Françoise Beck
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.
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.