As you might expect, Montaigne has something to say about walking.
Every place of retirement requires a walk: my thoughts sleep if I sit still: my fancy does not go by itself, as when my legs move it: and all those who study without a book are in the same condition.
My walking is quick and firm; and I know not which of the two, my mind or my body, I have most to do to keep in the same state.
That’s the Charles Cotton translation on Gutenberg (the same Charles Cotton of Bereford Hall who helped Isaak Walton on The Compleat Angler. But this seems to suggest the idea of keeping in trim, while the context is all about restlessness. The translation given in Jean Starobinski’s Montaigne in Motion is more convincing:
and I know not which of the two, my mind or my body, I have had more difficulty in keeping in one place.
I have never succeeded in keeping some part of me from always wandering.
That speaks to me not just of the way both the body and the mind experience life as as series of impressions/thoughts, and of how, for me at least, it’s easier to concentrate on lots of little things in succession than one thing for a long time; it also reminds me of mind-wandering, and my interest in how understanding this phenomenon might help me to write better.