As someone who has not read the Harry Potter books, I can watch this movie with a sense of mystery, watching for clues and hints, things that will, no doubt, reveal themselves invaluable within the plot of the movie. By the way, did I mention that I'm a Star Trek fan too? Why is this important? One of more popular plots used on Star Trek is temporal travel (time travel); just because something hasn't happened doesn't mean that didn't already happened. Confusing -- I know, but that's time travel for you. You'll see this effect too in Harry Potter -- it'll seen confusing at first but as the movie continues on, you'll understand. What you see isn't really what happened until you reach the later parts of the film
Special effects played heavily on this movie, from the magical map that can track everyone's movement to the dreadful wraith-like guards of Azkaban; from the "floating" aunt to the grumpy old tree just outside the grounds of Hogwarts. One of the better effects that I've seen done from one Harry Potter movie to the next was used in the Quidditch games. The rich detail of the environment, the weather and fast-paced depiction of the game brings plausibility and realism to the movie. I know, it's still a movie.
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