Affect of the Zollner Illusion on the Muller-Lyer

Joshua J Moffat, 10jjmoff@alma.edu, Alma College, Alma, Michigan


Introduction:

The Muller-Lyer illusion is simply constructed by two parallel lines of the same length, one with outward fins, and one with inward fins. The line with the outward fins (obtuse angled) is almost always perceived as being longer than the inward (acute) (fig 1). One aspect of the illusion is that the angle of the fins affects the strength of the illusion (e.g., Lewis, 1909; Dewar, 1967; Presey & Martin, 1990). It has been found through several experiments that the illusion of the obtuse and acute angled stumuli are directly affected by the angle of the fins. (Presey & Martin (1990)).


(Fig 1) The Classic Muller-Lyer Illusion

The Presey and Martin experiment was done with the test lines (with fins) next to a control line of the same length (no fins) If the illusion is strengthened directly by adjusting the angles of the fins, then why not see if something like the Zollner illusion will affect the angles of the fins which will in turn affect the strength of the illusion. The Zollner illusion can be several parallel lines with cross hatching intersecting the lines. The cross hatchings will be at different angles on each line. This illusion makes the parallel lines look nonparallel (fig 2). If we were then to put these Zollner like cross hatchings on the obtuse or acute angled fins of the Muller-Lyer illusion, would it affect our appearance of the angle of the fins? In study done by Chung Chiang (1968), it was found that when two objects are close enough, their two images overlap so as to form one image located at a position somewhere between the two original images. So in the Zollner illusion, the line you see is somewhere in between the angle of the actual line and the angle of the cross hatch and no longer looks parallel to the other lines. However, will the shorter length fins still be affected as much as the longer parallel lines in the Zollner illusion? If they are, will the crosshatches ultimately affect the strength of the illusion?


(Fig 2) The Classic Zollner Illusion




Methods:

Hypothesis: The addition of the Zollner illusion will directly affect the appearance of the angle of the fins and ultimately change the length of the line as we would see it.

Participants: Fifteen fellow classmates to be test subjects.

Apparatus and Stimuli: To make the experiment I started by using a computer program designed by Dr. Walter Beagley from Alma College Called Eye Lines. This program allowed one to create an illusion from an existing illusion or a new one, and then run the experiment. The participant has the responsibility of adjusting the control variable with a mouse to match the experimental variable.

Procedure: The fifteen participants came in one at a time to look at the appearance of three different stimuli. They first compared the control line to the experimental line and adjusted it with a mouse to where they thought their lengths were the same (Fig 1:Experimental). The experimental line had Zollner like cross hatches set at 40 degrees on the fins. They then adjusted the opposite control line the same way (Fig 2: Opposite).This line had Zollner cross hatches set at 70 degrees. After the participant adjusted the control line in both the experimental and opposite (Fig 1 & Fig 2) they were then asked to adjust the control line in the basic version (Fig 3:Basic) of the Muller-Lyer Illusion. This tested the strength of the Illusion itself, without the Zollner cross hatches.


Fig 1(Experimental)


Fig 2(Opposite)


Fig 3 (Basic)

Results:

After reviewing the data I concluded that the Zollner cross hatches do actually affect the angle of the fins in the Muller-Lyer. However they affected them in a different way, and only showed a difference on the experimental (Fig 2) stimulus.The figure labeled (Opposite) who had cross hatches set at 70 degrees had an illusion strength of almost the same as the normal tails in version of the Muller-Lyer. The basic figure was simply the normal Muller-Lyer (tails in version). The figure labeled (Experimental) however, showed some what of a difference in the strength of its illusion. The experimental figure had cross hatches set at 40 degrees. Although it showed a difference, it was not what I expected. The illusion of this figure was actually weakened. Therefore the cross hatches made the subject perceive the arrows being wider than what they really were, in return making it appear larger. So they pretty much counteracted the affect of the Muller-Lyer illusion. As you can see in the line graph below (Graph 1) the (experimental) figure was perceived as being 85mm longer than the (opposite) figure. There for the Zollner cross hatches on the (experimental) figure actually weakened the illusion.


(Graph 1) Illusion Strength of the Three Stimuli


Discussion: 

Though I expected that adding the Zollner illusion to the Muller-Lyer would have an affect on the strength of the illusion, it was surprising to find that it affected it how it did. The best answer to this problem is that the Zollner cross hatches made the angle of the fins greater on the experimental line (Fig 1), thus making the illusion weaker. However, why did it not have the opposite affect on the opposite stimulus (Fig 2)? The Zollner cross hatches should have strengthened the illusion making the angle of the fins less, which then would make the line shorter. This is surprising, I can see what probably happened to Fig 1 (experimental stimulus). It would be interesting to see if the results would differ with a larger sample. Maybe you would see the opposite affect if one were to use the fins out version.

References:

Chiang, Chung. (1968). A New Theory to Explain Geometrical Illusions Produced by Crossing Lines, Perception & Psychophysics, Vol 3(3-A), 174-176

Predebon, John. (2000). Length Illusions in Conventional and Single-Wing Muller-Lyer Stimuli, Perception & Psychophysics, Vol 62(5), 1086-1098

Presey, A.W. & martin, N.S. (1990). The effects of varying fins in Mueller-Lyer and Holding illusions.Psychological Research, Vol 52, 46-53.

Lewis, E. O. (1909). Confluxion and contrast effects in the Muller-Lyer illusion.British Journal of Psychology, Vol 3, 21-41.

Dewar, R.E. (1967). Stimulus determinants of the magnitude of the Muller-Lyer illusion.Perceptual and Motor Skills,Vol 24, 708-710.



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