illustration (attribution, if any possible, is at the end of the article)
Traditionally, the eyes of the Buddha are represented half-open half-shut. Sometimes, the eyes appear almost shut, because the gaze is directed downward.
This is not some unfocused perception, where the Buddha is cutting himself off from reality: this symbolises an attitude to the world both 'open' and 'guarded.'
Quite obviously, 'open' relates to being present to here&now: open-mindedness…
"Guarding the sense-doors" relates to actively engaging with how the present is grasped, relates to choosing not to let proliferations (born from stimulus) grow unchecked.
Unchecked mental proliferations (stimulus leading to an idea then another idea then another idea —which might be 'concentric' ideas: getting into finer and finer details) might easily take you away from here&now: you'd then be 'mesmerised' by what you perceive, and would quickly dissociate yourself from all else. You'd not be present anymore (you might e.g. be deaf to the sound of someone hurting themselves near you and needing assistance, because you're so captured by what you're looking at).
Presence is not in being 'engrossed' in the experience, there's mindful restraint: you're present but you remain free from clinging to the stimulus. The stimulus doesn't decide, for you, what you do (or don't do) next!
Half-open half-shut also represents being attentive to the mind (mindfulness, meditation) and to the external world (ethical life).
But there's a critical key word in the above: 'represent'.
Initially, the preferred representation of the Buddha was an absence: footprints, empty throne, wheel… capturing the idea of self-less-ness.
The Buddha did not spend his time with half-open eyes… And contrarily to what's easily seen on the web, half-open half-shut is not simply a 'recommended' guideline for meditation.
It is a 'representation', a visual message related to deeper teachings than just a meditative 'technicality': "free and open to the world, not transfixed."
Photo: © Vera & Jean-Christophe, flickr.com/photos/magical-world
For those interested in 'representations', may I recommend today's tidbit from : plus.google.com/u/0/106803428216413544405/posts/irBc8Tyw8Vd