While most of our daily endeavors require our direct attention, and preferably concentration, there are certain activities for which it's beneficial for our attention to be directed elsewhere. Like safely viewing an eclipse, it's better to look at them indirectly. Take, for example, the placebo effect. If we know that medication we are taking may be just be a placebo, it is best not to think too much about that possibility because doing so will undermine its effectiveness. Yet I have found, much to my surprise, that holding such knowledge in passive awareness is not detrimental.
I experience this on a regular basis when I take Melatonin pills to help me sleep at night. I take them and immediately, when my head hits the pillow, I go to sleep. I know that it's not possible for the pills to work that quickly-- it has to take at least 20 minutes for the hormone to be absorbed into my bloodstream. Yet it works. And oddly, my knowing that it is just a placebo effect and acknowledging that fact to myself somehow does not undermine it. I suppose if I were to dwell on it, it would. But I hold that knowledge instead in a sort of passive awareness, a knowledge held in check, given a nod and passed over without too much deliberation. I think this type of awareness can be useful in other arenas as well.
One arena that is directly related to my Melatonin example is the process of falling asleep itself. There come these moments every night when I am aware that my mind is slipping off into a sort of dreamlike consciousness. Thoughts will begin to occur in nonsensical patterns, with images and feelings and words falling out of joint into new relationships with each other. I know in those moments that I am in the process of falling asleep and soon will be slipping away from my own consciousness. I used to think that if I were to acknowledge to myself that I was falling asleep in those moments, it would break the spell and I would rouse myself back to full wakefulness, but again, to my surprise, that doesn't happen if I hold my knowledge of my impending sleep state in a sort of passive awareness, where I give it a silent nod and then don't deliberate on it.
It strikes me that this same sort of passive awareness is useful in all kinds of activities where we are pushing our minds to do something; recognize that we could undermine our own mental process; and need to step out of our own way. This applies to coming up with a solution to a complex problem, a situation in which often, after conscious weighing of pros and cons, need to "sleep on it," to let the unsolved problem lie dormant in our subconscious mind and not pick it up again until sleep has done its work of sorting the issue out in our minds. Often we wake up with a clear answer, or a clearer one when we have let our minds do this work away from our direct gaze. It's often tempting to pick these problems back up for conscious deliberation (often in the middle of the night), but doing so will only hinder the work our minds must do without our interference. In those cases it's best to give the silent nod to the existence of the problem, and then turn away again from direct deliberation so that we do not interfere.