In the books, Arya spends Lord Tywin's time in Harrenhal as a peon who only catches the occasional norms regarding sex and marriage. I think it's important to remember that Littlefinger has nothing to gain from strengthening Tywin's hand at this point. His objective is to foster. Tywin is correcting Arya so that she can make sure her disguise will in a power position - as such it is a genuine advice on how to maintain her cover. . Tywin's relationship with Arya is reflective of and consistent with his.
Her use of the term proper was improper in that context.
She did this on purpose so that she could subsequently correct herself in an attempt to outwit Tywin. He obviously wasn't fooled, being quite cunning himself. One of my favorite scenes in the entire series thus far.
To me, there is a significant difference: Not sure if that distinction is intended to be carried through to the Throniverse, though. Tywin has figured out probably pretty fast that Arya is a highborn posing as a commoner, but he clearly cannot know who exactly she is, otherwise he'd immediately secure her in custody.
He has multiple reasons for correcting her disguise: Tywin doesn't want anyone else finding out Arya's secret, since only him knowing about it keeps him in a power position - as such it is a genuine advice on how to maintain her cover. At the same time it is a power play move. Since Arya is trying to hide an important secret from Tywin, she considers herself in an empowered position to him.
That could be ok for a while, but he doesn't want her to get too comfortable thinking she's outsmarted him - he's reminding her that he's the one in power. Even further, he shows that even though she'd had a secret from him he has chosen to both ignore her mistrust and keep her secret safe from others.
The move also places Arya in subtle social debt. Tywin has now revealed a secret to her, while at the same time making sure she no longer has a chance to reveal it herself. These two definitely have a better relationship with each other than almost any other set of siblings in Westeros, with the exception of the Starks.
Unlike Cersei, Jaime actually likes his little brother and has done his best to look out for him. We can recall that it was because of Tyrion being kidnapped in season one, that Jaime attacked Ned on the street, and he was willing to give up being a Kingsguard for him. Tyrion, himself, helps Jaime when he returns to King's Landing without as much as a right hand with emotional support and a sword teacher.
Romantic relationships have been built on less In what universe would this ever happen? These two have never had a scene together, and even if they had, I'm not seeing the chemistry. If Sansa didn't go for Tyrion, despite his sheer awesomeness because he's a Lannister even while they were married, then she'd never go for the Lannister most notoriously known as the Man Without Honor.
He's also known as the guy who has never had sex with anyone except his sister Still, it's an interesting concept. Jaime obviously cares enough about her to honor his oath to a deceased Catelyn Stark and sent Brienne after her instead of following Cersei's orders and hunting her down.
They were on the right track before the Red Wedding came and screwed everything up.
With him protecting her from his horrible family members and her giving him advice on how to prank courtiers, it was a match in weird Westeros heaven. In any other situation, these two would've eventually gotten along very well. In fact, I have a theory that they are going to end up re-married by the end of the season.
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The Stark-Targaryen is easy: The Stark-Lannisters can be solved by Sansa and Tyrion's re-marriage—so long as Sansa stays out of the next assassination attempt. Can you imagine the sass in the pillow talk between these two? It definitely would not be a very romantic relationship, what with Bronn's blunt "I like you, truly.
I just like myself more" attitude.
- Why Arya Stark and Tywin Lannister was a really good idea
Although, maybe if there had been romance, he would've taken on the Mountain for Tyrion's trial by combat. He's as fast and as good as Oberyn Martell, but not nearly as arrogant in his skills or dead-set on getting a confession about a year-old war crime. And Tyrion wouldn't have hired Shae if he had Bronn, so we wouldn't have had to go through that horrible betrayal.Game of Thrones S02E04: Arya Stark meets Tywin Lannister