I'm not going to respond to any individual comments here but will share a statistic from the December 2014 month of the Prodigy Program. Note that all of these instructors are excellent.
I no longer have time to teach many lessons but I try to occasionally teach in the Prodigy Program due to this and many other statistics we've collected from students.
Human coaches are 2800 at best. Computers are 3300.
A true prodigy will learn by example from the computers, without need for explanation, and will eventually be able to force a draw or better every game against the machine.
I did it to PacMan, Space Invaders, Centipede, Ms. PacMan, Asteroids, Defender, and can sure as hell do it to chess. If I can do it, so can others. Carlsen is going to be a joke in five years tops.
At least he has 5 years, you're a joke now.