Other mistake: At the end of the film when they arrive in NYC looking for the library, we know that they survived because they are inside with a roaring fire burning. But where is the smoke up above, as Jack Hall approaches? There must be a chimney, or else they would have all died of asphyxiation.
The Day After Tomorrow (2004)
Plot summary
Directed by: Roland Emmerich
Starring: Dennis Quaid, Jake Gyllenhaal, Ian Holm, Emmy Rossum, Sela Ward, Dash Mihok, Jay O. Sanders
The Earth experiences a major climate shift, caused by global warming, which pushes the planet into a new ice age. It is a race for survival as the whole northern hemisphere begins an evacuation to the south where it is warmer.
WampaLord
More mistakes in The Day After Tomorrow
Vice President Becker: I don't accept that abandoning half of the country is necessary!
Tom Gomez: Maybe if you'd listened to him sooner, it wouldn't be.
Vice President Becker: Bullshit! It's easy for him to suggest this plan. He's safely here in Washington.
Tom Gomez: His son is in Manhattan. I just thought you should know that before you start questioning his motives.
Trivia: Before the film was released, N.A.S.A. sent a memo out to all of its employees stating that they were not allowed to comment on the likelihood of the events portrayed in this movie.
Question: Why would Sam and his friends go to the library?
Answer: Possibly because it was the closest building with height to it as they are about to be hit by a gigantic wave of water. There was no snow yet, so I don't believe burning books or snow was on anybody's mind yet. It turned out to be a great idea as snow soon starts to fall and those books were literally a life saver.
Answer: It was the closest building they could access. While the smarter move would have been to just go back to JD's apartment (which Brian and Laura suggest) it may have been too far a walk to get out of the flooding streets.
Why did they burn the books and not the wooden shelves that the books were on?
As for burning books rather than shelves, it was just easier. They would have had to expend more energy to break down the shelves into manageable size.
They burn books instead of the wooden shelves because burning books is a quicker and more efficient way to generate heat in a desperate situation, as the paper readily catches fire and produces a substantial amount of heat compared to solid wood, which might take longer to burn properly.
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Suggested correction: As already corrected, just because we can't see an outlet for the smoke doesn't mean there isn't one. White smoke against white snow is very hard to see.
Nik Rolls
But they were still burning the books, which meant the smoke should be black, if they stop burning the books, the smoke would have been white, which isn't the case in the movie.
Just looked at a boatload of videos of burning books, including one in a fireplace, and the smoke was indeed white.