Visual Perception: Monovision Can Bias the Apparent Depth of Moving Objects

Unusual Mathematical Approaches Untangle Nervous Dynamics

The massive amount of available neurodata suggests the existence of a mathematical backbone underlying neuronal oscillatory activities. For example, geometric constraints are powerful enough to define cellular distribution and drive the embryonal development of the central nervous system. We aim to elucidate whether underrated notions from geometry, topology, group theory and category theory can assess neuronal issues and provide experimentally testable hypotheses. The Monge’s theorem might contribute to our visual ability of depth perception and the brain connectome can be tackled in terms of tunnelling nanotubes. The multisynaptic ascending fibers connecting the peripheral receptors to the neocortical areas can be assessed in terms of knot theory/braid groups. Presheaves from category theory permit the tackling of nervous phase spaces in terms of the theory of infinity categories, highlighting an approach based on equivalence rather than equality. Further, the physical concepts of soft-matter polymers and nematic colloids might shed new light on neurulation in mammalian embryos. Hidden, unexpected multidisciplinary relationships can be found when mathematics copes with neural phenomena, leading to novel answers for everlasting neuroscientific questions. For instance, our framework leads to the conjecture that the development of the nervous system might be correlated with the occurrence of local thermal changes in embryo–fetal tissues.

The magnitude of monocular light attenuation required to elicit the Pulfrich illusion

In the Pulfrich illusion, the depth of a moving object is misperceived due to induced retinal disparity and/or interocular velocity differences arising from differences in luminance, contrast, or spatial frequency between the two eyes. These effects have been shown to occur both for visual deficits and for optical corrections that introduce significant binocular differences between the retinal images. However, it remains unknown to what extent the illusion might arise given normal variation between the eyes, such as natural interocular variation in pupil diameter (anisocoria). To assess this, we examined the threshold interocular retinal illuminance difference required to experience illusory depth in two random-dot fields moving in opposite directions in 24 normally-sighted observers with dilated pupils. Interocular difference in retinal illuminance was induced by placing neutral density filters of different intensities before the left eye. A minority of subjects (n = 8) did not provide meaningful data on changes in the experience of illusory depth with interocular difference in retinal illuminance and four subjects showed biases >±10% from the 50% point of subjective equality in the psychometric function. For the remaining 12 participants, the retinal illuminance had to differ by approximately 40% for the depth between the planes to become visible at threshold levels. This difference was approximately constant over a range of absolute luminance levels from 10 to 80 cd/m2. Our results suggest that while motion-in-depth illusions due to interocular differences in retinal illuminance may be pronounced in certain ophthalmic diseases or following certain optical interventions, it is unlikely to be manifest as a result of normal interocular variations in retinal illuminance. Further, our results also point towards the existence of substantial individual differences in the experience of what is otherwise thought of as a readily appreciable motion-in-depth illusion.