Yes in three specific environments for varying durations. Lying down to sleep, showering and driving.

Each last for a different amount of time and you generally can’t write or even read anything. But in my personal experience, all three lead to solving the most difficult software problems.

Fair. But in all 3 did you very quickly write down the solution as soon as you were able?

My best thinking is when I am going for very long runs, when I write down the thought, my brain stops thinking about it, considers it done and moves on.

When writing, thoughts become forced and linear in my view as opposed to floating in a specific way from point to point. Like I lose the natural creativity.

Writing is about remembering or communicating, so it is summarizing the thoughts, but it is not thinking itself, it is more so thinking about how to communicate efficiently or how to make a note so you don't forget. It is not creativity for me.

Kind of imagine building an idea in your head while running and then you write down the summary of it.

I see, I'm the same too. Throughout my day my thoughts would be flying and zooming around. Some of them good, most of them not good or otherwise useless.

When I sit down to try and write them down, I blank out. Or the thoughts that I thought were good/useful, I second guess when writing them down. Perhaps it's just lack of practice on writing them down (I'm trying to use a typewriter to do so recently).

You will get to a point that you have to write it down so you don't forget but more importantly check if it even compiles.

writing is a way to get your brain to put thoughts into a form that someone else will be able to reach the same understanding as yourself. The effort to explain oneself often leads to better understanding: Duck Debugging basically.