Measuring the Strength of an Illusion

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

Although the two red bars are identical in length and width, the top bar appears significantly larger. but how much larger?

When I ask this question to students in my illusions seminar at UC Santa Cruz, they give a variety of answers: “much larger,” “slightly larger,” or “about 20 percent larger.” While these answers provide an intuitive assessment of the illusion’s strength, they are somewhat arbitrary and subjective. One student’s “something” is difficult to compare to another student’s “much.”

Point of Subjective Equality: A group activity

A clever method can be used to actually quantify the strength of this illusion by finding the strength of each observer 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 Gauge Kit” consisting of (1) a printout of railroad tracks with a solid horizontal bar near the top of the tracks and (2) a set of nine different size comparison bars placed individually near the bottom of the traces. 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.

Source: Cameron Casey/Pexels

In the 30-minute activity, students take turns as experimenter and observer. The experimenter selects one of the comparison bars (e.g. the 140 percent bar) and places it at the bottom of the tracks. The viewer then makes a simple judgement: does the comparison bar look smaller, larger, or the same as the top bar? Depending on the answer, the experimenter chooses a smaller or larger comparison bar, replacing the one at the bottom of the traces, and the observer makes another size comparison, and so on.

Over the course of several trials, the experimenter identifies which bar causes the observer to judge the two bars to be of equal size. At this point the observer point of subjective equality is reached. For example, if it is judged that the 120 percent comparison bar looks the same as the top bar, then one can say that this student’s “illusion strength” is 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 each student play the role of observer, students see how much variability there is between observers: some students’ illusion strength is as low as 10 percent, while others are as high as 40 percent.

Testing a new hypothesis

To expand the activity, I ask each group of students to come up with a manipulation or variation of the illusion and hypothesize whether this manipulation will increase or decrease the strength of the illusion. For example, a 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 chooses 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 examined, and whether the manipulation resulted in a stronger or weaker illusion than the base state. Finally, students address limitations they encountered while measuring the illusion. Here, students identify issues such as 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 to quantify the strength of a perceptual fallacy, finding the point of subjective equality provides a simple and reliable way to do so. In addition, students learn that they can carry out a simple scientific study in a short time using very simple tools. Finally, students can see firsthand that perceptions can vary significantly from person to person.