@ Marcin,

I am not sure you are getting the point:

It started when I invented a way of completing a tricky level of Monty on the Run (Commodore game ;) on a walk to church

This sounds as if you were aware your brain was working on the problem. However, TheIowaKid says it very well:

SOAKING™. "It's what your doing when your not."

As an example: when I need to come up with a design or a choice that needs some work, I go out into the garden (I work as an independent software developer and work from home) and do some pruning. Now pruning isn't just clipping away branches. You need to understand the growth of different types of plants and you need to know where you want to go with the plant, especially if you want to use some of the material for propegation. It is an activity that requires you to concentrate on only one thing. However, at some point, the original dilemma that I faced, the one why I went outside, will pop up and at that moment I will know I have a solution. If I get back at the keyboard I will continue as if I always knew what to do next. I am completely unaware of the process that went on from problem to solution. This is a completely passive soak.

Sometimes, if a problem is bigger, there is a phase where you collect anything that is even remotely related to the subject and where you try to organise what you have. Let it flow naturally: try to find it's inherent structure. Things have a natural tendency to organise themselves (I know, it doesn't like a firm foundation to base a design on, but at this point the goal is only to understand the problem. Anyway, this is how life started, so it is something to respect). Collecting/organising is active soaking. Active soaking, however, comes before passive soaking.

Just see this as good news. If you are trapped in a long meeting that is going nowhere: unfocus. Your brain will be soaking on problems that need to be solved. Back at your desk, you'll probably be able to do some important work done.