In the movie Eternal Sunshine of the Spotless Mind (2004), Joel gets a message from 'Clementine' in his dream inside his head, and since even that dream was erased how do the real Clementine as well as the 'new' Joel know that they were supposed to meet each other in Montauk the next morning?
The question answered here as follows,
She doesn't, exactly. The whole experience is in his head, and it was the memory of her that told him to go to Montauk.
We are supposed to take a guess at what her memory erase experience was like, and assume that she had a similar experience to his, so maybe when they were clearing her memory, he said the same thing to her. But remember, she did it weeks before he did, so the real question is: how did they know to come on the same day? Fate, maybe?
Montauk was an important place in their relationship. That's where they had a night picnic on the frozen pond, and they were very close at the time... which is important because it was shortly after that when their relationship went sour. It suggests that there are some things that cannot be forgotten, no matter how powerful the science used against it may be, especially with memories tied to very strong emotions like Love.
I just saw this wonderful movie a few months ago, so this question had gripped me seriously since quite lately.
I think perhaps if we follow a bit of logical train of thought we might arrive at the answer in a more satisfied manner , now before we draw any conclusions let's have some assumptions and facts sorted out ;
Assumptions and facts :
let's say the memory erasing was completely successful on everyone!!, but that doesn't mean people who have undergone such treatment won't start feeling the same way again, remember Mary svevo falling for doc Howard yet again or when Patrick was wooing Clementine (with the same words, style to that of Joel), she suddenly started feeling all strange.
However may you think otherwise, but this registers as a fact that the Clementine we see in Joel's memory is a figment of imagination by Joel's mind only of how the real clementine was, more simply put the real Clementine may not be entirely the Clementine that Joel's mind had remembered, although I still think the virtual Clementine was almost 95% of the real clementine but still there must have been trivial gaps between them.
let's say you are a chess player, and a rival defeats you by a secret unknown trick, so what do you do then, ? You most probably will try to figure out a way, to develop a resistance to this trick at any point of the game in your further matches, that's how our brain works unconsciously, no I am no brain expert or neurologist but have a read through this book, it's very insightful about this topic : thinking fast and slow
Clementine and Joel know each other's ways, manners and daily life routine quiet most thoroughly, after all they were in a intimate relationship, so yes such details will be saved by brain quiet intimately.
the dream where Joel was involved when he was undergoing while memory erasing was also itself erased, in the morning, for it weren't, then surely Joel would have remembered actually how did he erase Clementine
after the erasing process, he would be there at that point of his life just after Naomi left him.
the virtual Clementine had actually figured out a way to develop a resistance to this process for a while, which is by tampering the memory which is to be erased, by linking or mixing it with some other target memory which isn't mapped to be erased.
Even though Clementine had actually undergone this same treatment, there's no credible evidence in the film or any possible scientific suggestion that in her dreams too she could actually connect with the real Joel, same could be said of Joel.
montauk was the place they met first time, and also while Joel waited for the train to his work place everyday, there was a train to montauk everyday at the adjacent platform.
note that as the virtual Clementine was just a creation of his mind only, so actually Joel's brain had figured out a way of this erasing process for a while, but later his brain and Joel both realize, this method won't work till a further point.
His brain too realizes that relentless trying to retain those lovely memories, will too not work here however romanticised that notion may be.
but there's actually a way that brain may have found, note that(as stated under assumptions and facts) people start behaving strangely when superimposed with things, that give them a feeling of deja vu, the memories may have been erased but the familiar stimuli remains.
so perhaps the only way again Joel might again get to reunite, with her is to possibly have a hint regarding her, now there were many such special places(like that iced lake), why only montauk serve as that hint ? Look at the last point under the assumption and facts, yes somehow his mind must have thought of giving a hint that's closely related to his daily life routine, and which is also associates Clementine, otherwise from his everyday routine, and that place is montauk.
So brain gave Joel a hint through the virtual Clementine because it knew Clementine must have known this feature or coincidence of how a train departs for montauk regularly as Joel sets out for his workplace.
quite expectedly as Joel waits for his train next morning in that station, as it's announced there that " the train to MONTAUK lives in 4 minutes", Joel surely must have felt uncomfortably familiar (like clementine behaved whenever Patrick said her she was "nice"), although I didn't expect him straight away run for that train.
As to how Clementine and Joel met there on same day, is all I can say fate, yes fate don't tell me there was some telepathic import of intent, there was no real or reel evidence to suggest this.
there goes another argument as to how they would meet at same time and catch the same train back ? Isn't that too coincidental ? But didn't you see how much montauk was deserted(except on holidays) ? So perhaps there was only 1 train there that ran between where both Joel and Clementine lived and montauk, so while Joel caught the train to montauk, she must have been in the same train in a different coach perhaps so they arrive there at same time, and yes there must be only 1 good and nearby restaurant in a place like that.
I may have had made my reasons too 'brainological', but I think that was my viewpoint or how I deduced. Nevertheless the script, dialogues, theme, direction and acting was really mesmerizing.
I think it is also worth noting that in the beginning of the film where Joel and Clementine meet on the frozen beach in Montauk it is in fact Valentines day. It might have some significance to both of them as Joel buys a gift for Clementine because he wants to resolve their fight before Valentine's Day arrives. After they both have their memories erased of each other they both end up in Montauk on Valentine's Day. Montauk has a significance to both of them as it was the first, earliest memory that they have of one another and it was the location where they met for the first time. I can only conclude that right before Clementine has her last memory of Joel erased, her memory of Joel asked her to meet him in Montauk too on Valentine's Day. It's also worth noting that Clementine does in fact recognize Joel (as she states in the beginning of the film while they are on the train) as Joel did previously go to her work with her gift while unaware that she had her memory erased of him.