Improvisation in music is probably one of the most mystifying of the many skills which can be developed by a pro musician.  People who can do it at a high level make it look effortless, leaving all the square cats not in-the-know exclaiming, “They did that without reading music, and they made it up as they went…and it was good?  IMPOSSIBRU!”  Likewise, many musicians (especially those who begin with a regimented course of study) are reduced to being no better than blundering fourth graders when asked to improvise a passage of music, briefly mumbling that they don’t know how to improvise before sitting down and churning out some Paganini.