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Ecological Psychology , 26:283–300, 2014
Copyright © Taylor & Francis Group, LLC
ISSN: 1040-7413 print/1532-6969 online
DOI: 10.1080/10407413.2014.957999
Department of Psychology
University of Southern Mississippi
School of Health Professions
University of Alabama at Birmingham
Department of Psychology
University of South Alabama
Department of Kinesiology
Auburn University
This study shows that perceived geographical slant affects postural stability. In 2 experimental conditions participants stood on a force platform that measured center of pressure (COP) during quiet stance while looking at a rigid, flat ramp surface of varying geographical slants. Using an otherwise identical procedure, participants in the second condition also provided verbal estimates of the steepness of the surface in degrees. Several measures of postural stability offered converging evidence that
COP sway gradually increased as geographical slant decreased to 0 (horizontal ground). Specifically, COP was sensitive to changes in surface slant. Both the range
Correspondence should be addressed to Alen Hajnal, Department of Psychology, University of Southern Mississippi, 118 College Drive #5025, Hattiesburg, MS 39406. E-mail: alen.hajnal@ usm.edu
Color versions of one or more of the figures in the article can be found online at www.tandfonline.
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283

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HAJNAL, RUMBLE, SHELLEY-TREMBLAY, LIU and the standard deviation of COP showed the same trend of increased variability with decreasing geographical slant angles in both conditions. The area of the ellipse covering COP sway (based on a principal components analysis) showed the same tendency: ellipse area got larger for smaller, more horizontal slants.
Nonlinear fractal dynamics of COP sway, as measured by the Hurst exponent of
COP, pointed in the same direction: more fractal patterns, known to be correlated with increased muscle activity and decline in postural stability, were measured for shallower surface slants. There were no effects of verbal estimates on any of the measures, suggesting that explicit awareness of slant does not bias postural stability above and beyond the effects of visual environment.
Visual information is one of several ambient energy patterns that contribute to postural stability. How do people maintain stable upright stance based on visual information about their surroundings? The spatial surroundings are constituted by a complex arrangement of nested surfaces at different distances and different orientations. Is posture affected by the visual layout of surfaces in front of the observer? Does visual perception of such layout help, hinder, or share no relation to postural stability? These questions, which are critical to understanding control of posture in normal and clinical populations, motivated our present research.
There are at least three basic aspects of the configuration of surfaces that may pertain to postural stability: surface orientation, surface distance from observer, and surface texture. A person may choose to stand on a slanted or horizontal surface, and he or she may stand near or far from other surfaces, such as a wall or the slope of a hill. In this study the paradigm required observers to stand on flat, horizontal ground and instructed them to visually inspect a large, door-size rigid static surface in front of them that was propped up at a geographical slant angle ranging from 0 to 90 degrees. The experiment was designed to determine whether exposure to a slanted surface would change participants’ postural stability. We chose to manipulate geographical slant as it is one of the most basic spatial properties of the visual world. Most surfaces that people encounter in daily life are slanted upward, downward, or to the side, and so it makes sense to expect the spatial layout of surfaces to have a profound impact on our ability to maintain upright posture.
Lishman and Lee (1973) offered early evidence that visual information in an optic array constituted by the layout of vertical surfaces had dramatic influence on postural stability. Testing the postural effects of surfaces at geographical slants other than the vertical may provide researchers with a broader understanding of the exact nature of their effects on visual kinesthesis than the single vertical wall used by Lishman and Lee in their seminal study. We have intentionally used a static stimulus array, instead of a dynamically changing optic flow field, to provide for the most basic test of the influence of visual environment on postural stability.

POSTURE AND GEOGRAPHICAL SLANT
285
Differential effects of geographical slant and elevation on posture have been demonstrated in applied settings such as construction sites (roofs and building scaffoldings; see Simeonov, Hsiao, Dotson, & Ammons 2003; Simeonov, Hsiao,
& Hendricks, 2009). Specifically, Simeonov et al. (2009) have shown that looking at vertical reference objects such as a vertical bar while standing on an inclined roof increases postural stability and that posture becomes even more stable when the visual reference bar is placed nearby. A more basic question that has not been evaluated is whether such visual reference structure would have an effect on posture even when standing on flat extended ground. Put plainly, does the sight of a reference object alone affect posture even under safe conditions such as standing on a horizontal, firm surface at ground level? Our present empirical work was designed to offer such a basic test of the influence of a visual array of surfaces on posture.
In precarious circumstances, such as standing on a cliff or on the balcony of a tall building, dizziness and vertigo might cause a complete breakdown of postural stability due to the absence of nearby visual anchors, such as near support surfaces, walls, and other rigid objects that may provide safety by engaging the visual system (Hsiao & Simeonov, 2001; Hsiao et al., 2005). The sight of a wall or other nearby surface may actually stabilize posture to a larger extent than a distant surface or other wide-open spaces. Following Simeonov et al. (2009), we hypothesized that during unconstrained viewing, increased
(i.e., more vertical) geographical slant of an extended surface would result in greater postural stability.
A considerable body of literature demonstrates that distance to visual targets influences postural stability. Stoffregen, Smart, Bardy, and Pagulayan (1999) showed that looking at nearby targets makes posture more stable compared with looking at distant targets or no targets at all. This evidence suggests that objects and surfaces in the environment may serve as visual anchors that play a role in maintaining upright stance. If this is true, potential applications are boundless: engineers and architects can construct “smart environments” such as scaffoldings at construction sites and hospital rooms and corridors that may lower fall risk for patients. Such “smart environments” have already been built and applied in vehicular traffic control (e.g., perceptual countermeasures to speeding;
Fildes et al., 2005) and demonstrated in the visual guidance of locomotion of insects (Srinivasan, 1998) and humans (Elliott, Vale, Whitaker, & Buckley,
2009). Furthermore, T. M. H. Dijkstra, Gielen, and Melis (1992) discovered that distance to a surface might play a central role in postural sway, as optic flow patterns are larger and more discernible nearby, thus providing more detailed and precise information for maintaining postural stability. Bonnet, Temprado, and
Berton (2010) explicitly tested how distance to visual targets affects posture.
They showed that visual exposure to near objects stabilizes posture. In these tasks, the act of paying attention to a target is considered suprapostural, that is,

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HAJNAL, RUMBLE, SHELLEY-TREMBLAY, LIU purposeful above and beyond the mere exposure to the surrounding optic array, and may exert its effect on postural stability independent of other factors. In our present contribution we take a step back and study the most basic postural task, that of standing upright and viewing a uniform frontal surface that may be more simply indicative of the effects of visual exposure to surface layout.
In addition to traditional measures of postural variability such as range and standard deviation, we sought to include complementary measures, such as fractality, that tap into the complex dynamics of center of pressure (COP) sway (Collins & De Luca, 1993, 1995; Duarte & Zatsiorsky, 2001). Recent research has revealed intricate connections among sensory stimulation, perception, and postural control by using fractal and other nonlinear measures (for examples see Bonnet, Kinsella-Shaw, et al., 2010; Bonnet, Temprado, et al.,
2010; Palatinus, Dixon, & Kelty-Stephen, 2013; Stambolieva, 2011; for related findings in a perceptual learning task that parallel fractal signatures observed in postural tasks see Stephen & Hajnal, 2011). Our choice of dependent measures sought to reaffirm the utility of nonlinear fractal analyses of postural stability in describing postural control as a function of sensory exposure and interaction with structured stimulus arrays in the environment. In a seminal study Collins and
De Luca (1993) found COP measures in the anterior-posterior (AP) direction to be the most informative and sensitive measures related to postural sway due to the inherent asymmetry of the lower limb. We therefore based all our measures on COP in the AP direction and expected no systematic variation of
COP in the medio-lateral (ML) direction. The same authors described postural control as a combination of open-loop and closed-loop motor control strategies.
They discovered that open-loop control produced variability corresponding to a highly fractal signal that is correlated with decreased postural stability, and as a consequence, heightened muscle activity, whereas closed-loop control generated signals that were indicative of larger postural stability, close to a biomechanical equilibrium point, less fractal in nature, and characterized by less active postural adjustments (Amoud et al., 2007; Lin, Seol, Nussbaum, & Madigan, 2008). To remain consistent with the literature, our predictions were in line with Collins and De Luca’s (1993) findings: we expected highly fractal signals to reflect open-loop control and to indicate less postural stability as a function of visual information of the layout of surfaces. Specifically, wide-open spaces provided by lower geographical slant angles were expected to be related to less stability and elevated fractality.
Within the literature on the perception of geographical slant, considerable debate exists about the status of various measures of slant (for details see
Proffitt, Bhalla, Gossweiler, & Midgett, 1995). Verbal estimates are usually shown to be exaggerated and interpreted as reflecting cognitive processes such as future action planning, whereas more direct measures of perceived slant
(haptic matching) are considered purely perceptual. However, there is growing

POSTURE AND GEOGRAPHICAL SLANT
287 evidence (Durgin, Hajnal, Li, Tonge, & Stigliani, 2010) that verbal and nonverbal measures of slant do not reflect such division between cognition and perception.
We sought to test whether verbal and nonverbal perception of slant may influence the stability of upright stance in different ways. Specifically, it was expected that the addition of a suprapostural task, such as verbal estimation, would stabilize posture and reduce variability similar to the findings of Stoffregen et al.
(1999). The results will be relevant for the potential interpretations of postural control as “cognitively impenetrable” (Pylyshyn, 1999) and have repercussions for the discussions related to the embodiment of cognition during postural tasks, such as postural sway effects observed between individuals involved in verbal communication during quiet stance (Shockley, Richardson, & Dale, 2009;
Shockley, Santana, & Fowler, 2003).
METHOD
COP sway was measured in two groups of participants as they stood on horizontal ground and observed a large, uniformly textured surface placed in front of them. It was positioned at one of seven different geographical slant angles between 0 and 90 degrees. One group was asked to estimate the geographical slant of the board in front of them using verbal numerical reports expressed in degrees, whereas the other group was not asked to provide verbal estimates.
Thus, the experimental design was a 2 (Condition: No Verbal Report, Verbal
Report) 7 (Slant: 0, 15, 30, 45, 60, 75, 90 degrees) mixed design, with
Condition as a between-subjects variable and Slant as a within-subjects variable.
Participants
Approval to conduct this study was obtained from the Institutional Review Board at the University of South Alabama. Participants were from the University of South Alabama subject pool. All participants were undergraduate students enrolled in a psychology course. Using random assignment 14 participants (9 males, 5 females) took part in the No Verbal Report group and 17 participants
(3 males, 14 females) in the Verbal Report group. Participants had no known neurological, vestibular, or neuromuscular impairments. They all had normal or corrected to normal vision. Participants were given credits for a lab research course to participate.
Apparatus
An incline was constructed out of a Styrofoam board ( 122 239 5 cm) covered with a green outdoor carpet of uniform texture that was able to adjust to different

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HAJNAL, RUMBLE, SHELLEY-TREMBLAY, LIU
FIGURE 1 Experimental setup. Geographical slant angle ( ˛ ) is the angle between the horizontal ground and the surface propped up in front of the participant. The horizontal surface is defined as ˛ D 0 ı , whereas vertical orientation corresponds to ˛ D 90 ı . Anteriorposterior direction corresponds to COPAP whereas medio-lateral direction to COPML.
geographical slant angles in 15-degree increments in a 0- to 90-degree range, with 0 being perfectly horizontal frontal direction and 90 representing a vertical orientation (see Figure 1 for a schematic of the experimental apparatus). An
AMTI (AMTI, Inc., Newton, MA) force platform ( 463:5 508 mm) sampled at 1000 Hz was used to measure the pressure patterns below the feet. The data were collected and processed via the VICON Nexus 1.6.1 motion capture system
(VICON Motion Systems Ltd., Oxford, UK) and exported as Microsoft Excel
Comma Separated Values Files.
Procedure
After signing the consent form participants would step onto the force platform facing the incline. Prior to each trial, participants were coached to close their eyes and relax while the ramp was set up. The trial began when participants were instructed to open their eyes. They were told to look straight ahead at the board and not to move their head, hands, legs, or any other body parts during the trial. If movement occurred during the trial, the recording was stopped, the data discarded, and the trial was repeated. Their stance was to be relaxed during each trial with no intentional movement. The bottom end of the board was 20 cm in front of the feet. This meant that in the 90-degree condition (vertical orientation) the board was approximately 20 cm in front of the person’s head.
Each trial lasted 30 s with seven different geographical slant angles (0, 15, 30,
45, 60, 75, and 90 degrees) repeated three times in a fully randomized order, with a short break every six trials. In the No Verbal Report group participants

POSTURE AND GEOGRAPHICAL SLANT
289 were simply told to remain as still as possible for the duration of each trial. In the
Verbal Report group participants were asked to provide a numerical estimate of the geographical slant in degrees after each trial. No talking was allowed during the trial recording of COP sway. Participants were asked to close their eyes between trials. Following the end of the last trial, participants were debriefed on the study and were asked for their subjective experience with the task. The first and last 5 s of the COP time series were truncated prior to statistical analysis to remove any effects of transiency.
Participants were not told anything about the physical properties of the ramp surface (e.g., rigidity, material) and were not encouraged to think of the surface as stand-on-able or as a visual reference. At the beginning of each experimental session the experimenter mentioned that the ramp surface was propped up at the back and would not be moved during any trials. The task description was left underspecified with respect to any behaviorally meaningful function (e.g., affordance of stand-on-ability; Fitzpatrick, Carello, Schmidt, & Corey, 1994;
Kinsella-Shaw, Shaw, & Turvey, 1992).
Measures of COP Sway
Our dependent measures were based on time series of the two-dimensional trajectory of center of pressure (COP). The result of vertical forces acting on the surface of support, COP is the collective outcome of the activity of the postural control system and the force of gravity. The recorded data allowed us to compute the standard deviation of COP (measure of the variation in the distribution of the COP position), the range of COP (measure of range of motion of the COP position), the Hurst exponent of detrended fluctuation analysis (DFA; useful to characterize the fractal nature of time series data; for more details see
Peng et al., 1994; Peng, Havlin, Stanley, & Goldberger, 1995), and skewness
(to determine the shape of the distribution of COP displacements). We analyzed the anterior-posterior (COPAP) and medio-lateral (COPML) component of COP separately, except for one measure (COP Ellipse Area) that used the actual twodimensional COP displacement path time series. We expected COPAP to be the most informative measure, as it captured COP sway along the dimension that was most relevant to the experimental manipulation of geographical slant.
Standard deviation of COPAP.
Standard deviation was defined as the average spread around the mean COPAP value for each trial:
SDCOPAP
D v u u u
N
X
.
COPAP n
COPAP / 2 u t n D 1
;
N where N is the number of samples on a given trial.

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HAJNAL, RUMBLE, SHELLEY-TREMBLAY, LIU
COP Ellipse Area.
On each trial the COP displacement time series can be represented as a scatterplot of consecutive COP locations. We defined COP
Ellipse Area as the area of an ellipse covering 85.35% of COP displacement data points based on principal components analysis (PCA; Duarte & Zatsiorsky,
2002). Small values of the ellipse area were interpreted as indicative of more postural stability and vice versa (Chiari, Rocchi, & Cappello, 2002; Huxhold,
Li, Schmiedek, & Lindenberger, 2006).
Hurst exponent of COP time series.
Fractality of COP sway was assessed by the method of detrended fluctuation analysis (DFA), which measures the nature of the total variability in the COP signal. First, the COP time series was converted into a time series of Euclidian distances .d / between subsequent data points (see Figure 2). The next step was to subtract the average value from each sample and thus effectively detrend the nonstationary signal. The Hurst exponent ( H ) is the slope of the regression line that fits the total variability at all measured scales. If H
D
0:5 , then the COP signal exhibits no signs of fractality and can be considered random white noise; if 0:5 < H < 1:0 , then the signal is considered in fractal range. If 0 < H < 0:5 , the signal exhibits antipersistence, or negative long-range correlations, and is considered not random. According to several research groups (Collins & De Luca, 1995; Lin et al., 2008) COP
FIGURE 2 Time series of COP (top part of figure) is converted into time series of
Euclidian distances .d D j COP .i
C 1/ COP .i/ j / , where i indicates the i th sample. DFA computes the Hurst exponent ( H ) that indicates the degree of self-similarity of variability at all timescales. The top part of the figure shows an exemplary COP path in two dimensions, whereas the bottom part of the figure shows how this time series is converted into a onedimensional series of Euclidean distances.

POSTURE AND GEOGRAPHICAL SLANT
291 fluctuations with a Hurst value close to 1 are correlated with increased muscle activity and decline in postural stability.
RESULTS
All analyses employed a 7 (Slant: 0, 15, 30, 45, 60, 75, 90 degrees) 3
(Repetition) 2 (Condition: No Verbal Report, Verbal Report) mixed design analysis of variance (ANOVA). There were no significant effects in the ML direction for any of the dependent measures. In addition, there were no main effects of Condition, suggesting that cognitive activity expressed through verbal reports did not alter the pattern of COP sway. No main effects of Repetition were observed, suggesting that repeated exposure to the task did not result in explicit learning or recalibration to task demands or the experimental manipulation.
Finally, no significant interactions were observed among any of the variables, indicating that the effect of geographical slant might be the result of an additive perceptuomotor process.
Range of COPAP
Range was the crudest measure of variability and highly correlated with standard deviation .r
D
:94/ . We computed range of COPAP as the absolute difference between the two most extreme scores in every trial. The smallest average range occurred in the Verbal Report condition when exposed to a 90 ı ramp ( M
D
14:80 mm, SD
D
7:82 mm). The largest average range was observed in the
No Report condition when viewing a horizontal 0 ı ramp ( M
D
23:49 mm,
SD
D
12:04 mm).
Standard Deviation of COPAP
The main effect of Slant was significant, F .6; 150/
D
7:81 , p < :001 , indicating a steady decrease from 0 to 90 degrees of geographical slant angle (see Figure 3).
A post hoc test using Bonferroni correction (with a criterion p < :0024 ) revealed significant differences between 0 ı versus 45 ı
, 0 ı versus 60 ı
, 0 ı versus 75 ı
, 0 ı versus 90 ı
, 15 ı versus 75 ı
, 15 ı versus 90 ı
, and 30 ı versus 90 ı
.
COP Ellipse Area
The main effect of Slant was significant, F .6; 150/
D
2:56 , p < :022 , indicating a decrease from 0 to 90 degrees of geographical slant angle (see Figure 4), although this decrease was noisier than the range and standard deviation. No post hoc comparisons among geographical slant angles were significant.

292
HAJNAL, RUMBLE, SHELLEY-TREMBLAY, LIU
FIGURE 3 Standard deviation of COPAP. In this and all subsequent figures the No Verbal
Report condition is indicated by “No Report” (full circles), whereas the Verbal Report condition is labeled “Verbal Report” (empty circles) in the legend. Error bars correspond to ˙ 1 standard error.
Hurst exponent of COP time series.
The main effect of Slant was significant, F .6; 150/
D
6:10 , p < :001 , indicating a steady decrease from 0 to
90 degrees of geographical slant angle (see Figure 5). Large geographical slant angles resulted in increased fractality (with values closer to 1) compared with smaller angles. A post hoc test using Bonferroni correction (with a criterion
FIGURE 4 Ellipse area of total COP sway. Error bars correspond to ˙ 1 standard error.

POSTURE AND GEOGRAPHICAL SLANT
293
FIGURE 5 Hurst exponent of the time series of COPAP based on detrended fluctuation analysis. Error bars correspond to ˙ 1 standard error.
p < :0024 ) revealed significant differences between 0 ı
90 ı
, 15 ı versus 90 ı
, 30 ı versus 90 ı
, and 60 ı versus 90 ı
.
versus 75 ı
, 0 ı versus
Verbal Reports
Figure 6 plots perceived geographical slant against actual geographical slant angles and indicates that perceived geographical slant was linearly correlated with actual geographical slant .r
2
D
:952/ . Perception was well calibrated to actual slant (with regression slope near 1), albeit with a large intercept (18.0
degrees). This large offset might have been due to a number of factors, including lack of knowledge about geometry and other cognitive biases not controlled for in the study.
DISCUSSION
Several standard measures of postural stability offered converging evidence that COP sway gradually decreased as geographical slant increased from zero
(horizontal ground) to 90 degrees (vertical wall). The nonlinear fractal dynamics of COP sway, as measured by the Hurst exponent of COPAP, pointed in the same direction: more fractal patterns, known to be correlated with increased muscle activity and decline in postural stability, were measured for shallower surface slants (Amoud et al., 2007; Collins & De Luca, 1993; Lin et al., 2008).
There were no effects of Condition in any of the measures, suggesting that

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HAJNAL, RUMBLE, SHELLEY-TREMBLAY, LIU
FIGURE 6 Perceived versus actual slant. Error bars correspond to ˙ 1 standard error.
explicit perception of slant (expressed through the cognitive process of verbal estimation) does not bias postural stability above and beyond the effects of visual environment.
We see our work as an extension of the classic demonstration of “optical push” (Lishman & Lee, 1973; Shaw & Kinsella-Shaw, 2007) in which visual information influences bodily posture through visual kinesthesis. In Lishman and
Lee’s (1973) demonstration subtle changes in optic flow patterns were generated by a moving a vertical surface in front of the observer that brought about postural adjustments. Even though in our study the visually inspected surface remained static during each trial, we believe that minute postural sway still occurred due to subtle body movements. Upright quiet stance exhibits dynamic stability that undergoes continuous postural adjustments. These adjustments are performed by minute body movements that include head movements as well. For the most part these are not conscious movements; however, they still generate optic flow patterns as a function of our surroundings. This is true for both static and dynamically changing surroundings. As such, upright stance cannot be considered an absolutely static case of perceptuomotor control. One way to describe upright stance would be to say that the body is an inverted pendulum that is inherently unstable and would be in constant danger of falling or collapsing if muscular forces did not continuously adjust body segments.
These bodily adjustments generate optic flow. The rate of change of such optic flow is faster when looking at nearby objects and surfaces. One way to become more stable would be to generate less optic flow at a slower rate of

POSTURE AND GEOGRAPHICAL SLANT
295 change. This can be accomplished by moving (swaying) less around the basis of support. When the geographical slant angle gets closer to zero (horizontal ramp orientation) the optic flow changes more slowly for the same amount of body sway compared with steeper (and nearer) ramp surfaces. That is perhaps why the postural system can afford to generate sway of larger amplitudes at geographical slant angles close to zero without measurable decrease in perceived postural stability. These slower optic flow patterns specify potential impact with a surface at a later time than do steeper nearby surfaces. According to the geometrodynamical interpretation of Shaw and Kinsella-Shaw (2007) this specification of impact (future contact) activates more varied inertial forces in wide-open spaces than at close quarters.
Here is how a typical sequence of postural adjustments might take place:
Sway forward creates diverging optic flow. Because the person is not aware of his or her own miniscule movements he or she interprets the optic flow pattern to specify a surface that is approaching the eye. Thus, visual information specifies that one should lean backward to zero out the expanding optic flow. This work is done by activating the inertial force that “optically pushes” the individual backward. The person usually overcompensates and creates a converging optic flow that specifies a surface moving away from the observer. This cycle of oscillation repeats many times during the course of a trial, and the cycle is
“fueled” by the inertial forces that work to balance out optically specified postural configurations. It is plausible to assume that a significant part of visual control of upright stance involves the just described dynamic process of “keeping tabs” on the miniscule changes in optic flow patterns by way of nonconscious postural sway.
What is the nature of the visual information that specifies postural sway?
Although our study did not address this issue directly, it is safe to say that detecting subtle changes in optic flow are crucial to maintaining postural stability. Is the optic flow generated during postural sway a function of distance, geographical slant, or both? Although the effect of distance of visually perceived objects on postural stability is well documented (Bonnet, Temprado, et al., 2010;
Stoffregen, Pagulayan, Bardy, & Hettinger, 2000), it is not clear whether our present results are exclusively accounted by this effect. In past research on the effects of distance on posture target objects were relatively small and clearly delineated with respect to the background surface. In our experiment there were no explicit targets apart from the ramp surface that covered large portions of the visual scene. It is possible that surface slant has an effect on posture that is independent of the effect of distance. Is the effect of geographical slant the result of changes in orientation or distance? In our task, we did not have an explicitly delineated target that participants had to focus on. As a result, we do not know which part of the surface participants looked at during any given trial.
It is possible that on some occasion they could have looked down and near, or

296
HAJNAL, RUMBLE, SHELLEY-TREMBLAY, LIU far and up, or at any other location on the surface. It is also possible that their gaze direction may have changed several times during a single trial. Thus, the eye-surface distance was underspecified, and any correlation between eye gaze location and geographical slant was considered unsystematic, as it would under natural circumstances during visual inspection of ambient surfaces. However, the potential effect of distance cannot be discounted altogether because the average eye-surface distance was highly correlated with geographical slant.
Distance would be perfectly correlated with geographical slant angle if the participant chose to fixate his or her gaze at the same relative location on the ramp at all times. For example, suppose that the participant always chose to look at the midpoint of the ramp (4 ft from the base of the ramp). Then the correlation between distance and geographical slant angle would be 1. But because the experimental instructions did not specify where one should look, it was highly unlikely that participants consistently looked at the same spot.
If we assume that gaze direction was random, then the distance-geographical slant angle correlation would end up being somewhat lower (between 0.8 and
0.93, for a person of average height, 1.65 m, based on our calculations that included random gaze direction on each trial). However, it is also possible and very likely that participants looked at several locations during each trial, thus compounding the difficulties in mapping distances to geographical slant angles.
Allowing unrestricted eye movements would weaken the distance-geographical slant angle correlation even further. In everyday circumstances, such as viewing real hills and slopes, the eye-surface distance and the geographical slant angle are naturally highly correlated. In fact the information for perceiving the affordance most intimately related to geographical slant, namely, stand-on-ability, has to be inherent in the texture gradient pattern of the surface. This is true for both visual gradients and haptic gradients of tool use (see p. 281 in Fitzpatrick et al., 1994).
Furthermore, thanks to the thoroughgoing geometrical analyses undertaken by
Cutting and Millard (1984) the definitions describing various types of texture gradients include both geographical slant angles and distance (e.g., see Equations
1, 2, and 3 in Cutting & Millard, 1984). In summary, the question of whether perception relies on distance or geographical slant is superseded by the question of how perception is specified by the higher order variable of texture gradient that contains both lower order variables of distance and geographical slant.
The optic flow patterns generated by postural sway specify actions (such as the direction of sway) but also contain information about the spatial layout of surfaces via projections of changes in texture gradients that modulate the magnitude of postural sway. It is also worth noting that the detection of global optic flow patterns and global texture gradients is not completely viewpoint specific. This means that the same optic flow information can be detected by looking at many different parts of the ramp surface. As a consequence, in the present task optic flow and texture gradient patterns of slanted surfaces may be

POSTURE AND GEOGRAPHICAL SLANT
297 invariant over eye movements. Participants in our study stood still and did not make large postural adjustments; nevertheless our data showed that posture was differentially influenced by a variety of static visual surroundings in subtle ways.
Our results are not without precedent in recent investigations of postural sway.
Palatinus, Kelty-Stephen, Kinsella-Shaw, Carello, and Turvey (2014) showed that even the most minimal postural adjustments carry significant meaning and are specific to well-defined perceptual tasks, such as judging whole and partial length of objects. Paralleling our present findings, these postural adjustments were exhibited through complex patterns of COP fluctuations as revealed by multifractal measures. We consider our present contribution an existence proof that changes in pseudostatic optic arrays constituted by slanted surfaces engage the postural system and influence its variability even in the absence of focal visual targets, or explicit tasks beyond that of maintaining upright stance.
What is the role of fractality in postural control? Several researchers have pointed out that fractality emerges in postural control whenever active management of sway is needed, such as in the case of moving visual fields (Isableu,
Fourre, Vuillerme, Giraudet, & Amorim, 2011). Collins and De Luca (1993) suggested that there are two basic neuromuscular control strategies for maintaining upright stance: open-loop and closed-loop strategies. Open-loop strategies are associated with higher levels of stochasticity and carry a higher level of fractal signature. We observed higher fractality during exposure to wide-open visual fields (close to zero degree geographical slant). We concluded that in the absence of nearby visual anchors and detailed visual arrays the postural system utilizes fractality to establish and maintain postural stability.
Our results are consistent with Collins’ and De Luca’s (1993) findings and point to the need for more extensive empirical investigation beyond the scope of the present article. It is worth noting that in our study there were no targets that could have served as visual anchors. Therefore, it is unclear whether visual anchors play an active role in stabilizing posture or is it the nearby surfaces themselves, or perhaps both.
We found that COP sway is not explicitly influenced by the cognitive activity of assessing slant magnitude. The absence of effects of Verbal Report may indicate that the proposed neuromuscular control strategies are fairly autonomous.
After all, during quiet stance posture is usually maintained automatically by the peripheral nervous system that receives minimal input from conscious volitional centers in the brain. This finding is an intriguing counterpoint to a host of recent studies that argue for the embodiment of cognition as revealed by postural adjustments (K. Dijkstra, Eerland, Zijlmans, & Post, 2012; Riley, Mitra, Saunders,
Kiefer, & Wallot, 2012; Shockley et al., 2009) and to interpretations that consider the postural control system dependent on suprapostural tasks (Stoffregen et al.,
2000). Whereas Stoffregen et al. (1999) showed that merely attending to a visual target can significantly stabilize posture, K. Dijkstra et al. (2012) demonstrated

298
HAJNAL, RUMBLE, SHELLEY-TREMBLAY, LIU that implicit body orientation to the right or left had an effect on categorization of political affiliation using a spatial metaphor (right- vs. left-wing party), an example of high-level abstract thought influenced by posture. The fact that the addition of verbal judgments in our study did not result in significant postural changes indicates that not all cognitive activity is embodied in the same way, if at all, and that further studies are needed to uncover the diversity of linkages between cognition and bodily states.
The long-term goal of the present demonstration was to lay the foundation for applied research in ergonomics for the design of safe environments whose surfaces and orientations could potentially stabilize posture and gait (e.g., diminish vertigo and motion sickness and decrease fall risk) through visual and somatosensory control. Static and dynamic visual arrays are a powerful source of information for postural stability worth investigating for the benefit of many patient populations. The present experimental paradigm was also conceived of as a foundation for future studies of affordance perception (such as stand-onability). Indeed, one of the long-term goals of this paradigm is to explain how information in static visual arrays constituted by surfaces at different distances and orientations factors into affordance perception, an issue first raised by Gibson
(1979/1986). Along the way, we also wanted to test how explicit cognition about our environment (such as judging the slant of surfaces) may or may not factor into our embodied presence and behavior. The hope is that postural effects of visual arrays similar to those found in the present study will contribute to the understanding of the interplay of perception, action, and cognition in goaloriented behavior.
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