Sharing Paradoxes: Impossible Spaces, Impossible Times and Impossible Facts. The Function of Self-Contradictory Structures in Arts, Sciences and Philosophy. (Part 3)

We can classify visual paradoxes into two categories: the simply self-contradictory ones and the ambigrams. In looking at most of Maurelius C. Escher’s optical illusions, the spatial design seems to be both true and false. As pointed out by Biederman, since the shapes preserve adequate angle constructions, the objects seems to be credible. That is a direct result of the importance of line intersection in object recognition. Nevertheless, the overall conceptualisation of the object seems not acceptable as being true (Biedermann, 135-140). In this case, these visual paradoxes are simply self-contradictory because the macroscopic veracity statement contradicts the microscopic ones (as in the two sentence: The next sentence is true. The last sentence is false (Hofstadter, 19)) Many artists have found multiple interesting ways to produce these types of paradoxes. Escher indeed is well known for such constructions, but we can name as well graffiti artist Damien Gilley, Dutch artist Ramon Bruin and Istvan Orosz (Figure 3) Having met quite a wide popularity, it is normal that these simply self-contradictory visual objects have appeared in various situations. For instance, Penrose’s triangles has appear on post stamps, tattoos and many everyday objects.

Inception stair scene

Figure 4: Inception.s stairs scene by Christopher Nolan

These self-contradictory visual objects can contribute solving other artistic problems. In Christopher Nolan’s movie Inception the infinite stairs illusion is used and as real instance within the diegetic world to trap the enemy. In this case, it is a use of a visual paradox to solve of narrative problem. (Figure 4) On his hand, Cameron Browne have found interesting ways to merge the optical illusion construction with another old problem; the paving of the plane (Browne, 2007). Browne has constructed infinite patterns of self-contradictory visual objects that can be used to fulfill the entire plane. He worked as well with contradictory fractal structures (Figure 5)

Camron Browne.jpg

Figure 5: Impossible Fractal by Cameron Browne. Source: http://www.cameronius.com/graphics/impossible-fractals-figures/

Ambigrams are figures that show two incompatible information at the same time, inasmuch a paradox, they work on a scale more nuanced than the dichotomic paradoxes[1]. The figure of a young-old lady is a popular example of ambigram due to H.H. Hill (Delahaye, 91). In this image we can actually perceive two different portraits. One pictures a young lady and one offers the profile view of an old lady. It is a paradox since it contradicts itself, not in the previous case straightforward manner, but by ricochet. If it is a young lady, then it is impossible to be the old lady at the same time and vice versa. In the other hand, we can interpret the image as containing two informations, two different images. Ambigrams, working on a larger scale; they can contain more information. For instance, in figure 5 one can find six apparitions of the word palindrome, all put upside-down and to be read in both directions.

The advantage of using a word like ambigram is that it underlines an interesting property of paradoxes, that fact of being containing multiple statement that would usually not appear in general in a coherent manner. To go further in this sense, we have to go back to an analysis made by Mexican sociologist and writer Octavio Paz. In an analysis of complementary and dual concepts existing in various societies, Paz stresses the importance of considering such pairs as a whole by focusing on the relation between them. For instance, body and no-body are not to be considered as specific meanings except to express contraries (Paz, 55). This perception of duals as a whole can lead to interesting results when applied to paradoxes.

Palindrome

Figure 6: Ambigram

[1] We mean by this that the information is not straight opposite, like true and false, up and down, etc.

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