Perceptual axioms are irreconcilable with Euclidean geometry.

There are different definitions of axioms, but the one that seems to have general approval is that axioms are statements whose truths are universally accepted but cannot be proven; they are the foundation from which further propositional truths are derived. Previous attempts, led by David Hilbert, to show that all of mathematics can be built into an axiomatic system that is complete and consistent failed when Kurt Gödel proved that there will always be statements which are known to be true but can never be proven within the same axiomatic system. But Gödel and his followers took no account of brain mechanisms that generate and mediate logic. In this largely theoretical paper, but backed by previous experiments and our new ones reported below, we show that in the case of so-called 'optical illusions', there exists a significant and irreconcilable difference between their visual perception and their description according to Euclidean geometry; when participants are asked to adjust, from an initial randomised state, the perceptual geometric axioms to conform to the Euclidean description, the two never match, although the degree of mismatch varies between individuals. These results provide evidence that perceptual axioms, or statements known to be perceptually true, cannot be described mathematically. Thus, the logic of the visual perceptual system is irreconcilable with the cognitive (mathematical) system and cannot be updated even when knowledge of the difference between the two is available. Hence, no one brain reality is more 'objective' than any other.

A clinico-anatomical dissection of the magnocellular and parvocellular pathways in a patient with the Riddoch syndrome.

KEY MESSAGE: The Riddoch syndrome is thought to be caused by damage to the primary visual cortex (V1), usually following a vascular event. This study shows that damage to the anatomical input to V1, i.e., the optic radiations, can result in selective visual deficits that mimic the Riddoch syndrome. The results also highlight the differential susceptibility of the magnocellular and parvocellular visual systems to injury. Overall, this study offers new insights that will improve our understanding of the impact of brain injury and neurosurgery on the visual pathways. The Riddoch syndrome, characterised by the ability to perceive, consciously, moving visual stimuli but not static ones, has been associated with lesions of primary visual cortex (V1). We present here the case of patient YL who, after a tumour resection surgery that spared his V1, nevertheless showed symptoms of the Riddoch syndrome. Based on our testing, we postulated that the magnocellular (M) and parvocellular (P) inputs to his V1 may be differentially affected. In a first experiment, YL was presented with static and moving checkerboards in his blind field while undergoing multimodal magnetic resonance imaging (MRI), including structural, functional, and diffusion, acquired at 3 T. In a second experiment, we assessed YL's neural responses to M and P visual stimuli using psychophysics and high-resolution fMRI acquired at 7 T. YL's optic radiations were partially damaged but not severed. We found extensive activity in his visual cortex for moving, but not static, visual stimuli, while our psychophysical tests revealed that only low-spatial frequency moving checkerboards were perceived. High-resolution fMRI revealed strong responses in YL's V1 to M stimuli and very weak ones to P stimuli, indicating a functional P lesion affecting V1. In addition, YL frequently reported seeing moving stimuli and discriminating their direction of motion in the absence of visual stimulation, suggesting that he was experiencing visual hallucinations. Overall, this study highlights the possibility of a selective loss of P inputs to V1 resulting in the Riddoch syndrome and in hallucinations of visual motion.