We determined how much motion coherence was needed to detect a target group of four moving dots in a dynamic visual noise (DVN) background. The lifetimes of the trajectories of the target and that of the noise dots were the same. In addition to parallel trajectories and collinear dot arrangements, divergent, convergent, or crossing trajectories and non-collinear dot arrangements were also tested. Performance saturated at a lifetime of approximately 600 ms. It was best for parallel trajectories and collinear dots, and worse for crossed trajectories with non-collinear dots, where it approached performance in a no-motion, form-only control experiment. Results illustrate the importance of common fate in motion perception in DVN, when other factors are equated.

A number of recent as well as classic ideas suggest that there are constraints and limits on the explanatory role that computational, mathematical, and neural net models of visual and other cognitive processes can play that have not been generally appreciated. These ideas come from mathematics, automata theory, chaos theory, thermodynamics, neurophysiology, and psychology. Collectively, these ideas suggest that the neural or cognitive mechanisms underlying many kinds offormal models are untestable and unverifiable. Models may be good descriptions of perceptual and other cognitive processes, but they cannot in principle be reductive explanations nor can we use them to predict behavior at the molar level from what we know of the neural primitives. This discussion is an effort to clarify the appropriate meanings of these models, not to dissuade workers from forging ahead in the modeling endeavor, which I acknowledge is progressing and is making possible our increasingly deep appreciation of plausible and interesting cognitive processes. 188What do formal models of cognitive processes mean? What can models do, and what can they not do? My purpose in this article is to consider these questions for a wide variety of formal models-mathematical, computational, neural network, statistical, cognitive flowchart, and symbolic, as well as others that are just arriving on the scene.' The past decade, in particular, has seen an explosion of interest in the development of formal models of cognitive processes. But it must not be overlooked that this kind of modeling has been with us virtually since the first availability of digital computer technology. (See, e.g., Farley & Clark, 1954;Rosenblatt, 1962;Selfridge, 1959; and Widrow, 1962, among others; and for a comprehensive review of the history of this field and the mathematical relationships among the various theories, see also Grossberg, 1988. Anderson & Rosenfeld's 1988 compendium of significant papers in neurocomputing is also a good review of the history of one cluster of formal models.) The recent impetus for the renewed interest in computer simulations and mathematical models of cognitive proThis work was supported by Contract NOOOI4-88-K0603 from the Office of Naval Research. I would like to express my thanks to several anonymous reviewers of an earlier draft of this article. In addition, I wish specifically to thank Stevan Hamad, Joseph Lappin, and James T. Townsend for their detailed and insightful commentaries, which helped make this document a clearer and more worthwhile contribution than it otherwise would have been. Correspondence should be sent to the following address: William R. Utta1,

The detectability of forms embedded within random visual noise has been found to be predictable from the autocorrelation transform of the stimulus pattern (Uttal, 1975). A basic assumption in the autocorrelation theory of form detection is that detectability is determined by the organization of the stimulus pattern, irrespective of the observer's prior knowledge or expectations about the characteristics of the form. This assumption was tested by determining the effect of the size of the set of alternative target forms on performance of a forced-ehoice detection task. The targets were composed of dots in a straight line, appearing in one of a specified set of 2, 4, or 8 alternative positions in a pattern of randomly distributed masking dots. Detection accuracy was found to decrease as set size increased, but this decrease was close to what was predicted on the assumption that the random background was independently confusable with the target at each of the alternative positions. Thus, prior knowledge of the set of alternative targets appeared to have no effect on the visual process, but only on the decision process by virtue of the features that were relevant criteria for deciding which of the two patterns on each trial was most likely to contain the target. This result is consistent with the autocorrelation theory. This experiment may illustrate how the decision process has influenced the performance in many other experiments that have been assumed to demonstrate an effect of prior knowledge on perception.A significant development in contemporary research on visual form perception is the use of complex spatial and temporal patterns that are generated and displayed under control by a computer. The concept of "form" or "pattern" can thus be defined by the relational organization of a large number of identical elements.This technique is illustrated in Uttal's (1975) research program on the detection of simple forms embedded in random patterns of dots that serve to mask or camouflage the form. Both target form (a deterministically defined pattern) and noise (a statistically defined masking pattern) are patterns of dots displayed on a cathode ray tube-the target being regular and periodic in some way, and the noise being random with uniform distribution in Reprint request should be addressed to Joseph S. Lappin, Department of Psychology, Vanderbilt University, Nashville, Tennessee 37240. We would like to express our appreciation to Ms. Thelma Eskin, who helped greatly in the running of the experiment and in the data analysis, and to V. R. Carlson and Sandra McNabb for their helpful comments on earlier drafts.

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