most fruitfully in linguistic domains, such as reading and speech perception. For example, the amount of processing resources subjects have available has been shown to influence the resolution of syntactic ambiguity ( MacDonald, Just, & Carpenter, 1992). The capacity framework is an intuitively plausible theoretical lens through which to view language processing, because the sequential, serial nature of language imposes a continuous load on attentional and memorial processing resources.
Language, however, is not the only type of stimulus that occurs through time. Kinematic events also occur through time. To perceive and understand these events, observers must not only process and store the kinematic system's successive momentary states, but also integrate the states over time. Capacity theory suggests that a system's momentary states are processed, stored, and integrated in working memory using a finite supply of activation ( Just & Carpenter, 1992). Because the supply is finite, an increase in either the storage or the processing requirements of one aspect of a motion causes the deallocation of activation from other aspects, which may be processed more slowly or lost from working memory. Capacity theory also proposes that individuals vary in the supply of activation. High-capacity individuals, with more activation, are less prone than low- capacity persons to processing slowdowns or the displacement of items from working memory when a task involves storing and computing multiple items.
The general capacity framework may be applied to the CCI by developing a specific, capacity-based process account of the illusion. The cycloid and curtate cycloid trajectories are distinguished mainly by their bottom portions: The curtate cycloid contains a loop, whereas the cycloid does not. Whether the trajectory contains a loop reflects how the wheel pivots when the perimeter point contacts and leaves the surface. To accurately derive the trajectory, the wheel's pivoting must be correctly processed when the point contacts the surface. Here, the point is the wheel's instant center, the point about which the entire wheel is rotating at that instant. One way subjects can correctly represent the bottom portion of the point's trajectory is to derive an instant center when the point contacts the surface. The CCI may arise when activation is deallocated from updating translation to computing the wheel's instant centers when the point contacts and leaves the surface. This deallocation begins only when the dot contacts the surface and continues until the dot reaches approximately seven or eight o'clock in its rotational path.
Three experiments investigated the instant center hypothesis. Susceptibility to the CCI was assessed by the degree to which a normally rolling wheel's translation was exaggerated in the attempt to make a perimeter dot follow a cycloid. Because the dot is already following a cycloid, subjects who exaggerate its translation must perceive the wheel as undertranslating and the does path as the curtate cycloid.
Experiment 1 compares the effects on CCI susceptibility of practice at computing instant centers to the effects of experience with a task that does not involve instant center computation. Practice should reduce the demand imposed by instant center computation, increasing the activation available to update translation and reducing susceptibility to the CCI.
Thirty-six subjects viewed rolling wheels or tumbling batons. Trials occurred in blocks in which either only wheel or only baton trials were viewed. There were four block sequences, each viewed by nine subjects: wheel-wheel-wheel (WWW), baton-baton-baton (BBB), baton-baton-wheel (BBW), wheel-baton-wheel (WBW). Because continued experience with rolling wheels allows subjects to practice instant center computation, they should be less prone to the CCI on the third than on the first block of the WWW sequence. By contrast, they should be as prone to the CCI on the third as on the first block of the WBW sequence. The bottom portion of the path of a dot at one end of a tumbling baton may be derived by assessing the dot's horizontal displacement along the surface. If there is no displacement, the baton's translation/rotation ratio is 1:1, but if the dot slips forward or backward, the translation/rotation ratio is greater than or less than one, respectively.
White wheel rims or batons (9.3° of visual angle) rolled or tumbled across a black computer screen. A small dot appeared on the inside of the wheel's rim or at one end of the baton. The objects rolled on a white band (width = 7.6° of visual angle) extending the width of the screen.
Subjects viewed 33 trials arranged in three blocks of eleven. The object's translation/rotation relationship was 1:1 on five of the trials in each block, overtranslating on three, and overrotating on three. On 1:1 trials, the wheel's rotational velocity was 0.38 rev/s, and its translational velocity was 5.65 cm/s (10.70/s). On overrotating trials, the wheel's rotational speed was increased by factors of 1.15, 1.20, or 1.25. On overtranslating trials, its translational speed was increased by factors of 1.25, 1.35, or 1.50.
Subjects were shown a drawing of a cycloid and were instructed to change the motion until the dot's path matched the drawing if they did not think the dot was already following the cycloid. Subjects used a mouse button to move a pointer along a horizontal scale that controlled the wheel's translation/rotation ratio. The scale appeared in the top center of the screen and was 8.0 cm (14.9°) long. The pointer was positioned at the scale's midpoint at the beginning of each trial. The scale's extremes were labeled "more spin" and "more slide". Moving the pointer from the point where the wheel's rolling was normal toward the "spin" extreme maintained a translational velocity of 5.65 em/s, but increased the wheel's rotational velocity. Moving the pointer from the normal point toward the "slide" extreme kept the rotational velocity at 0.38 rev/s, but increased the wheel's translational velocity. Subjects could make as many adjustments as they wished.
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Publication information: Book title: Proceedings of the Seventeenth Annual Conference of the Cognitive Science Society. Contributors: Johanna D. Moore - Editor, Jill Fain Lehman - Editor. Publisher: Lawrence Erlbaum Associates. Place of publication: Mahwah, NJ. Publication year: 1995. Page number: 50.
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