When I described the black circle technique to my wife, she became curious and decided to give it a try herself. For the last week we have both been experimenting with this visualization as we went to sleep.
Has it been effective? The evidence so far is fairly neutral. I haven’t been lying awake, but I’ve also been staying up too late, so I’m pretty tired when I actually get into bed for the night. My wife has been sick, and she had one bad bout of insomnia that the exercise did nothing to alleviate.
I plan to continue the visualizations for at least a month. The fact that I have been so tired while going to sleep is, I think, a net positive: I hope that my brain has been associating black circles with falling asleep.