The reason we don't notice the darkening of the visual world when we blink may be because corollary discharge signals the visual centers to discount such darkening when blinks occur. In support of this hypothesis, it has been found that

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The hypothesis suggests that the visual center receives a corollary discharge signal when a blink occurs, which helps in discounting the darkening of the visual world. If this hypothesis is correct, then sensitivity to light would be reduced around the time of a blink, as the visual center is already ignoring the changes caused by the blink.

The Reason We Don't Notice the Darkening of the Visual