Pattern-contingent color aftereffects, or McCollough effects (MEs), are used to probe the visual brain's operations psychophysically. Their neural substrate is unknown, however, and theories about them are weak. Our theory proposes a strong functional role for MEs and a neuropsychological basis that accounts for "top-down" (global) constraints ignored by other theories. The functional aspect of the theory is based on the concept of contingent adaptation level, following Helson (1964), and on the "error-correcting device" of Andrews (1964), which tracks and adjusts internal representation to external-world contingencies. The neuropsychological part of the theory postulates that global properties are the result of MEs being generated not at the individual detector level but in vectorfields of which the detectors are elements. It is an implementation of Lie transformation group theory (Hoffman, 1966). Evidence for this model is assessed.
The Lie transformation group model of neuropsychology (LTG/NP) purports to represent and explain how the locally smooth processes observed in the visual field, and their integration into the global field of visual phenomena, are consequences of special properties of the underlying neuronal complex. These properties are modeled by a specific set of mathematical structures that account both for local (infinitesimal) operations and for their generation of the "integral curves" that are visual contours. The purpose of this tutorial paper is to expound, as nontech· nically as possible, the mathematical basis for LTG/NP, and to evaluate that model against a reasonable set of criteria for a neuropsychological theory. It is shown that this approach to spatial vision is closer to the mainstream of current theoretical work than might be assumed; recent experimental support for LTG/NP is described.
A study of spatial concepts in nearly 200 children between the ages of five and eleven years old showed that the types of thinking and problem-solving described by Piaget for children of this age range occur quite generally. However, it was not possible to characterize the great majority of the children studied as being in any one of the particular stages of spatial concept development described by Piaget. The over-all ability to deal correctly with spatial concepts improves with age, as one might expect, but no clear-cut progression from one type of thinking about space to another could be identified in the data. The pattern of development is probably influenced by a variety of different factors, and it is suggested that more intensive longitudinal studies are required to determine what these influences may be.
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