Measuring the Strength of an Illusion

The Ponzo perspective illusion was discovered in 1911 by Mario Ponzo. One version of the illusion can be seen below:

Although the two red bars are identical in length and width, the top bar clearly appears to be bigger. But how much bigger?

When I pose this question to the students in my seminar on "Illusions" at UC Santa Cruz, they provide a variety of answers: "a lot bigger," "somewhat bigger," or "about 20 percent bigger." While these responses provide an intuitive assessment of the illusion's strength, they are somewhat arbitrary and subjective. One student's "somewhat" is difficult to compare to another student's "a lot."

Point of Subjective Equality: A Group Activity

A clever method can be used to actually quantify the strength of this illusion by finding each observer's point of subjective equality. To demonstrate this method, I divide the class into groups of five or six students and provide each group with a "Ponzo measurement kit" that consists of (1) a print-out of train tracks with a fixed horizontal bar near the top of the tracks and (2) a set of nine variably sized comparison bars to be placed one at a time near the bottom of the tracks. The comparison bars are scaled versions of the fixed bar, at 80, 90, 100, 110, 120, 130, 140, 150, and 160 percent of its size.

In the 30-minute activity, students take turns being the experimenter and the observer. The experimenter selects one of the comparison bars (say, the 140 percent bar) and places it near the bottom of the train tracks. The observer then makes a simple judgment: Does the comparison bar look smaller, larger, or the same as the top bar? Depending on the answer, the experimenter selects a smaller or larger comparison bar and replaces the one near the bottom of the tracks, and the observer makes another size comparison, and so on.

Over the course of several trials, the experimenter identifies which bar leads the observer to judge the two bars as being the same size. At this point, the observer's point of subjective equality is reached. For example, if the 120 percent comparison bar is judged to appear the same as the top bar, then that student's "illusion strength" can be said to be 20 percent. That is, the bottom bar needs to be 20 percent larger than the top bar for them to look the same size. By having every student play the role of the observer, students see how much variability there is across observers: Some students' illusion strength will be as small as 10 percent while others' is as high as 40 percent.

Testing a New Hypothesis

To extend the activity, I challenge each student group to come up with one manipulation or variation of the illusion and to hypothesize whether that manipulation will increase or decrease the illusion's strength. For example, one group may decide to turn the train tracks upside-down and measure whether the unusual perspective of upside-down tracks weakens the illusion (and if so, by how much). Another group may ask whether observing the illusion with one eye closed changes its strength compared to observing it with both eyes open. Another group might vary the distance from which the illusion is observed.

At the end of the activity, each group selects a representative to share their findings with the rest of the class. As part of their presentation, students report the average strength of the illusion in their group, the manipulation they chose to examine, and whether the manipulation led to a stronger or weaker illusion than the baseline condition. Finally, students bring up limitations they encountered in the process of measuring the illusion. Here, students identify issues like observer bias, lack of randomization, and other technical limitations.

As a result of the lesson, students learn that although it may seem difficult at first glance to quantify the strength of a perceptual illusion, finding the point of subjective equality provides a simple and reliable way to do so. In addition, students learn that they can conduct a simple scientific study in a short amount of time using very basic tools. Finally, students are able to see first-hand that perception can vary substantially across individuals.