Most Findings Obtained With Untimed Visual Illusions Are Confounded

Participants

To provide robust power and reproducibility, we ran two independent studies and enrolled as many participants as feasible—in light of the constraint that they were all unpaid volunteers, separately recruited and tested individually in the same laboratory. Most were university students of various scientific disciplines. Data were collected over 6 years (Study 1: 2014–2015; Study 2: 2016–2019) by experimenters blind to the study hypotheses. A total of 263 adults (138 women and 125 men; median and mean age = 22 years, range = 18–30) participated in Study 1, and a total of 290 adults (195 women and 95 men; median and mean age = 23 years, range = 19–62) participated in Study 2. Each sample therefore included more than twice the number of participants used in Bressan and Kramer’s (2013) study. The experimental procedures were approved by the University of Padova’s Psychological Research Ethics Committee and were in accordance with the Declaration of Helsinki (seventh revision). All participants gave written informed consent.

Apparatus and stimuli

In both studies, stimuli were presented in a dark or dimly lit laboratory on a calibrated Perfect Color 22 CRT monitor (manufactured by Quato) with a 22-in. screen shielded by a custom black hood. We used a pairwise-comparison paradigm with a fixed stimulus and a variable one with four possible values. In the two studies, we presented slightly different values at the ends of each spectrum so as to expand the overall stimulus range and increase measurement sensitivity.

The stimuli for the Ebbinghaus illusion (Fig. 1, left) were two white target disks centered on adjacent black squares (15.5 × 15.5 cm). One target was surrounded by large disks (diameter: 50 mm in Study 1 and 45 mm in Study 2) and the other by small ones (diameter: 12 mm in Study 1 and 10 mm in Study 2). The size of the target surrounded by large disks was fixed (diameter: 25 mm). The diameter of the other target—which tends to look larger—varied and was 21, 22, 23, or 24 mm in Study 1 and 20, 21, 22, or 23 mm in Study 2. The position (left vs. right) of the variable half of the stimulus was counterbalanced within and between participants.

The stimuli for the lightness illusions (Fig. 1, right) were two small target squares (both 6.4 × 6.4 cm) centered on two large background squares (both 16 × 16 cm) sitting side by side and surrounded by a dark frame (gray-scale value = 55). In the case of double decrements, the backgrounds were white (gray scale = 255) and medium gray (gray scale = 153). The gray-scale value of the target on gray was fixed (gray scale = 102). The gray-scale value of the target on white—which tends to look darker—varied and was 117, 122, 125, or 127 in Study 1 and 123, 125, 127, or 129 in Study 2. In the case of double increments, the backgrounds were black (gray scale = 0) and light gray (gray scale = 200 in Study 1 and gray scale = 180 in Study 2). The gray-scale value of the target on gray was fixed (gray scale = 222). The gray-scale value of the target on black—which tends to look lighter—varied and was 205, 208, 211, or 214 in Study 1 and 211, 213, 215, or 217 in Study 2. The position (left vs. right) of the variable half of the stimulus was counterbalanced within and between participants.

Procedure

Data were collected as part of two larger studies, but the experiment reported here was always presented first. Each illusion (double increment, double decrement, and Ebbinghaus, in that order) was shown in two blocks of four trials each, for a total of eight trials per illusion and 24 trials overall. Presentation time was a single second in one block and unlimited (allowing “ad-libitum” inspection) in the other, and the order of the two blocks was counterbalanced across participants. In both the 1-s and ad-libitum conditions, the participants were to press a key if they perceived the target on the left (“Z” key) or the right (“M” key) to be lighter in the double-increment illusion, darker in the double-decrement illusion, or larger in the Ebbinghaus illusion. At the start of each block (1 s or ad libitum), participants were presented with the general instructions for that block and pressed the space bar to begin. Before each stimulus, they were shown a 2,500-ms reminder about whether they had 1 s or unlimited inspection time.

In the 1-s block, the stimulus disappearance was followed by the instruction to press either the left or the right key. In the ad-libitum block, participants were asked to hit the space bar as soon as they had decided which target was lighter, or darker, or larger. There was no time pressure. After hitting the space bar, participants were shown the instruction to press either the left or the right key.

Methodological implications: mix-ups in global-local processing

A series of well-cited studies investigated global versus local processing of visual stimuli and compared seminomadic Himba tribesmen from Namibia with British undergraduates (and other urbanites; see Caparos et al., 2020). The Ebbinghaus illusion was smaller (Caparos et al., 2012) and classical lightness contrast larger (Linnell et al., 2018) among the Himba than among the British. These effects were attributed to a stronger local (as opposed to global) bias among the former than the latter, ascribed in turn to their traditional rather than urban lifestyle. The implication that urban experience may influence visual illusions is remarkable, particularly as regards something so very basic as lightness contrast.

Yet because inspection time in these studies was neither controlled nor considered, a less provocative interpretation presents itself. Traditional Himba are so removed from the modern world that they even lack names for geometric shapes such as circles and squares (Davidoff et al., 2008). Understandably, they are also quite unaccustomed to being asked to perform exotic cognitive tasks in exchange for sugar and flour. It thus seems likely that they would find participating in such experiments more interesting than do British university students. One way in which greater engagement can express itself is more time spent on the task (Huang et al., 2012; Wise & Kong, 2005). In reaction time experiments, in fact, the Himba proved significantly slower and less distractible than British undergraduates (de Fockert et al., 2011; Linnell et al., 2013). Hence, it is perfectly possible that the Himba might also have taken longer than the British to inspect the illusions. Our own findings suggest that this would lead precisely to a weaker Ebbinghaus illusion and a stronger lightness contrast.

Three separate findings suggest that the unusual performance of the Himba may indeed be driven not by some “local bias” rooted in their intimate relationship with nature but, more simply, by their greater attentional engagement. First, the Himba matched constellations of squares and crosses (after Navon, 1977) more by their local elements than by their global shapes; but such “local” choices turned out to be uncorrelated with the allegedly “local” choices they had previously made with the Ebbinghaus illusion (Caparos et al., 2012), calling into question whether these two sets of responses truly have the same cause. Second, when explicitly asked to identify either the local elements or the global shape of such constellations, the Himba outperformed British psychology students in both tasks (Caparos et al., 2013). Third, in reaction time experiments that required attending to a target and ignoring distractors (Linnell et al., 2013), the Himba outperformed the British when the task was relatively boring to students (determining whether an arrow points left or right) but not when it was “engaging or interesting” (p. 1245) to the Himba and British both (determining whether a face is Black or White).

In our present study, as well as in most of the Himba studies, optimal performance requires disregarding context, which takes effort. One can expend this effort by looking at the stimulus for longer or by concentrating on it harder. Thus, we predict that participants’ motivation to respond carefully (their response effort; Huang et al., 2012) will change visual illusions in much the same way as does spontaneous inspection time, even when such time is held constant. This implies that the strategy of matching subgroups of Himba and urbanites by their response times (as has been done, for example, to allay concerns of speed/accuracy trade-offs in reaction time experiments; de Fockert et al., 2011; Linnell et al., 2013) is inadequate for dismissing engagement as an explanation. And of course, whereas the idea that urbanization could affect visual illusions is very provocative, the idea that urbanization could affect engagement and engagement affect visual illusions is rather less so—especially if “urbanization” turned out to simply reflect a different attitude of urbanized and nonurbanized people toward experiments.

Theoretical implications: the timeline of grays

Our finding that lightness contrast depends on inspection time for increments but not for decrements has important repercussions for theories of lightness. As far as we can tell, none of them is capable of accommodating this finding except the double-anchoring theory (Bressan, 2006, 2007).

The primary problem in lightness perception is that we cannot “see” the percentage of light a region reflects (its reflectance or gray shade) but only the amount of light it reflects (its luminance), which depends on both reflectance and illumination. To tell them apart, we must rely on a regularity of nature: Light sources tend to illuminate not only the region of interest but also nearby ones. Thus, taking into account the target’s luminance relative to that of its neighbors helps discount the illumination they share. Double-anchoring theory proposes a mechanism to determine which regions are likely to be sitting under a common illumination. Within this shared-illumination framework, the target’s luminance is anchored twice: once to the other regions (the target’s surround) and once to the highest luminance. The target:surround and target:highest-luminance ratios are then averaged. Note that both anchors are defined as white (though neither necessarily appears white in the end). Thus, anchoring establishes not only the target’s relative luminance but also its specific lightness—which in the model can range from black to luminous superwhite. (For a discussion of highest-luminance anchoring by itself, see also Gilchrist et al., 1999; Wallach, 1948.)

Surround anchoring is weighted relative to highest-luminance anchoring to express the surround’s importance: how much information about the illuminant it is likely to be supplying and how reliable this information is. For example, a larger and more irregular surround tends to provide more information than a small, uniform one. And a bright surround (which is likely to be getting plenty of light) tends to provide more detailed, better-quality information than one that is dim (and likely to be poorly lit). In the exact same vein, a surround that is inspected for longer tends to provide more accurate and reliable information than one that is seen only very briefly.

In the model, decremental and incremental lightness contrasts are rather different. The double-decrement illusion (Fig. 1, top right) is brought about in full by either anchoring. Surround anchoring computes the target as darker when it sits on white rather than on gray, because the target:surround luminance ratio is lower. Highest-luminance anchoring does that too, because—for decremental targets—the local highest luminance is the surround itself. When the relative weight of surround anchoring increases, therefore, the double-decrement illusion is expected to neither increase nor decrease. Instead, the double-increment illusion (Fig. 1, bottom right) is entirely due to surround anchoring: The target is computed as lighter when it sits on black rather than on gray, because the target:surround luminance ratio is higher. Highest-luminance anchoring produces no illusion, because both targets are the local highest luminances and thus defined as white. When the relative weight of surround anchoring increases, therefore, the double-increment illusion is expected to increase as well.

Both predictions are corroborated by evidence that whatever one does to augment the weight of the surround (e.g., enlarge it or make it less homogeneous; Bressan & Actis-Grosso, 2006; Schirillo & Shevell, 1996) increases contrast illusions with increments but has no effect on those with decrements. Exactly the same is expected to happen if the illusion-inducing surround acquires more weight by being looked at for longer than a glimpse.

Thus, double-anchoring theory accounts effortlessly for two counterintuitive findings. First, a longer inspection time—which is bound to increase the visual information available for processing, at least over the first few seconds—can make lightness perception less rather than more veridical. Second, this general effect entirely depends on whether the object whose color is being assessed is brighter or dimmer than its surroundings.

Conclusion

Much research relies on visual illusions to either build theories of them or explore differences in people’s perceptual or cognitive styles. Here, we have shown that the experience of visual illusions depends on how long they are looked at—in ways that are specific to each illusion and can be highly counterintuitive. Theories that cannot account for this fact are incomplete; studies that ignore it, confounded.