So, the order in which the people are seen, seem to have some significance. To me at least ;) They always show up in the same order: Michiru -> Ruka -> Takeru -> Eri -> Sosuke.
From the little I know, it appears that each person 'likes' the preceding person. For example:
1. Michiru likes Sosuke... check, this is correct. (I had to revert back to the last name, because she was first in the list).
2. Ruka likes Michiru... check, this is correct.
3. Takeru likes Ruka... I'm going to say this is also correct, from the way it's been hinted in the series...
4. Eri likes Takeru? This I have no idea... so is pure speculation, but since I really know nothing about this character, it could be true? Mind you, she did apparently spend the night with Ogura (from what it showed in Ep 3 during the 'wake up to coffee' scene), so that might not work, but since he's not in the opening sequence, and this is my screwed up mind taking over, then whatever. I'll just run with it for now...
5. Sosuke likes Eri? Now this one is hard for me to believe, but I'm not really sure if his love for Michiru is real, or he's just in love with the idea of someone that will stay with him? (Because she's had a bad life and apparently thinks he's the best she can do) If Sosuke is only in love with the idea of not being alone... then pairing up with "solitude" might be good for the both of them... so long as he works out his issues first, and starts acting like a decent guy.
Okay, so that might have been pushing it a bit at the end, but since the pattern worked so well at the beginning, I thought, why not run with it, and see where it takes us?
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Next idea...
From the section where we first see them all walking solo, and coming through the curtains... I noticed a couple things worth mentioning.
1. Everyone is walking, except for Sosuke. Does that imply that everyone is pushing forward in their life and their problems, but he's stuck at a stand-still?
2. As the camera cuts away from each person, the only person to be "blurred out" is Ruka. Is this a foreshadow to her "fading away", ie. dying?
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Okay, and here goes another one of my 'order' predictions. I feel more and more crazy as I type this. Is anyone still reading by this points?
Anyway... this is what I was getting from the part where they were all passing through their "Love", "Liberation", "Agony", etc. for the 'sum-me-up-in-one-word' section.
1. Michiru ("Love"), cut to scene with Takeru and Ruka (in that order, from left to right of screen... I have a thing for order ;))
If you'd care to notice... that seems to follow the 'who loves who' order. Michiru -> Takeru -> Ruka. ie. Michiru likes Takeru (or so says the correlation chart with the heart going from her to him), and Takeru likes Ruka (or so it appears through his actions).
So, that first one works. Also, since Ruka, was the last in line, she's up next
2. Ruka ("Liberation"), cut to scene with Michiru and Takeru (again, left to right).
Same thing appears to work. Ruka -> Michiru -> Takeru. All like each other in that order (from what I've come to know anyway.)
Again, my last in line theory work... Takeru was last, so he's next in line...
3. Takeru ("Agony"), cut to scene with a 'mystery' person walking away from Eri (Again, left to right people!)
Now, this mystery person is not one of the people wearing a dress... so that gets rid of Michiru, and Eri (mind you, I didn't think Eri was walking away from herself... so yea
). That leaves us with Ruka, Takeru, or Sosuke.
If it was Ruka... Then the order would be Takeru -> Ruka -> Eri...
Now, the Takeru liking Ruka thing works... but I don't see Ruka liking Eri... since she seems pretty hooked on Michiru. But you never know... Eri is also a member of the 'home team' so to speak, so it might make sense.
If the mystery person was Takeru... then it would be Takeru -> Takeru -> Eri...
That would just be silly... Takeru likes himself lol... (after all, he seems to have a phobia of relations with other people due to his past trauma, so -maybe-, but it's a stretch)... but then he'd also like Eri. Anything is possible, but I'm thinking not. Probably not lol... Two Takeru's might just confuse the matter lol...
If the mystery person was Sosuke... then it would be Takeru -> Sosuke -> Eri...
If I follow my theory of "A" likes "B" who likes "C", then that would be Takeru likes Sosuke... (I'm thinking so far, he doesn't have the best impression on the guy... knowing how he treats Michiru... so probably not going to happen, but if he -did- manage to change and become a good guy, then -maybe- seeing as Takeru does have that 'gay' image about himself... and the coveted "teletubbie purple" cup ;) I'm stretching it again, aren't I?), so and then Sosuke would have to like Eri... which I have no idea. It's possible, by the reasoning I came up with about 20,000 words ago.
The first two options are sounding a lot more plausible than this last one, but none of them in this segment sit quite right with me lol... anyway, moving on... Since Eri was last in line, she's next to go (at least one part of my ordering theory seems to be working out ;))
4. Eri ("Solitude"), cut to a Michiru/Sosuke scene. Eri -> Michiru -> Sosuke
Eri liking Michiru? It could happen, since I really don't know enough about Eri to prove it wrong... other than he 'one night' with Ogura. And we all know Michiru likes Sosuke... so that half definitely works.
Then since Sosuke was last... he's up next
5. Sosuke ("Contradiction"), cut to scene of everyone walking together and ignoring one another.
Wait? What... Sosuke doesn't get to have his own love path? Okay, that might make sense too, since I can't see him really loving anyone if he's going to get all DV on them. Mind you, he did have that white coffee cup with the black coffee spilling over just before he was shown. So that might a metaphor about the "badness" building up inside him, waiting to overflow once it hits the breaking point. (Again, am I reading too much into things?)
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I so feel like one of the too long/didn't read posts... sorry guys. Thanks if you have stuck with me this far
Sorry if I'm just insane, and this all means nothing!
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Now, my last speculation is about the final shot with the 'red ribbon' that ties them to ones another. Call it the 'red line of fate' or whatever...
Ribbon 1: Comes from outside of the frame, twists around Eri's wrist, and then once again leaves the frame, not connecting her to anyone. This is a nod to her 'solitude'?
Ribbon 2: Comes from outside of the frame, and then connects Takeru to Michiru to Ruka. Each of those that are connected have a 'deeper connection' so as they are tied by fate to be together. The ribbon seems to end at Ruka, as it doesn't seem to leave the frame. Could this be foreshadowing that her 'fate' has a definite end in sight, where she dies? Then again, Ruka also has a second ribbon (ribbon 3?) on her other wrist that comes and goes from outside the frame, without giving her a connection to anyone else. Perhaps signifying that without her connection to Michiru, she's also be in 'solitude'?
I also find it strange that Takeru doesn't have a ribbon that connects him to Ruka, since there seems to be something shaping up in that direction... but maybe since he knows her feelings towards Michiru, things never progress between the two of them for that "deeper connection" that seems to be needed for the red ribbon to connect?
Ribbon 4: Connects Michiru to Sosuke, and then trails out of the frame. Again, there's the definate Michiru / Sosuke connection, but that also shows that he doesn't have that deep connection to any of the others.
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A couple additional points that I noticed, but don't really have a place to fit them here...
1. Everyone in the final shot (with the red ribbon) is facing someone... or at least is facing in the direction of someone. All except for Sosuke. Does that mean that everyone has someone to turn to for help with their 'issues' except for Sosuke, who is left alone with no one to listen?
2. Sosuke is the only one wearing anything that isn't white. Now this is obvious to say ... that's because he's a bad guy... black=bad. Okay, well, I was thinking about that a little more deeply. Perhaps that bit of black that he wears represents the small part of himself that he doesn't like - I shall refer to that part as evil-Sosuke.
Since he is the only one that is wearing anything other than white, it makes me think that he's the only one showing his true colours. He knows he has a problem, but hasn't found anyway to deal with it. He doesn't hide his problem (at least, he isn't hiding it very well, from all the DV he's showing) and so he wears a bit of black.
The rest wear nothing but white - effectively hiding their "true colours".
Michiru hides the pain from her relationship with Sosuke, so she can feel a bit of that "love" she's never felt before. (Though by the end of the third episode, she doesn't seem to be hiding it any longer... for the time being at least, I can see he going back to him again... starting the cycle once more.)
Ruka hides her feelings about Michiru - loving her the only way she knows how to ... from afar, stealing a kiss when the chance surfaces. She's also apparently hiding some sort of medical condition from everyone, judging by the website she's been visiting.
Takeru is hiding the 'agony' that he feels inside from his past traumas.
And Eri is hiding her solitude, by trying to act all happy-go-lucky. I suspect her owning a rooming house is a way to try to rid herself of solitude, but that doesn't work well when everyone moves out on her.
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Again, sorry for the length... didn't realize I'd gone so in depth with my theories here. Feel free to skim past this one if you want ;)