Françoise Beck

Waterloo, Belgium
Free-lance writer and Italianist, I express in animal painting my immense love and respect for our so-called 'inferior' friends. In a math-art community, why not try to capture participants' interest in aspects of animality close to mathematics, through the emotional appeal of the representation medium?

This time I want to share a discovery I made last year: while accustomed to seeing cats' eyes retracting their pupils into vertical slits, so different from the more widespread circular shape I read that for certain animals such as horses, goats, sheep, ibexes, mouflons, common toads, Ahaetulla and Thelornis snakes (respectively vine and twig snakes), octopuses, the shape of their horizontal rectangular pupils results in a different way of perceiving the world.

Hence the following drawing that invites to a geometrical reading but also to a metaphoric one close to my understanding of animals versus humans.
Horses enjoy wider viewing than Humans
9 X 14 cm in 24 x 28.5 cm frame
Color pencils on cartonboard and black ink
The stange pupil shape retains the complete angle of vision over the horizon for the animal to better be able to spot predators. This broad peripheral vision, allowing the animal to see behind without turning its head (sheep), occurs at the expense of depth of field of vision. When excited, their eyeball muscles contract and their eyes retract, thereby deepening the shadows and hence increasing panic. Goats got a reputation for clear-sightedness, even sorcery in the Middle Ages, but many civilizations attributed to this a divine dimension, friendliness and generosity or embedding the richness of Nature.
In physical terms, the phenomenon is described by the Fraunhofer diffraction resulting from interference fringes according to the Fresnel-Huygens principle. These theories involve high math boiling down to a 'simple' Fourier transform of the pupil transmitttance. On the drawing are superposed the idealized geometrical shapes of the pupils of horses/goats/sheep, cats, and ourselves.