So i've been reading Brian Greene's The Elegant Universe, and I'm not quite sure I understand general relativity. This is the way it was roughly presented in the book. Two friends are throwing a baseball back and forth at 20 m/s. However, when one of the friends begins to run away from the ball at 12 m/s when the ball is approaching him, the ball really only approaches him at 8 m/s. Seems simple enough so far. But if a beam of light approaches you at 670 million mph and you hop in your space ship and fly away from that beam of light at 100 million mph, the beam of light will still be approaching you at 670 million mph. This seems to imply that the beam of light "speeds up" by 100 million mph to maintain it's approach of 670 million mph. But shortly after this description, the book says that the speed of light never speeds up or slows down, it is always constant. Well how can that be? If the beam of light didn't "speed up" in order to maintain an approaching speed of 670 million mph towards the space ship, then the space ship would still be speeding away at 100 million mph and the beam of light would only be approaching at 570 million mph. Can somebody clarify this please? Thanks much.