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This article contains plot details from the latest books.
Blinking is when elves let light pass through them and they disappear. Vanishers do it naturally as they move, but other elves can do it with practice. Fitz does it the day he finds Sophie when she doesn't believe she's an elf. Once, Sophie uses a brain push and accidentally ends up flying through the air. At the time Fitz think she's blinking but it turns out it is from her Teleportation ability.
In Flashback, Della and Biana are pictured to blink out of sight for longer periods than normal at Alvar's tribunal. This indicates that Vanishers blink out of sight for longer periods when they are in particularly negative moods.