Leaning tower illusion
| Frederick A. A. Kingdom et al. (2007), Scholarpedia, 2(12):5392. | doi:10.4249/scholarpedia.5392 | revision #170055 [link to/cite this article] |
The Leaning Tower Illusion is the phenomenon in which an image of a tower viewed from below appears lopsided when placed next to a copy of itself. The illusion’s name is a pun on ‘Leaning Tower’ because it was first noticed in a pair of identical images of the Leaning Tower of Pisa, as shown in Figure 1. The illusion works however for any image of a receding tower, as well as with other receding objects (see below). The illusion is best described as a visual, not optical illusion, because the ‘trick’ is in the mind not the light.
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The brain reconstructs the third dimension
In the Leaning Tower Illusion, the mind is tricked by its own mechanism for constructing a mental 3D (three-dimensional) image from a flat, 2D (two-dimensional) image. The outlines of objects that recede from view tend to converge towards a common point when projected onto a 2D (two-dimensional) surface. The pattern of converging lines is referred to as the perspective view. Objects in the visual scene are imaged onto the retinae at the back of our eyes, then encoded into electrical signals that are sent to the brain for further analysis. Because our retinae are surfaces, the images cast upon them are in perspective. Our brains however have learnt to reconstruct the third dimension from the images on the retinae, and as a result we tend to perceive objects ‘as they are’, i.e. not with converging outlines. It is not well understood how and when our brains acquire this ability, but most likely it develops during infancy from the feedback obtained by young infants as they interact, visually and manually, with a physical world of 3D objects. The brain's remarkable ability to reconstruct the third dimension is not only effortless but unconscious, an example of what the famous 19th century physicist and physiologist Helmholtz referred to as ‘unconscious inference’. So good are we at reconstructing a 3D world in our heads, and so unaware are we of doing it, that one can understand why it was not until the Renaissance, many thousands of years after humans began to make drawings, that artists worked out how to represent perspective graphically.
The brain is able to reconstruct the third dimension not only from retinal images, but from paintings, photographs and television images. Figure 2 shows a cube drawn in perspective. It looks like a proper cube, with parallel sides and right-angled corners, even though in perspective view the sides and corners are neither parallel nor right-angled. Paradoxically, one can perceive a proper cube while at the same time being aware of the distortions due to perspective.
Reason for the illusion
Consider the photograph of the Petronas twin towers in Quala Lumpur shown in Figure 3. Even though the corresponding outlines of the two towers converge due to perspective, our brain perceives the towers rising at the same angle, which in reality they do. It follows that if one has an image where the corresponding outlines of two receding towers do not converge but are parallel, the only reasonable interpretation is that the towers must be diverging. This is precisely what is seen in Figure 4, where the right hand tower has been replaced by a copy of the one on the left. The same principle applies to the Pisa towers.
Significance of illusion
The Leaning Tower Illusion reveals that the brain’s mechanism for reconstructing the third dimension is applied to the image as a whole, rather than to separate parts of it. If reconstruction was applied separately to the two images of the Pisa towers, they would be perceived to rise at the same angle. It is as if it is impossible to see the two images as separate, albeit identical versions of the same image. Instead one sees the ‘Twin Towers of Pisa’, with the ‘correct’ interpretation that one tower leans more than the other.
Does the Leaning Tower illusion mean that our brains are flawed ? Would it not be better to reconstruct the 3D image separately for different parts of the scene and thus avoid the misperception of the Pisa towers ? No. The visual system is designed to help us navigate through a complex but unitary 3D world. The brain’s mechanism for reconstructing the third dimension is not perfect and if it were applied separately to different parts of the scene rather than to scene as a the whole there would be an accumulation of errors that would make navigation much more difficult.
Other explanations for the illusion
Some visual illusions have been explained by ‘acute-angle expansion’ (Kitaoka & Ishihara, 2000), the phenomenon in which acute angles tend to look larger than they actually are. If the acute angle subtended by the two inner sides of the Pisa towers in Figure 1 was expanded perceptually, this could produce the impression of the towers diverging. Akiyoshi Kitaoka designed Figure 5 to test this idea. The arrangement of angles in the figure is similar to the Pisa towers, but unlike the Pisa towers the two figures are not of receding objects. If the illusion was due to acute-angle expansion a similar illusion should occur, whereas if the perspective explanation given above is correct there should be little or no illusion. The illusion is almost non-existent in the cartoon figure of the two children, thereby supporting the perspective explanation.
The illusion does not accumulate
It might be supposed that if a series of Pisa towers were placed next to one another the illusion would accumulate, with the comical result that the tower on the far right would topple over altogether! Figure 6 however shows this does not happen. The illusion can still be experienced when focusing on any adjacent pair of towers, but the towers do not become increasingly lopsided as one proceeds from left to right. There are a number of possible reasons for this. First, even if the illusion did accumulate, either tower at the end of the series could in principle be the one that topples, depending on which one served as the 'anchor' for the other towers. Since there is no reason why either of the end towers should be the anchor, there is no basis for the other to topple. Second, if the hypothesis that our brains reconstruct the third dimension across the scene as a whole is correct, the illusion should be the same magnitude for any pair of towers in the series, including the end towers, and this would conflict with either of them toppling. Third, there is an inherent limit to our geometric misperceptions that is imposed by the visual system's more-or-less accurate representation of the spatial layout of the scene. The tower on the far right would never be seen to topple because this would conflict too much with the relatively accurate encoding of its spatial layout.
The illusion works with any image of a receding object
The illusion works with any image of a receding tower, or other receding object, such as the identical pair of photographs of tram lines shown in Figure 7.
Principle applied to a single object
The illusion found with side-by-side replicas of an image of a receding object applies also to a single object, as in Figure 8. The figure is drawn with parallel sides, yet the impression is of an object that becomes fatter with distance. Should one think of Figure 8 as an illusion? What you see - an object that gets fatter with distance - is arguably the correct interpretation given that the image is of a receding object. The Leaning Tower illusion on the other hand is arguably a genuine illusion because what we perceive contradicts what we otherwise know, namely that the two images are identical.
References
Kingdom, F. A. A., Yoonessi, A. & Gheorghiu, E. (2007). The Leaning Tower illusion: a new illusion of perspective. Perception, 36, 475-477.
Kitaoka, A. and Ishihara, M. (2000). Three elemental illusions determine the Zollner illusion. Perception & Psychophysics, 62, 569-575.
Wikipedia references: Perspective (visual); Perspective (graphical); Hermann von Helmholtz;
Internal references
- Valentino Braitenberg (2007) Brain. Scholarpedia, 2(11):2918.
- John Dowling (2007) Retina. Scholarpedia, 2(12):3487.
