In early modernity, one can find many spatial logic diagrams whose geometric forms share a family resemblance with religious art and symbols. The family resemblance these diagrams bear in form is often based on a vesica piscis or on a cross: Both logic diagrams and spiritual symbols focus on the intersection or conjunction of two or more entities, e.g. subject and predicate, on the one hand, or god and man, on the other. This paper deals with the development and function (...) of logic diagrams, their analogy to religious art and symbols, and their modern application in artificial intelligence. (shrink)

In this thesis, I both analyze the phenomenology of vision from a geometrical point of view, and also develop certain connections between that geometrical analysis and the mind body problem. In order to motivate the need for such an analysis, I first show, by means of a refutation of direct realism, that visual space is never identical with any of the physical objects being indirectly "seen" by constituting color arrangements in it. It thus follows that the geometry of visual (...) space may be quite different from the Euclidean geometry of physical space, and I proceed to analyze that geometry. ;I argue that topologically, visual space is two dimensional, inasmuch as regions of it are capable of being bounded by a line, such as the borders around the various objects constituted in it. An apparent paradox arises here though, inasmuch as we posess phenomenal depth perception, which is particularly striking during binocular vision, and thus the question arises as to how the binocular depth cue of retinal disparity is registered phenomenally in a two dimensional space. I resolve this apparent paradox by arguing that the internal metric struture of this space can be apprehended phenomenally, and can serve as such a phenomenal depth cue. It is shown that holistically, this metric structure is elliptical, since for example marginal distortions in wide-angle photography are not present in visual space, and it is also noted that there is a tendency towards size constancy in visual perception. It is shown from these geometrical considerations that visual space posseses a variable curvature, with that curvature being determined by the physical depths of objects constituted in the space. ;Finally, I investigate what bearing the preceding geometrical conclusions have on the question of how events in visual space may be causally determined by neural events in the brain. The classical isomorphic theory of Gestalt psychology is then reinterpreted in light of my analysis of the geometry of visual space. (shrink)

Notch is a mechanosensitive receptor that requires direct cell–cell contact for its activation. Both the strength and the range of notch signaling depend on the size and geometry of the contact sites between cells. These properties of cell–cell contacts in turn depend on cell shape and polarity. At the molecular level, the E3 ubiquitin ligase Neuralized links receptor activation with epithelial cell remodeling. Neur regulates the endocytosis of the Notch ligand Delta, hence Notch activation. It also targets the apical (...) polarity protein Stardust to promote the endocytosis of the Crumbs complex, thereby contributing to epithelium remodeling. Here, we review the interplay between Notch signaling and cell polarity and discuss the possible significance of linking Notch signaling with epithelial cell polarity via a common regulator. Notch receptor activation depends on direct cell–cell contacts that in turn depends on cell shape and cellular polarity. The size and geometry of cell–cell contacts have an impact on the strength and range of signaling. The E3 ubiquitin ligase Neuralized regulates the endocytosis and signaling activity of Delta. The activity of Neuralized is tightly regulated during development. Neuralized also modulates epithelial cell polarity by targeting the apical polarity protein Stardust and by promoting the endocytosis of Crumbs. Thus, the cell-specific expression of Neuralized couples Notch receptor activation with cell polarity regulation in epithelia. (shrink)

Symmetry in biological and physical systems is a product of self-organization driven by evolutionary processes, or mechanical systems under constraints. Symmetry-based feature extraction or representation by neural networks may unravel the most informative contents in large image databases. Despite significant achievements of artificial intelligence in recognition and classification of regular patterns, the problem of uncertainty remains a major challenge in ambiguous data. In this study, we present an artificial neural network that detects symmetry uncertainty states in human observers. (...) To this end, we exploit a neural network metric in the output of a biologically inspired Self- Organizing Map Quantization Error (SOM-QE). Shape pairs with perfect geometry mirror symmetry but a non-homogenous appearance, caused by local variations in hue, saturation, or lightness within and/or across the shapes in a given pair produce, as shown here, a longer choice response time (RT) for “yes” responses relative to symmetry. These data are consistently mirrored by the variations in the SOM-QE from unsupervised neural network analysis of the same stimulus images. The neural network metric is thus capable of detecting and scaling human symmetry uncertainty in response to patterns. Such capacity is tightly linked to the metric’s proven selectivity to local contrast and color variations in large and highly complex image data. (shrink)

What is consciousness? Conventional approaches see it as an emergent property of complex interactions among individual neurons; however these approaches fail to address enigmatic features of consciousness. Accordingly, some philosophers have contended that "qualia," or an experiential medium from which consciousness is derived, exists as a fundamental component of reality. Whitehead, for example, described the universe as being composed of "occasions of experience." To examine this possibility scientifically, the very nature of physical reality must be re-examined. We must come to (...) terms with the physics of spacetime-as described by Einstein's general theory of relativity, and its relation to the fundamental theory of matter-as described by quantum theory. Roger Penrose has proposed a new physics of objective reduction: "OR," which appeals to a form of quantum gravity to provide a useful description of fundamental processes at the quantum/classical borderline.hz Within the OR scheme, we consider that consciousness occurs if an appropriately organized system is able to develop and maintain quantum coherent superposition until a specific "objective" criterion (a threshold related to quantum gravity) is reached; the coherent system then self-reduces (objective reduction: OR). We contend that this type of objective self-collapse introduces non-computability, an essential feature of consciousness which distinguishes our minds from classical computers. Each OR is taken as an instantaneous event-the climax of a self-organizing process in fundamental spacetime-and a candidate for a conscious Whitehead "occasion of experience." How could an OR process occur in the brain, be coupled to neural activities, and account for other features of consciousness? We nominate a quantum computational OR process with the requisite characteristics to be occurring in cytoskeletal microtubules within the brain's neurons. In this model, quantum-superposed states develop in microtubule subunit proteins ("tubulins") within certain brain neurons, remain coherent, and recruit more superposed tubulins until a mass-time-energy threshold (related to quantum gravity) is reached.. (shrink)

_dualism_ (consciousness lies outside knowable science), _emergence_ (consciousness arises as a novel property from complex computational dynamics in the brain), and some form of _panpsychism_, _pan-protopsychism, or pan-experientialism_ (essential features or precursors of consciousness are fundamental components of reality which are accessed by brain processes). In addition to 1) the problem of subjective experience, other related enigmatic features of consciousness persist, defying technological and philosophical inroads. These include 2) the “binding problem”—how disparate brain activities give rise to a unified sense (...) of “self” or unified conscious content. Temporal synchrony—brain-wide coherence of neural membrane electrical activities—is often assumed to accomplish binding, but _what_ is being synchronized? What is being coherently bound? Another enigmatic feature is 3) the transition from pre-conscious processes to consciousness itself. Most neuroscientists agree that consciousness is the “tip of an iceberg”, that the vast majority of brain activities is. (shrink)

The cognitive basis of geometry is still poorly understood, even the ‘simpler’ issue of what kind of representation of geometric objects we have. In this work, we set forward a tentative model of the neural representation of geometric objects for the case of the pure geometry of Euclid. To arrive at a coherent model, we found it necessary to consider earlier forms of geometry. We start by developing models of the neural representation of the geometric (...) figures of ancient Greek practical geometry. Then, we propose a related model for the earliest form of pure geometry – that of Hippocrates of Chios. Finally, we develop the model of the neural representation of the geometric objects of Euclidean geometry. The models are based on the hub-and-spoke theory. In our view, the existence of specific models opens the possibility of addressing the relationship between geometric figures and geometric objects, in a novel way, in terms of their neural representation. (shrink)

Statistical regularities of the environment are important for learning, memory, intelligence, inductive inference, and in fact, for any area of cognitive science where an information-processing brain promotes survival by exploiting them. This has been recognised by many of those interested in cognitive function, starting with Helmholtz, Mach, and Pearson, and continuing through Craik, Tolman, Attneave, and Brunswik. In the current era, many of us have begun to show how neural mechanisms exploit the regular statistical properties of natural images. Shepard (...) proposed that the apparent trajectory of an object when seen successively at two positions results from internalising the rules of kinematic geometry, and although kinematic geometry is not statistical in nature, this is clearly a related idea. Here it is argued that Shepard's term, “internalisation,” is insufficient because it is also necessary to derive an advantage from the process. Having mechanisms selectively sensitive to the spatio-temporal patterns of excitation commonly experienced when viewing moving objects would facilitate the detection, interpolation, and extrapolation of such motions, and might explain the twisting motions that are experienced. Although Shepard's explanation in terms of Chasles' rule seems doubtful, his theory and experiments illustrate that local twisting motions are needed for the analysis of moving objects and provoke thoughts about how they might be detected. Key Words: Chasles' rule; evolution; geometry; perception; redundancy; statistics; twisting. (shrink)

In this article, I revisit Landau and Jackendoff's () paper, “What and where in spatial language and spatial cognition,” proposing a friendly amendment and reformulation. The original paper emphasized the distinct geometries that are engaged when objects are represented as members of object kinds, versus when they are represented as figure and ground in spatial expressions. We provided empirical and theoretical arguments for the link between these distinct representations in spatial language and their accompanying nonlinguistic neural representations, emphasizing the (...) “what” and “where” systems of the visual system. In the present paper, I propose a second division of labor between two classes of spatial prepositions in English that appear to be quite distinct. One class includes prepositions such as in and on, whose core meanings engage force-dynamic, functional relationships between objects, with geometry only a marginal player. The second class includes prepositions such as above/below and right/left, whose core meanings engage geometry, with force-dynamic relationships a passing or irrelevant variable. The insight that objects’ force-dynamic relationships matter to spatial terms’ uses is not new; but thinking of these terms as a distinct set within spatial language has theoretical and empirical consequences that are new. I propose three such consequences, rooted in the fact that geometric knowledge is highly constrained and early-emerging in life, while force-dynamic knowledge of objects and their interactions is relatively unconstrained and needs to be learned piecemeal over a lengthy timeline. First, the two classes will engage different learning problems, with different developmental trajectories for both first and second language learners; second, the classes will naturally lead to different degrees of cross-linguistic variation; and third, they may be rooted in different neural representations. (shrink)

The program of “neurophenomenal structuralism” is presented as an agenda for a genuine structuralist neuroscience of consciousness that seeks to understand specific phenomenal experiences as strictly relational affairs. The paper covers a broad range of topics. It starts from considerations about neural change detection and relational coding that motivate a solution of the Newman problem of the brain in terms of spatiotemporal relations. Next, phenomenal quality spaces and their Q-structures are discussed. Neurophenomenal structuralism proclaims a homomorphic mapping of the (...) structures of self-organized neural maps in the brain onto Q-structures, and it will be demonstrated how this leads to a new and special version of structural representationalism about phenomenal content. A methodological implication of neurophenomenal structuralism is that it proposes measurement procedures that focus on the relationships between different stimuli (as, for instance, similarity ratings or representational geometry methods). Finally, it will be shown that neurophenomenal structuralism also has strong philosophical implications, as it leads to holism about phenomenal experiences and serves to reject inverted qualia scenarios. (shrink)

A successful vision system must solve the problem of deriving geometrical information about three-dimensional objects from two-dimensional photometric input. The human visual system solves this problem with remarkable efficiency, and one challenge in vision research is to understand howneural representations of objects are formed and what visual information is used to form these representations. Ideal observer analysis has demonstrated the advantages of studying vision from the perspective of explicit generative models and a specified visual task, which divides the causes of (...) image variations into the separate categories of signal and noise. Classification image techniques estimate the visual information used in a task from the properties of “noise” images that interact most strongly with the task. Both ideal observer analysis and classification image techniques rely on the assumption of a generative model. We show here how the ability of the classification image approach to understand how an observer uses visual information can be improved by matching the type and dimensionality of the model to that of the neural representation or internal template being studied. Because image variation in real world object tasks can arise from both geometrical shape and photometric (illumination or material) changes, a realistic image generation process should model geometry as well as intensity. A simple example is used to demonstrate what we refer to as a “classification object” approach to studying three-dimensional object representations. (shrink)

In this paper we first recall geometrical models of neurogeometical in Lie groups and we show that geometrical properties of horizontal cortical connectivity can be considered as a neural correlate of a geometry of the visual plane. Then we introduce a new model of non isotropic cortical connectivity modeled on statistics of images. In this way we are able to justify oblique phenomena comparable with experimental findings.

I have argued here for a change in a scientific world-view, from that of the study of forms to that of process. In doing so we need to understand as to how process creates form. In showing this I have at first drawn from the history of Buddhist philosophy; with its concepts of ‘Sunyata’ (Emptiness) and radical interdependency (Huayen). Then showed its parallel with modern Fractal geometries, which thru’ rather simple mathematics, shows as to how process could derive form. I (...) have then gone on to Quantum constructions, which is without doubt the most advanced scientific development in modern times, and attempted to show two vital directions which contradict the classical scientific world view. The usual scientific view retains a Descartian, ‘out there’ deterministic framework. I argue that with the break down of determinism, and the non locality of phenomena suggested by Quantum Mechanics allows for an independent functioning of consciousness; which then is not a mere epiphenomena of neural activity within the brain. Such a view has wide implications on how we live and how we die. (shrink)

: This commentary focuses on the scientific status of perceptual projection-a central feature of Pereira’s projective theory of consciousness. In his target article, he draws on my own earlier work to develop an explanatory framework for integrating first-person viewable conscious experience with the third-person viewable neural correlates and antecedent causes that form conscious experience into a bipolar structure that contains both a sense of self and a sense of the world. I stress that perceptual projection is a psychological effect (...) and list many of the ways it has been studied within experimental psychology, for example in studies of depth perception in vision and audition and experiences of depth arising from cues arranged on two-dimensional surfaces in stereoscopic pictures, 3D cinemas, holograms, and virtual realities. I then juxtapose Pereira’s explanatory model with two other models that have similar aims and background assumptions but different orientations, Trehub’s Retinoid model, which focuses largely on the neural functioning of the visual system, and Rudrauf et al’s Projective Consciousness Model, which draws largely on projective geometries to specify the requirements of organisms that need to navigate a three-dimensional world, and how these might be implemented in human information processing. Together, these models illustrate both converging and diverging approaches to understanding the role of projective processes in human consciousness. Resumo: Este comentário enfoca o status científico da projeção perceptiva - uma característica central da teoria da consciência de Pereira. Em seu artigo alvo, ele recorre ao meu trabalho anterior para desenvolver uma estrutura explicativa para integrar a experiência consciente visível em primeira pessoa com os correlatos neurais visíveis de terceira pessoa e as causas antecedentes que formam a experiência consciente em uma estrutura bipolar que contém tanto um sentido de eu e um sentido do mundo. Enfatizo que a projeção perceptiva é um efeito psicológico e relaciono modalidades de seu estudo na psicologia experimental, por exemplo em estudos de percepção de profundidade em visão e audição, experiências de profundidade em superfícies bidimensionais em imagens estereoscópicas, cinemas 3D, hologramas e realidades virtuais. Eu então justaponho o modelo explicativo de Pereira com dois outros modelos que têm objetivos e suposições similares, mas orientações diferentes, o modelo do sistema retinóide de Trehub, que se concentra principalmente no funcionamento neural do sistema visual, e o modelo de consciência projetiva de Rudrauf et al., que estabelece raciocínios geométricos para especificar os requisitos de organismos que precisam navegar em um mundo tridimensional, e como eles podem ser implementados no processamento de informação no contexto humano. Juntos, esses modelos ilustram abordagens convergentes e divergentes para compreender o papel dos processos projetivos na consciência humana. (shrink)

An original quantum foundations concept of a deep learning computational Universe is introduced. The fundamental information of the Universe (or Triuniverse)is postulated to evolve about itself in a Red, Green and Blue (RGB) tricoloured stable self-mutuality in three information processing loops. The colour is a non-optical information label. The information processing loops form a feedback-reinforced deep learning macrocycle with trefoil knot topology. Fundamental information processing is driven by ψ-Epistemic Drive, the Natural appetite for information selected for advantageous knowledge. From its (...) substrate of Mathematics, the knotted information processing loops determine emergent Physics and thence the evolution of super-emergent Life (biological and artificial intelligence). RGB-tricoloured information is processed in sequence in an Elemental feedback loop (R), then an Operational feedback loop (G), then a Structural feedback loop (B) and back to an Elemental feedback loop (R), and so on around the trefoil in deep learning macrocycles. It is postulated that hierarchical information correspondence from Mathematics through Physics to Life is mapped and conserved within each colour. The substrate of Mathematics has RGB-tricoloured feedback loops which are respectively Algebra (R), Algorithms (G) and Geometry (B). In Mathematics, the trefoil macrocycle is Algebraic Algorithmic Geometry and its correlation system is a Tensor Neural Knot Network enabling Qutrit Entanglement. Emergent Physics has corresponding RGB-tricoloured feedback loops of Quantum Mechanics (R), Quantum Deep Learning (G) and Quantum Geometrodynamics(B). In Physics, the trefoil macrocycle is Quantum Intelligent Geometrodynamics and its correlation system is Quantum Darwinism. Super-emergent Life has corresponding RGB-tricoloured loops of Variation (R), Selection (G) and Heredity (B). In the evolution of Life, the trefoil macrocycle is Variational Selective Heredity and its correlation ecosystem is Darwin’s ecologically “Entangled Bank”. (shrink)

Machine generated contents note: Cajal and Consciousness: Introduction. By PEDRO C. MARIJUAN1 -- Part I. Consciousness, One Hundred Years after Textura -- Progress in the Neural Sciences in the Century after Cajal (and the Mysteries -- That Remain). By THOMAS D. ALBRIGHT, THOMAS M. JESSELL, -- ERIC R. KANDEL, AND MICHAEL I. POSNER11 -- Part II. Biological Complexity and the Emergence of Consciousness -- Consciousness, Reduction, and Emergence: Some Remarks. -- By MURRAY GELL-MANN41 -- The Epistemic Paradox of Mind (...) and Matter. By HAROLD J. MOROWITZ50 -- The Conscious Cell. BY LYNN MARGULIS55 -- Complexity and Tinkering. By FRANCOIS JACOB71 -- Consciousness, the Brain, and Spacetime Geometry. By STUART HAMEROFF. 74 -- Consciousness, the Brain, and Spacetime Geometry: An Addendum-Some -- New Developments on the Orch OR Model for Consciousness. -- By ROGER PENROSE105 -- Part III. From Primary to Higher-level Consciousness -- Consciousness: The Remembered Present. By GERALD EDELMAN111 -- Consciousness and the Binding Problem. By WOLF SINGER123 -- Cajal on Neurons, Molecules, and Consciousness. By JEAN-PIERRE CHANGEUX 147 -- A Neuronal Model of a Global Workspace in Effortful Cognitive Tasks. By -- STANISLAS DEHAENE, MICHEL KERSZBERG, AND JEAN-PIERRE -- CHANGEUX152 -- Consciousness and the Brain: The Thalamocortical Dialogue in Health and -- Disease. By RODOLFO LLINAS AND URS RIBARY166 -- The Neuroanatomy of Phenomenal Vision: A Psychological Perspective. -- ByPETRA STOERIG176 -- Co-evolution of Human Consciousness and Language. By MICHAEL A. ARBIB 195 -- From Computing with Numbers to Computing with Words-From -- Manipulation of Measurements to Manipulations of Perceptions. -- By LOTFI A. ZADEH221 -- Part IV. Closing Remarks -- Who Was Cajal? By ALBERTO PORTERA-SANCHEZ253 -- Index of Contributors259 -- Subject Index261. (shrink)

Scientific theories of consciousness identify its contents with the spatiotemporal structure of neural population activity. We follow up on this approach by stating and motivating Dynamical Emergence Theory, which defines the amount and structure of experience in terms of the intrinsic topology and geometry of a physical system’s collective dynamics. Specifically, we posit that distinct perceptual states correspond to coarse-grained macrostates reflecting an optimal partitioning of the system’s state space—a notion that aligns with several ideas and results from (...) computational neuroscience and cognitive psychology. We relate DET to existing work, offer predictions for empirical studies, and outline future research directions. (shrink)

The essay brings a summation of human efforts seeking to understand our existence. Plato and Kant & cognitive science complete reduction of philosophy to a neural mechanism, evolved along elementary Darwinian principles. Plato in his famous Cave Allegory explains that between reality and our experience of it there exists a great chasm, a metaphysical gap, fully confirmed through particle-wave duality of quantum physics. Kant found that we have two kinds of perception, two senses: By the spatial outer sense we (...) perceive phenomena, objects in space. Our temporal inner sense lets us perceive our inner state, noumena . Kant's two senses are fully confirmed through bilateral brain duality of cognitive science. The bilateral brain serves inner, temporal sense, logic & noumena in the left hemisphere. The right brain half is for the outer, spatial sense, geometry & phenomena. We form a whole system, a bilateral interior cosmos, a kind of world model, expressing what may lie beyond the metaphysical gap. In the right brain we build a phenomenal cosmos, to resemble the outer environment. In the brain's left hemisphere a noumenal cosmos, a model of our private world including Saint Teresa of Avila's castillo interior. The cosmos is regularly updated with novel sense data integrated into our memory banks. This was recognized early by Helmholtz (1860s). Our lives, health & well-being depend on us keeping our interior cosmos in good order. This used to be seen as saving one's precious soul from perdition. While we endeavour to keep our phenomenal cosmos neat & orderly by protecting the environment from harm, our noumenal cosmos to be livable requires us to engage in ethical conduct. This bilateral cosmos is responsible for our common sense judgment power, that we depend on for being able to lead a good & benign life. The 200 million neurons of BA10 in the prefrontal lobe have global access to the interior cosmos, & apply massive feedback to identify environmental conditions rapidly. The global access also gives conscious presence of the individual to itself, all that is present in the interior cosmos, for total freedom of action. In the left brain private ego, we are guarded by faith in divine mercy, & guided to choose the best course of action, able to survive under the most adverse conditions. For this, we receive directions from the Holy Ghost in Saint Teresa's castillo interior. (shrink)

Excitation at widely dispersed loci in the cerebral cortex may represent a neural correlate of consciousness. Accordingly, each unique combination of excited neurons would determine the content of a conscious moment. This conceptualization would be strengthened if we could identify what orchestrates the various combinations of excited neurons. In the present paper, cholinergic afferents to the cerebral cortex are hypothesized to enhance activity at specific cortical circuits and determine the content of a conscious moment by activating certain combinations of (...) postsynaptic sites in select cortical modules. It is proposed that these selections are enabled by learning-related restructuring that simultaneously adjusts the cytoskeletal matrix at specific constellations of postsynaptic sites giving all a similar geometry. The underlying mechanism of conscious awareness hypothetically involves cholinergic mediation of linkages between microtubules and microtubule-associated protein-2 . The first reason for proposing this mechanism is that previous studies indicate cognitive-related changes in MAP-2 occur in cholinoceptive cells within discrete cortical modules. These cortical modules are found throughout the cerebral cortex, measure 1–2 mm2, and contain approximately 103–104cholinoceptive cells that are enriched with MAP-2. The subsectors of the hippocampus may function similarly to cortical modules. The second reason for proposing the current mechanism is that the MAP-2 rich cells throughout the cerebral cortex correspond almost exactly with the cortical cells containing muscarinic receptors. Many of these cholinoceptive, MAP-2 rich cells are large pyramidal cell types, but some are also small pyramidal cells and nonpyramidal types. The third reason for proposing the current mechanism is that cholinergic afferents are module-specific; cholinergic axons terminate wholly within individual cortical modules. The cholinergic afferents may be unique in this regard. Finally, the tapering apical dendrites of pyramidal cells are proposed as primary sites for cholinergic mediation of linkages between MAP-2 and microtubules because especially high amounts of MAP-2 are found here. Also, the possibility is raised that muscarinic actions on MAP-2 could modulate microtubular coherence and self-collapse, phenomena that have been suggested to underlie consciousness. (shrink)

The open rhabdoms of the fly's eye enhance absolute sensitivity but to avoid compromising spatial acuity they require precise optical geometry and neural connections.1 This neural superposition system evolved from the ancestral insect eye, which has fused rhabdoms. A recent paper by Zelhof and co‐workers2 shows that the Drosophila gene spacemaker (spam) is necessary for development of open rhabdoms, and suggests that mutants revert to an ancestral state. Here I outline how open rhabdoms and neural superposition (...) may have evolved via nocturnal intermediates, and discuss the implications for the role of spam in insect phylogeny. BioEssays 29: 111–115, 2007. © 2007 Wiley Periodicals, Inc. (shrink)

Age-old battle lines over the puzzling nature of mental experience are shaping a modern resurgence in the study of consciousness. On one side are the long-dominant "physicalists" who view consciousness as an emergent property of the brain's neural networks. On the alternative, rebellious side are those who see a necessary added ingredient: proto-conscious experience intrinsic to reality, perhaps understandable through modern physics (panpsychists, pan-experientialists, "funda-mentalists"). It is argued here that the physicalist premise alone is unable to solve completely the (...) difficult issues of consciousness and that to do so will require supplemental panpsychist/pan-experiential philosophy expressed in modern physics. In one scheme proto-conscious experience is a basic property of physical reality accessible to a quantum process associated with brain activity. The proposed process is Roger Penrose's "objective reduction" (OR), a self-organizing "collapse" of the quantum wave function related to instability at the most basic level of space-time geometry. In the Penrose- Hameroff model of "orchestrated objective reduction" (Orch OR), OR quantum computation occurs in cytoskeletal microtubules within the brain's neurons. The basic thesis is that consciousness involves brain activities coupled to a self-organizing ripples in fundamental reality. (shrink)

Analyzing geometric properties of high-dimensional loss functions, such as local curvature and the existence of other optima around a certain point in loss space, can help provide a better understanding of the interplay between neural network structure, implementation attributes, and learning performance. In this work, we combine concepts from high-dimensional probability and differential geometry to study how curvature properties in lower-dimensional loss representations depend on those in the original loss space. We show that saddle points in the original (...) space are rarely correctly identified as such in expected lower-dimensional representations if random projections are used. The principal curvature in the expected lower-dimensional representation is proportional to the mean curvature in the original loss space. Hence, the mean curvature in the original loss space determines if saddle points appear, on average, as either minima, maxima, or almost flat regions. We use the connection between expected curvature in random projections and mean curvature in the original space (i.e., the normalized Hessian trace) to compute Hutchinson-type trace estimates without calculating Hessian-vector products as in the original Hutchinson method. Because random projections are not suitable to correctly identify saddle information, we propose to study projections along dominant Hessian directions that are associated with the largest and smallest principal curvatures. We connect our findings to the ongoing debate on loss landscape flatness and generalizability. Finally, for different common image classifiers and a function approximator, we show and compare random and Hessian projections of loss landscapes with up to about 7×10^6 parameters. (shrink)

This paper reports on the investigation of the effects of neuronal shape, at both individual cell and network level, on the behavior of neuronal systems. More specifically, two-dimensional biologically realistic neuronal networks are obtained that take explicity into account the position and morphology of neuronal cells, with the respective behavior for associative recall being simulated through a diluted version of Hopfield's model. While a specific probability density function is used for the placement of the cell bodies, images of real neuronal (...) cells (namely alpha and beta ganglion cells from the cat retina) are used to obtain biologically realistic models. Several morphological measures – including fractal dimension, the excluded volume, and integral geometry functionals–are estimated for the considered cells, and their values are correlated with the potential of the network for associative recall, which is quantified in terms of the overlap between distorted version of the trained patterns and their original version. Such an approach allows the quantitative and objective characterization of the relationship between neuronal shape and function, an important issue in neuroscience. The obtained results substantiate interesting relationships between the neural morphology and function as determined by the performance of the network. (shrink)

This paper presents an enquiry into the essential nature of phenomenal consciousness and its relation to the neural correlates of consciousness in the brain . It first combines critical accounts of current ideas about the nature of NCCs themselves and about what constitutes phenomenal consciousness. This is followed by an examination of how these two may be related with a particular focus on pointing out the defects in the currently most popular hypothesis in this field, namely the identity theory. (...) The conclusion is that we need a better theory. A candidate for this theory is presented in some detail that involves higher-dimensional geometry. (shrink)

One major problem many hypotheses regarding the neural correlate of consciousness, face is what we might call “the why question”: why would this particular neural feature, rather than another, correlate with consciousness? The purpose of the present paper is to develop an NCC hypothesis that answers this question. The proposed hypothesis is inspired by the cross-order integration theory of consciousness, according to which consciousness arises from the functional integration of a first-order representation of an external stimulus and a (...) second-order representation of that first-order representation. The proposal comes in two steps. The first step concerns the “general shape” of the NCC and can be directly derived from COI theory. The second step is a concrete hypothesis that can be arrived at by combining the general shape with empirical considerations. (shrink)

This paper introduces the Cummins Functions Approach to neural representations, which aims to capture the notion of representation that is relevant to contemporary neuroscientific practice. CFA shares the common view that “to be a representation of X” amounts to “having the function of tracking X,” but maintains that the relevant notion of function is defined by Robert Cummins’s account. Thus, CFA offers a notion of neural representation that is dependent on explanatory context. I argue that CFA can account (...) for the normativity of neural representations, and defend its dependence on explanations. (shrink)

Computationalism about the brain is the view that the brain literally performs computations. For the view to be interesting, we need an account of computation. The most well-developed account of computation is Turing Machine computation, the account provided by theoretical computer science which provides the basis for contemporary digital computers. Some have thought that, given the seemingly-close analogy between the all-or-nothing nature of neural spikes in brains and the binary nature of digital logic, neural computation could be a (...) species of digital computation. A few recent authors have offered arguments against this idea; here, I review recent findings in neuroscience that further cement the implausibility of this view. However, I argue that we can retain the view that the brain is a computer if we expand what we mean by “computation” to include analog computation. I articulate an account of analog computation as the manipulation of analog representations based on previous work on the difference between analog and non-analog representations, extending a view originally articulated in Shagrir :271–279, 2010). Given that analog computation constitutes a significant chapter in the history of computation, this revision of computationalism to include analog computation is not an ad hoc addition. Brains may well be computers, but of the analog kind, rather than the digital kind. (shrink)

ABSTRACTWe discuss the thesis of universality of geometric notions and offer critical reflections on the concept of “natural geometry” employed by Spelke and others. Promoting interdisciplinary wor...

Over many centuries, the homing pigeon has been selectively bred for returning home from a distant location. As a result of this strong selective pressure, homing pigeons have developed an excellent spatial navigation system. This system passes through the hippocampal formation, which shares many striking similarities to the mammalian hippocampus; there are a host of shared neuropeptides, interconnections, and its role in the storage and manipulation of spatial maps. There are some notable differences as well: there are unique connectivity patterns (...) and spatial encoding strategies. This review summarizes the comparisons between the avian and mammalian hippocampal systems, and the responses of single neurons in several general categories: location and place cells responding in specific areas, path and goal cells responding between goal locations, context-dependent cells that respond before or during a task, and pattern, grid, and boundary cells that increase firing at stable intervals. Head-direction cells, responding to a specific compass direction, are found in mammals and other birds but not to date in pigeons. By studying an animal that evolved under significant adaptive pressure to quickly develop a complex and efficient spatial memory system, we may better understand the comparative neurology of neurospatial systems, and plot new and potentially fruitful avenues of comparative research in the future. (shrink)

Modern color science finds its birth in the middle of the nineteenth century. Among the chief architects of the new color theory, the name of the polymath Hermann von Helmholtz stands out. A keen experimenter and profound expert of the latest developments of the fields of physiological optics, psychophysics, and geometry, he exploited his transdisciplinary knowledge to define the first non-Euclidean line element in color space, i.e., a three-dimensional mathematical model used to describe color differences in terms of color (...) distances. Considered as the first step toward a metrically significant model of color space, his work inaugurated researches on higher color metrics, which describes how distance in the color space translates into perceptual difference. This paper focuses on the development of Helmholtz’s mathematical derivation of the line element. Starting from the first experimental evidence which opened the door to his reflections about the geometry of color space, it will be highlighted the pivotal role played by the studies conducted by his assistants in Berlin, which provided precious material for the elaboration of the final model proposed by Helmholtz in three papers published between 1891 and 1892. Although fallen into oblivion for about three decades, Helmholtz’s masterful work was rediscovered by Schrödinger and, since the 1920s, it has provided the basis for all subsequent studies on the geometry of color spaces up to the present time. (shrink)

ObjectiveRetinal vein occlusion (RVO) is the second most common retinal vascular disorder after diabetic retinopathy, which is the main cause of vision loss. Retinal vein occlusion might lead to macular edema, causing severe vision loss. Previous neuroimaging studies of patients with RVO demonstrated that RVO was accompanied by cerebral changes, and was related to stroke. The purpose of the study is to investigate synchronous neural activity changes in patients with RVO.MethodsA total of 50 patients with RVO and 48 healthy (...) subjects with matched sex, age, and education were enrolled in the study. The ReHo method was applied to investigate synchronous neural activity changes in patients with RVO.ResultsCompared with HC, patients with RVO showed increased ReHo values in the bilateral cerebellum_4_5. On the contrary, patients with RVO had decreased ReHo values in the bilateral middle occipital gyrus, right cerebelum_crus1, and right inferior temporal gyrus.ConclusionOur study demonstrated that patients with RVO were associated with abnormal synchronous neural activities in the cerebellum, middle occipital gyrus, and inferior temporal gyrus. These findings shed new insight into neural mechanisms of vision loss in patients with RVO. (shrink)