The brain is an amazing thing, and recently on Twitter, I read about how the brain does something really clever in the tiny bit of time when you move them.
When we move them in short fast bursts (which are called saccades), our vision goes all blurry, which is not ideal considering the amount of time we (in)voluntarily do it, so our brains hide it from us.
What the brain does is basically pauses your visual processing, and when you finish your eyes finish moving, it shows you what you now see at the new position. What gets crazy is that you see the image at the new point, but equivalently processes it in such a way that the brief microsecond that your visual processing was paused, it seems like you were seeing it the whole time your eyes were moving, but since the system was paused, you would not have seen the blurriness or blackness.
You can see this happen if you watch a flashing light (for example a warning light in your car – been there, did it). Look away by moving just your eyes, keeping your head relatively still, then look back to the warning light – it will seem like the light has either been on longer, or off longer (either giving you more of a panic or brief relief).
This effect has been known for over 100 years, called Saccadic Masking, and more specifically Chronostasis. Another example of Saccadic Masking is when you look at yourself in a mirror – no matter how close you bring it to your eyes, and how much you look around, you will never see your eyes move. You’re blind during those moments. But you still think you are seeing.