It's pretty crazy the number of times I've banged my head against the wall trying to fix something... and then I'll either step away for an hour, or just come back the next day, and I'll have it fixed in minutes. It really does work sometimes.
When I was trying to learn to code as a kid, I struggled for days trying to wrap my head around the concept of a variable.
I the concluded that programming isn't for me and left the bloodshed ide untouched.
Two weeks later, I was watching TV. And out of nowhere it just hit me. I finally understood what variables are! I ran to the computer to test my assumption, and it was spot on.
To this day, 20+ years later, I still remember the feeling of everything suddenly falling into place!
I was lead dev once and the unofficial "rubber duck." I'd always get called over when someone was stuck on a thorny problem, lean over their shoulder and ask them to explain it and it was always instantly "Oh! I see it now, thank you!" and I had done nothing.
I remember playing a logic game which required lots of thinking to solve it. Then at some point I stopped trying to actively solve it, I just simply stared at the game without trying to solve it, and after a while I tried to solve it. Guess what? I solved it at first attempt, without knowing how! This was really curious and it made me excited so I tried to keep doing it this way and turns out it was not a fluke, this method seemed to work consistently.
I did some research on it and this phenomenon is called "incubation" which is a core concept in the psychology of creativity and problem solving. Apparently it's frequently observed in puzzles, mathematical problems, and design tasks that require restructuring rather than mere computation.
In your case, conscious and effortful thinking can lead to functional fixedness or mental set, where you become stuck on an unproductive strategy, so taking a break allows these rigid patterns to weaken, making space for more flexible or creative approaches.
In psychology, incubation refers to the unconscious processing of problems, when they are set aside for a period of time, that may lead to insights. It was originally proposed by Graham Wallas in 1926 as one of his four stages of the creative process: preparation, incubation, illumination, and verification. Incubation is related to intuition and insight in that it is the unconscious part of a process whereby an intuition may become validated as an insight. Incubation substantially increases the odds of solving a problem, and benefits from long incubation periods with low cognitive workloads.
In my day, when you encountered a tough problem, you'd go outside and have a cigarette, and the solution would magically come to you. Thank God I quit that poison, and have since learned that a brisk walk can accomplish the same goal. But back then it was a joke amongst peers - cigarettes will solve your problems!
