by Richard Crews
I first stumbled on this phenomenon about 25 years ago. Each week on Wednesday my son would bring home from high school a difficult math problem. He and I would work on it together--sometimes for hours. The answer, if we came up with one, would go into school with him Friday morning.
One Wednesday evening, working long into the night, we had one problem reduced to a complicated formula that had only about a dozen possible solutions--each solution took nearly an hour to test. We checked a couple of possible solutions. No dice. We went to bed. When I awoke the next morning, I kind of "knew" which solution to test next, and darned if that solution didn't work.
Ten years later I was trying to figure out an equation to determine how many perfect shuffles it took to return a deck of playing cards (of varying numbers of cards) to its original card order. Several times I lay down in near-sleep to think about the problem, and in this state I could keep the pieces straight and solve the problem, but when I awoke I could not remember the solution. I learned that when my mind was "asleep" and had solved the problem, I had to take careful note of the steps in the solution and of the final form of the equation in order to capture it again when I was fully conscious.
Nowadays I regularly solve math or other problems in this semi-sleep state. I get the parts of the puzzle straight in my mind, I lie down in bed, and I find I can generally sort my way into the puzzle and out the other end with the solution. Sometimes I drift in this semi-sleep state for a couple of hours. While I drift, I keep coming back, again and again, to the start of the problem, and--again and again--I mentally walk into it, carefully keeping all the pieces as straight as I can.
I believe this mental state is close to meditation, although when I meditate, I try to clear and calm my mind--I repeat a mantra, or focus on my breathing, or calmly put to rest the tensions that have built up since the last time I meditated. And when I meditate, I sit--back supported, head not supported--in a dark and quiet place. Each distraction that comes up, internal or external, I notice, accept, enjoy, and set aside.
On the other hand, to access this problem-solving state, I lie in bed, the room is dark and quiet, my head is on a pillow--everything is set to take a nap--and sometimes I do take a nap, but whether I fall asleep or not, the solution is generally in the front of my mind when I awake.
In recent years numerous scientific studies have validated these phenomena that I have observed.
I have also come to understand, through these experiences, how dreams are formed. I lie down to go to sleep. I sort through the memories of the day, or choose a fantasy to develop. And then I put myself into the scene again and again, varying the action and the outcome. The "dream," when I awake, is the result of exploring and testing dozens of different, minor changes in the fantasy, gradually settling on one that is the most satisfying.
Bun Gladieux, president of the Presssure Positive Company, has a blog with an interesting series of topics.
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