We already know from Prinzmetal et al. (2001) that tilting the Ponzo, Zollner and Poggendorf illusions increase the magnitude of the illusion. We also know that tilting the participant increases their perception of the illusion strength. Combining these two processes, tilting both the stimuli and the participant also increases the magnitude of these particular visual illusions. This is known as the tilt-constancy theory. These findings contradict explanations of these illusions, that are based on linear perspective theories (Gillam, 1980; Gregory, 1963) and fatigue and inhibition of orientation detecting cells (Blakemore et al., 1970). The data presented in the Prinzmetal et al. (2001) study suggest the most significant aspects of these illusions is our ability to perceive orientation. However, when tested in the same experimental process, the Brentano version of the Muller-Lyer illusion did not produce statistically significant results to support the tilt-constancy theory.
Could this effect be due to the complexity of that particular version of the Muller-Lyer illusion? The Brentano version of the Muller-Lyer has two segments, each pushing in opposite directions from one another, which creates a far more complex illusion than any version of the Muller-Lyer illusion. Also, the Muller-Lyer illusion is most often associated with (Gregory & Harris, 1975) constancy scaling theory, rather than mechanisms relying on orientation. However, previous findings (Asch & Witkin, 1948) as well as the results of the Pinzmetal et al. 2001 study, indicate that when a person is not in their usual upright position, they rely more on information obtained from their visual system. Perhaps the complex Brentano version of the Muller-Lyer illusion produced a stronger illusion than simpler versions of the illusion, thus reducing the effects of tilting.
Therefore, the experiment tests simpler variations of the Muller-Lyer illusion to find first, if the tilt-constancy theory holds true with any variation of the Muller-Lyer illusion and secondly, if it does produce an effect, where the effect appears strongest.
Participants. Twenty-five participants who are all students from Alma College between the ages of 18-22. The ratio of males to females was about equal. All participants had normal or corrected eyesight.
Apparatus. The stimuli were presented on a Macintosh computer with screen dimensions of 32 cm x 44 cm, through the EyeLines 3.2 program. Participants were seated in a plastic chair, approximately 72 cm from the computer screen. In the tilted condition of the experiment, each participant was tilted 10 degrees clockwise by placing a wooden platform underneath the chair. The dimensions of the platform are 55cm x 30 cm x 10 cm, and the computer screen will be tilted 10 degrees clockwise. The participants were told to keep their head aligned with their body. In the untilted condition, the participant was seated in the chair with no ramp underneath the chair and the computer screen was in its usual upright position. Both experimental conditions were done on a computer in a dark room.
Stimuli. The stimuli were presented as white lines against a black background. They were presented twice, once in a tilted condition and again in an untilted condition. The order in which each participant undergoes a particular experimental condition was randomized. Each experiment contains exactly the same images, however, each time the experiment was done, and the order in which each stimulus was presented was random.
The stimuli include the Zollner illusion as well as a Zollner control to measure the effect of tilting. Both Zollner illusion and Zollner control are 159 mm, with approximately 19.13 mm between each intersecting line. The lengths of the intersecting lines vary, but average to 14.3 mm (see figures 1 & 2). Included as well are three simple variations on the tails-in Muller-Lyer illusion as well as a control for the Muller-Lyer. The length of the tails on the Muller-Lyer illusion 25.5 mm and the long segment is 127.5 mm (see figures 3, 4, 5 & 6). Each stimulus will be presented twice in each experimental condition.
Fig. 1 Zollner Illusion
The bottom line in both figures 1 and 2 will be moved up and down to adjust parallelism.
Fig. 2 Zollner Control
Fig. 3 Muller-Lyer Control
The bottom line, in figures 3-6, will be moved left and right to adjust lenght.
Fig. 4 Muller-Lyer Single Tail
Fig. 5 Muller-Lyer Two Tails
Fig. 6 Muller-Lyer Four Tails
Procedure. Each participant was presented with a total of 18 stimuli per experiment, which made a total of 36 stimuli presented total. The participant first underwent either a tilted condition or an untilted condition, and then underwent the other condition. In either case, the participant entered their initials into the Eyelines program and pressed a key on the keyboard to advance to the experiment.
To adjust each stimuli, the participant moved the mouse either up or down to adjust parallelity in the case of the Zollner illusion and the Zollner control or left or right to adjust the length in any of the Muller-Lyer variations or control. Once satisfied with the image on the screen, the participant was instructed to press any key, excluding the space bar key, on the keyboard to move on to the next image. When the participant completed one experimental condition, the physical environment was changed to meet the criteria for the next condition, either tilted condition to untilted condition or the untilted condition to the tilted condition and they will underwent the same process.
Tilting did not appear to have a significant effect on either the Zollner illusion (see figure 7) or the Muller-Lyer illusion (see figure 8).
Fig 7. Strength of the Zollner Illusion in the upright condition compared to the strength of the Zollner Illusion in the tilted condition.
As illustrated by Figure 7, tilting the Zollner Illusion did not have much of an effect on the magnitude of the illusion. The mean value for the control illusion in the tilted condition is approximately .5 degrees, while the mean value for the Zollner illusion in the tilted condition was approximately .64 degrees, a little higher. These results suggest that tilting did not have much of an effect on the Zollner illusion. However, several participants did mention that they could determine parallelism by simply lining up the pixels of the line on the screen, rather than allowing the illusion to influence their perception, which may account for the non-significant results.
Figure 8 illustrate the results from the Muller-Lyer trials, after the control values have been subtracted from them to find the error purely due to the illusion itself.
Fig. 8 Strength of the Muller-Lyer Illusion in the upright (horizontal) condition compared to the strength of the Muller-Lyer Illusion in the titled condition based on the number of tails
The effects of tilting do not seem to have much, if any, effects on the strength of the Muller-Lyer illusion. For the horizontal condition, the mean value of the one-tailed variation of the Muller-Lyer illusion was approximately 7 mm too short; for the two tailed variation, approximately 70 mm too short; and for the four tailed variation, approximately 131 mm too short. For the tilted condition, the mean value for the one tailed variation of the Muller-Lyer illusion was approximately 10 mm too long; for the two tailed illusion, approximately 80 mm too short; and for the four tailed variation, approximately 175 mm too short. The only values that appeared as though they could possibly be significant were the two values for the four tail Muller-Lyer. A paired T-test showed that the results were not significant, with t(22) = -.184 and p > .05.
I hypothesized that tilting the participants would increase the magnitude of the Muller-Lyer illusion with two tails and four tails, because the one tail variation is very similar in appearance to the control stimuli. It appears, that there is a slight effect with the two-tail Muller-Lyer, and a stronger effect in the four-tail Muller-Lyer; however, the difference is not significant. This is consistent with the results found by Prinzmetal et al. (2001), and in their article, they suggested several reasons as to why tilting may create such and increase in illusion magnitude. They suggested that tilting the observer increases their reliance on visual cues, while decreasing the impact of gravity on perception. However, this suggestion raises the notion that any position not in line with gravity would affect perception. Goodenough et al. (1981) tested this theory on the rod and frame effect by having participants complete the rod and frame task in an erect position as well as a supine position, and found that lying in a supine position does increase the rod and frame effect, which suggests that the interference of gravity would similarly affect other illusions. This did not affect the Muller-Lyer illusion, most likely because this illusion is thought to operate on other mechanisms, such as size-constancy theories (Gregory & Harris, 1975).
The difference between illusions that rely on visual cues, orientation and linear perspective, as do illusions such as Zollner, Ponzo and Poggendorf illusions, and illusions that are a result of size-constancy theories, such as the Muller-Lyer illusion by Prinzmetal et al (2001). They found that illusions that had significant results in tilt-orientation experiments produced opposite effects in experiments that tested size constancy, suggesting that these two theories work by completely opposite mechanisms, which accounts for non-significant results in the Muller-Lyer illusions.
Another suggestion put forth by Prinzmetal et al. (2001), is how one perceives eye level and how that relates to their perception of horizontal and vertical. This concept has been tested in numerous studies, and they have all found that environment will affect where one will perceive eye level, for example, when participants are looked at something that is pitched down, they will indicate that their eye level is lower than it really is. Many wonder whether that the neural mechanisms that detect eye-level are the same as the ones involved in detecting horizontal and vertical. As far as I know, no research on this topic has been done. However, if this is the case, it offers some explanation as to why tilting may increase illusion strength. If a person is tilted, then their concept of horizontal and vertical would be thrown off, which may somehow affect where they perceive eye-level, so when they feel as though they are looking directly at the stimuli, they may actually be looking a little above or a little below the actual stimuli, which could impact their ability to perceive length. Since this does not produce a particularly strong effect, that could explain the slight, but not significant, differences found in this experiment.
The most prominent theory discussed by Prinzmetal et al. (2001) consist of a family of theories put forth by many other researchers, such as assimilation theory (Pressey, 1971) and normalization theory (Gibson, 1937). These theories look at the neural mechanisms that may be involved in tilting and perception, and the fact that some studies (Sauvan and Peterhaus, 1995) found that in animals, that visual cues regarding orientation may be taken more from the environment rather than from retinal images. What this basically means is that if a particular neuron increases itŐs firing rate when exposed to vertical stimuli, and from lateral inhibition, it will also respond to nearly vertical stimuli. So, if the stimuli contains a nearly vertical line, then neurons that respond to vertical lines, would also fire, which may somehow trick the brain into processing the nearly vertical line as a vertical line.
How would this affect the tilted Muller-Lyer illusion? When the participants attempted to adjust the lengths of the lines in the Muller-Lyer illusion, they would often draw imaginary vertical lines with their eyes or their fingers down from the top of the line to the adjustable line to gauge distance. However, if their orientation and perception of vertical and horizontal were warped, then perhaps when the imaginary vertical lines were drawn, they were not truly vertical, but pushed slightly inward. Since neurons that respond to vertical lines also respond to nearly vertical lines, the brain could have believed that these lines were, in fact vertical and they had accurately judged the length of the lines, when in reality, they had estimated the line length to be too short, which again, could account for the slight difference found in the two and four tailed variations of the Muller-Lyer.
This theory also provides insight as to why the original testing of the Brentano version of the Muller-Lyer illusion, which not only provided non-significant results, but also results that showed the illusion had weakened due to tilting. Since the Brentano version has tails pushing both in and out, and participants were asked to move the middle tail, that creates both a tails in and tails out effect, to bisect the line, any imaginary vertical line they may have drawn to gauge the lengths would have been countered by the two forces of pushing in and pushing out. This also explains why the results were less noticeable in the one tail and two tailed variations in this test. Since there were no other forces acting on the perception of vertical or horizontal other than the forces described above, participants were able to more accurately gauge length. However, the effect of tilting on any variation of the Muller-Lyer illusion thus far, has proved to be not significant.
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Prinzmetal, W. and Beck, D. M. (2001). The tilt-constancy theory of visual illusions. Journal of Experimental Psychology: Human Perception, 27, 205-217.
Sauvan, X. M., & Peterhaus, E. (1995). Neural integration of visual information and direction of gravity in prestriate cortex of the alert monkey. In T. Mergner & G. Hlavacka (Eds.), Multisenory control of posture (pp. 43-49). New York: Plenum Press. In Prinzmetal, W. and Beck, D. M. (2001). The tilt-constancy theory of visual illusions. Journal of Experimental Psychology: Human Perception, 27, 205-217.
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