James L. Dannemiller

On Catching Fly Balls

Michael K. McBeath et al. (1) make several statements about the process that fielders use to determine where to run to catch a fly ball: (i) that optical acceleration cancellation (OAC) (2) would require the fielder to precisely discriminate optical accelerations-a task at which, McBeath et al. argue, humans are not very good; (ii) that, because of this poor sensitivity to acceleration, fielders turn the problem of catching a fly ball from a temporal one of detecting velocity differences into a spatial one of detecting optical curvature-a task at which, McBeath et al. say, humans are very good; and (iii) that maintaining a twodimensional projection of the ball on a linear optical trajectory (LOT) is sufficient to get the fielder to the right place at the right time to catch the ball. The first statement is not correct when the velocities and accelerations of fly balls typically encountered by a fielder are used. The second statement may be correct, but it is not supported by the types of studies that McBeath et al. cited in their report. Finally, we show that the third statement is incorrect by presenting an example in which a LOT is maintained, yet the fielder arrives 5.7 m away from the balls landing site at the instant the ball hits the ground. OAC models do not require a precise ability to discriminate accelerations, only the ability to detect acceleration (and deceleration). Several of the studies cited by McBeath et al. in support of the statement that humans are poor at detecting accelerations (3) used velocities and accelerations that are not typically encountered by an outfielder. When more representative values are used, observers can discriminate approximately a 20% change in average velocity over a period of about 1 s (4). A more recent study (5) also showed that humans can detect successive differences in speed better than McBeath et al. Thus, rejecting OAC models because of a supposed poor sensitivity to successive speed differences is not warranted by existing data. McBeath et al. argue that a fielder runs in such a way as to maintain the fly ball on a LOT with respect to home plate: The fielder adjusts his position so that he prevents the ball from taking a curved optical path. Humans are purported to be much better at detecting optical trajectory curvature than they are at detecting changes in speed. But the studies cited by McBeath et al. in support of this position (6, 7) required subjects to respond to straight versus curved lines, and one of these (7) had human infants discriminating large arcs with different radii of curvature. Because fly balls do not leave trails in the sky, this line curvature sensitivity (a spatial problem) is of questionable relevance to the trajectory curvature sensitivity (a spatiotemporal problem) required by the LOT model. More relevant data show that humans require a deviation of approximately 50 at low temporal frequencies to detect perturbations from a straight path for a slowly moving object (5). Whether this is sufficient sensitivity to support the LOT model remains to be determined. Consider two paths of a fielder running toward a fly ball (Fig. 1). The fielder starts in straight-away center field at a distance of 67 m from home plate. The ball is launched at a speed of 24.38 m/s, at an elevation angle of 500, and at an azimuthal angle of 200 (toward left field) from the line connecting home to second base. The ball is in the air for 3.83 s and it lands 23.1 m from the fielders starting position-20.5 m to the fielders right and 10.6 m in front of his starting position (8). The path ending away from the landing point results in an error, while the path ending at the landing point gets the fielder in position in time to catch the ball (Fig. 1). We discuss the erroneous path first. To generate it, we simulated a fielder running in depth (toward home) at 50% of the speed necessary to null the vertical optical acceleration. We calculated the corresponding constant lateral running speed that would keep the lateral component of the optical projection proportional to the vertical component and maintain the initial angle of launch in the projection (what McBeath et al. call T). Two path images (Fig. 2) were derived by projecting the fly ball onto a plane that remained perpendicular to the ground lineof-sight to the ball and that was 1 unit (arbitrary) behind the nodal point of the fielders eye; that is, the projection plane rotated, and the nodal point moved with the fielder. These images can be thought of as retinal projections and correspond to scaled versions of what the fielder would see over time (9). The curved trajectory (Fig. 2) shows what the fielder would see if he stood still. The straight projection (Fig. 2) is that which results when the fielder takes the erroneous path (Fig. 1). This latter projection is linear over the entire flight, and maintains the initial angle (T) in the projection. The fielder has thus followed the LOT strategy, yet is far from the ball when it hits the ground. The LOT strategy results in this error because it provides too weak a constraint on Home

Infant habituation criteria: I. A Monte Carlo study of the 50 % decrement criterion

The statistics of the 50% decrement habituation criterion (.5DC) were investigated using Monte Carlo techniques. The bias. variability. and false alarm rate of this criterion were influenced by the amount of error in fixation times. The results preclude the use of trials to criterion as an index of rate of habituation. habituation rate criterion error

A failure to observe negative preference in infant acuity testing

Held et al. (1979) Vision Res. 19, 1377-1379, reported that infants psychometric functions in preferential looking experiments exhibit a region of below chance performance or negative preference. They argued from this that previous preferential looking experiments may have systematically underestimated acuity because they ignored this negative preference. We present data from an experiment designed to reveal negative preference in the version of the preferential looking paradigm used in our laboratory. The results do not exhibit negative preference apart from random variations about 50%. Gwiazda et al. (1980) Am. J. Optom. physiol. Opt. 57, 420-427; 428-432, developed a psychophysical procedure for infant testing that is designed to yield accurate threshold estimates in a short period of time. We present the results of computer simulations of more conventional psychophysical procedures. The simulations demonstrate that an up-down staircase procedure is more efficient than the Gwiazda et al. procedure.