Deb, I think it is actually "eddy line", but either eddy, or eddie line, it's the line on the surface of the water that is created by the faster and slower running waters and even water that is running reverse to the main stream. If your steam has such characteristics, obviously it is much much easier if you are able to take advantage of it when paddling upstream. I guess if your river is really crooked, you're most likely right about cutting the corners, but still you have to read the water and hope you choose the right course.