Why can you sit 2 hours trying to solve a programming/math problem, give up, go to bed & then when you wake up, solve the problem in 10 minutes?
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I’ve often solved seemingly intractable problems, especially at work, by waking up at 3am with the solution. Not just math problems, either.
When you keep trying to solve a problem for a long time you often get stuck in some dead-end area of thought which doesn’t lead to any solutions. After you’ve rested you often can take a different approach which leads to victory. And it might be fast, because really many such problems have rather simple solutions once you know them.
Lots of problems can be solved with a good night’s sleep. It’s hardwired into us. During sleep, the brain takes the day’s events and decides what to store in memory. This is an evolutionary advantage because our ancestors could remember where the food was found.
If you had been working on a problem, the brain assumes that it is important to your survival, so it makes attempts to solve that problem and store the solution in memory. There was a recent episode on PBS’ Nova about this process. It monitored the brains of rats and showed how they tried to solve a previously unknown maze to get to food. Those that had slept after exposure to the maze performed much better than those who just kept trying without sleep.
One of the other findings was that the very young and seniors should be taking short afternoon naps in order to increase their retention and to not worry about problems so much.
There is a great book on this subject and I think it is called Why We Sleep. One of the most fascinating things revealed was an experiment measuring brain activity. I may get details wrong but the concept is correct. The experiment was on awake monkeys. Scientists wanted to see how their brains responded to certain stimuli. As the story goes, someone forgot to shut off the recorder device one night and came back the next morning to a pile a data that exceeded data collected during waking hours. It opened a whole new area of study for scientists.
Are brains are not inactive when we sleep, they are more active. Our brains process a days worth of input and the next morning usually results in more clarity regarding the previous days problems.
I rely on the above phenomena for all tough problems. I will spend a day testing solutions for something, go to bed thinking about it as I fall asleep and wake up confident that I will have a new perspective that solves the issue at hand. Sometimes it takes 2 nights but I usually find an answer. This of course is worthless for emergency decisions that need an immediate answer but luckily, that scenario does not happen often.
By working on the same thing hours on end, you start presuming that you only have a complex problem and that alll simple solutions have already been tried.
You go to sleep and start frrom the real beginning with extra awareness and suddenly, the solution sticks out.
This is also why “fresh eyes” work so well. Sometimes it’s not about stupid errors bit just that the bigger picture solves more.
Crossword puzzles are the same way. You can get stuck, then come back to it an hour later and suddenly know the answers to clues that stumped you before.
I know nothing about the psychology, but to me it seems as if your mind is also like a muscle. It needs a rest after being worked. It also helps break you from a train of thought that is probably wrong, which is why you’re stuck.
I think this is an example of a general pattern of problem solving that also explains why you can sometimes magically solve problems the moment you try explaining the problem to somebody else: **You’re benefiting from having to start over again.**
In the time you distanced yourself from the problem, you “lost your place”, and basically end up having to re-trace your trail of though to where you got before. Usually, if we’re stuck on a problem and can’t find the mistake in our thinking, it’s when the mistake happened so far back that we already forgot about it. Forcing you to re-trace your steps makes you notice the mistake.
I find a good way to do this deliberately is by trying to formalize my chain of reasoning to see if I can “prove” why my problem is impossible to solve. (Of course, such a proof usually fails – but the point is that in trying to make the proof rigorous, I can figure out what the error was.)
It also works great for puzzle games!
A large part of the sleep process is consolidating daytime info and rearranging problems to try to find new solutions. When you wake up you are benefitting from your brains processing capabilities during your sleep.
It takes time for something to be encoded into long term memory, you can’t rush it. Unless you’ve been traumatized; that one’s kind of a built in shortcut.
Your brain continues to work on the problem while you sleep. It gives your mind a break from terrorizing you with bad dreams.
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