Modelling the visual world of a velvet worm

In many animal phyla, eyes are small and provide only low-resolution vision for general orientation in the environment. Because these primitive eyes rarely have a defined image plane, traditional visual-optics principles cannot be applied. To assess the functional capacity of such eyes we have developed modelling principles based on ray tracing in 3D reconstructions of eye morphology, where refraction on the way to the photoreceptors and absorption in the photopigment are calculated incrementally for ray bundles from all angles within the visual field. From the ray tracing, we calculate the complete angular acceptance function of each photoreceptor in the eye, revealing the visual acuity for all parts of the visual field. We then use this information to generate visual filters that can be applied to high resolution images or videos to convert them to accurate representations of the spatial information seen by the animal. The method is here applied to the 0.1 mm eyes of the velvet worm Euperipatoides rowelli (Onychophora). These eyes of these terrestrial invertebrates consist of a curved cornea covering an irregular but optically homogeneous lens directly joining a retina packed with photoreceptive rhabdoms. 3D reconstruction from histological sections revealed an asymmetric eye, where the retina is deeper in the forward-pointing direction. The calculated visual acuity also reveals performance differences across the visual field, with a maximum acuity of about 0.11 cycles/deg in the forward direction despite laterally pointing eyes. The results agree with previous behavioural measurements of visual acuity, and suggest that velvet worm vision is adequate for orientation and positioning within the habitat.

Kazimir Malevich’s Negative Theology and Mystical Suprematism

This article examines Kazimir Malevich’s Suprematist art in the context of negative (apophatic) theology, as a crucial tool in analyzing both the artist’s theoretical conclusions and his new visual optics. Our analysis rests on the point that the artist intuitively moved towards recognizing the ineffability of the multidimensional universe and perceiving God as the Spiritual Absolute. In his attempt to see the invisible in the formulas of Emptiness and Nothingness, Malevich turned to the primary forms of geometric abstraction—the square, circle and cross—which he endows with symbolic concepts and meanings. Malevich treats his Suprematism as a method of perceiving the ineffability of the Absolute. With the Black Square seen as a face of God, the patterns of negative theology rise to become the philosophical formula of primary importance. Malevich’s Mystical Suprematism series (1920–1922) confirms the presence of complex metaphysical reflection and apophatic thought in his art. Not only does the series contain icon paraphrases and the Christian symbolism of the cross and mandorla, but it also advances the formulas of the apophatic faith of the modern times, since Suprematism presents primary forms as the universals of “the face of the future” and the energy of the non-objective art.