Meta-Invariant Structure in Stimulus Arrays: A Response to Mace's Zetetic Challenge to Ecological Perceptual Researchers

ABSTRACT

Ecological perception, per James Gibson's theory, avows that perception depends on informative structure in stimulus arrays, where information is defined as stimulus array invariants. Gibson, however, was somewhat vague about the nature of such structure. Consequently, ecological perceptual research—even acknowledging some remarkable successes—has generally been ad hoc: Lacking principled heuristics, researchers examine array structure, which, by some means, they have come to discover as (or believe to be) informative. Here, I propose a series of heuristic principles potentially useful for the discovery of informative structure in stimulus arrays, with examples to suggest how those principles might apply. The major benefit of principled search for stimulus array invariants is more efficient elaboration of their function in perception. While admittedly preliminary, the principles outlined may both guide perceptual investigations and prompt additional consideration of how to approach the search for stimulus array invariants.

Notes

¹ The wording represented by the ellipsis here is: “The psychophysical task is [original emphasis] simplified inasmuch as one would limit the patterns used to those that might correspond to selected environmental properties. Otherwise Gibson's insight that ‘higher order’ variables of stimulation could function as stimuli for perception would have opened a Pandora's box of possibilities.” Apparently, Mace is suggesting two separate concepts here: (a) that principled limitations would be useful for finding informative patterns of stimulus array structure; and (b) that the choice among identified patterns for empirical study should focus on selected environmental properties, presumably those that have some behavioral relevance. The “Pandora's box of possibilities” might suggest that attempting to address both concepts would be an overwhelming task. Because my aim is stimulus array analysis, I omitted the statements that appear to refer to the empirical issue. Parenthetically, although James Gibson (1966, 1979) uses the phrase “higher-order” repeatedly, one searches in vain in those sources for any explicit definition of what the term actually means.

² In passing, with the exception of cylindrical vessels filling with water (Cabe & Pittenger, 2000) and acoustic information for an approaching sound source (e.g., Neuhoff, 1998; Shaw, McGowan, & Turvey, 1991), the examples proposed in Cabe (1993) have not, to the best of my knowledge, actually been subjected to experimental test in perceptual studies. They remain good targets for such research.

³ AS, defined as array structure, is taken directly from Cabe (2001). In that paper I defined the symbol WS for world structure. Here, ES for environmental structure suggests a more limited purview. In point of fact, some of the ideas in the present paper were introduced in Cabe (2001).

⁴ The history of the development of measurement theory is complicated, contentious, and essentially contemporaneous (e.g., Marley, 1992). Several authors (e.g., Diez, 1997; Michell, 2004) have reviewed the historical development of measurement theory. Michell, in particular, sharply criticizes the logic Stevens used in deriving his scales of measurement.

⁵ It is true, of course, that the degree of apparent movement of nontarget objects, with respect to the target object, defines ordinal relative depth relationships. With additional assumptions (see Cutting & Vishton, 1995), metric information may also be available from motion parallax.

⁶ Theories of measurement typically begin with the assumption that objects to be measured are perceptually differentiable. The assumption often appears to be tacit.

⁷ I thank Suellen Cabe for pointing this example out to me.

⁸ The relationships between environmental properties and stimulus array properties that specify those environmental properties are often not absolute, but rather constrained by contextual variables.

⁹ In fact, while the curves have asymptotic forms mathematically, physical constraints (e.g., friction) mean they reach absolute end points, rather than continuing to some nonzero limit at infinity.

¹⁰ Astronomers distinguish degrees of relative position of the sun below and above the horizon in terms such as nautical twilight, civil twilight, and astronomical twilight (see definitions in Seidelman, 1992).

¹¹ The rapidity with which the sun sets (or rises) is a function of season and latitude. Seasonal difference occur because the axis of the earth is tilted relative to the plane of the ecliptic, the effects of which on sunrise and sunset change across the year as the earth revolves around the sun. Thus, the sun approaches the horizon at different angles at different times of the year (which in itself might be seen as optical information for the season). Latitude influences the length of time that sunsets and sunrise take, due to the differing tangential velocities at differing points between the poles and the equator. A common observation is that sunset occurs very rapidly in the tropics. It does, because tangential velocity at the equator is greater than 1600 km/h, while at 45 degrees latitude, it is less than 1200 km/h. It follows that the time that it takes for the sun to set is optical information for latitude.