Science, 268(5218). 1681-1685 and Science, 273(5272). 256-259
In these publications, several letters and technical comments address our article "How baseball outfielders determine where to run to catch fly balls", and we reply. We point out that the outfielder problem can be described from many different scientific perspectives and this accounts for some of the differences of opinion expressed. The principal points raised in each letter or technical comment and our replies are summarized below.
1. Henry Pollack points out that the Linear Optical Trajectory (LOT) model that we introduced is related to the nautical strategy of maintaining optical constancy when trying to intersect the path of another boat. We agree and add that similar control theory principles are used by animal predators and ballistic tracking systems. We note that the outfielder problem is somewhat more complicated in that the pursuer must intersect the path of the ball at a particular time and place in space.
2. Robert Adair criticizes the LOT model based on the result of two thought experiments. Adair goes on to suggest that through practice, fielders learn to maintain lateral alignment, and achieve a location where the ball is vertically descending straight toward them. We point out that Adair's thought experiments are flawed and conflict with our empirical findings. We comment on how Adair's proposed method of arriving at the correct destination requires information not available from the fielders vantage, and we describe how it implies that balls hit to the side should be computationally more difficult to catch. We suggest that Adair's perspective does not address the perceptual questions that we are trying to answer and conclude that the empirical evidence supports the LOT model.
3. Richard Jacobs points out that in Willie Mays' famous 1954 world series catch pictured in Science, Mays did not appear to use the LOT strategy. We replied that first, our model addresses the behavior of recreational level players and leaves open the possibility that trained professionals might learn alternate strategies to enhance their performance. Second, Mays' extraordinary behavior and deviation from the LOT model during this play may be part of the reason that it is considered by many to be one of the greatest in the history of the sport.
4. Chodosh, Lifson, and Tabin argue that professional players do not catch the ball on the run as the LOT model seems to direct, but rather they run ahead and wait for the ball at the destination point. We again argue that our model looks principally at recreational players and allows for the possibility that trained professionals might learn some tricks that allow them to run ahead. We also reiterate that the LOT model specifies only how to get near the landing point by arrival time and that evidence supports that fielders use other depth cues that become available near then to determine final positioning. Finally, we comment on how in contrast to the authors' claims, our observations of professional fielders support that they typically reduce their running speed for closer balls and they have little time to spare after arriving at their destination. We conclude by reminding readers that the LOT strategy utilizes the perceptual invariant of constancy of relative angle of motion, a principle that can be generalized to areas as diverse as designing cockpit displays to herding livestock.
5. Dannemiller, Babler, and Babler point out that temporal cues cannot be fully ignored and question our choice to constrain the temporal optical conditions to a monotonic function rather than a linear one as specified by the Optical Acceleration Cancellation (OAC) model. They also question why fielders would use the spatial information specified by the LOT model when a linear temporal strategy should work alone. They argue that the traditional OAC model is superior be cause it specifies both a unique solution and the shortest running path whereas the LOT model does neither. We reply that much evidence supports that viewers are poorer at discriminating temporal accelerations than they are at spatial curvature. The LOT model therefore solves why balls hit to the side are easier to catch. We chose the monotonic temporal constraint as a worst case scenario to demonstrate the robustness of the LOT strategy. We argue that there is no reason to assume that fielders must abandon either the temporal or spatial cues in favor of the other . We point out that the empirical evidence supports neither that fielders run in a straight line, nor that fielders determine a unique solution.
6. Jacobs, Lawrence, Hong, Giordano, & Giordano (JLHGG) argue that fielders run along substantially curved paths and run ahead to arrive at the destination early. They point out that fielders typically do not run along the precise minimally curved path prescribed by an ideal LOT solution (based on maintaining a constant rate of increase in the vertical tangent of the ball image). They also provide evidence that in the case of a single high fly ball, fielders did not appear to maintain optical linearity as specified by the LOT model. They suggest a strategy similar to that of Adair in which fielders try to position themselves so that the ball directly approaches them. We reiterate that the LOT strategy first brings the fielder close to the destination, but other depth cues probably take over near termination. We also point out that in the one case shown, time of arrival was a mere 0.2 seconds ahead of time, evidence against the strategy of running ahead. We further clarify that the LOT strategy does not specify a unique solution, so comparing empirical findings to one particular LOT-consistent path is inappropriate. We conclude that JLHGG's data remain consistent with a LOT solution provided that linearity within the picture plane is a function of the vertical and lateral optical angles rather than the vertical and lateral tangents.
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