I am really not very tidy. And I come from a family of not-very-tidy people (my mother even has a sign that says "Neatness causes cancer in laboratory rats"), and generally I've considered neatness to show a certain lack of creativity and of a mind in a rut.
Well... I've been rethinking that and am now prepared to say I was wrong.
I think what changed my mind was reading David Allen's fine book, Getting Things Done, in which he advocates a very rigorous tidiness. One of his main themes, as I recall, is that if you put (and keep) everything in its place - especially schedules of things to do - then your mind can switch itself off on these topics because it knows that your "system" is doing the remembering. (My wife looked at the book and kind of yawned. She's been living this for years and kind of wonders what's taken me so long to see it.)
Anyway, so now I realize the value of mindlessness. If I'm tidy, I won't have to think about where I put my pen, or the sander, or the crescent wrench, or the computer files I've been working on for Ann. If I just put things where they belong, I can mindlessly grab them and do what I need to do with them. If I already thought once about where to keep the harmonica, why waste my time thinking about it again? Just put it back in its place when I'm done with it!
So I was wrong. Tidiness doesn't cause me to be uncreative or put my mind in a rut or cause cancer in laboratory rats. In fact, it helps by giving me more time to think and be creative; time I wouldn't have if I always had to spend it thinking about where I put stuff.