Convergence-divergence: the Muller-Lyer Illusion

In 1860, Zollner proposed the optical mechanism of convergence-divergence.  It states that our assessment of a geometrical quantity is strongly affected by the nature of the surrounding territory.  This was first illustrated in 1889, in what is known as the famous Muller-Lyer illusion.

Fig. 60 The Muller-Lyer illusion.  The two horizontal lines are of equal length. 

On sight, it appears that the line with the converging arrowheads is shorter than the one with the diverging arrowheads.  Surprisingly, they are actually equal in length.  Convergence has an effect of shortening a geometrical quantity, while divergence lengthens it.  The combined effect yields the Muller-Lyer illusion.

Fig. 61 A modification of the Muller-Lyer illusion.   

In Fig. 61, the line appears to be equally bisected.  In fact, the portion with the diverging arrowheads is about 28% shorter. 

Convergence-divergence can be exploited in dress design to give the appearance of a reduced waist.  Schematically, we have the waistlines of two ladies in Fig. 62.  In the upper waistline, the diverging lines on the dress make the waist appear bigger than it actually is.  The lower waistline appears smaller than the upper one, due to convergence.  In fact, both have the same size. 

Fig. 62 Dress patterns influence the
apparent size of the waistline.

Another famous example related to convergence-divergence is the Ponzo illusion, first presented by Mario Ponzo in 1913.   

Fig. 63 The Ponzo Illusion.

Fig. 63 shows a railway converging into the distance.  Notice that the upper block appears bigger than the lower one.  In fact, they are of the same size.  The converging railway tracks have clouded our judgement of size.