Try this little experiment:

Look at yourself in the mirror from a distance of about 20 cm.

Alternately look at your left and right eye.

Not much to see, is there? And that's exactly it: You don't see your eyes moving! Yet eye movements are clearly visible. You can verify this with a variation on the same experiment:

Look at yourself in the front-facing camera of a phone (or any webcam).

Again, alternately look at your left and right eye.

Now you clearly see that your eyes move, in small jerky movements called saccades. So what's the difference? Why can you see your eyes move in a webcam, but not a mirror?

When one does the second experiment, it is imperative that one duckfaces. (Source)

The answer is that your phone's camera shows things with a slight delay; therefore, you see your eyes move only after they have already stopped moving. In contrast, a mirror has no delay; therefore, to see your eyes move in a mirror, you have to see while your eyes move. And you usually can't—a phenomenon that is often called saccadic suppression. (Because vision is suppressed during saccades.)

An intuitively attractive theory is that saccadic suppression prevents you from seeing a dizzying movement of the world whenever your eyes move. The idea is simple: The eye is a camera, and when a camera moves too rapidly, the viewer gets dizzy. (Think of found-footage movies, which are recorded with a hand-held camera, preferably while the lead character runs naked and screaming through the woods.) Therefore, to avoid the little man in our head from getting dizzy, vision shuts down when our eyes move. Or so the idea goes.

But this theory has a problem: Vision doesn't really shut down during eye movements. This is what we showed in a recent study that just appeared in the journal PeerJ. (Similar studies have been before. The main novelty of our study was that we used a physiological measure: pupil size.)

Our experiment was simple but very cool. We used an old trick that was developed in the 80s by Heiner Deubel (I think). First, we took vertical stripes that moved continuously and horizontally across a computer display. We then increased the speed until the pattern moved too fast to be seen: It was all blurred, and looked like a uniform gray display. Next, we asked participants to make eye movements from the left to the right side of this display. And—here's were it gets clever—we set the speed of the stripes so that it matched the top speed of the participants' eyes. Therefore, for a brief moment during the eye movement, the stripes formed a static image on the retina, the light-sensitive layer in the back of the eye.

Get it? This trick is a bit like tracking a running person with a camera: Even though the person moves, you can create a more-or-less static camera image by matching the runner's speed with the camera. But instead of a moving camera, we used eye movements at a really, really high speed—about the speed of a cruising airplane flying by at 50 m distance. Yes, your eyes are that fast.

The result of this trick was that the stripes, which were normally invisible, became clearly visible for a brief moment during the eye movement. This is called intrasaccadic perception, and is a very strange and powerful phenomenon.

Intrasaccadic perception had been shown before, but always through subjective report; that is, participants indicated verbally or manually whether or not they had seen something. This means that participants were never naive: To participate, they more-or-less needed to know what the experiment was about.

To get around this, we measured pupil size; that is, we compared pupil size in a condition with intrasaccadic perception, with pupil size in a control condition. The prediction was simple: We expected intrasaccadic perception to trigger a constriction (shrinkage) of the pupil, just like normal stimuli do .

You can see the results below:

The effect of intrasaccadic perception on pupil size. Adapted from Mathôt et al. (2015).

This figure shows pupil size over time, separately for the intrasaccadic-perception (blue) and control (orange) conditions. On the timeline, 0 corresponds to the midpoint of the eye movement. You can see a few things in this figure, not all of which are related to intrasaccadic perception:

Before the eye movement, the pupil starts to dilate (becomes bigger). This reflects movement preparation.

About 0.2 s after the eye movement, the pupil starts to constrict in both conditions. This always happens after an eye movement—intrasaccadic perception or no.

And the crucial finding:

The pupil constricted more when participants experienced intrasaccadic perception (the blue line) than when they did not (the orange line). This effect arose with the pupil's typical delay of about 0.2 s after intrasaccadic perception had occurred.

In other words, intrasaccadic perception affected the size of the pupil. After the experiment, we also asked participants verbally whether they had experienced intrasaccadic perception. And they had.

So what to make of this? Why don't you see the world move when your eyes move, while experiments such as ours show that you can see perfectly well during eye movements?

The key, I think, is to realize that there is no paradox. There just seems to be one, because we tend to think that visual perception is directly linked to the retina. Therefore, if there is movement on the retina, as there is during eye movements, it seems that we should perceive movement.

But perception doesn't work that way. It's better to think of perception as the brain's best guess of what the world is like. If there is movement on the retina while the eyes are moving, the brain simply doesn't interpret this as movement in the world. Your brain isn't fooled that easily. In other words, there is no need whatsoever for vision to shut down during eye movements . Not as long as the brain makes sensible guesses.

This also explains why intrasaccadic perception occurs, but only in very contrived laboratory settings such as ours. Your brain does not expect a static retinal image when the eyes are moving at top speed. That doesn't ordinarily happen in the real world; so when it does, your brain's best guess is that something odd must be going on. And, subjectively, this gives rise to intrasaccadic perception.

So to answer the question from the title of this post: Yes, you can see while your eyes move, but your brain isn't easily fooled into seeing things that aren't there.