Academic journal article Psychonomic Bulletin & Review

Subjective Randomness and Natural Scene Statistics

Academic journal article Psychonomic Bulletin & Review

Subjective Randomness and Natural Scene Statistics

Article excerpt

Accounts of subjective randomness suggest that people consider a stimulus random when they cannot detect any regularities characterizing the structure of that stimulus. We explored the possibility that the regularities people detect are shaped by the statistics of their natural environment. We did this by testing the hypothesis that people's perception of randomness in two-dimensional binary arrays (images with two levels of intensity) is inversely related to the probability with which the array's pattern would be encountered in nature. We estimated natural scene probabilities for small binary arrays by tabulating the frequencies with which each pattern of cell values appears. We then conducted an experiment in which we collected human randomness judgments. The results show an inverse relationship between people's perceived randomness of an array pattern and the probability of the pattern appearing in nature.

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People are very sensitive to deviations from their expectations about randomness. For example, the game Yahtzee involves repeatedly rolling 5 six-sided dice. If you were to roll all sixes 6 times in a row, you would probably be quite surprised. The probability of such a sequence arising by chance is 1/630. However, the low probability of such an event is not sufficient to explain its apparent nonrandomness, since any other ordered sequence of the same number of dice rolls has the same probability. Consequently, recent accounts of human subjective randomness (our sense of the extent to which an event seems random) have focused on the regularities in an event. These regularities suggest that a process other than chance might be at work (Falk & Konold, 1997; Feldman, 1996, 1997; Griffiths & Tenenbaum, 2003, 2004). The basic idea behind these accounts is that stimuli will appear random when they do not express any regularities.

An important challenge for any account of subjective randomness based on the presence of regularities is to explain why people should be sensitive to a particular set of regularities. In the example given above, systematic runs of the same number may suggest loaded dice or some other nonrandom process influencing the outcomes. However, for other kinds of stimuli, such as the one- or twodimensional binary arrays used in many subjective randomness experiments, explanations are more difficult to come by. A common finding in these experiments is that people consider arrays in which cells take different values from their neighbors (such as the one-dimensional array 0010101101) more random than arrays in which cells take the same values as their neighbors (such as 0000011111) (Falk & Konold, 1997). This result makes it clear that people are sensitive to certain regularities, such as cells having the same values as their neighbors. However, it is difficult to explain why these regularities should be more important than others that seem a priori plausible, such as neighboring cells differing in their values.

In this article, we explore a possible explanation for the origins of the regularities that influence subjective randomness judgments for one class of stimuli: two-dimensional binary arrays. These stimuli are essentially images, with the cells in the array having the appearance of a grid of black and white pixels (see Figure 1). We might thus expect that the kinds of regularities detected by the visual system should play an important role in determining their perceived randomness. A great deal of recent research suggests that the human visual cortex efficiently codes for the structure of natural scenes-scenes containing natural elements, such as trees, flowers, and shrubs, that represent the visual environment in which humans evolved (Olshausen & Field, 2000; Simoncelli & Olshausen, 2001). We consider the possibility that the kinds of regularities that people detect in two-dimensional binary arrays are those that are characteristic of natural scenes. …

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