Just today I've heard a theory, that when you walk around brain is more able to try new ways of thinking and solving problems, because the 'motion center' in the brain is doing what it's supposed to do: handling one's movements. On the contrary when we are not moving, this center can often overwhelm the thought process with already established habits, which makes trying new things harder.
I thing it works - even in offices many people start walking in circles when they have an important decision to make.
Funny, in my language the word meaning 'reflexively', 'instinctively' is in a form which can be literally translated 'out of the movement', which quite fits this theory.
I didn't look for the scientific background, but I know from the context of how I've heard this, that it was taught at the univ on a psychology specialization.