This can be chopping wood, taking a shower, walking, hiking, running, riding a bike, taking the dog for a walk, doing the dishes, etc.
The key is:
1. No particular mental focus
2. Some kind of physical movement
Your mind eventually starts to spin on autopilot, which is when it is able to mix things it can't while you're focused.
My theory, unencumbered by evidence, is the movement shakes the thoughts around until they find a pattern where they fit together.
These are all games that require some type of intense focus but where I surely begin making mistakes the moment I consciously think about my actions in the game. Sometimes this means getting in the zone and not thinking about anything at all, but sometimes my mind is instead allowed to wander it a way it doesn't normally, and without judgment.
When using such tool, at some point where there is no need to focus on keys or words, mind will drift into thinking something else.
Much of our thought is based on metaphor of body movement.
It happened so much that when I quit smoking I made sure to continue the routine of getting up to go outside for a few minutes every two hours or so.
If you look at all the “it just came to me” stories, they are talking about step 2 while glossing over the sweat and tears that went into step one.
The way I see it, finding a shortcut in a mental landscape requires that landscape to be setup in some sufficient detail.
This is also the advantage of iterative development. Build a prototype, if you see a better solution, rewrite it. Rinse and repeat if time permits.
I also work at home, so I guess my shower is like your commute.
In the other cases (shower), I can think about the problem without pressure and in a more free way. No one will care what I think or what I could propose about the problem in that situation, it's just my mind and me.
It's wonderful to see it formalised and be able to communicate its value.
Naps, walks and gentle bike rides hold the answers to so many puzzles.
Thinking actively about a problem is often all we have time for, but if you can let something stew and let your brain work on it, especially while working on other problems that might turn out to have some similar structure, the results can be quite satisfying.
On a similar note, I realised pen and paper -away from any computer, works wonders to organise my thoughts.
The other thing I've noticed is how it's sometimes hard to concentrate on something else when you're going through a significant cognitive process (changing jobs, arguments, work hassles...), even if you are not actively thinking about it. As if your brain's cycles were taken by something else.
I've started to notice the pattern (hard to focus, distracted), attribute it to backprocess, realize that whatever triggered it must be significant, and expect to yield results at some point.
The one downside is the fact that I can't write stuff down, so I oftentimes forget these revolutionary thoughts ;-)
1) The book Your Brain at Work by David Rock does a great job explaining the brain and how to tilt it in your favor, more often.
2) I have solved more problems and had more great ideas 3+ miles into a run than any place else. There's something to be said for thinking less and not forcing the brain into a corner.
I find myself unable to focus on my audiobooks while running once the pace is high enough. I imagine all I would be thinking of while running without content to distract me would be the number of the miles left of the run.
Opposite for me, I go for easy problems and then let my mind wander while I play a mindless game of Chess or HoMM3, then when I restart work one hour later the solution writes itself in 5 minutes.
Multiplayer games of high action, like overwatch similarly are bad.
Other games that don’t work well for me are zachtronic likes, too hard, and too much like the problems I’m trying to solve.
Suprisingly, though, dark souls is a good game to play. Something about the combat is meditative, especially the corpse runs from dying to an easy mob, that focuses my attention in ways I find other activities don’t.
Homm3 seems like a good meditative game. Lots of relatively brainless combat, especially if you use save games to avoid truly stupid moves. Many one more turn type games can fall under this historically. Newer strategy games I find lack this quality though. It seems that modern game design generally avoids the dominant and dominated strategies that I used to enjoy finding and exploiting mindlessly decades ago.
By and large though, I personally try to avoid games until I’m done for the day. I find it hard to go back to work, and my working sessions are shorter and shorter the earlier I allow myself to play any games...
I've written in the past about this, let me copy an old comment of mine:
"Let me share a tip that might work for you as well then: some times you will procrastinate heavily because you're have a hard problem with no solution in sight. You'll want to make some semblance of progress, but you just can't sit down and concretely work on it.
It's by design! Your subconscious keeps working in the background, thinking outside the box until one day out of nowhere you get the solution right before your eyes.
I'm not sure it's possible to think outside the box if you're not procrastinating, since you need other types of unrelated input for your brain to make a different type of association and reach a conclusion from another perspective.
I'd like to read more about this phenomenon but has been one of my best tricks up my sleeve in my career. Recently I've been trying to write down a complex piece of code, the corner stone of my application critical to the whole business. I've spent weeks on that problem, tried and failed to design a working solution, spent hours reading papers during working time instead of writing anything, browsing HN mindlessly, until after 2 months, out of the blue at 4am looking at cat pics on reddit I found the answer. And I'm now enjoying this newfound wave of productivity until my next hard problem"
Or maybe it's even simpler: conscious mind stuck on hard problem starts to work as broken record - you are repeating the same thoughts, reconsidering the same wrong solutions all over again. Focusing on something unrelated frees your uncounciousness to try something else.