. However, it is a variable because we don’t know it, not because it hasn’t happened.

I am not talking about fate, I am merely talking about the past. This is, again, at the heart of Time Index. In the original Lavos timeline, pre-time travel (the various timelines are illustrated in the following document: http://www.chronocompendium.com/images/wiki/b/b1/Timelines.png ) did have a child at time point X, which we know because the Guardia line does in fact exist in 1000 AD. She lived her life, she had her child, she made her choices resulting from freewill, and she died. By Time Index standards, however, ALL of the original, pre-time travel timeline is in the past. The timeline was that way, but something new happened; time travel was introduced. Ayla having a child can be treated as having already happened simply because it has already happened, in the pre-time travel timeline. When she joins up with Chrono and the others, even though having children is in her future, it is still in the past.

Time Travel is introduced into the timeline by the Entity. This doesn’t necessitate change (indeed, it can’t necessitate as that would be fate) but it allows for change to occur. These changes, however, cannot occur until they occur. Ayla having a child can’t change until it changes. Until a future for the future is established, the future is based on the past. It makes sense if one follows Time Index, but not normal time.

To offer a different example: Chrono doesn’t defeat Lavos until he actually defeats him. Time Travel allows for this change, but it is a variable, it is potential. Until that change is made, Lavos remains undefeated, just as in the original pre-time travel timeline. Once Lavos is defeated, we have a new timeline. 2300 AD on the pre-time travel timeline, according to Time Index, is in the past compared to 12000 BC on the new, post time travel timeline.

So to my original argument, in the original, pre-time travel timeline, Ayla had a child. Her travels in time allow for the possibility for that event to change. However, that event doesn’t change until it changes. This isn’t because she is fated to have a child; it is because she DID have a child in the past (even though the past is her future). At point X on the original pre-time travel Ayla had a child, thus in the post-time travel timeline point X cannot be changed until it is changed, and it can’t be changed until Ayla reaches point X. Even though point X is in the future for Ayla according to normal time, it is in the past for Ayla according to Time Index and it can’t be changed until that past (her future) is overwritten by her present (which from the game’s perspective will be in the future).

This isn’t to say that due to time travel she couldn’t have children later or earlier or not at all, just that the events that proceed from Point X can’t change until Point X itself changes, and that change can’t occur until Ayla reaches Point X. This isn’t fate, this is how the timeline existed before time travel was introduced and how it remains to exist until changed.

Thus, I am not talking about a predetermined future for Ayla; rather I am talking about a post-established past that continues to exist until changed.

As I explained before, and to make it even clearer: A Time Index for each time traveler is actually what the Time Error stands for. We just never really see this in-game because you are always traveling in a party of three! (As stated by Gaspar, because otherwise it would cause a disrpution in the time-space continuum, which is why you ended up there in the first place)

Partially correct; Time Error relates to locations, Time Index relates to Time Travelers and how they interact with timelines (both current and past). Time Error cannot exist for specific individuals as this would allow Chrono, Marle, and Lucca to travel through time only to have Frog, Ayla, and Robo follow after changing the very events that C, M, & L changed. Time Error must be universal and impersonal.

Problem #3

Now to address Problem 3, which is actually easier to respond to than anything yet. You are stating that having the entirety of a person’s life as it would be, from the moment before they are effected by time travel to the point that they would have died (and any subsequent effects that life would have had on history), pre-time travel, would create a major problem for the timeline. As you said, “just imagine what it would be like to keep tags on everything at every single moment in a time traveler's life just so that a major event can be kept in existence for that person's sake.” Well actually, it would be for time’s sake, not the person’s sake, and it would be so that all events, not just major event, remain in existence. They remain simply because they do not change until changed. Essentially, you are claiming that it would be a major problem to keep tabs of a bunch of stationary objects (things that currently aren’t changing). Yeah, that isn’t that difficult.

But I made the mistake of using the word “flux” when I should have said something more along the lines of “infused with potential.” The events in traveler’s Time Index beyond their point of departure remain exactly as they were until changed, the only difference now is that they have the potential to change (remember, by Time Index standards these events are in the past, not the future, and remain in the past until the present overwrites them to create a future).

To offer a real life example of the underlying principles: take a bowling ball from the 1st floor of a building to the roof. You just gave it a good amount of potential energy. The bowling ball is exactly the same, nothing changed about it, only in its relation to everything else; it now has potential. In the same way, Time Index events after a time traveler’s departure remain exactly the same, only with potential for change. As there is only a potential change, they are no more difficult to keep tabs on than before that potential was introduced.

If you still find this to be a major problem, then I would recommend reading up on Schrodinger’s Cat and the Heisenberg Uncertainty Principle. Given that at any moment most of the Universe exists in multiple states until observed (seemingly), it is really a small thing for a comparatively few moments of comparatively few people in just one out of countless worlds to be held in a state of “flux,” or potential.

Problem #4

As for problem 4, I must confess that I have no idea what you mean by:

Everything that you are suggesting can be equitable to one other concept that has been established by another medium, in which this theory would actually make sense: Back to the Future. You just presentend in a very organized and succinct manner, so that it could be also applied to this game.

Which “other concept” from Back to the Future is my theory equitable to? Additionally, why does it matter?

At its heart, Time Index can be summarized as “things don’t change until they change.” Everything else I have said is just an explanation of that concept and how it (maybe?) makes sense. Indeed, the explanations themselves could be summarized by the phrase “The enemy’s gate is down,” a quote taken from the book Ender’s Game, which essentially means that when a frame of reference has been removed (gravity in the book, a set direction of time for the Chronoverse) and no other references are necessitated but a frame of reference is still needed in order to act, then one should choose the frame of reference that best suits the situation. The GRL Paradox is avoided by the future happening in the past, a different frame of reference than has yet been suggested.

Problem #5

Problem 5 is easier to address than problem 3. As I have laid things out, Robo’s personal Time Index is messed up at the end of the game. All the events left over from the original, pre-time travel timeline, from between 2300 and 2700, have been rewritten. You find this to be a problem.

As per what your theory states, everything that he actually did from year 2300 to 2700 AD would have to be rewritten. Unfortunately this would also include all the events that took place during Chrono Cross. Meaning no 'Prometheus Circuit', and therefore no designation of Serge as 'Arbiter' of Time. Quite a big problem it poses, wouldn't you say?

This is quite easy because the posed problem is coming from a misunderstanding. Everything he did from 2300 to 2700 on the original, pre-time travel timeline would have to be rewritten. Chrono Cross, however, does not take place on that timeline. Any rewriting of Robo’s history resulting from the Time Index theory would have been re-rewritten due to the successful defeat of Lavos and the saving of the future. Thus, the Prometheus circuit would have no problem existing because even though Robo’s 2700 is being rewritten, as that is in the past when compared to the Prometheus Circuit in 2400, via Time Index.

Problem #6

And finally, because I haven’t written a long enough response, allow me to address the 6th problem. The Entity did it argument essentially states that an outside force prevents the GRL Paradox from happening. Time Index, however, essentially states that the [GRL Paradox doesn’t need to be prevented since the events that could trigger such a thing haven’t occurred. Such events might occur in the future (from a Time Index POV), but nothing in the game necessitates that they have or will occur. If my theory is valid, it doesn’t circumvent the problems presented by the Entity Did It argument, it fully stops before we get to an “it” that the Entity may or may not have done.

Occam’s Razor is happy because the theory really is quite simple; things don’t change until they change (and nothing has changed to cause the GRL Paradox, so the GRL paradox hasn’t happened).

[dankun]

Dankun, thank you for taking the time for such a thorough response. Before I launch into a response to your response, please let me make sure I am clear on your points (makes no sense to address an issue if no one thinks it is an issue).

Thought, thank you for taking the time to write such a thorough refutation to my already in-depth reply to your theory. And to answer your first question; yes, you understood all of my points perfectly, it seems.

That is a lot to respond to. I will try to do so in a concise and ordered manner, but I am afraid this is a friggenly huge post.

I'm afraid that it's only going to get worse with my current reply. But I will also try to do so in an orderly fashion, while trying to be as clear as possible on everything I say. I also apologize again for taking such a long time to even consider replying to your post. However, as you so adequately put: it was a HUGE post to reply to, and as such, not an easy challenge to take on.

Solution #1

I reread the article and I must maintain that my original interpretation is correct and that, indeed, your take on it does not conform to the article that you linked to.

My understanding of Time Error does not differ or contradict anything of what is already stated in the Compendium's current definition . The only thing that I suggested (that you misinterpreted) is that, instead of thinking of it as a separate mathematical equation from normal time; to simply view it as a sort of 'tracking' to a any given personal timeline, once that person has time traveled and effected changes to his life.
Think of it as a track record accessible to all time travelers, so that they can actually modify the things that they want changed. Also, so that they don't cause any time-traveling related problems like paradoxes and such.

The Principles of Time and Dimensional Travel article (which you linked to) states, under the Theories Section, Sub section Time Error (1.2.2), 1st bullet point, states “time portals within the standard time axis flow through time and Time-Error at equal rates.” An example is then given: “A time portal is created at time X and Time-Error 0. At time X+T, the Time-Error of the Portal is T.”

I stated the following: “Time Error, as I understand it, is that the specific instance a gate will open up into is its original period + the time error.”

I can find no significant divergence between my statement and the article’s in this instance. Mathematically, they are saying the same thing.

Yes, you are indeed correct. So far, everything you said about Time Error holds true under that definition. However, later on, you go on and add several other observations that actually twist the definition of Time Error and therefore make this statement a fallacy.  You do all this, in order for you to try claiming that there is absolutely nothing wrong with your theory and that it effectively resolves the Guardia Royal Line Paradox. When in fact, the only thing that you manage to pull off up by doing this is contradict yourself. How? By stating two completely different things, and at the same time, holding them both to be true statements.

Now, correct me if I'm wrong, but isn't that what is actually called an incorrect foundation for a fact? Basically, you can't say something is true if what originated your 'thought' in the first place is an incorrect observation. Simple logic, that states that anything deduced in this manner automatically makes it a false observation and therefore not a valid argument for your theory. And I do believe that it indeed is your central argument for it, as you base everything else you say off from it. So, in consequence if it can be proven to be wrong time and time again, there should be no questions left as to the 'status' of your theory as a bogus one.

This does not match up with the article on time error. Going back to the example used in the article itself, “at time X+T, the Time-Error of the Portal is T.” To represent this a little more simply, we have a basic equation: X+T=I. Time X is the exact point in time at which the portal was originally created, the article clearly states that Time-Error is T, and I am proposing that Time Index is essentially I (the result of that equation). Time Index cannot be the same as Time Error since Time Index is Time Error+X.

You purposely misrepresented what that equation would really look like, so that you could actually differentiate what Time Index is from the definition of Time Error.
In the formulae that you propose you state the following: [TI]= X+T. Of which, TI is Time Index, X represents the timeline and T stands for the amount of Time spent added to the original timeline.

This is the part that never gets justified with the rest of your explanations!
You did a very poor job on trying to validate your whole theory solely through this argument. Indeed, everything else you say is in direct opposition of what you’re trying to say here by trying to make them look as two different concepts.
Let's us take a look at the very same example you used, for the sake of argument.

In that example of the article, the formulae that can be deduced from it would actually look like this: (X)+(x+T) = X'. As explained by the article, x is the modified timeline, T is the amount of time spent during Time Error that needs to be added to said timeline, which in turn then needs to be added to X or the original Time at which the timeline started; and the result of that equation is X', which is a different location as to where the timeline initiated at which is also known as: TE (Time Error).

Now let's compare both formulas. Shall we?
[TI]=X+T & [TE]=(X)+(x+T)
Isn't that essentially the same exact formulae?

However, a more precise formulae can be created to correctly address all problems. Or at least, that actually explains what I was trying say in the first place. To calculate a Time Record (or 'track') the formulae for Time Error would have to be modified and it would then read as: TE = (X)+[R(x+T)]. Wherein: TE is Time Error. X is the original location at which a timeline is accessed and R (which is the result of x+T, representing the amount of time spent added to a personal time on that timeline) is the 'record' of the whole endeavor (what that traveler actually did to his timeline), kept by Time itself, the Entity, or whatever.

Furthermore, Time-Error is not a record of what a Time Traveler has done. To quote the article again, paragraph 1, sentence 2: “Time Error is the way time flows in places like the End of Time compared to the way it flows in the rest of the world.”  Time Error represents time in a place, not for a person.

Not according to what the article currently says about Time Error, fair enough. However. I believe that the above explanation of what a time track/record actually is, does not contradict anything already stated by the Time Error theory, as opposed to your cheap, soundless theory which almost invalidates it.

A person can experience Time Error but only in a place that already has Time Error and only as the result of Time Error on a portal. Time Error is how time flows for portals and locations, not people.

Not entirely. That is, at least not when you consider other suggested possibilities, like how a Time Record can be applied to Time Error concept. A Time Record isn't just everything that a traveler will do while in reaches of places with a Time Error flow principle. It is a complete duplication of what the Time Error timeline would look like for every time traveler.

Thus, Time Error cannot be a record of what a Time Traveler has done. At best, it could be described as a record of a Time Traveler’s actions while in areas of Time Error, but not in normal time.

Apparently, it would seem that you didn't quite misunderstood what I was trying to say. However, as each person can be said as to having their own individual timeline, a record needs to be created for each and every one of them. Thus, exonerating the idea that the Time Error concept needs not only be applied to portals, places or locations.

That is really the heart of my argument; previously Time-Error was a concept that can only be applied to locations, I am proposing that a variation on that theory could also be applied to animate objects (aka, people like Chrono and Ayla). To be fair, I am not using Time Error exactly as expressed in that article either. I am using Time Error as the difference between one value and another (that is, the moment that Time Travel has been introduced into a specific section a timeline and any event that follows after). This value will always be equal to the article’s exact definition of Time Error, but I am applying it in a manner that wasn’t expressed by the article.

I'm afraid not. Not according to what I just pointed out. My initial critiques and observations are still very much valid. You didn't exactly differentiate much of anything! The only thing you did was change the nomenclature of what the result of the equation would have to be called.

To try to illustrate what I am proposing Time Index is, allow me to compare it to Time Error. If Time Error flows perpendicular to normal time, then Time Index potentially flows in (essentially) a scribble to normal time. It doubles back on itself, it skips ahead, it falls behind, etc. Despite this, Time Index still flows in a straight line; it is only in comparison to normal time that it takes an odd shape. Compared to Time Error it is also a straight line.

Hardly. A time'line' wouldn't exactly be a line if it isn't straight, now would it? Is just doesn't make sense... at all! Think about it, you first claim that Time Index isn't really a line, more so than it is a scribble, but then you say "Time Index still flows in a straight line"! Now, I don't know about you, but if you can’t see that as a contradictory statement I honestly believe there must be something wrong with your head. Just listen to how that last sentence actually sounds like... or better yet, read this again and tell me that it actually rings logical to you:

Time Index represents the Time Traveler’s travels through time in chronological order, which do not necessarily match up with the chronological order of normal time. According to normal time, Chrono and Co enter 600 AD (Marle disappears in the teleporter accident), leave 600 AD (after rescuing her), leave 1000 AD (Marle disappears in the teleporter accident), enter 1000 AD (their successful return from saving Marle). According to Time Index, these events happen more along the lines of how the player sees them; Chrono and Co leave 1000 AD, enter 600 ad, leave 600ad, and enter 1000 ad. From the perspective of normal time, Chrono and Co arrived in 600 AD before they left in 1000 AD (specifically, they arrived 400 years before they left). From the perspective of Time Index, just before Marle steps onto the teleporter, 600 AD is actually in the future. Just after Chrono goes through and enters 600 AD, 1000 AD is then in the past.

...Preposterous, indeed.

Solution #2

I actually quite agree that fate does not exist in the series and that one cannot determine the point in Ayla’s future that she will have children. However, my argument is actually drawing from the past in order to determine a hypothetical “when” for Ayla to have children. The specific “when” that I used (30) is just for the ease of discussion. Really, if we assume that Ayla is the ancestor of the Guardia line, and the Guardia line exists, then we know that Ayla must have had a child at time X. I merely assigned an arbitrary value to that variable, but we can leave it as a variable if you prefer. However, it is a variable because we don’t know it, not because it hasn’t happened.

Wrong again!
It isn't a variable just because we don't know it, but also as a result of not knowing when/how/where or whether or not it's even going to happen! Why? Because if it isn't assigned any value (as it should, cause there is no Fate in the Chronoverse), as a variable it should remain as such, simply for the reason that we don't know what the outcome is going to be if, and when is replaced by an actual value in the equation. Why should it matter then, that because of this the variable may be negated existence? Because that number can also be a negative value! Or maybe, if you prefer, simply one that's beyond her lifespan or even better, one that is actually just past the point in her life in which she can in fact, have those children!

I am not talking about fate, I am merely talking about the past. This is, again, at the heart of Time Index. In the original Lavos timeline, pre-time travel (the various timelines are illustrated in the following document: http://www.chronocompendium.com/images/wiki/b/b1/Timelines.png ) did have a child at time point X, which we know because the Guardia line does in fact exist in 1000 AD. She lived her life, she had her child, she made her choices resulting from freewill, and she died. By Time Index standards, however, ALL of the original, pre-time travel timeline is in the past. The timeline was that way, but something new happened; time travel was introduced. Ayla having a child can be treated as having already happened simply because it has already happened, in the pre-time travel timeline. When she joins up with Chrono and the others, even though having children is in her future, it is still in the past.

This is an assumption (and an incorrect one) made by you. As is demonstrated by the very same document that you provide, such point X is never mentioned in either Timeline. Ayla's exact role in the Lavos-timeline is ultimately unknown. We pretty much don't know anything about this timeline. As a result, you can't assume that she did, in fact, have children and was actually the one who started the Guardia Royal Line. Time Index is a crackpot theory that would only make sense in Yuji Hori's head, I'm afraid.

Time Travel is introduced into the timeline by the Entity. This doesn’t necessitate change (indeed, it can’t necessitate as that would be fate) but it allows for change to occur. These changes, however, cannot occur until they occur. Ayla having a child can’t change until it changes. Until a future for the future is established, the future is based on the past. It makes sense if one follows Time Index, but not normal time.

Says who? Only you and your ludicrous Time Index theory.
And since Time Index does not make any sense at all whatsoever... Yeah, you're right, I guess this could make sense, if you’re crazy enough to believe all that nonsense.

To offer a different example: Chrono doesn’t defeat Lavos until he actually defeats him. Time Travel allows for this change, but it is a variable, it is potential. Until that change is made, Lavos remains undefeated, just as in the original pre-time travel timeline. Once Lavos is defeated, we have a new timeline. 2300 AD on the pre-time travel timeline, according to Time Index, is in the past compared to 12000 BC on the new, post time travel timeline.

Bad example. As this is even used for an explanation of what Time Error is. You are basically stating that Time Index and Time Error are, indeed, the exact very same thing. Hmm.. Now doesn't that completely invalidate what you had previously said about what Time Error and Time Index represent? Precisely.

Let me quote you again, so as to remind you of a little something you said earlier:

previously Time-Error was a concept that can only be applied to locations, I am proposing that a variation on that theory could also be applied to animate objects (aka, people like Chrono and Ayla). To be fair, I am not using Time Error exactly as expressed in that article either. I am using Time Error as the difference between one value and another...

See what I mean? If that is not a self-contradiction of your theory, I don't know what is! Thank you for proving my point, by using that example.

So to my original argument, in the original, pre-time travel timeline, Ayla had a child. Her travels in time allow for the possibility for that event to change. However, that event doesn’t change until it changes. This isn’t because she is fated to have a child; it is because she DID have a child in the past (even though the past is her future). At point X on the original pre-time travel Ayla had a child, thus in the post-time travel timeline point X cannot be changed until it is changed, and it can’t be changed until Ayla reaches point X. Even though point X is in the future for Ayla according to normal time, it is in the past for Ayla according to Time Index and it can’t be changed until that past (her future) is overwritten by her present (which from the game’s perspective will be in the future).

And now, what you're just basically doing is to claim that while Point X is not supposed to be determined with a value, it should only rather have a definite location point in her personal timeline that does not actually move around that much (read: not at all). Yeah, that makes sense. About as much sense as what you said when you assigned a specific value to the variable!

This isn’t to say that due to time travel she couldn’t have children later or earlier or not at all, just that the events that proceed from Point X can’t change until Point X itself changes, and that change can’t occur until Ayla reaches Point X. 
This isn’t fate, this is how the timeline existed before time travel was introduced and how it remains to exist until changed.

The point of this paradox is that due to time travel she can't be expected to either 'have children later or earlier or not at all'. Not that there somehow exists a specific point X which in some strange bizarre way isn't malleable to anything else that can or could ever be modified in her own timeline. Think about it that way. Doesn't that sound ridiculous to you? Or at least on some level, as something that completely obliterates all known Principles of Time mechanisms currently known for this game?

Thus, I am not talking about a predetermined future for Ayla; rather I am talking about a post-established past that continues to exist until changed.

That cannot be ultimately changed, right? And only has the 'potential' to be changed?
Like I said... Yeah, this makes perfect sense.

Solution #3

Now to address Problem 3, which is actually easier to respond to than anything yet. You are stating that having the entirety of a person’s life as it would be, from the moment before they are effected by time travel to the point that they would have died (and any subsequent effects that life would have had on history), pre-time travel, would create a major problem for the timeline. As you said, “just imagine what it would be like to keep tags on everything at every single moment in a time traveler's life just so that a major event can be kept in existence for that person's sake.” Well actually, it would be for time’s sake, not the person’s sake, and it would be so that all events, not just major event, remain in existence. They remain simply because they do not change until changed. Essentially, you are claiming that it would be a major problem to keep tabs of a bunch of stationary objects (things that currently aren’t changing). Yeah, that isn’t that difficult.

Not if you factor in the idea that everyone has a personal timeline (within the multiple 'dimensions' of the Chronoverse Timelines)! Which you have, personally, alluded to in your own theories. You're saying that it wouldn't only be done just for one person's but for all of Time's sake, but if your consider this fact what the word 'Time' is only referring to, is to Ayla's Time. In other words, her very own personal timeline. An argument based on a semantic difference of what a word could potentially mean is by no means a good one.

All you've done so far is evaded providing an answer to this question: How can her timeline (Ayla's) have any possibility of remaining in a constant state of 'flow', if and when all of her future events are indeterminate? Not a big enough problem for you? How about doing that very same thing, for all events of every time travelers' personal 'Time' that could ever show up in a given Timeline? What do you think would happen if that were true? Time would most definitely cease to flow! At least as far any of the Time Travelers’' is concerned. Talk about a real Time's scar. And that's just to say the least of what could happen, as many other potential problems would definitely arise!

But I made the mistake of using the word “flux” when I should have said something more along the lines of “infused with potential.” The events in traveler’s Time Index beyond their point of departure remain exactly as they were until changed, the only difference now is that they have the potential to change (remember, by Time Index standards these events are in the past, not the future, and remain in the past until the present overwrites them to create a future).

Potential to change = No change at all! That is, at least, until another external force is made present in that person's life (which should be read as Fate). This may actually sound stupid to you, but, the potential to anything isn't really anything until it actually is! It's non-existent, it doesn't matter, it doesn't make any difference... because it isn't there! Or even if it would be there, it can go away just as easily!! I'm sorry, but that is just the way it is, and will continue to be so as long as something (anything) else is needed in order to help generate the actual change in that person/object/timeline.

To offer a real life example of the underlying principles: take a bowling ball from the 1st floor of a building to the roof. You just gave it a good amount of potential energy. The bowling ball is exactly the same, nothing changed about it, only in its relation to everything else; it now has potential. In the same way, Time Index events after a time traveler’s departure remain exactly the same, only with potential for change. As there is only a potential change, they are no more difficult to keep tabs on than before that potential was introduced.

And to help you understand what I'm saying, I will use the very same example you provided.
That bowling ball is still just going to sit there at that roof, no matter how much time passes. It will always be there sitting, waiting, doing absolutely nothing at all! Sure, it has potential to crack someone's head open. But will that eventually ever happen, unless something else causes this ball to fall down? I.e. the wind, some mischievous brat, whatever?

If you still find this to be a major problem, then I would recommend reading up on Schrodinger’s Cat and the Heisenberg Uncertainty Principle. Given that at any moment most of the Universe exists in multiple states until observed (seemingly), it is really a small thing for a comparatively few moments of comparatively few people in just one out of countless worlds to be held in a state of “flux,” or potential.

I'm not the one who matters here; at least not as to what should even be considered a potential problem to your theory! What constitutes a problem to a theory can't be as simple as a different point of view of any given person. Problems exist because of the simple fact that when and if a legitimate question is raised that simply can't be answered without leaving any shadow of a doubt as to its validity as a theory.

Furthermore, while both of those theories have very little application to the real problem (the Guardia Royal Line Paradox) at hand, they have absolutely nothing to do with what is being discussed at the moment. And even if they did, they still would offer no solution whatsoever to this problem in particular, as they are in fact also just theories!

Solution #4

Which “other concept” from Back to the Future is my theory equitable to?

I don't believe that it has an established concept or name, by which it can be easily distinguished from any other; or at least not in the sense of canon. But I think you know exactly as to what part I was referring to. There was a previous poster on this thread that summarized it pretty well.

Additionally, why does it matter?

It matters because, if indeed you were trying to adapt rules and time traveling mechanics from a different source you are faced with the problem of bending somewhat another concept or theory that has already been previously established by the medium that we are currently discussing (in this case, the Time Error Theory and part of Chrono Trigger's Time Traveling Mechanics and Principles).

At its heart, Time Index can be summarized as “things don’t change until they change.” Everything else I have said is just an explanation of that concept and how it (maybe?) makes sense. Indeed, the explanations themselves could be summarized by the phrase “The enemy’s gate is down,” a quote taken from the book Ender’s Game, which essentially means that when a frame of reference has been removed (gravity in the book, a set direction of time for the Chronoverse) and no other references are necessitated but a frame of reference is still needed in order to act, then one should choose the frame of reference that best suits the situation. The GRL Paradox is avoided by the future happening in the past, a different frame of reference than has yet been suggested.

No it can't. It doesn't. I believe I have demonstrated to you enough that this really is NOT the case! And apparently, perhaps it was a different source altogether, which gave you this idea. My mistake. It's still a valid point though, even if I 'thought' that the source was originally a different one.

Solution #5

Problem 5 is easier to address than problem 3. As I have laid things out, Robo’s personal Time Index is messed up at the end of the game. All the events left over from the original, pre-time travel timeline, from between 2300 and 2700, have been rewritten. You find this to be a problem.

Ha! Again with this? I find it to be a problem?.... Yeah right, as if that matters as to what constitutes a problem.
Not at all! This is a real problem that still needs to be addressed, just as much as all the other ones, before your theory can even be considered a valid one.

Okay, I admit that perhaps I exaggerated a bit as to this problem's status as the biggest problem of your theory. There are many other bigger problems, which have (curiously in descending order) already been listed; and that, as of yet,  not one of them has been successfully solved.

Unfortunately for you, as will be shown, Problem #5 still poses a pretty big problem to your theory! Indeed, the very fact that you can't even see it as a problem doesn't help your theory at all... and it questions your logical reasoning, even further.

Now, allow me to quote the core issue of this problem, so as to not to repeat myself:

As per what your theory states, everything that he actually did from year 2300 to 2700 AD would have to be rewritten. Unfortunately this would also include all the events that took place during Chrono Cross. Meaning no 'Prometheus Circuit', and therefore no designation of Serge as 'Arbiter' of Time. Quite a big problem it poses, wouldn't you say?

As such it would seem that the timeline proceeding from the point that an individual leaves their timeline and the point in which they would have naturally died (if they hadn't time traveled) must be in a state of flux until such a point as the specific Time Index of the time traveler matches the Time Index of the event. Only then can the event’s flux be resolved into a definite outcome. So, for every second Ayla is trekking through time, the timeline is actually being re-written with Ayla being missing from her own era for that one extra second.

Let it be noted than, that you are indeed claiming that the Robo whose Time Index should have to be rewritten, would be the one who stays behind to fix Fiona's Forest. Therefore, as one who has actually time traveled, in as much as for he stays there as long as he does, should have his personal Time Index be rewritten accordingly to his new actions in the Middle Ages, for all of the 400 years that correspond to his own time period; that is from 2300 AD to 2700 AD.

So what does this all mean, exactly? It means that this Robo, has very much so, time traveled before (and with the Team, as well) and is not the 'original-timeline' Robo that you so conveniently claim wouldn't have this problem because of never having time-traveled before.

Now, it is true that once he returns to the future, all time traveling methods become unavailable to him, as all the gates are closed to him after that point. However, this by no means equals to, having his old 'Time Index' not be overwritten by a new different one. Remember, this is only as per what your theory states, as all of the 'rewriting' actually takes place during the time in which they remain time traveling (in this case the 400 years he spent in the Middle Ages).

Now, allow me to quote yourself, so as to establish what your theory has previously stated in this regard:

As most characters aren’t gone from their timeline long enough to really miss out on any major events, the GRL Paradox doesn’t manifest. There is only one exception to this; Robo. He “travels” through time for more than 400 years. Thus, any event that the original-timeline Robo did from 2300 AD to 2700 AD would be erased. Alas, Crono and the gang never travel so far into the future in order to test this theory. As Robo is back in 2300 by the end of the game, presumably all the events in his life from 2300 to 2700 would be changed to have a new Time Index.

The 'original-time-line' Robo is the only one that doesn't time travel. He has nothing to do with this problem! So why don't you just leave him alone gathering up dust at Proto Dome, where he belongs? You also seem to believe, for whatever reason, that once he goes back to 2300 AD at the end of the game, everything that he did should return to normal; his whole time traveling experience should go up in smokes, as if it never even happened. Do you even know how absurd that is? It's almost as moronic as saying that he wasn't in fact, time traveling at that very instant in order to get to his own time period!

This is quite easy because the posed problem is coming from a misunderstanding. Everything he did from 2300 to 2700 on the original, pre-time travel timeline would have to be rewritten. Chrono Cross, however, does not take place on that timeline. Any rewriting of Robo’s history resulting from the Time Index theory would have been re-rewritten due to the successful defeat of Lavos and the saving of the future. Thus, the Prometheus circuit would have no problem existing because even though Robo’s 2700 is being rewritten, as that is in the past when compared to the Prometheus Circuit in 2400, via Time Index.

I'm afraid that the only misunderstanding here came from your end.
I never said that Cross took place in the exact same timeline that Trigger did. You, however, did misinterpreted almost every single event in which Robo actually travels through time. That is, in as much to say, because you actually claimed that Keystone-T1 Robo had never time traveled before or that in some mysterious way, it would be just as if he never did by the end of the game, just so that you could validate your own theory. This of course is wrong; not just for the reason that only the Robo from the original-timeline (the one in which Crono never interferes because there aren't any time gates, called the Lavos-timeline) never actually time travels (just like Crono), but also because it is impossible to even consider that after Lavos is destroyed all other time related side-effects would simply disappear (especially considering Chrono Cross' revealing plot).

Solution #6

And finally, because I haven’t written a long enough response, allow me to address the 6th problem. The Entity did it argument essentially states that an outside force prevents the GRL Paradox from happening. Time Index, however, essentially states that the [GRL Paradox doesn’t need to be prevented since the events that could trigger such a thing haven’t occurred. Such events might occur in the future (from a Time Index POV), but nothing in the game necessitates that they have or will occur. If my theory is valid, it doesn’t circumvent the problems presented by the Entity Did It argument, it fully stops before we get to an “it” that the Entity may or may not have done.

Finally, you're right! Only because this isn't nearly long enough yet! Yeah right.... I think I may have reasoning problems myself.
Except that only everything about common sense would necessitate such events from actually occurring! Otherwise what you are indeed claiming is that random things can actually happen as a predetermined occurrence... and that things don't need to change at all because all they need is to have the potential for it, and thus don't actually need to be random at all!
And this is where you leave Occam's Razor Principle to rest, I believe.

Occam’s Razor is happy because the theory really is quite simple; things don’t change until they change (and nothing has changed to cause the GRL Paradox, so the GRL paradox hasn’t happened).

No. Occam's Razor will never be 'happy', as long as all of this problems aren't completely solved in this particular theory.

And with that said, I declare this the biggest post the Chrono Compendium's Forum has ever seen!!!

[Radox Redux]

I know I'm late to this thread, but I once posted a time-clone theory about the idea of time-clones; that their purpose is to preserve the timeline if the time-traveler would leave time. I actually dislike this theory a lot now, but it something to concider methinks:

It was originally made, becuase from what I understand Crono, Lucca and Marle travel to 2300 AD despite the fact that it is the future of their present. This shouldn't happen, since the minute they leave their time, the timeline would be altered, menaing Crono, Lucca and Marle shouldn't have been able to visit the future, especially a future with Marle's future relative.

The simple theory is those nifty clones we see are used as placeholders for the time-travellers (perhaps put in place by the entity, as a kinf of reverse-time-bastard.) to live their life for them, in order to preserve the future. This was based on observations of the use of the Crono dummy, as well as their presense in the Black Omen, were they'd be used to preserve th Omen's own existance.

It's not my favourite theory, since it's an extention of an 'entity did it' approach, but what do you guys think?

[Thought]

It's not my favourite theory, since it's an extention of an 'entity did it' approach, but what do you guys think?

It is a theory that certainly fits the necessary parameters of explaining your situation (why 2300 doesn't change as soon as Marle, Lucca, and Chrono leave 1000) but anything that seems like "the entity did it" or an extension there-of leaves a bad taste in my mouth (despite the fact that, at least for Dinopolis, the entity DID do it). However, this clone theory would help "solve" the Marle Paradox too. Even if Marle is removed from time, regardless of TTI, her "time clone" would preserve history as Chrono and Lucca knew it, so they could still function as seen in the game.

However, I would still maintain that timelines don't change until they change. That is, the timeline doesn't change to take into account that Chrono, Lucca, and Marle are no longer in their present (say, 1001 AD) until such a time as they aren't there (essentially, for 1001 AD, Chrono and Co's absence would only matter if they were gone for a full year). To try to sum up my "Time Index" theory, discussed above, I'd maintain that until Chrono himself is at an age that matches when an event "would have" happened, sans time travel, that event is preserved in the timeline. As we see, time doesn't change on potential alone, only actual actions. Thus, for the future to change just because Chrono and the others travel in time, their bodies would have to reach those time points that would change and either do or not do whatever the original timeline would have had them do.

[Radox Redux]

Correct me if I'm wrong here, but according to your theory, wouldn't Ayla technically be able to meet her future-self, so long as she time-travels to a point beyond her total Time Error count?

Herein lies the problem, it wouldn't just apply to removing someone from a timeline, it would apply to all changes made by a time traveller. Essentially all this does is introduce the idea that time changes at the same rate as the displaced item's Time Error, as opposed to instantly. According to your theory, if Crono and crew defeated Lavos in 1999 AD, 2300 AD would change extremely slowly. The time-travellers have to wait 301 Time Error years (After defeating Lavos) before they could access the 'good future' version of 2300 AD.

Whilst this would solve the 'Doan paradox', Robo makes it clear at the end of CT that they're travelling to a 'new' future which, I'm afraid to say, blows your theory out of the proverbial water, unless you can provide a reason.

[Thought]

Correct me if I'm wrong here, but according to your theory, wouldn't Ayla technically be able to meet her future-self, so long as she time-travels to a point beyond her total Time Error count?

Herein lies the problem, essentially all this does is introduce the idea that time changes at the same rate as the displaced item's Time Error, as opposed to instantly. According to your theory, if Crono and crew defeated Lavos in 1999 AD, 2300 AD would change extremely slowly. The time-travellers have to wait 301 Time Error years (After defeating Lavos) before they could access the 'good future' version of 2300 AD.

Whilst this would solve the 'Doan paradox', Robo makes it clear at the end of CT that they're travelling to a 'new' future which, I'm afraid to say, blows your theory out of the proverbial water.

I guess Ayla could meet her future self, but alas there are no examples of this (though Robo, Magus, and Lucca sort of meet their past selves).

But I never said that changes to the timeline don't happen instantly; indeed, I maintain that they do. But I also maintain that the changes have to happen before they can effect the timeline. Chrono can't change an event that would have happened when he was 30 years old until he is 30 years old. By leaving the timeline, Chrono is actually rewriting history second by second, but the changes to the timeline are instantaneous. For every day he is gone, for every second, time is changed so he is gone for that one extra second/day (as it can only be when that event is reached that Chrono can either be or not be there). There isn’t one change, there are countless changes to the timeline as it can resolve itself.

Defeating Lavos in 1999 AD (technically 12,000 BC) instantly changes the future even for Robo and the others for three reasons:

1) Because Lavos isn't a time traveler and therefore not subject to Time Index.

2) Even if Lavos were subject to Time Index, Time Index arises out of unresolved potential. After Chrono first leaves in 1000AD, he may be presented in 1001 AD to perform an event that the original timeline has him performing, but he might not be present. There is potential for both outcomes and so time cannot resolve which to function off of. As no change is possible based on possibilities, the old timeline remain until changed (a concept clearly stated in the games). Death, however, is the end of possibilities (unless we want to get spiritual). Even assuming that Lavos were subject to Time Index, the moment he dies his potential is resolved. Thus, his Time Index collapses and his personal future (and the whole future based on his personal future) can be resolved.

3) Even assuming Lavos is effected by Time Index, and even assuming death doesn’t resolve his potential, after Lavos dies he never leaves his timeline. Thus, he has reintegrated to his own timeline and I would propose that Time Error is no longer a valid factor (Time Error effecting Gates, extra-temporal locations, and as I propose it Time Index). Not that Time Error ceases to exist; rather it just isn’t important for non-time travelers.

Consider that Janus leaves 12,000 BC, travels to approximately 580ish AD, ages until he is Magus, yet can still travel back to 12,000. Even Time Error would indicate that if a gate originally opens to 12,000 BC, after 20ish years of Time Error it should open to 12,020 BC. Janus/Magus appears to be on a different Time Error than Chrono and Co (but still on some semblance of Time Error). From this example, it is implied that Time Error doesn’t need to be universally uniform. However, to offer a counter-argument, it isn’t like Janus left 12000 BC through a standard gate. I may well be drawing too much significance from a potentially anomalous event.

Anywho, if Time Error is no longer a factor, the Time Index Equation changes from Original Time + Time Error = Time Index to Original Time = Time Index.

This is a bit of a curiosity as we never definitively see what happens AFTER a time traveler stops time traveling, so I am sure some people will disagree with this point.

[Radox Redux]

Correct me if I'm wrong here, but according to your theory, wouldn't Ayla technically be able to meet her future-self, so long as she time-travels to a point beyond her total Time Error count?

Herein lies the problem, essentially all this does is introduce the idea that time changes at the same rate as the displaced item's Time Error, as opposed to instantly. According to your theory, if Crono and crew defeated Lavos in 1999 AD, 2300 AD would change extremely slowly. The time-travellers have to wait 301 Time Error years (After defeating Lavos) before they could access the 'good future' version of 2300 AD.

Whilst this would solve the 'Doan paradox', Robo makes it clear at the end of CT that they're travelling to a 'new' future which, I'm afraid to say, blows your theory out of the proverbial water.

I guess Ayla could meet her future self, but alas there are no examples of this (though Robo, Magus, and Lucca sort of meet their past selves).

But I never said that changes to the timeline don't happen instantly; indeed, I maintain that they do. But I also maintain that the changes have to happen before they can effect the timeline. Chrono can't change an event that would have happened when he was 30 years old until he is 30 years old. By leaving the timeline, Chrono is actually rewriting history second by second, but the changes to the timeline are instantaneous. For every day he is gone, for every second, time is changed so he is gone for that one extra second/day (as it can only be when that event is reached that Chrono can either be or not be there). There isn’t one change, there are countless changes to the timeline as it can resolve itself.

Dude, listen to what your saying. This is a complete and utter contradiction. You say they happen instantanously, and then you say that Chrono can't change an event that he does when he is 30 years old until he is 30. Thus the changes now have to happen gradually, as Crono's Time Error clocks up. Sorry, but it just doesn't work.

Defeating Lavos in 1999 AD (technically 12,000 BC) instantly changes the future even for Robo and the others for three reasons:

1) Because Lavos isn't a time traveler and therefore not subject to Time Index.

But Chrono is, and he defeats Lavos, just as Ayla gives birth the Guardia Line. It's not about a person being a time-traveller it's about the changes that occur as a result, otherwise the Guardia Line Paradox wouldn't exist.

Besides the Lavos example was just one, I could apply it to every instance of time-travelling in the game: If your theory is true then the heroes wouldn't be able to make any change in the timeline at all, since they would have to wait for time-error to catch up to them again.

2) Even if Lavos were subject to Time Index, Time Index arises out of unresolved potential. After Chrono first leaves in 1000AD, he may be presented in 1001 AD to perform an event that the original timeline has him performing, but he might not be present. There is potential for both outcomes and so time cannot resolve which to function off of. As no change is possible based on possibilities, the old timeline remain until changed (a concept clearly stated in the games). Death, however, is the end of possibilities (unless we want to get spiritual). Even assuming that Lavos were subject to Time Index, the moment he dies his potential is resolved. Thus, his Time Index collapses and his personal future (and the whole future based on his personal future) can be resolved.

This is where your mistake stems from: The idea that Chrono can't be assumed to come back, but neither can it assume that he WON'T come back. But of course, your overcomplicating it. This isn't about potential, it's about the actions that the team make. Causality. Chrono dissapears from history, becuase he makes the choice to leave his timeline. Cause and effect; nothing 'potential' about it. Randomly habving him reappear in the future before he has even made the choice to come back, is breaking this causality.

My point: No assumptions are being made when a time-traveller leaves, the timeline doesn't include them becuase they physically left. Cause and effect.

3) Even assuming Lavos is effected by Time Index, and even assuming death doesn’t resolve his potential, after Lavos dies he never leaves his timeline. Thus, he has reintegrated to his own timeline and I would propose that Time Error is no longer a valid factor (Time Error effecting Gates, extra-temporal locations, and as I propose it Time Index). Not that Time Error ceases to exist; rather it just isn’t important for non-time travelers.

Once agian: this isn't anything to do with Lavos. It's all about Chrono, who changed history.

Consider that Janus leaves 12,000 BC, travels to approximately 580ish AD, ages until he is Magus, yet can still travel back to 12,000. Even Time Error would indicate that if a gate originally opens to 12,000 BC, after 20ish years of Time Error it should open to 12,020 BC. Janus/Magus appears to be on a different Time Error than Chrono and Co (but still on some semblance of Time Error). From this example, it is implied that Time Error doesn’t need to be universally uniform. However, to offer a counter-argument, it isn’t like Janus left 12000 BC through a standard gate. I may well be drawing too much significance from a potentially anomalous event.

Yeah it was a different gate. Imagine, the gates as timeless windows with time progressing on both sides equally. If he touched the gate he came to 580 AD from,  in 600 AD, then yes he would arrive 20 years after the Zeal incident. (Which BTW is 11,980, not 12,020, don't forget we're dealing with BC years here.)

[Thought]

Ah, terribly sorry I hadn't responded earlier; I just now noticed that you had posted.

Dude, listen to what your saying. This is a complete and utter contradiction. You say they happen instantanously, and then you say that Chrono can't change an event that he does when he is 30 years old until he is 30. Thus the changes now have to happen gradually, as Crono's Time Error clocks up. Sorry, but it just doesn't work.

Changes don't happen until they happen, but when those changes happen they effect all of time instantly. How is that a "complete and utter contradiction"? Let us imagine a real life situation; Bob will go to the store. He can’t go to the store until he is actually going to the store (it isn’t like he can arrive there before he leaves), but once he goes to the store he then is going to the store. This is a bit repetitive, but it is only so because the Guardia Royal Line Paradox seems to inherently assume that someone like Bob went to the store before he actually did so, arriving before he left (or, in terms of the paradox, that Ayla didn’t give birth to the royal line at age 30 before she was even age 29).

And of course Chrono can't change an event that he does when he is 30 until he is 30; can you change an event that you'll do in 10 years until those 10 years have passed? How would that even work?

Now we could imagine that Chrono at age 16 might be able to travel into the future and meet himself at age 30, however here we have a curious problem; the series never has a person meet their future self (only past selves), so we really don't know how this would effect things. But in this case, we'd actually have two Chronos; young Chrono might change the events surrounding old Chrono, but he isn't directly changing old Chrono or old Chrono's actions. Indeed, by time index, things change because what Chrono 16 is doing would be in the past, for both himself and Chrono 30, after he has done them. At no point would he be changing Chrono 30 at 30 while himself at 16.

But Chrono is, and he defeats Lavos, just as Ayla gives birth the Guardia Line. It's not about a person being a time-traveller it's about the changes that occur as a result, otherwise the Guardia Line Paradox wouldn't exist.

What in the who now? Could you try explaining your point? It is entirely about being a time traveler because the changes that occur as a result of time traveling only occur as a result of time traveling. If there is no time traveling, there are no changes.

Lavos is defeated, thus he doesn't exist in the future. Action happened, thus the result effects the timeline. Ayla has neither given nor not given birth to the Guardia line, therefore the action hasn't been addressed and therefore there are no results to effect the timeline. Time Index happens specifically at the individual level.

Besides the Lavos example was just one, I could apply it to every instance of time-travelling in the game: If your theory is true then the heroes wouldn't be able to make any change in the timeline at all, since they would have to wait for time-error to catch up to them again.

Time-Error is a universal constant that seems to sync the various gates and extra-temporal locations of the game. That is, spend 3 days in 600AD and you've spent 3 days away from 1000AD. Let us say that an event happens at Time Index Q (such as the change that occurs to the Mayor of Porre). Time Index is a function of two values; the state of the timeline at the point of a time traveler's departure and time error. This results in a value that can then be matched up with an event in that time traveler's future (like an index of a book). So, then, the Mayor's ancestor is not a time traveler so the first value is Null (not even 0). This leaves only time error. Not the time error that is the universal constant, but what time error will be at the time of the event. Ah, but as the Mayor's ancestor is not a gate or an extra-temporal location, she isn't effected by time error either. That means the equation can't work and Time Index does not apply to her (as, indeed, Time Index does not apply to ANY non-time-traveler). Thus, there is no "time error" that needs to catch up to them (or anyone else). Even happens, it effects the timeline.

Now, from Chrono's perspective, he can only give the Mayor's ancestor jerky (and thus, change the future) when his personal time index matches up with the event. The event is at original departure point + X, where X is a value equal to the time between the two. At X-1 or less, Chrono cannot change the Mayor's ancestor. At X, Chrono gives her jerky. All points in time that are equal to or greater than X+1 will then be effected by this action. You can test this in the game yourself if you don't believe me; go, play Chrono Trigger and see if you can change the Mayor of Porre before X (X being when Chrono gives his ancestry the jerky). You can't. Chrono's time index only effects what HE will do in his life, not what other people will do (though, to the extent that they will react to his actions, they are effected).

As this is my theory and it does allow for changes to occur, I must propose that you did not understand my theory. I am terribly sorry; if you can identify where my theory looses you I will try to elucidate the matter.

This is where your mistake stems from: The idea that Chrono can't be assumed to come back, but neither can it assume that he WON'T come back. But of course, your overcomplicating it. This isn't about potential, it's about the actions that the team make. Causality. Chrono dissapears from history, becuase he makes the choice to leave his timeline. Cause and effect; nothing 'potential' about it. Randomly habving him reappear in the future before he has even made the choice to come back, is breaking this causality.

My point: No assumptions are being made when a time-traveller leaves, the timeline doesn't include them becuase they physically left. Cause and effect.

Actually, I am being terribly simple. If you haven't noticed, time index matches up exactly with the player's sense of time (rather than the internal sense of time of the game). Time Index is as simple as playing the game.

Time Travel is what gives Chrono and the others an option; it is what brings the potential of change to time. If it wasn't for time travel, 2300 could never change. But introducing time travel doesn't change the future, it merely offers the possibility of change. Thus, my theory's claim is similar. Time travel is what gives a person an option; it is what brings the potential of change to their personal timeline. If it wasn't for time travel, Ayla would give birth to the Guardia line. But introducing time travel doesn't change the future, it merely offers the possibility of change. Ayla's time traveling adventures no more inherently destroy the guardia royal line than Chrono's time traveling adventures inherently destroy Lavos. It can happen, but only (everyone say it with me) when it happens, and not a moment before.

Yes, Chrono leaves 1000 AD and "disappears from history." Cause and Effect. But that is just one action, so you are extending that "effect" too far, going into predetermination (which is inherently contrary to the game). The effect of Chrono leaving 1000AD is that he is not in 1000AD, cause and effect. However, the effect of Chrono having been absent for 3 days has a different cause, and that cause is Chrono spending those three days elsewhere. He can't be gone for three days until he is gone for three friggen days. When he has only been gone for two, he hasn’t yet been gone for three. When he has been gone for four days, he has already been gone for three. Five is right out.

Once agian: this isn't anything to do with Lavos. It's all about Chrono, who changed history.

Then perhaps we need to define what "this" is. I confess, I have been working under the assumption that "this" is my theory, Time Index, and if it is a plausible explanation to the Guardia Royal Line Paradox. As Time Index is always personal and specific to the time traveler in question, "this" is always about the individual in question. As you brought Lavos up, "this" is then about Lavos. However, "this" can also just as easily be about Chrono (but the two are separate).

Your original supposition is that after Chrono and the others killed Lavos they'd have to wait 301 years before 2300 would change from its post-apocalyptic state. Chrono and the others kill lavos as a very specific point; their original departure point + X, where X is the amount of time that passes between that departure and Lavos' death. At any point before X, 2300 is a wasteland. At any point after X, 2300 never had an apocalypse (until Serge somehow changed it back in ways that I don't understand). Indeed, it could be said that Lavos' death changes Chrono's personal timeline entirely; gone is the Chrono at Age 30 in a world with Lavos, and come is the Chrono at Age 30 in a world without Lavos. Doesn't mean that whatever Chrono would have done at age 30 (in either timeline) is set in temporal stone. It changes the possibility, but it doesn't resolve that possibility. There is no waiting; Time Index, like Time-Error, is apart from the normal flow of time. Indeed, I am not even sure where you are getting the idea that waiting would be necessary for non-personal effects to happen (and for personal effect, there would be no way of observing that wait except through living; in which case the objection is nonsensical).

To be honest, I am not seeing where your objection is stemming from. Perhaps we should start over?