Hands are also very good at remembering.
Thinking with our hands is essentially another way of saying 'turning off our mind'.
It describes a way of walling where we are no longer thinking about what we are doing.
We are not aware of the weather or the time or that we are hungry or thirsty, too hot or too cold.
There is no sense of time, and usually after we look back on the day of 'good walling' we see that 'time' has gone much slower or faster than we imagined.
It is our hands that have taken over from our minds and although they have done a great job during these mind-in-neutral phases, they aren't as well wired as our minds to keep a proper account of the passing of time.
There are times when our brain should do all the thinking
but there are times when it should just switch off !
Sleep is one of those times, it is on the low activity side of the scale.
The automated, skilled movement of satisfying work is the active side of the scale and usually in this mode, the brain gets to switch off or at least ponder other things.
This is fairly common occurrence in most activities of manual labour. And walling is a lot of, just that, 'manual' labour - working with our hands. It is in fact often labour intensive but usually it is not back-breaking, and while it is time consuming too you may not notice that part of it. With a desk job letting the mind 'switch off' rarely happens. If it is engrossing desk work there may be a sense of time flying but there is often associated with that the sense of not having got enough done. A section of wall after a day of building can look pretty magnificent and usually it's pretty surprising even for a beginner, how much work he or she accomplished.
What makes dry stone walling (and thinking with our hands) such an interesting phenomena is
that there is this strange combination of ongoing object-specific spacial decision making combined with the repetition of routinely having to create the same pattern and shape over the length of the wall. Hands are very good at grasping this shape and seeing that the job gets done.