3M3 | Jelena Mitrović: Spheric mirror

November 21st - December 5th, 2016

Our perception of space is strictly articulated by linear perspective, but the curvature of our spherical world was destined to be revealed.

People from the ancient times knew of this curvature. When looking at the elements of ancient architecture, we find curves to be straight lines or the straight ones to be curved: columns that would visually distort in our eyes are subjected to entasis, epistyle and stylobate must be arched so as not to relax, and the curves of Doric temples confirm the practical implications of these findings.

The ancient optics was dismissive of linear perspective. Even when they did not understand the spherical distortion of form, it was to respond to the even more important recognition of the distortion in length. The ancient perspective always reflected on the apparent size (projection of objects onto the spherical field of view). The ratio of size was expressed by angle, rather than length. In perspective, the apparent difference is created based on the angle; as the Eighth theorem of Euclid explicitly requires: an obvious difference between the two of the same size as seen from different distance is determined by the ratio (coefficient) of viewing angles, and not by the ratio (coefficient) of distance.

This is completely different from the doctrine behind the construction of modern perspective, which declares size and distance proportionally commensurable. The Eighth theorem was either ignored or effaced during the Renaissance. There was a discrepancy between the Euclidean perspective naturalis (or communis), which sought to find the mathematical laws of natural perception (that is why it linked apparent size with the coefficient of angle), and artificialis on the other hand, a perspective that was used to create appropriate methods of representing space on a two-dimensional surface. This has resulted in abandoning the axiom: to recognize it was to leave the creation of the image to the impossible, because a plane simply cannot be projected onto a sphere. - Jelena Mitrovic