An edge in a painting is like a pause between two musical phrases: it marks the ending of one shape and the beginning of another. The two sides of any edge can be isolated from each other or transitioned into each other, depending upon how the artist has handled the painting of the edge itself.
Whereas sharp edges bring shapes to an abrupt halt, calling our attention to them, soft and lost edges enable shapes and images to flow from one area of the painting to another. The soft edge makes a gentle transition, but in the lost edge, we don't see a break between where one shape begins and the other one ends.
Now, look specifically at just the sharp edges you found. Notice how your eye migrates to them. Next focus on the soft edges. Notice how they create a transition from one area to another. Finally, the lost edges. Imagine how stilted the painting would be if these were clearly defined rather than being lost.
Our eyes want to participate, to become involved in paintings we view. We want to be challenged, not spoon fed. When an artist uses just enough sharp edges to bring us into the painting, then employs soft and lost edges, our eyes become involved. We feel like we've been invited to become a part of what the painting is all about.