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Goodfellas is actually presented chronologically. The important point here is the exact wording: It is PRESENTED chronologically, even if the voice-over narration is technically non-linear. The narrator explains in chronological sequence the events of his life.
This narrative technique affects the audience by making presenting the main character, a criminal, in a sympathetic light. The audience first identifies with Henry as someone normal-- he has a family, grows up like most normal kids, and the era in which he was born is widely considered to be "the good old days". It softens the edge of his criminal career.
Ultimately the impact of the storytelling method is used to soften the edges of what we know to be Henry's ultimate fate. How he arrives there is foreshadowed by his admiration for the culture he is exposed to. His ultimate fate as a character, the trials he puts his family through, and the consequences of his choices develop a character along a path that this storytelling method is used to present as inevitable. It is not that Henry himself is a bad person, but rather, this storytelling technique is used to imply that given his surroundings, this is where he (and by extension, the audience) see as natural for themselves.
Presentation of the story in a nonlinear method would be very effective at shifting the blame from nurture to nature. If we first saw Henry as a hardened criminal killing people, we would view any presentation of his childhood under a very different light. It would be the most effective method for saying it was Hill's nature, not his surroundings, that inevitably led to his life of crime. This presentation of his adult life out of sequence is used very effectively to eliminate any audience sympathy.Please let me know if you need any clarification. I'm always happy to answer your questions.
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