Skilled fielders were filmed as they ran backward or forward to catch balls projected toward them from a bowling machine 45 m away. They ran at a speed that kept the acceleration of the tangent of the angle of elevation of gaze to the ball at 0. This algorithm does not tell fielders where or when the ball will land, but it ensures that they run through the place where the ball drops to catch height at the precise moment that the ball arrives there. The algorithm leads to interception of the ball irrespective of the effect of wind resistance on the trajectory of the ball. The everyday nature of the act of running to catch a ball can obscure the remarkable predictive ability that it re-quires. Figure 1 shows the trajectories of three balls pro-jected at 45 ° and approximately 22, 24, and 26 m/s toward a stationary fielder 45 m away. They will land 5 m in front of, at, or 5 m behind the fielder, respectively. The solid line shows the trajectory of each ball in the first 840 ms; the dashed line shows the rest of the flight. Within 840 ms, most competent fielders would have started running forward for the ball on the lower trajectory and backward for the ball on the higher trajectory. 1 Yet, the only difference between these two flights at this time is the difference between the longest and shortest solid lines. How is the fielder able to work out where to go from so little information? Precise calculation of the trajectory is not possible be-cause the essential ball flight parameters of projection angle, velocity, and wind resistance are available to the fielder only as, at best, crude estimates. Nor, given the infinite variation of trajectory, does it seem possible that learning to catch involves learning individual trajectories. An alterna-tive is that an algorithm exists that links the visual infor-mation obtained from watching the bali's flight to a running speed that will bring the fielders to the correct place, irre-spective of their starting position or the bali's trajectory. Learning to catch would involve the discovery of this algorithm.

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When an object’s motion is influenced by gravity, as in the rise and fall of a thrown ball, the vertical component of acceleration is roughly constant at 9.8 m/sec 2. In principle, an observer could use this information to estimate the absolute size and distance of the object (Saxberg, 1987a; Watson, Banks, von Hofsten, & Royden, 1992). In five experiments, we examined people’s ability to utilize the size and distance information provided by gravitational acceleration. Observers viewed computer simulations of an object rising and falling on a trajectory aligned with the gravitational vector. The simulated objects were balls of different diameters presented across a wide range of simulated distances. Observers were asked to identify the ball that was presented and to estimate its distance. The results showed that observers were much more sensitive to average velocity than to the gravitational acceleration pattern. Likewise, verticality of the motion and visibility of the trajectory’s apex had negligible effects on the accuracy of size and distance judgments. People need to process the absolute distance and size of objects in order to act in the environment. For example, in order to catch and grasp a thrown ball successfully, a person must place his/her hands in the appropriate

Linear optic trajectory theory claims that people catch balls by running in a direction that keeps an optic trajectory of the ball linear. The authors show a range of ball trajectories for which departures of the optic trajectory from linearity do not predict which direction people will run, and the direction they choose does not correct these departures. Data from a wide range of ball trajectories show that people run so that the angle of elevation of gaze to the ball increases at a decreasing rate. But it is not yet known why people choose the particular path they do from the many that would achieve this. Thirty years have passed since the pioneering work of Chapman (1968) on how the information obtained from watching a ball that was hit into the air might control a fielder's interception strategy. Although there is general agreement about the control strategy used by fielders when running backward or forward to catch a ball thrown directly toward them, there is no consensus on the strategy used in the more general case in which the fielder must run to the side as well. Considering the ease with which some children learn to catch—just by watching ball flights and trying to catch the

This thesis is about the reconciliation of realistic views of rationality with inferential-intentional theories of communication. Grice (1957; 1975) argued that working out what a speaker meant by an utterance is a matter of inferring the speaker’s intentions on the presumption that she is acting rationally. This is abductive inference: inference to the best explanation for the utterance. Thus an utterance both rationalises and causes the interpretation the hearer constructs. Human rationality is bounded because of our ‘finitary predicament’: we have limited time and resources for computation (Simon, 1957b; Cherniak, 1981). This raises questions about the explanatory status of inferential-intentional pragmatic theories. Gricean derivations of speakers’ intentions seem costly, and generally hearers are not aware of performing explicit reasoning. Utterance interpretation is typically fast and automatic. Is utterance interpretation a species of reasoning, or does the hearer merely act as if reasoning? Within the framework of cognitive science, mental processing is understood as transitions between mental representations. I develop a traditional view of rationality as reasoning ability, where this is essentially the ability to make transitions that preserve rational acceptability. Following Grice (2001), I claim that there is a ‘hard way’ and a ‘quick way’ of reasoning. Work on bounded rationality suggests that much cognitive work is done by heuristics, processes that exploit environmental structure to solve problems at much lower cost than fully explicit calculations. I look at the properties of heuristics that find solutions to open-ended problems such as abductive inference, particularly sequential search heuristics with aspiration-level stopping rules. I draw on relevance theory’s view that the comprehension procedure is a heuristic which exploits environmental regularities due to utterances being offers of information (Sperber & Wilson, 1986). This kind of heuristic, I argue, is the ‘quick way’ that reasoning proceeds in utterance interpretation.

The generalized optic acceleration cancellation (GOAC) theory of catching proposes that the path of a fielder running to catch a ball is determined by the attempt to satisfy 2 independent constraints. The 1st is to keep the angle of elevation of gaze to the ball increasing at a decreasing rate. The 2nd is to control the rate of horizontal rotation necessary to maintain fixation on the ball. Depending on the lateral velocity of the ball relative to the fielder, this rate may be zero or constant at a negative or positive value. The authors show that a simulated fielder implementing the GOAC strategy follows a path indistinguishable from that of real fielders running to catch balls thrown on the same trajectories.