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Although I like Daniel's theory that people are the variables because they have free will, I think that their status as variables in any given equation (e.g., the incident = ax +by +cz…) is, well, variable. In other words, some people may be able to affect real change while others cannot.
The ‘D’ variable
I’ve believed for a long time that Desmond can change the past. And for a long time I thought he was, as Dan said, uniquely and miraculously special this way. In Flashes Before Your Eyes he came unstuck in time and was able to “relive” part of his pre-island timeline while being aware that he was reliving it. Mrs. Hawking seems to be particularly anxious about keeping him on the path to his destiny of button-pushing on the island. Her anxiety over it leads me to believe that Desmond’s destiny is no certain thing. Additionally, in The Variable, she apologizes to Penny for Daniel leading him to become involved in the situation which led up to his being shot. I don’t see her doing that if she believed him to be destined to be involved. Finally, she asserts that Desmond’s destiny is uncertain (whether he’ll recover or not) and that this is the first time she is not sure what will happen next. It would seem that Desmond is a very powerful variable and his involvement (post-hatch) through Faraday may indeed change everything.
But can anyone else be a variable?
My first thought, while watching The Variable was - Daniel. Like Desmond, Daniel has been exposed (in his case through his experimental research) to powerful energy which may have unstuck him in time. We don’t know the exact nature of his memory problems, but they may be due (see AngriBhuddist’s blog) to being unstuck in time. Daniel, however, came to the island on the freighter, which would not have happened if the incident hadn’t led to the button pushing and subsequent failure to push the button, etc. (see AngriBhuddist’s comment on Harcourt’s “Whatever Happened Is Drama” blog). So Daniel cannot prevent the incident because it would create a paradox.
Who can’t be a variable?
Extending this line of reason, it seems that none of the Losties who remained on the island and experienced the effects of Ben turning the wheel and Locke turning the wheel, sending them back to the 1970’s, can prevent the incident without causing a paradox. After all, they only ever came to the island because Desmond’s failure to push the button (which we know was installed because of the incident) caused 815 to crash on the island… which means Sawyer and… well Sawyer… can’t prevent the incident.
What about the others (no not the Others)?
I always wondered why Ben was so ridiculously adamant in preventing the Losties from leaving the island when he clearly had no intention of letting them join his community. But I realize that keeping them on the island in effect zeroed out their ability to change the past. Mathematically speaking, it’s like putting a zero constant before each variable x=ay + bz… if a and b are set to zero, then the effects of y and z are eliminated and no matter what value they take on, they will have no effect on the outcome of the equation. Whether on his own initiative or in response to Jacob’s orders, Ben desperately tried to zero out the Losties as variables and eliminate their power to change the past.
What about the Oceanic 6?
But in the end Ben was unsuccessful in keeping them all there, and as a result, six of them escaped the island (plus Desmond and Frank). Once they left the island, the possibility opens up for them to come back to the island for reasons unrelated to the crash of 815 and therefore independent of the incident having happened.
So perhaps the Losties who left the island and then ‘’returned’’ via Ajira 316 – Jack, Kate, Hurley, and Sayid in particular – retained their variable status. I think it depends on why they chose to return to the island and what caused them to flash back to 1977. Kate chose to return to find Claire for Aaron’s sake. This is dependent on the chain of events set off by the incident so Kate cannot be a variable in this case. (incidentally I do think Kate was a variable in the case of little Ben – Richard told her what would happen if he healed Ben and gave her the option of deciding what to do, and she freely chose to hand him over to Richard). Sayid was brought back unwillingly by Ilana, so he may be a variable. We still don’t really know why Hurley came back, so his status is uncertain, but I’m going to hazard a guess that he can’t be a variable because his whole association with the island is wrapped up with the numbers, which are so integrally related to the swan hatch that it is almost certain that Hurley cannot change the past without creating a paradox. And Jack came back because of a vague sense of his purpose being tied to the island. Technically, he wouldn’t know about the island if 815 hadn’t crashed, but he may have taken a ride on 316 to find his destiny even if 815 had never landed. We know his pre-island life was already in shambles, with his wife divorcing him and marrying another man. He was already well on the way to a miserable life of obsessively fixing things but devoid of any real deeper purpose. So I think he could possibly be a true variable.
And then there were none
But what about the Dharma folks? They came to the island ‘’before’’ the incident. What if their space-time experiments at the Orchid enabled them to travel back in time. Could they then prevent the incident from happening? I think it would depend on why they went back in time. If they only went back to prevent the incident, then that would create a paradox, since preventing the incident would negate their reason for going back in the first place. If, however, they also had another significant reason to go back, or if they went back by accident then they could prevent the incident without creating a paradox. But of course, they’re all dead now so they presumably can’t serve as variables.
In fact, their status as variables may be the reason why they were purged. Ben, Richard, and the others may have murdered them specifically to prevent them from ever changing the past.
Where oh where is Claire?
Before the island moved, Claire disappeared into the jungle, was seen briefly, hanging out with her dad in Jacob’s cabin, and hasn’t been seen since. Many fans believe she may be existing in a state outside of time, along with Jacob. Could this enable her to be a variable? Probably not, since she is still on the island solely because of 815, which crashed because of the hatch, which was built because of the incident. So no, she can’t be a variable in changing the incident. But she can in a way be an ‘’indirect’’ variable – by giving birth to her son Aaron who could be a variable. Aaron is no longer on the island, and so his “on the island because of 815” stint is over. He could, however, come back to the island for an unrelated reason and serve as a variable the second time around.
The writers have heaped loads of importance around his character from before he was ever born. Mr. Malkin gave vague but terrified predictions about his future if anyone but Claire raised him. Ethan and the others went to extreme measures to get their hands on Aaron. Dead Charlie sent Jack a message that he wasn’t supposed to raise him. Kate went back to the island to bring Aaron’s real mom, Claire, back. Hurley’s comment that “Australia’s the key to the whole game” during the game of Risk may be a hint for the show in a broader sense, and I only counted two Australian among the survivors of 815 – Claire and Aaron. So Aaron may be a variable.
What lies in the Shadow of the Statue?
Speaking of kids, what about the children of the dead Dharma people? If Aaron could be a variable, could the Dharma kids sent away with Miles and Charlotte shortly before/after the incident be variables? I think they could. Many fans believe that Brahm, Ilana, and their buddies who keep asking what lies in the shadow of the statue are the lost kids of Dharma. Perhaps this is what they have returned to the island for – to try to change the past and prevent the incident. Of course, they are still in 2007, but perhaps they know the secret of the frozen donkey wheel. In fact, I’m going to guess that that is what lies in the shadow of the statue. It would make a lot of sense, since the time-traveling Losties saw the statue appear fairly close to the Orchid when the island skipped back to ancient times. If they can turn the wheel and get back to 1977, then perhaps they can do something.
Where does faith come into the equation?
All in all, however, I am of the opinion that intention counts. It is possible that a paradox would be created in any case where it is a character’s intention to change the past, and prevent the incident from happening. This is because if the incident never happened they most likely would not have taken whatever action they took to prevent it from happening. If, however, a character like Locke, a man of faith, took action based not on science (if we do this then we can prevent the incident) but on faith (I will do this because it is what I’m supposed to do, though I don’t know why), then there would be no paradox. If Locke has a knowledge through faith of what he should do and follows it, then that is not based on an intention of changing the past, and therefore could conceivably alter the past without creating a paradox, since his decision was independent of what happened in the past.
If this is the case, Locke may be the most powerful variable and the key to the whole equation.