How is it possible for a batter to have enough time to hit the ball?

According to this article, it can take less than a half second for the ball to get to the batter, and reaction time is three quarters of a second. It says that the batter starts to swing before the ball is released and makes adjustments afterwards. Is this really possible? How long does it take to make an adjustment? It would be interesting to see the pitcher and batter in slow motion.