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.

The neural determinants of abstract beauty.

We have enquired into the neural activity which correlates with the experience of beauty aroused by abstract paintings consisting of arbitrary assemblies of lines and colours. During the brain imaging experiments, subjects rated abstract paintings according to aesthetic appeal. There was low agreement on the aesthetic classification of these paintings among participants. Univariate analyses revealed higher activity with higher declared aesthetic appeal in both the visual areas and the medial frontal cortex. Additionally, representational similarity analysis (RSA) revealed that the experience of beauty correlated with decodable patterns of activity in visual areas. These results are broadly similar to those obtained in previous studies on facial beauty. With abstract art, it was the involvement of visual areas implicated in the processing of lines and colours while with faces it was of visual areas implicated in the processing of faces. Both categories of aesthetic experience correlated with increased activity in medial frontal cortex. We conclude that the sensory areas participate in the selection of stimuli according to aesthetic appeal and that it is the co-operative activity between the sensory areas and the medial frontal cortex that is the basis for the experience of abstract visual beauty. Further, this co-operation is enabled by "experience dependent" functional connections, in the sense that currently the existence and high specificity of these connections can only be demonstrated during certain experiences.

The neural determinants of beauty.

The perception of faces correlates with activity in a number of brain areas, but only when a face is perceived as beautiful is the medial orbitofrontal cortex (mOFC) also engaged. Here, we enquire whether it is the emergence of a particular pattern of neural activity in face perceptive areas during the experience of a face as beautiful that determines whether there is, as a correlate, activity in mOFC. Seventeen subjects of both genders viewed and rated facial stimuli according to how beautiful they perceived them to be while the activity in their brains was imaged with functional magnetic resonance imaging. A univariate analysis revealed parametrically scaled activity within several areas, including the occipital face area (OFA), fusiform face area (FFA) and the cuneus; the strength of activity in these areas correlated with the declared intensity of the aesthetic experience of faces; multivariate analyses showed strong patterns of activation in the FFA and the cuneus and weaker patterns in the OFA and the posterior superior temporal sulcus (pSTS). The mOFC was only engaged when specific patterns of activity emerged in these areas. A psychophysiological interaction analysis with mOFC as the seed area revealed the involvement of the right FFA and the right OFA. We conjecture that it is the collective specific pattern-based activity in these face perceptive areas, with activity in the mOFC as a correlate, that constitutes the neural basis for the experience of facial beauty, bringing us a step closer to understanding the neural determinants of aesthetic experience.

The Paton prize lecture 2021: A colourful experience leading to a reassessment of colour vision and its theories.

In this lecture, given in honour of Sir William Paton, a brilliant scientist and one of Britain's great patrons of biology, I give a personal account of the fundamental issues in colour vision that I have tackled since 1973, when I discovered a cortical zone lying outside the primary visual cortex that is rich in cells with chromatic properties. I do not provide an exhaustive review of colour vision but summarise how my views on colour vision and theories surrounding it have changed in light of that discovery.

"Multiplexing" cells of the visual cortex and the timing enigma of the binding problem.

In this opinion essay, I address the perennial binding problem, that is to say of how independently processed visual attributes such as form, colour and motion are brought together to give us a unified and holistic picture of the visual world. A solution to this central issue in neurobiology remains as elusive as ever. No one knows today how it is implemented. The issue is not a new one and, though discussed most commonly in the context of the visual brain, it is not unique to it either. Karl Lashley summarized it well years ago when he wrote that a critical problem for brain studies is to understand how "the specialized areas of the cerebral cortex interact to provide the integration evident in thought and behaviour" (Lashley, 1931).

The Bayesian-Laplacian brain.

We outline what we believe could be an improvement in future discussions of the brain acting as a Bayesian-Laplacian system. We do so by distinguishing between two broad classes of priors on which the brain's inferential systems operate: in one category are biological priors (ß priors) and in the other artefactual ones (α priors). We argue that ß priors, of which colour categories and faces are good examples, are inherited or acquired very rapidly after birth, are highly or relatively resistant to change through experience, and are common to all humans. The consequence is that the probability of posteriors generated from ß priors having universal assent and agreement is high. By contrast, α priors, of which man-made objects are examples, are acquired post-natally and modified at various stages throughout post-natal life; they are much more accommodating of, and hospitable to, new experiences. Consequently, posteriors generated from them are less likely to find universal assent. Taken together, in addition to the more limited capacity of experiment and experience to alter the ß priors compared with α priors, another cardinal distinction between the two is that the probability of posteriors generated from ß priors having universal agreement is greater than that for α priors. The two categories are distinct at the extremes; there is, however, a middle range where they merge into one another to varying extents, resulting in posteriors that draw upon both categories.

The biological basis of the experience and categorization of colour.

We used the Land Colour Mondrian experiments in a Bayesian context to test the degree to which subjects vary in categorizing the colour of different patches, when each patch is made to reflect light of the identical wavelength-energy composition. The brain uses a ratio-taking mechanism to determine the ratio of light of every waveband reflected from a surface and from its surrounds. Our (Bayesian) hypothesis was that this ratio-taking mechanism is similar in all humans and therefore leads to a constant categorization of colours that differs little between them. The similarly categorized colours are the initial priors, with initial hues attached to them. Twenty subjects of different ethnic and cultural backgrounds, for all but one of whom English was not the primary language, viewed eight patches of different colour in two Mondrian displays; each patch, when viewed, was made to reflect identical ratios of long-, middle- and short-wave light. Subjects were asked to match the colour of the viewed patch with that of the Munsell chip coming closest in colour to that of the viewed patch, without using language. In terms of hue, there was less variability in matching warm hues than cool ones. In terms of colour categorization, there was little variability overall. We take the lack of significant variability between subjects in the matches made as a pointer to similar computational mechanisms being employed in different subjects to perceive colours, thus permitting them to assume that their categorization of colours has universal agreement and assent.

The experience of beauty derived from sorrow.

We studied the neural mechanisms that are engaged during the experience of beauty derived from sorrow and from joy, two experiences that share a common denominator (beauty) but are linked to opposite emotional valences. Twenty subjects viewed and rerated, in a functional magnetic resonance imaging scanner, 120 images which each had classified into the following four categories: beautiful and sad; beautiful and joyful; neutral; ugly. The medial orbito-frontal cortex (mOFC) was active during the experience of both types of beauty. Otherwise, the two experiences engaged different parts of the brain: joyful beauty engaged areas linked to positive emotions while sorrowful beauty engaged areas linked to negative experiences. Separate regions of the cerebellum were engaged during experience of the two conditions. A functional connectivity analysis indicated that the activity within the mOFC was modulated by the supplementary motor area/middle cingulate cortex, known to be engaged during empathetic experiences provoked by other peoples' sadness. Hum Brain Mapp 38:4185-4200, 2017. © 2017 Wiley Periodicals, Inc.

Early visual cortical responses produced by checkerboard pattern stimulation.

Visual evoked potentials have been traditionally triggered with flash or reversing checkerboard stimuli and recorded with electroencephalographic techniques, largely but not exclusively in clinical or clinically related settings. They have been crucial in determining the healthy functioning or otherwise of the visual pathways up to and including the cerebral cortex. They have typically given early response latencies of 100ms, the source of which has been attributed to V1, with the prestriate cortex being secondarily activated somewhat later. On the other hand, magnetoencephalographic studies using stimuli better tailored to the physiology of individual, specialized, visual areas have given early latencies of <50ms with the sources localized in both striate (V1) and prestriate cortex. In this study, we used the reversing checkerboard pattern as a stimulus and recorded cortical visual evoked magnetic fields with magnetoencephalography, to establish whether very early responses can be traced to (estimated) in both striate and prestriate cortex, since such a demonstration would enhance considerably the power of this classical approach in clinical investigations. Our results show that cortical responses evoked by checkerboard patterns can be detected before 50ms post-stimulus onset and that their sources can be estimated in both striate and prestriate cortex, suggesting a strong parallel input from the sub-cortex to both striate and prestriate divisions of the visual cortex.

Multiple asynchronous stimulus- and task-dependent hierarchies (STDH) within the visual brain's parallel processing systems.

Results from a variety of sources, some many years old, lead ineluctably to a re-appraisal of the twin strategies of hierarchical and parallel processing used by the brain to construct an image of the visual world. Contrary to common supposition, there are at least three 'feed-forward' anatomical hierarchies that reach the primary visual cortex (V1) and the specialized visual areas outside it, in parallel. These anatomical hierarchies do not conform to the temporal order with which visual signals reach the specialized visual areas through V1. Furthermore, neither the anatomical hierarchies nor the temporal order of activation through V1 predict the perceptual hierarchies. The latter shows that we see (and become aware of) different visual attributes at different times, with colour leading form (orientation) and directional visual motion, even though signals from fast-moving, high-contrast stimuli are among the earliest to reach the visual cortex (of area V5). Parallel processing, on the other hand, is much more ubiquitous than commonly supposed but is subject to a barely noticed but fundamental aspect of brain operations, namely that different parallel systems operate asynchronously with respect to each other and reach perceptual endpoints at different times. This re-assessment leads to the conclusion that the visual brain is constituted of multiple, parallel and asynchronously operating task- and stimulus-dependent hierarchies (STDH); which of these parallel anatomical hierarchies have temporal and perceptual precedence at any given moment is stimulus and task related, and dependent on the visual brain's ability to undertake multiple operations asynchronously.

Varieties of perceptual instability and their neural correlates.

We report experiments designed to learn whether different kinds of perceptually unstable visual images engage different neural mechanisms. 21 subjects viewed two types of bi-stable images while we scanned the activity in their brains with functional magnetic resonance imaging (fMRI); in one (intra-categorical type) the two percepts remained within the same category (e.g. face-face) while in the other (cross-categorical type) they crossed categorical boundaries (e.g. face-body). The results showed that cross- and intra-categorical reversals share a common reversal-related neural circuitry, which includes fronto-parietal cortex and primary visual cortex (area V1). Cross-categorical reversals alone engaged additional areas, notably anterior cingulate cortex and superior temporal gyrus, which have been posited to be involved in conflict resolution.

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.

Functional specialization and generalization for grouping of stimuli based on colour and motion.

This study was undertaken to learn whether the principle of functional specialization that is evident at the level of the prestriate visual cortex extends to areas that are involved in grouping visual stimuli according to attribute, and specifically according to colour and motion. Subjects viewed, in an fMRI scanner, visual stimuli composed of moving dots, which could be either coloured or achromatic; in some stimuli the moving coloured dots were randomly distributed or moved in random directions; in others, some of the moving dots were grouped together according to colour or to direction of motion, with the number of groupings varying from 1 to 3. Increased activation was observed in area V4 in response to colour grouping and in V5 in response to motion grouping while both groupings led to activity in separate though contiguous compartments within the intraparietal cortex. The activity in all the above areas was parametrically related to the number of groupings, as was the prominent activity in Crus I of the cerebellum where the activity resulting from the two types of grouping overlapped. This suggests (a) that, the specialized visual areas of the prestriate cortex have functions beyond the processing of visual signals according to attribute, namely that of grouping signals according to colour (V4) or motion (V5); (b) that the functional separation evident in visual cortical areas devoted to motion and colour, respectively, is maintained at the level of parietal cortex, at least as far as grouping according to attribute is concerned; and (c) that, by contrast, this grouping-related functional segregation is not maintained at the level of the cerebellum.

Parallelism in the brain's visual form system.

We used magnetoencephalography (MEG) to determine whether increasingly complex forms constituted from the same elements (lines) activate visual cortex with the same or different latencies. Twenty right-handed healthy adult volunteers viewed two different forms, lines and rhomboids, representing two levels of complexity. Our results showed that the earliest responses produced by lines and rhomboids in both striate and prestriate cortex had similar peak latencies (40 ms) although lines produced stronger responses than rhomboids. Dynamic causal modeling (DCM) showed that a parallel multiple input model to striate and prestriate cortex accounts best for the MEG response data. These results lead us to conclude that the perceptual hierarchy between lines and rhomboids is not mirrored by a temporal hierarchy in latency of activation and thus that a strategy of parallel processing appears to be used to construct forms, without implying that a hierarchical strategy may not be used in separate visual areas, in parallel.

Neural patterns of conscious visual awareness in the Riddoch syndrome.

The Riddoch syndrome is one in which patients blinded by lesions to their primary visual cortex can consciously perceive visual motion in their blind field, an ability that correlates with activity in motion area V5. Our assessment of the characteristics of this syndrome in patient ST, using multimodal MRI, showed that: 1. ST's V5 is intact, receives direct subcortical input, and decodable neural patterns emerge in it only during the conscious perception of visual motion; 2. moving stimuli activate medial visual areas but, unless associated with decodable V5 activity, they remain unperceived; 3. ST's high confidence ratings when discriminating motion at chance levels, is associated with inferior frontal gyrus activity. Finally, we report that ST's Riddoch Syndrome results in hallucinatory motion with hippocampal activity as a correlate. Our results shed new light on perceptual experiences associated with this syndrome and on the neural determinants of conscious visual experience.

The primary visual cortex, and feedback to it, are not necessary for conscious vision.

A compelling single case report of visual awareness (visual qualia) without primary visual cortex would be sufficient to refute the hypothesis that the primary visual cortex and the back-projections to it are necessary for conscious visual experience. In a previous study, we emphasized the presence of crude visual awareness in Patient G.Y., with a lesion of the primary visual cortex, who is aware of, and able to discriminate, fast-moving visual stimuli presented to his blind field. The visual nature of Patient G.Y.'s blind field experience has since been questioned and it has been suggested that the special circumstances of repeated testing over decades may have altered Patient G.Y.'s visual pathways. We therefore sought new evidence of visual awareness without primary visual cortex in patients for whom such considerations do not apply. Three patients with hemianopic field defects (Patient G.N. and Patient F.B. with MRI confirmed primary visual cortex lesions, Patient C.G. with an inferred lesion) underwent detailed psychophysical testing in their blind fields. Visual stimuli were presented at different velocities and contrasts in two- and four-direction discrimination experiments and the direction of motion and awareness reported using a forced-choice paradigm. Detailed verbal reports were also obtained of the nature of the blind field experience with comparison of the drawings of the stimulus presented in the blind and intact fields, where possible. All three patients reported visual awareness in their blind fields. Visual awareness was significantly more likely when a moving stimulus was present compared to no stimulus catch trials (P < 0.01 for each subject). Psychophysical performance in Patient F.B. and Patient G.N. was consistent with the Riddoch syndrome, with higher levels of visual awareness for moving compared to static stimuli (P < 0.001) and intact direction discrimination (P < 0.0001 for two- and four-direction experiments). Although the blind field experience of all three subjects was degraded, it was clearly visual in nature. We conclude that the primary visual cortex or back-projections to it are not necessary for visual awareness.

Top-down modulations in the visual form pathway revealed with dynamic causal modeling.

Perception entails interactions between activated brain visual areas and the records of previous sensations, allowing for processes like figure-ground segregation and object recognition. The aim of this study was to characterize top-down effects that originate in the visual cortex and that are involved in the generation and perception of form. We performed a functional magnetic resonance imaging experiment, where subjects viewed 3 groups of stimuli comprising oriented lines with different levels of recognizable high-order structure (none, collinearity, and meaning). Our results showed that recognizable stimuli cause larger activations in anterior visual and frontal areas. In contrast, when stimuli are random or unrecognizable, activations are greater in posterior visual areas, following a hierarchical organization where areas V1/V2 were less active with "collinearity" and the middle occipital cortex was less active with "meaning." An effective connectivity analysis using dynamic causal modeling showed that high-order visual form engages higher visual areas that generate top-down signals, from multiple levels of the visual hierarchy. These results are consistent with a model in which if a stimulus has recognizable attributes, such as collinearity and meaning, the areas specialized for processing these attributes send top-down messages to the lower levels to facilitate more efficient encoding of visual form.

Judgments of mathematical beauty are resistant to revision through external opinion.

We here address the question of the extent to which judgments of mathematical beauty (which we categorize as biological beauty) are resistant to revision through external opinion. A total of 100 mathematicians of different national and ethnic origins were asked to rate 60 mathematical equations for their beauty; after being presented a fictitious "expert rating," they were asked to re-rate the same equations. Results showed that the judgments of mathematical beauty had a high level of resistance to external opinion. This is in line with the resistance to revision of a judgments for other categories of biological beauty.

On the necessity of importing neurobiology into mathematics.

In Gödel's Incompleteness Theorems, for every mathematical system there are correct statements that cannot be proven to be correct within that system. We here extend this to address the question of axiomatic statements that are perceived (or known) to be correct but which mathematics, as presently constituted, cannot prove. We refer to these as perceptual axioms.

Human faces and face-like stimuli are more memorable.

We have previously suggested a distinction in the brain processes governing biological and artifactual stimuli. One of the best examples of the biological category consists of human faces, the perception of which appears to be determined by inherited mechanisms or ones rapidly acquired after birth. In extending this work, we inquire here whether there is a higher memorability for images of human faces and whether memorability declines with increasing departure from human faces; if so, the implication would add to the growing evidence of differences in the processing of biological versus artifactual stimuli. To do so, we used images and memorability scores from a large data set of 58,741 images to compare the relative memorability of the following image categories: real human faces versus buildings, and extending this to a comparison of real human faces with five image categories that differ in their grade of resemblance to a real human face. Our findings show that, in general, when we compare the biological category of faces to the artifactual category of buildings, the former is more memorable. Furthermore, there is a gradient in which the more an image resembles a real human face the more memorable it is. Thus, the previously identified differences in biological and artifactual images extend to the field of memory.