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Perhaps the most common reason to tell a story out of order is to put an exciting scene at the beginning to get the reader interested. Then go back and put in all the exposition to explain how that...
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Source: https://writers.stackexchange.com/a/10252 License name: CC BY-SA 3.0 License URL: https://creativecommons.org/licenses/by-sa/3.0/
#2: Initial revision
Perhaps the most common reason to tell a story out of order is to put an exciting scene at the beginning to get the reader interested. Then go back and put in all the exposition to explain how that scene came to happen. Another reason is if telling the story in order would give away important information to soon. Others have mentioned mystery stories. If you're writing a mystery where the reader is supposed to be trying to figure out who the villain is along with the detective, than of course starting out with the scene where the villain commits the crime could give it all away. Of course many stories have a "mystery" without being mystery stories in the sense of being about a crime, and the same reasoning might apply. Some stories involve numerous flashbacks as information is progressively revealed. Any given story might naturally call for non-linear time for any number of reasons. A story about an old man reminiscing about the past would quite naturally involve flashbacks. Perhaps you want to display the chaotic state of the hero's mind. Etc. As John Smithers says, if you do write a non-linear story, be careful that it is clear what is the present and what is the past. I have occasionally read stories where something was supposed to be a flashback and I didn't realize it, and the story was confusing until I figured it out. This can be done as simply as putting a date at the front of each section or giving clear introductions to the flashbacks, like "Jack thought back to when ..." Remember to also make it clear when the flashback is over, by the way.