As an ME and a baseball player, it is obvious to me that the parabolic trajectory in Figure 4b is one and the same "cliff" that batters complain about. The cliff is about 20ft from the batter; before this point, deviation from a line or smooth trajectory is small (1ft); after, is large (2ft), and this only in the last 1/3rd of the pitch! The problem is that almost every baseball player swings at their first curve ball well before they learn what acceleration is in physics class, let alone what causes the acceleration. They can only relate to what they know - "smooth" parabolic trajectories due to gravity. Anything with additional acceleration will "break". The majority of baseball players simply do not understand the fluid dynamics behind the curve ball, so it is no wonder that there is a mystique surrounding it.

The other problem here is control systems - in order to catch up with an accelerating curve ball, you need to increase the order of the control compensator (while maintaining bandwidth), which the human body has a really hard time doing (arguably impossible to do with feedback in that timeframe; must use prediction or feedforward compensation).

The problem is, unless the batter understands the parabolic trajectory and the cause for the acceleration, the batter will almost always dig in at the back of the batter's box, reasoning that additional time will be to his advantage - when it is most definitely not! This is the exact opposite of what should be done when expecting a curve ball (i.e. 0-2 count), in which case the batter should stand at the front of the box, to "hit it before it breaks". (up-up-and-up is best - choke up, up in the box, up on the plate)

A similar situation: the case where a catcher seems to grossly misjudge a ball that is popped straight up, even though to him he was under it for 95% of the time and at the last second it drifted away due to spin-related acceleration.

There is no perceived "discontinuity" by the batter for a curve ball; it does not instantly change positions, perceptually or physically. That is what a knuckle ball does, for very different fluid dynamic reasons.

The swf demo is excellent, but perhaps better describes an outfielder taking his eye off a fly ball to find a fence, and missing the catch by 10 ft.

I firmly believe the "key to understanding the break of the curveball" is education, rather than "the difference between central and peripheral vision", any affect of which is minor in comparison for the vast majority of baseball players.