On the right is another interesting exercise in perception I did a few years ago from the highly recommended book "Drawings on the right side of the brain" by Betty Edwards. I had to copy the lines of an artwork upside down so that my left brain couldn't figure out what was going on and my right brain could function unimpeded ! Amazingly, it was all perfectly proportioned when I turned it around. She gives a good explanation for the process of learning to draw with direct perception rather than relying on memory and symbols of how you think things look but not as they really are. This book really helped me gain a lot of confidence in my drawing abilities when I worked through it almost ten years ago now, and the exercises were mostly interesting.
"Be clear in your mind why learning to draw well is important. Drawing enables you to see in that special, epiphanous way that artists see, no matter what style you use to express your special insight. Your goal in drawing should be to encounter the reality of experience... to see ever more clearly, ever more deeply." (Betty Edwards)
Here is a good explanation of Betty Edwards' Left brain / Right brain theory if you are unfamiliar with it. It's really very interesting !
It can be difficult to shut off that left brain at times, so I find doing these types of exercises when I get a chance keeps my brain practiced in that right brain mode and this kind of perception definately becomes easier the more you practice. It's like brain training for artists....