Shepard's analysis of how shape, motion, and color are perceptually represented can be generalized. Apparent motion and shape may be associated with a group of spatial transformations, accounting for rigid and plastic motion, and perceived object color may be associated with a group of illuminant transformations, accounting for the discriminability of surface-reflectance changes and illuminant changes beyond daylight. The phenomenological and mathematical parallels between these perceptual domains may indicate common organizational rules, rather than specific ecological adaptations. [Barlow; Hecht; Kubovy & Epstein; Schwartz; Shepard; Todorovič]

Tenenbaum and Griffiths' paper attempts to subsume theories of similarity – including spatial models, featural models, and structure-mapping models – into a framework based on Bayesian generalization. But in so doing it misses significant phenomena of comparison. It would be more fruitful to examine how comparison processes suggest hypotheses than to try to derive similarity from Bayesian reasoning. [Shepard; Tenenbaum & Griffiths]

Based on concepts of self-organization, we interpret apparent motion as the result of a so-called non-equilibrium phase transition of the perceptual system with the stimulus-onset asynchrony (SOA) acting as a control parameter. Accordingly, we predict a significantly increasing variance of the quality index of apparent motion close to critical SOAs. [Shepard]

To balance Kubovy & Epstein, I evaluate the relationship between Shepard and Gestalt theorists along three dimensions. First, both discover internal universals by reducing external support. Second, they share strengths and weaknesses of the minimum principle. Third, although their attitudes toward an evolutionary account of perception is superficially different, they are fundamentally similar with respect to the internalization process. [Kubovy & Epstein; Shepard]

It is argued that color constancy is only one of the benefits of color vision and probably not the most important one. Attention to a different benefit, chromatic contrast, suggests that the features of the environment that played a role in the evolution of color vision are properties of particular ecological niches rather than properties of naturally-occurring illumination. [Shepard]

Shepard provides an account of mechanisms underlying perceptual judgment or representation. Ought we to interpret the account as revealing principles on which those mechanisms operate or merely an account of principles to which their operation apparently conforms? The difference, invisible so long as we remain at a high level of abstraction, becomes important when we begin to consider implementation. [Shepard]

The great advantage of Tenenbaum and Griffiths's model is that it incorporates both specific and general prior knowledge into category learning. Two phenomena are presented as supporting the detailed assumptions of this model. However, one phenomenon, effects of diversity, does not seem to require these assumptions, and the other phenomenon, effects of sample size, is not representative of most reported results. [Tenenbaum & Griffiths]

In the course of evolution organisms change both their morphology and their physiology in response to ever-changing environmental selection pressures. This process of adaptation leads to an “internalization,” in the sense that external regularities are in some way “imitated” by the living system. Countless examples illustrate the usefulness of this metaphor. However, if we concentrate too much on Shepard's “universal regularities in the world,” we run the risk of overlooking the many more fascinating evolutionary details which alone have made, and still make possible the evolution of diversity on earth. [Shepard]

The commentary is in general agreement with Roger Shepard's view of evolutionary internalization of certain procedural memories, but advocates the use of Lie groups to express the invariances of motion and color perception involved. For categorization, the dialectical pair is suggested. [Barlow; Hecht; Kubovy & Epstein; Schwartz; Shepard; Todorovič]

As Hecht points out, finding unequivocal evidence for phylogenetic knowledge structures is problematic, if not impossible. But if phylogeny could be dropped, then internalization starts to resemble the “theory theory” approaches of developmental psychology. For example, an appreciation of falling objects leads to a very strong bias that could be regarded as internalized knowledge acquired during ontogeny. [Hecht; Shepard]

Shepard's (1994) choice of kinematic geometry to support his theory is questioned by Todorovic, Schwartz, and Hecht. His theoretical framework, however, can be applied to another domain that may be less susceptible to some of their concerns. The domain is the representation of spatial layout. [Hecht; Schwartz; Shepard; Todorovič]

We argue four points. First, perception always relies on environmental constraints, not only in special cases. Second, constraints are taken advantage of by detecting information granted by the constraints rather than by internalizing them. Third, apparent motion phenomena reveal reliance on constraints that are irrelevant in everyday perception. Fourth, constraints are selected through individual learning as well as evolution. The “perceptual-concept-of-velocity” phenomenon is featured as a relevant case. [Hecht; Kubovy & Epstein; Shepard]

Hecht provides insights concerning the difficulty of empirically testing Shepard's internalization hypothesis, but his argument for an externalization hypothesis suffers from similar sins. [Hecht]

Shepard's internalization concept is defended against Hecht's criticisms. By ignoring both Shepard's evolutionary perspective and the fact that internalization does not preclude modularization, Hecht advances inconclusive evidence. Developmental research supports Shepard's conclusion that kinematic geometry may be more deeply internalized than physical dynamics. This research also suggests that the internalization concept should be broadened to include representations acquired during ontogeny. [Hecht; Shepard]

Behavioral regularities are open to both representationist (hence internalist) and non-representationist explanations. Shepard improvidently favors internalism, which is burdened with severe conceptual and empirical shortcomings. Hecht and Kubovy & Epstein half-heartedly criticize internalism by tracing it back to “unconscious” metaphors or by replacing it with weak externalism. Explanations of behavioral regularities are better relocated within a radical embodiment approach. [Hecht; Kubovy & Epstein; Shepard]

We review studies on catching that reveal internalization of physics for action control. In catching free-falling balls, an internal model of gravity is used by the brain to time anticipatory muscle activation, modulation of reflex responses, and tuning of limb impedance. An internal model of the expected momentum of the ball at impact is used to scale the amplitude of anticipatory muscle activity. [Barlow; Hecht; Shepard]

While Tenenbaum and Griffiths impressively consolidate and extend Shepard's research in the areas of stimulus representation and generalization, there is a need for complexity measures to be developed to control the flexibility of their “hypothesis space” approach to representation. It may also be possible to extend their concept learning model to consider the fundamental issue of representational adaptation. [Tenenbaum & Griffiths]

Shepard claims that “evolutionary internalization of universal regularities in the world” takes place. His position is interesting and seems plausible with regard to “default” motion detection and aspects of colour constancy which he addresses. However, his claim is not convincing with regard to object recognition. [Shepard]

Tenenbaum and Griffiths's article continues three disturbing trends that typify category learning modeling: (1) modelers tend to focus on a single induction task; (2) the drive to create models that are formally elegant has resulted in a gross simplification of the phenomena of interest; (3) related research is generally ignored when doing so is expedient. [Tenenbaum & Griffiths]

Roger Shepard's creativity and scientific contributions have left an indelible mark on Psychology and Cognitive Science. In this tribute, I acknowledge and show how his approach to universal laws helped Oden and me shape and develop our universal law of pattern recognition, as formulated in the Fuzzy Logical Model of Perception (FLMP). [Shepard; Tenenbaum & Griffiths]