This is a good question, and I'm surprised that nobody has responded yet. The Spirit of Aikido
is a great book.
Another great book actually addresses your question: The Gift of Fear
by Gavin DeBecker. His main point is that our conscious mind can either create anxiety ot minimize danger (sometimes both). In contrast, our intuition sub-consciously filters through the information collected by our senses, processes that info., and guide us in the right direction. This is what I think of when we talk about perception fo will.
Two examples: (1) When driving, most of us can pretty much divine what people are going to do if we pay attention to the other cars around us. We can tell when the person ahead is going to change lanes -- even when he doesn't use his turn signal -- by the way the car travels in the lane, the spacing of the cars around him, and even by the tilt of his head. Often, we don't even think about all the information we just took in at a glance to make that kind of divination.
(2) It seems that anyone I've talked to who has studies martial arts for a year or two ends up developing a much increased sensitivity to movement. We all have stories of dropping something or seeing something fall, and being able to catch it quicker than would seem possible to bystanders. I once put an empty coke bottle on a desk next to me in class, and as I drew my hand away, ended up knocking it off the desk. I quickly caught it before it hit the ground. It was cool, because I was sitting the the front so everyone saw my "amazing" feat. The instructor even commented.
Anyway, my point is that our training naturally increases our sensitivity to movement and body language.