Spatial Semantics: Tafereel, Einder and El Lissitzky

Abstract In visual awareness the expanse of pictorial space fills a slab of finite depth between a frontal plane and a backdrop at infinity. It paradoxically coexists with the flatness of a picture. The constructivist El Lissitzky (1890–1941) suggested that a formal account would therefore require paradoxical notions such as non-Euclidean geometry and imaginary numbers. Perhaps so, for pictorial and physical spaces have distinct ontological roots so they are incommensurable. Alberti’s perspective discards the third dimension. Depth is a mental quality that cannot be represented. Since the picture plane is flat, ‘depth’ has to be imaginary. Imaginary dimensions capture the ‘enchantment’ of pictorial vision. Pictures and Alberti’s perspective address the disenchanted (flat), objective aspect. Only arcane geometries with imaginary dimensions might possibly account for the phenomenology — as they indeed are found to do. Linguistic terms that refer to such imaginary objects — such as ‘tafereel’ and ‘einder’ in Dutch — are scarce.