Space (and Its Perception): The First

and Final FrontierM. T. TurveyCenter for the Ecological Study of Perception

and ActionUniversity of Connecticut

The primary test field for theories of perception has, over the centuries, been overwhelmingly the general problem of space perception and, in particular, distance perception. The first step in addressing this problem is a question of the most fundamental kind: what is space? It is not difficult to appreciate that resolution of the scientific problem of how space is perceived depends ultimately on the correctness of the scientific presumption of what space is apropos perception and action.

The question can be refined: what kind of concept is “space”? The most dominant answer is that space is a mathematical concept. The defining properties are those identified in a formal geometric system, with the system of Euclid the most typical choice. A subordinate, but nonetheless influential answer, is that space is a physiological/psychological concept. Here, the emphasis is on the spatial properties that brain/mind might be presumed to prescribe to the world. The synthetic a priori properties of Kantian philosophy and the spatial patterns of organization of Gestalt psychology are primary examples. A third answer, hardly ever entertained, is that space is a biological/ecological concept. For this latter answer, the defining properties of space are to be found

ECOLOGICAL PSYCHOLOGY, 15(1), 1-5Copyright © 2003, Lawrence Erlbaum Associates, Inc.

Requests for reprints should be sent to M. T. Turvey, CESPA U-20, University of Connecticut, Storrs, CT 06269-1020. E-mail: turvey@uconn.edu

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at the interface of animal and environment, where their respective properties are complementary. Gibson’s (1950, 1979) claim that our practical and formal understanding of space should be founded on the layout of substantial surfaces that support actions, rather than the points, lines and planes of abstract geometry, exemplifies the ecological stance.

The many strands of thinking about space and geometry in the past few centuries, though often motivated by the first two answers, have provided a collection of proposals that inform the third answer and encourage its pursuit. Figure 1 summarizes the contributions of Descartes, Berkeley and Kant, pictured in terms of Descartes’s “trialism” and the man-in-the-inner-room metaphor. The man’s perception of the world outside his house is based on a reasoned interpretation (3rd grade of sense) of the colors and sounds (2nd grade of sense) provided by a television set inside the room that receives inputs (1st grade of sense) from cameras and microphones attached to the house’s exterior. Despite Berkeley’s efforts in the New Theory of Vision, the willingness to accept Euclidean geometry as the ultimate definition of space and the willingness to ascribe knowledge of Euclid’s necessary truths to the perceiver were not truly threatened until the crisis in geometry. This crisis arose in the latter part of the 19 th century as a consequence of re-assessing Euclid’s parallel postulate (Cassirer, 1950). Figure 2 identifies the crisis and provides samples of the geometrical empiricism that resulted from it. The larger effect of geometrical empiricism was justification for physics and the other sciences to construct and test conceptions of space that fit the observations of the discipline.

The aforementioned collection of proposals on the nature of space, how to investigate space, and how to study its perception, follow from further historical considerations of the kind depicted in Figures 1 and 2. The proposals can be summarized briefly (Table 1). They do not, however, form a coherent whole and there is overlap. Nonetheless, they provide springboards for open-minded thinking about the definition of space befitting fact and theory in ecological psychology.

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FIGURE 1 The man in the inner room.

The “Man-in-the-Inner Room” model of Descartes’s trialism (three different substances as shown in parentheses). The 3rd grade of sense is endowed with necessary truths of Euclid’s geometry. For example: angle between light rays subtended by an object varies with its distance.

3rd Grade of Sense (mental)

1st Grade of Sense (physical)

2nd Grade of Sense(physical-mental)

Berkeley’s dismissal of the geo-metric theory of Descartes and Malebranche. His analogy for space perception: language not geometry.

Visual spatial perception is a matter of understanding visual signs, not solving geometric problems.

The function of a language is to signify. The function of vision as a language is to signify that by means of which we can regulate activity.

World

Cannot register the lengths, intersections, or angles of light rays; only points

No endowment of necessary geometric truths;only contingent “truths” (learned associations)

The “man-in-the-inner room” according to Kant’s metaphysical and transcendental arguments: Space as a synthetic a priori.

Space is not a material thing that one perceives but a mode (manner or form) in which one perceives material things.

Space is described in purely mathematical terms. Euclidean geometry is not a representation of space, it is space.

World-as-is

‘Synchronizing currents’ of inner room impose Euclidean spatial structure on TV images

World-as-known World-as-sensed

19th C. variations on the parallel postulate led to a plurality of geometries. Consequence 1. A crisis: Which geometry is ‘correct’?Consequence 2. A realization: Geometry is empirical.

D = 1

D = 2

D = 3

D = 1.5849

Geometrical empiricism allows icono-clastic questions: How many dimensions does space have? Is it always an integer number? A line, a square, and a cube are scaled up by a factor of two. This doubling similarity requires 2 copies of the line, 4 copies of the square and 8 copies of the cube. The dimensionality is calculated according to D = log(number of copies)/log(scaling factor). When the doubling similarity applies to the Sierpinski triangle (far right), the rule for dimensionality produces a noninteger value.

RiemannSpherical geometry

EuclidP

L

Exactly one line through P parallel to L Planar geometry

Lobachevsky and BolyaiL

P More than one line through P parallel to L Hyperbolic geometry

No lines through P parallel to L

P

L

More geometrical empiricism: How is a structure-less manifold endowed with geometric structure? Lotze’s local signs and ‘extensity from intensity’ as interpreted by Helmholtz (in the style of Riemann). Hypothesis: Movement is the source of these endowments (in the case of the retina and visual space, Donder’s and Listing’s Laws of eye rotation).

FIGURE 2 The crisis in geometry.

skin manifold

Patch of local signs

x2

x1

Space of real numbers

Endow with properties of parallelism, curvature, geodesic: Affine Connection

Endow with properties of length and angle: Metric

topology of R2

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One catches glimpses of Gibson’s (1979) disquisition on space in each of the above. But there is yet a further proposal, expressed in Figure 3, that is uniquely Gibson’s. Although revolutionary on several fronts, the referring of “space” to possibilities for action (affordances) is in keeping with geometrical empiricism. It is a further step in the progression toward a characterization of space befitting the facts of perceiving-acting entities. Gibson (1958/1982, p.161) wrote: “A terrestrial animal is always encircled…by a radiating set of paths or barriers. Each angular sector of the optic array specifies the possibility of locomotion in that direction. …To

Berkeley

Riemann, Lotze, Helmholtz

Kant, von Uexküll

Riemann, Clifford, Einstein

Gauss, Einstein

Mandelbrot

Pasch

Berkeley

Helmholtz, Klein

1. Space as suggested by conditions of successful visually guided action, not by abstract geometry.

2. Geometry of space as a posteriori, not a priori.

3. Space as space-for-agent, not space-as-is.

4. Space as dependent on its constituents, not absolute and container-like.

5. Space as local and intrinsic, not global and extrinsic.

6. Spatial forms as primarily irregular and fragmented rather than regular and connected.

7. Geometric elements as referring to material facts, not idealizations.

8. Visible properties as signifiers of types of environmental contact not as mathematical entities.

9. Properties of space as relative to trans-formations of space, as relative to degree of free mobility.

TABLE 1Proposals About Space and Geometry

Proposal Proponents

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the extent that the animal can respond to these variables of the encircling optic array, we may now conclude, he has locomotor orientation to his environment. He perceives the possibilities of locomotion surrounding him. And this is probably what should be meant by asserting that an animal has visual space perception.”

The possibilities for action, of course, are not frozen, as Figure 3 makes clear. They change from moment to moment as an animal changes its form or pace of locomotion and alters its order and metrical relations with the surrounding surface layout. Space as possibilities for action that are time-varying and action-dependent, will present many challenges, experimental and formal, to a maturing ecological psychology.

Space comprises time-varying, action-dependent, possibilities for action.

A brink that is uncross-able when approached by walking is cross-able when approached by running.

“Space-for-agent” changes when “space-in-itself” remains the same.

change action potential change space

cross-able

notcross-able

FIGURE 3. “Space” referred to affordances.

ACKNOWLEDGMENT

Preparation of this manuscript was supported by grant No. SBR 00-04097 from the National Science Foundation.

REFERENCES

Cassirer, E. (1950). The problem of knowledge. New Haven, CT: Yale University Press.

Gibson, J. J. (1950). The perception of the visual world. Boston: Houghton Mifflin.

Gibson, J. J. (1958/1982). Visually controlled locomotion and visual orientation in animals. British Journal of Psychology, 49, 182-194. (Reprinted in E. S. Reed and R. Jones (Eds.), Reasons for realism, Hillsdale, NJ: Lawrence Erlbaum Associates)

Gibson, J. J. (1979). The ecological approach to visual perception. Boston: Houghton Mifflin.

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