Repost, but still TOTALLY appriopiate (4yr redux)
...there was this bit of imagery that totally captured my imagination and illustrated my mental processes (so, like, maybe other people could see the machinery clattering about in my head!)
It said (italics mine):
A good programmer working intensively on his own code can hold it in his mind the way a mathematician holds a problem he's working on. Mathematicians don't answer questions by working them out on paper the way schoolchildren are taught to. They do more in their heads: they try to understand a problem space well enough that they can walk around it the way you can walk around the memory of the house you grew up in.
It said (italics mine):
A good programmer working intensively on his own code can hold it in his mind the way a mathematician holds a problem he's working on. Mathematicians don't answer questions by working them out on paper the way schoolchildren are taught to. They do more in their heads: they try to understand a problem space well enough that they can walk around it the way you can walk around the memory of the house you grew up in.