My father used to teach ADHD kids in his classes to juggle -- or sometimes he used other more physical exercises -- because forcing their mind to focus on multiple things helped dissipate their extra energy and focus on the material at hand. The use of walking suggested, strikes me as slightly milder, yet eerily similar, form or exercise therapy used with ADHD. With this connection, it makes perfect sense to me that we should focus better while walking. From there I find myself in a reflective state trying to find an experience or set of experiences relating to philosophizing while walking.
As I think through it, I can think of plenty of times I've gone on walks by myself without any electronics or other distractions. I do believe, as I sort through these memories, that I can even say it did put me in an almost meditative state of mind. However, the questions I contemplated always come back to math. While in school I usually worked through my latest math homework, particularly if there was a problematic question. If there wasn't math to do at hand, my thoughts consisted of the mathematical parts of my science classes. Lacking that, they always turned to physics or natural science questions relating to something I'd observed. Again, I more often than not found myself working through the math of them. I think this is more a testament to the way my mind works than the importance of walking itself, however I believe they're related. In short, I think about everything in math so that's where my mind wanders in its purest state.
When I was doing a particualrly difficult math problem, i always thought about it while I was walking in order to solve it as well. Usually it worked. Looking at this, walking as a way to stimulate thought and now philosophy has always been helpful to me no matter the difficulty of the time or the stress of the day. Walking seems to be the natural way to quiet and clear our minds for clear thinking
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