These speculations on the connection between the different definitions are all well, but the truth lies herein:

In Kansas City near the beginning of the twentieth century there was a young boy named William who was notoriously naughty. His father took him out in the backyard very often to punish him and the beatings were so painful that he literally rose from the ground each time he was hit. These punishments stayed with him all his life. When he grew up he became a wonderful pianist/bandleader and he immortalized the punishment in one of his songs, the Count Basie classic, "Jumpin' at the Woodshed."

I know, I know, it was bad . . .