What can you see? A horizontal line is enclosed between two arrows whose peaks coincide with the line ends and point (1) alternately to each other, (2) from each other or (3) in the same direction. Which line is longer – the upper line, the middle line or the lower line? For almost all viewers, the middle line seems longest, at the end of which the arrows point outwards. The lower line seems shorter, but the upper line, where the arrows point inwards, seems to be the shortest.

In fact, all three horizontal lines are the same length. So here is a geometrical-optical illusion. It has the name Müller-Lyer-illusion and is one of the most well-known optical illusions. It is named after the German psychiatrist Franz Müller-Lyer (1857-1916). His journal article appeared in 1889 with the title  »Optische Urteilsbildung« (Optical judgment formation). The title fits exactly, because when judging the length of the lines you can be pretty wrong. Müller-Lyer explains the wrong assessment by the fact that we do not only look at the horizontal line, but also at its immediate surroundings. If the oblique lines point outwards, the line appears stretched; if they point inwards, it appears compressed.

What can you do? Almost all parameters can be changed in the program. So you can reproduce the images above. You can change the length of lines and arrows (length_line, length_arrow), their thickness (thickness_line) and the distance between the three lines (gap). The angle of the legs of the oblique lines is determined by angle_arrow. Which parameter is decisive for the effect? The reduction of the distance to zero (gap = 0) is in any case proof that the three lines are always of the same length!

The program can be made even more flexible by introducing different colors (color_bg for the background, color_line for the line and the arrows) or different thicknesses for lines and arrows. For this you have to add corresponding variables to the program. If the space on the stage still allows it, you can offer corresponding slide controls.

A Müller-Lyer measuring lab: You can measure how well you or your visitors can estimate the distances. The easiest way is when we no longer have two horizontal lines, but only one line. On it a third arrow can be moved (which is the Brentano form of the illusion, see Grave, Franz & Gegenfurtner, 2006). Alternatively only a point can be moved (which is called the Judd illusion). In addition, the line can be hidden. This finally results in four different experiments: line + arrow (experiment_no. 1), line + point (experiment_no. 2), no line + arrow (experiment_no. 3), no line + point (experiment_no. 4).

All variables can be defined as usual. For the actual measurement the arrow/point in the middle follows your mouse. Whenever you think that the two sections to the left and right of this arrow/point are exactly the same length, i.e. that the moving arrow/point is at the center of the line, press the [space bar]. Then the position of the arrow/point is fixed and you get the deviation from the exact midpoint in pixels as well as in %. You can start a new measurement by pressing the green flag.

Related topics: Müller-Lyer extended

References:
Ocean, G. (2010). The Müller-Lyer, Poggendorff and More Illusions. 3, 729-742. Article on his website.
de Grave, D., Franz, V. & Gegenfurtner, K. (2006).The influence of the Brentano illusion on eye and hand movements. Journal of Vision, Vol.6. Available as download.