Aspects of perspective and ambiguous space in the work of M.C. Escher

Abstract

Cartographers, mathematicians and artists discovered many of the rules for linear perspective before the Renaissance, but the mathematical basis to represent objects three-dimensionally was developed only in the 15th century. Brunelleschi was the first to demonstrate geometric perspective with his famous experiments in 1425. The humanist Alberti recorded the geometrical principles for creating three-dimensional space on a two-dimensional surface during 1435. This was, in other words, the tools to translate mental vision onto paper. The fact that, in human vision, the parallel lines from the edges of objects converge at an infinite point (the vanishing point) on the horizon, is an illusion. Escher wanted to make concrete representations of infinity and he used traditional perspective to create impossible worlds.

Die ontwikkeling van perspektief en die gebruik daarvan in die werk van M.C. Escher. Kartograwe, wiskundiges en kunstenaars het sommige van die reëls vir lineêre perspektief intuïtief ontdek, maar die wiskundige gronde vir drie-dimensionele voorstelling is eers tydens die 15de eeu ontdek. Brunelleschi het tydens 1425 meetkundige perspektief gedemonstreer met behulp van sy bekende eksperimente. Die humanis Alberti het tydens 1435 die meetkundige beginsels vir die voorstelling van drie-dimensionele ruimte op ‘n twee-dimensionele oppervlakte gedokumenteer. Hierdie beginsels was die metode waarvolgens die kognitiewe visie omgesit word in ‘n voorstelling op papier. Die feit (volgens menslike visie) dat die ewewydige lyne vanaf die rand van voorwerpe by ‘n oneindige punt (die verdwyningspunt) op die horison konvergeer, is ‘n illusie. Escher wou konkrete voorstellings van oneindigheid maak en hy het tradisionele perspektieftekening gebruik om ‘n onmoontlike wêreld te skep.