"Observe patiently while attacking ruthlessly" -- a martial artist

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Recent technological advances are allowing people to analyze eye movements for various purposes. For example, Eye-Tracking Software May Reveal Autism or Eye Movements when Examining an Image or Eye Movements of Doctors Spotting Cancers orTracking Cricket and Baseballs to Hit Them.

Studies done long ago showed chess players who are better consider empty squares more than weaker players. Soccer pros seem to study the empty spaces between players more than do amateur audience watchers. Could it be the player is considering what COULD happen and their creative mind must consider all the area involved?

Then there is the 'secret' of boxing: Where to Look during a Fight and how that works compared to studying the gloves, shoulders or other parts of your opponent's body.

What these studies say in common is that the more expert people don't have quicker eyes which see everything, but that they have specific skills which help them focus on specific things related to their work. Ball hitters can't follow the ball if it's too fast, so they may see it as it leaves the pitcher's hand and judge a path for it with an attempt to see it somewhere else on the way. Chess players may look at open lines to see where pieces may soon move. Boxers may look at nothing specific to avoid being misled by feints. Each isn't being faster, but smarter.

It's also true chess experts (meaning certified masters of all kinds) are somehow faster at getting to the relevant bits. This may relate to their quicker ability to recognize (chunk) patterns in the position before them and then to move on to the logic of their task. One thing I'm curious to learn is how much of the thinking of a top player is about the dynamics (calculating variations) and how much is about imagining the creation of another position they consider as good or better than their current one. Do they move from position to position or are they always looking for the path forward which is better and better?

Recently I looked at a YouTube.com video of Radjabov and Carlsen discussing the latter stage of a game (I presume they had just played). In that they didn't seem to discuss abstract plans (and in particular Radjabov seemed completely to not understand Carlsen's one and only way to win), but to focus entirely on move sequences.

It is sometimes said you just need to focus on what's important to learn to become expert in something. But, it's not always obvious what is the important thing to learn. Maybe eye-movement analysis, and some other things, can help us figure it out.