Visual space can be distinguished from physical space. The first is found in visual experience, while the second is defined independently of perception. Theorists have wondered about the relation between the two. Some investigators have concluded that visual space is non-Euclidean, and that it does not have a single metric structure. Here it is argued that visual space exhibits contraction in all three dimensions with increasing distance from the observer, that experienced features of this contraction are not the same as (...) would be the experience of a perspective projection onto a fronto-parallel plane, and that such contraction is consistent with size constancy. These properties of visual space are different from those that would be predicted if spatial perception resulted from the successful solution of the inverse problem. They are consistent with the notion that optical constraints have been internalized. More generally, they are also consistent with the notion that visual spatial structures bear a resemblance relation to physical spatial structures. This notion supports a type of representational relation that is distinct from mere causal correspondence. The reticence of some philosophers and psychologists to discuss the structure of phenomenal space is diagnosed in terms of the simple materialism and the functionalism of the 1970s and 1980s. (shrink)

What is the relationship between complexity in the world and complexity in the mind? Intuitively, increasingly complex objects and events should give rise to increasingly complex mental representations (or perhaps a plateau in complexity after a certain point). However, a counterintuitive possibility with roots in information theory is an inverted U-shaped relationship between the “objective” complexity of some stimulus and the complexity of its mental representation, because excessively complex patterns might be characterized by surprisingly short computational descriptions (e.g., if they (...) are represented as having been generated “randomly”). Here, we demonstrate that this is the case, using a novel approach that takes the notion of “description” literally. Subjects saw static and dynamic visual stimuli whose objective complexity could be carefully manipulated, and they described these stimuli in their own words by giving freeform spoken descriptions of them. Across three experiments totaling over 10,000 speech clips, spoken descriptions of shapes (Experiment 1), dot-arrays (Experiment 2), and dynamic motion-paths (Experiment 3) revealed a striking quadratic relationship between the raw complexity of these stimuli and the length of their spoken descriptions. In other words, the simplest and most complex stimuli received the shortest descriptions, while those stimuli with a “medium” degree of complexity received the longest descriptions. Follow-up analyses explored the particular words used by subjects, allowing us to further explore how such stimuli were represented. We suggest that the mind engages in a kind of lossy compression for overly complex stimuli, and we discuss the utility of such freeform responses for exploring foundational questions about mental representation. (shrink)

Inferences about spatial, temporal, and other relations are ubiquitous. This article presents a novel model-based theory of such reasoning. The theory depends on 5 principles. The structure of mental models is iconic as far as possible. The logical consequences of relations emerge from models constructed from the meanings of the relations and from knowledge. Individuals tend to construct only a single, typical model. They spontaneously develop their own strategies for relational reasoning. Regardless of strategy, the difficulty of an inference depends (...) on the process of integration of the information from separate premises, the number of entities that have to be integrated to form a model, and the depth of the relation. The article describes computer implementations of the theory and presents experimental results corroborating its main principle. (shrink)

Children learn their native language by exposure to their linguistic and communicative environment, but apparently without requiring that their mistakes be corrected. Such learning from “positive evidence” has been viewed as raising “logical” problems for language acquisition. In particular, without correction, how is the child to recover from conjecturing an over-general grammar, which will be consistent with any sentence that the child hears? There have been many proposals concerning how this “logical problem” can be dissolved. In this study, we review (...) recent formal results showing that the learner has sufficient data to learn successfully from positive evidence, if it favors the simplest encoding of the linguistic input. Results include the learnability of linguistic prediction, grammaticality judgments, language production, and form-meaning mappings. The simplicity approach can also be “scaled down” to analyze the learnability of specific linguistic constructions, and it is amenable to empirical testing as a framework for describing human language acquisition. (shrink)

The arts are one of the most complex of human endeavours, and so it is fitting that a special issue on Complex Systems in Aesthetics and Arts is being published. As the editors of this special issue, we would like to thank the reviewers of the submitted papers for their hard work in making this issue possible, as well as the authors who submitted their work and were very responsive to the comments of the reviewers and editors.

We address the problem of predicting how people will spontaneously divide into groups a set of novel items. This is a process akin to perceptual organization. We therefore employ the simplicity principle from perceptual organization to propose a simplicity model of unconstrained spontaneous grouping. The simplicity model predicts that people would prefer the categories for a set of novel items that provide the simplest encoding of these items. Classification predictions are derived from the model without information either about the number (...) of categories sought or information about the distributional properties of the objects to be classified. These features of the simplicity model distinguish it from other models in unsupervised categorization (where, for example, the number of categories sought is determined via a free parameter), and we discuss how these computational differences are related to differences in modeling objectives. The predictions of the simplicity model are validated in four experiments. We also discuss the significance of simplicity in cognitive modeling more generally. (shrink)