A story has no beginning or end; arbitrarily one chooses that moment of experience from which to look back or from which to look ahead.
~ The End of the Affair, by Graham Greene
What does the author want to say through this sentence?
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I don't think there is anything mysterious about this. If you think about it, every story relies on something which happens before the telling of the story begins, and every situation related in a story continues to have consequences after the latest point related in the story.
To take the archetypal example of Genesis 1:1
In the beginning God created the heaven and the Earth.
At that start of that story, the main character already existed before the story began. If a story begins with the birth of the main character, they still needed parents and all their lineage to bring us to that point, all of those can also be regarded as part of the story.
Likewise when the story telling ends, there are still people and lives ongoing.
Existence is a continuum, and any story is just a snatched piece of the whole, which could have started sooner of finished later.