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*warning, possible spoilers below*

Nice deductions Rick, but dont forget that Kyon (or Tanigawa theyre both the same X-D) has juggling between his hands, 4 sci-fi characters viewed in a introspective manner. He has:

1.-A highly advanced being from the outside.
2.-A person from an advanced time and culture in the far future.
3.-A person with an advanced extrasensorial capabilities.
4.-A person with an almighty capability.

Aimed at the inexpert, i could resume this 4 beings as an alien, a time traveler, an esper and *gulp* a semi-god. Somehow i find it fun how Tanigawa plays with these 4 characters and the way he points at their flaws if hypothetically, they could exist and how would he react to these strange circumstances. He practically tried to invite us into a discussion where the main plot is "what if..." (this is, a "make your own hipotesis about the story") and he does it well in a manner. Bad thing of letting loose a lot the imagination of your readers is that everyone will whant to pour his opinion and feelings into his work, something that i thank him a lot since it gave me soo many thing to think of but it leaves other people with no clue of what is really happening in the story because in some of the events people will need to understand body languaje well and try not to let any detail done in the story as irrelevant.

For example, the last scene, after the credits, we can contemplate Nagato at the library, reading a book. Casually, she stares at two kids, a boy and a girl, as the girl says "thank you" to the boy while he is helping her with a library card. Nagato stares down, back at the book she is reading and then, she stares back at the kids again while trying to cover her expresion. In the movie we see Nagato giving thanks to kyon 2 times, one at her apartment explaining that she knew him before because one day at the library Kyon made a library card for her, and at the end of the movie. This can make that some of us imagine that theres a connection between those 2 events. Could it be that Nagato learned that giving thanks is a needed human protocol, and the action of "give thanks", is a complex action that means that you, as a person, acknowledged the efforts of others when they try to help you and approve them? How could she approve something and judge if it is right or wrong if theres no prupose to assign a value to an action? An Ai only serves the prupose of the programmer, and her prupose wasn't hers. But maybe a flaw could be developed if you try to make them learn from human behaviour, because human behaviour is controlled by the brain that is waaay more complex than any supercomputer in the entire universe. Human brain is programmed to achieve "balance" in the body, but it has some flaws, because we have feelings that can be corrupted by imperfections from the inside and also from the outside. Than might be misundesrtandings, altered state of consciousness cuz of drugs or just because we like to create (imagining things enters in this catherogy) in order to have something of our own that gives a sense of worth to our life. Creation envolves the action of develop new data from the data we had previously, a data that is incomplete since our senses cant perceive everythng in the universe (our senses aint so sharp to watch molecules whit no aid from microscopes) so this means that every information that humans gets can be interpreted in many ways since we, most of the time, cant see the things just like they are meaning that our feelings can deceive us (like when people use pain killers, they might make the pain calm, but they aint solving any problem outside of that because they dont heal the illness, or drugs...that can make the illusion of feeling better, but in reality youre poisoning yourself and deceiveng your own body and mind).

How can Nagato may be grateful if she didnt feel like it? How could she fulfill that protocol and still be herself? Only living beings can feel and thus they can answer to that expresing their wish. "Give thanks" = error. Because she dont have the need like the humans do and in order to feel, she needed to sense pain, need, joy, that crave for something and comprehend it. She neded to develop feelings to give thanks properly, like humans do. Cant fly like a bird, literally because youre not a bird. Maybe you could fly...but like a human and thats all the people can get (buy your plane tickets and vuala, you fly like most humans). The solution to all those impediments -> turn into a human, to start feeling and have wishes. And something so simple like giving thanks are triggered by many other aspects in human beings but we forget and get easily impressed. Just look at us, discussing over some events that never ocurred in real life, discussing over unreal characters that represent our wishes and toughts and trying to use complex symbols to communicate, aint that fun how we try to give some worth to our toughts?.