The speaker perceives “immortality” in the figure of the bird—a creature that, the speaker believes, is unplagued by human anxiety about the inevitable march of time towards death, and whose song has echoed across the centuries.
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Eventually, though, even the nightingale flies away—leaving the speaker with a deep sense of loss and a seeming reassurance that *everything* inevitably fades.
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The speaker’s ability to enjoy the world is dampened by the awareness that nothing will be around forever.