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Cognitive processes and their adaptive functions can hardly be understood if we look exclusively inside the mind, such as when we try to explain behavior with traits, attitudes, or preferences. Rather, it is essential to analyze the adaptive match between cognitive and ecological structures. This chapter shows that many phenomena that look like cognitive fallacies follow logically from a cognitive system well adapted to its environment. Specifically, the chapter presents an ecological analysis of judgment and choice in terms of the three moments of statistical distributions of information in environments. The chapter demonstrates that phenomena from various areas of psychology can be accounted for by people’s sensitivity to the three moments, and it also describes the implications of these moments in terms of the effect of regression toward the mean, the role of sample size, and the process of sampling.

Texture refers to the surface characteristics of an object resulting from the quality and arrangement of its particles or constituent parts. One extensive set of experiments focused on the segmentation into discrete regions of visual stimuli composed of dots or micropatterns. The original work contrasted different statistical distributions of the lightness of the dots, but soon shifted to the geometrical properties of the micropatterns. Another extensive set of experiments focused on the perception of emergent global surface properties created by the successive transformation of random noise patterns. For visual Glass patterns, transformations can lead to the perception of rotation, radial expansion, symmetry, contour, and linear movement. For auditory noise patterns, repetition can lead to the perception of pitch. It is important to distinguish between direct passive perceiving and attentive active perceiving. Structure in the physical world may not be perceivable.

The fourth chapter presents the quantitative findings for the categories of speech, writing, and thought presentation in the corpus of 19th-century narrative fiction and compares their statistical distribution with the findings by Semino and Short (2004) for 20th-century fiction. The author finds that the JLVeffects of particular categories of thought presentation are different from those of speech presentation in the 19th-century data. Further, the scales of speech and thought presentation in 19th-century narrative fiction are differently distributed compared to the 20th century, this giving quantitative evidence to Fludernik’s (1993) “direct discourse fallacy” according to which a character’s direct discourse should never simply be accepted as fully reliable because the narrator’s mediation is always a distortion.

This chapter discusses the ordering of color percepts, and starts by presenting an overview of the critical issues surrounding the topic and by examining the relationship between stimuli and percepts. Certain types of variability were found by experimental psychology in the relationship between stimulus and response as a result of observation conditions. In the twentieth century, the view that the normal human color-vision system has a standard implementation and that all perceptual data are appropriately treated with normal statistical distribution methodology became the standard paradigm. However, the idea that the large number of color percepts humans can experience must fit into some kind of ordering system is an old one, going as far back to Aristotle and his proposed color categories based on a scale of chromatic colors between white and black. The strengths and limitations of the more recently developed kinds of color order systems are also touched upon here.

Benford's law is a statement about the statistical distribution of significant (decimal) digits or, equivalently, about significands, namely fraction parts in floating-point arithmetic. Thus, a natural starting point for any study of Benford's law is the formal definition of significant digits and the significand function. This chapter contains formal definitions, examples, and graphs of significant digits and the significand (mantissa) function, and the probability spaces needed to formulate Benford's law precisely, including the crucial natural domain of “events,” the so-called significand σ‎-algebra.