Intuition, says R.S, is living in spiritual content and is what defines thinking. If you come to accept this, says R.S, you come to realize that the human organization (I read this as: the human brain) doesn't influence thinking, contrary to the common sense opinion. For example in the contemporary philosophy of mind, the reductionist would give this kind of explanations to sensations: the sensation of pain is the excitation of the c-fibers from the brain - and I suppose they had a similar conception on what thinking is.
Steiner says that thinking takes as a point of start the human organization, but then it makes it stop what it does and is occupying its space. Is maybe hard to imagine what is happening in the head when you think. But when I think most intensely sometimes I feel as I'm above my head and there's this flow of energy pouring in to me from above, and sometimes I start even to hear some non physical sounds that sound more like a wind blowing through a hole. The usual counter-image of thinking (as R.S calls it and which he describes as lifeless) stops its activity and makes place for real thinking!
Another phenomenological observation that I made is that when I read the brain is making thinking (the common opinion) something in me was quite satisfied with that thought. And most of my life, my double was very satisfied with the materialism-conception. I do wonder why :)