Models of Consciousness

One in a series of talks from the 2019 Models of Consciousness conference. John Barnden School of Computer Science, University of Birmingham, UK I assume that [phenomenal] consciousness is a property physical processes can have, and that it involves pre-reflective auto-sensitivity (PRAS), which is related to the much-discussed pre-reflective self-consciousness [3,4]. I then argue that PRAS requires conscious processes to be directly and causally sensitive to their own inner causation as such, and not merely to their own trajectories of physical states as ordinarily understood. That causal sensitivity is therefore metacausation. Metacausation here is where instances of causation are themselves, directly and in their own right, causes or effects. Metacausation (aka higher-order causation) is rarely discussed at all, and has apparently not previously been linked to consciousness. But the proposal is yet more radical as I merely use "causation" to mean microphysical dynamism. I assume (anti-Humeanly) that the universe's law-governed unfolding is a dynamism irreducible to sheer regular patterning over spacetime of familiar physical quantities (masses, charges, fields, curvatures, etc.). Furthermore, I strongly reify dynamism: spatiotemporally specific instances of it are a ``new'' realm of fundamental physical quantities, themselves dynamically interacting in their own right with other quantities (familiar or new). That dynamic interaction is a new level of dynamism, namely metadynamism, with its own laws explicitly mentioning dynamism instances. As causation is just dynamism, metacausation is metadynamism. The poster summarizes the arguments (revising earlier versions [1,2]) and sketches initial formalization steps for metadynamism. It also indicates how metadynamism might be co-opted to enrich other consciousness theories, notably IIT and Orch-OR. References: [1] Barnden, J.A. (2014). Running into consciousness. J. Consciousness Studies, 21 (5-6), pp.33-56. [2] Barnden, J.A. (2018). Phenomenal consciousness, meta-causation and developments concerning casual powers and time passage. Poster presented at 22nd Conference for the Association for the Scientific Study of Consciousness, 26-29 June 2018, Krakow. [3] Gallagher, S. & Zahavi, D. (2015). Phenomenological approaches to self-consciousness. In Edward N. Zalta (Ed.), The Stanford Encyclopedia of Philosophy (Spring 2015 Edition). [4] Sebastian, M.A. (2012). Experiential awareness: Do you prefer ``it'' to ``me''? Philosophical Topics, 40(2), pp.155-177." Filmed at the Models of Consciousness conference, University of Oxford, September 2019.

One in a series of talks from the 2019 Models of Consciousness conference. Pedro Mediano Department of Computing, Imperial College London In a seminal series of papers, Tononi, Sporns, and Edelman (TSE) introduced the idea that the neural dynamics underlying conscious states are characterised by a balance of integration and differentiation between system components. This idea remains prevalent in consciousness research today, influencing theoretical and experimental work. Such work has faced a number of challenges. For example, distinct measures designed to measure such a balance behave very differently in practice, making it hard to choose which is the "right one", and dynamics of conscious and unconscious brains defy some of the predictions of this framework. We argue that these problems arise, at least in part, from the non-specific nature of the concepts of integration and differentiation. Here, we present a revised mathematical theory of neural complexity: we introduce a new measure, called O-information, that quantifies the balance between redundancy and synergy within a system, and is more effective than TSE’s original measure at describing phenomena where large-scale correlation and short-scale independence coexist; and develop a formalism to decompose different "modes" of information dynamics, providing an exhaustive taxonomy of redundant and synergistic effects. These developments allow us to place previous measures within a common framework and explain their their similarities and differences. Filmed at the Models of Consciousness conference, University of Oxford, September 2019.

One in a series of talks from the 2019 Models of Consciousness conference. Inês Hipólito University of Wollongong Building on the modular architecture of mind (Fodor 1983), Modularity Networks is claimed as a theory well equipped to explain neural connectivity and reuse (Stanley et al.; 2019, Zerrili 2019). This paper takes the case of the oculomotor system to show that even if Modularity Network’s tools are useful to describe brain’s functional connectivity, they are limited in explaining why such connections are formed and dynamic. To show this, section 1 starts by laying down the reasons for adopting Modularity Networks as well suited for explaining neural connectivity. Section 2 introduces the oculomotor system as a dynamic integration of action and vision. Section 3 argues that however valuable in describing the functional connectivity of the oculomotor system, Modularity Networks fails to explain why such connections are formed and dynamic (dependent on activity). This failure is made evident by acknowledging a fundamental distinction in the metaphysics of inference. The nature of inference is taken differently in functional connectivity as a description of inference as opposed to effective connectivity as an explanation of inference (Friston 2011). Section 4 introduces Dynamic Causal Modelling (DCM) as a better resource to capture effective connectivity. It allows explaining how and why brain connections, as generative models of cognitive integration, are dependent on the dynamic activity within the environment. This conclusion speaks against modular arguments for encapsulation, innateness and specificity of cognitive organisation. Filmed at the Models of Consciousness conference, University of Oxford, September 2019.

One in a series of talks from the 2019 Models of Consciousness conference. Gustav Bernroider University of Salzburg, Dept. of Biosciences, Austria Are there knowable criteria for subjective entities such as conscious experience? I think there are, even physical ones. I advocate the view that the basic dualism between subject and object or mind and matter can be figured by an intuitively simple version of an inside out or inversion relation between two opposing physical domains. I propose a particular topology for subject-object relations and argue that we can find a physical realisation in the brain of living organism that provides a conformal transformation between both domains. The transformation combines two physical domains related by inversion or parity symmetry or simply by mirror reflections. This view puts topological aspects behind inversion and the associated hidden symmetries in physics into the foreground. I introduce the model along three steps: i) evidence and motivation for the role of mirror symmetries from psychobiology based on previous studies (Senso- motory invariance in animal feelings [Bernroider G, Panksepp J. (2011), Neurosci & Biobehav. Rev., 35, 2009-2016.] and mirror-writing in (my grand-) children), ii) an intuitive diagrammatic demonstrating subject-object together with cause and effect relations mapped onto an inversive plane geometry and iii) a more formal outline and extension into the algebraic topology of non- orientable surfaces, the real and complex projective plane. The concept suggested here offers several testable predictions for the relation of ionic brain function to inversion symmetries realised by the molecular architecture of excitable membranes. For example, this aspect seems to be evidenced by enantio-selective electronic transitions during ion conduction in the brain [Bernroider G. (2017) JIN 16, 105-113]. Going beyond these technical aspects, the present view on modelling subjectivity shifts the role of canonical coordinates together with their static dimensional geometry into the background. It favours ideas behind general covariance. A parity transformation, if purely defined at the level of Cartesian coordinates with changing signs, is discrete, the transient itself only inferential, non-physical, with no known conserved quantity associated with this transformation in the sense of Emmy Noether’s theorem. However, if the same transformation is laid out continuously on the geometry of non-orientable surfaces (e.g. on a Möbius band), the transients gain some physics and offer a conserved quantity. I will discuss this conserved quantity with respect to subjectivity and consciousness. Filmed at the Models of Consciousness conference, University of Oxford, September 2019.

One in a series of talks from the 2019 Models of Consciousness conference. Marc Ebner Universität Greifswald, Germany The seemingly hard problem of consciousness is the problem of explaining why subjective conscious experience exist. However, Qualia is nothing mysterious. Our subjective conscious experience is comparable across individuals because we are a product of evolution. It is grounded in reality and we use it to communicate with each other. Consciousness seems to be intertwined with language. Its primary role is to serve communication between individuals. We need Qualia to communicate with others. We perceive objects within our visual field relative to the orientation of our head. This information is then stored and can also be communicated to others either during perception or at a later time. The same holds for the perception of sounds or smells. According to the theory proposed here, an assembly of neurons in the brain is in charge of consciousness. The job of this assembly is simply (a) to look at what the body does, (b) to keep a record of it, and (c) to explain it to our peers. Filmed at the Models of Consciousness conference, University of Oxford, September 2019.

One in a series of talks from the 2019 Models of Consciousness conference. Diana Stanciu University of Bucharest; Berlin-Brandenburg Academy of Sciences and Humanities (BBAW) I will argue that epistemic structural realism (ESR) can offer a feasible theoretical framework for the study of consciousness and its associated neurophysiological phenomena. While structural realism has already been employed in physics or biology (cf. Tegmark 2007, Leng 2010, Ainsworth 2010, 2011, McArthur 2011, Pincock 2011, Woodin 2011, Landry and Rickels 2012, Bain 2013, Andreas and Zenker 2014, Schurz 2014), its application to the study of consciousness is new indeed. Out of its two variants: ontic structural realism (OSR) and ESR, I consider the latter more suitable when studying the neurophysiological bases of consciousness since the OSR drastically claims that ‘there are’ actually no ‘objects’ and that ‘structure’ is all ‘there is’, while the ESR more moderately states that all we can ‘know’ is the ‘structure of the relations between objects’ and not the objects themselves (cf. Van Fraassen 2006). Thus, while not denying the existence of ‘objects’ (even if they are hard to pinpoint when discussing the neurophysiological bases of consciousness), the ESR still emphasises ‘relations’ vs. ‘objects’ and the retention of structure across theory change. In other words, it emphasies the continuity across theory change through the structural or mathematical aspects of our theories (cf. Stanford 2006). Filmed at the Models of Consciousness conference, University of Oxford, September 2019.

One in a series of talks from the 2019 Models of Consciousness conference. Aïda Elamrani Institut Jean Nicod, ENS The young field of consciousness science involves highly interdisciplinary research. For this reason, it is producing heterogeneous results which are hard to compare. This emerging discipline could benefit from a unifying, theory- neutral framework for analytical purposes. To this end, we must firstly identify a common ground between concurrent models. A brief scan through history reveals that consciousness has consistently revolved around the mind vs matter dichotomy. This binary split can be argued to span a sufficiently broad and flexible domain to semantically hold any contemporary scientific formulation of the consciousness problem, since most of them strive to provide a physical account of subjective experience. Accordingly, our reverse- engineered general frame is expected to map elements from mind-space to elements from matter-space, accepting a simple functional notation: Consciousness (INPUT) = OUTPUT. Although this equation might evoke Hilary Putnam’s functionalism, essential differences with the meta-model are emphasized by introducing its relation to Shannon’s information. Finally, alternative implementations and applications of this representation are used to illustrate and compare current accounts of consciousness. Filmed at the Models of Consciousness conference, University of Oxford, September 2019.

One in a series of talks from the 2019 Models of Consciousness conference. Chetan Prakash California State University, San Bernardino A scientific understanding of the process whereby physical entities produce consciousness has not come about, despite decades of investigation. This suggests exploring the reversal of the celebrated “hard problem of consciousness,” i.e., take consciousness as fundamental and the physical world as emergent. We describe D. Hoffman’s Interface Theory of Perception in which perceptual experiences do not approximate properties of an “objective” world, but reside in simplified, species-specific, user interfaces. Building on this, the Conscious Realism Thesis states that the objective world consists entirely of a social network of ‘conscious agents’ and their experiences, which together create the objects and properties of our common physical world. Using evolutionary game theory, we justify interface theory by showing that perceptual strategies reporting the truth will be driven to extinction by those tuned instead to fitness. We state further theorems on fitness beating truth, by showing that perceived structures, such as symmetries, partial orders and probabilities, will likely not be possessed by a world. We define “conscious agents,” suggesting that space-time is a property of the perceptual interface of human conscious agents: physical “objects” are akin to icons on that interface; physical “phenomena” are properties of apparently interacting icons. Filmed at the Models of Consciousness conference, University of Oxford, September 2019.

One in a series of talks from the 2019 Models of Consciousness conference. Quanlong Wang Department of Computer Science, University of Oxford Natural science has a basic assumption that there exists a kind of objectivity in the world independent of any consciousness. But how could one verify such objectivity given the fact that human beings can only perceive any existence through their own consciousness? On the other hand, there is a possibility for the existence of pure consciousness which could support the appearance of all phenomena, as claimed by the Yogācāra school of Indian philosophy. Based on this philosophy, any consciousness consists of two divisions: the perceived division (nimittabhaga in Sanskrit) and the perceiving division (darsanabhaga in Sanskrit). The perceiving division can recognise the information presented by the perceived division, they interact with each other as a whole unity. It is based on these two divisions that objectivity and subjectivity are established. In this talk, we give a mathematical model for characterising the interacting processes between the perceived division and the perceiving division within the framework of ZW-calculus, which is a graphical language representing quantum processes in compact closed categories. We expect that using this model some key interacting processes between the perceived division and the perceiving division can be characterised, which then paves the way for further research on modelling consciousness. Filmed at the Models of Consciousness conference, University of Oxford, September 2019.

One in a series of talks from the 2019 Models of Consciousness conference. Pierre Baudot Median Technologies, Marseille, France. Elementary quantitative and qualitative aspects of consciousness are investigated conjointly from the biology, neuroscience, physic and mathematic point of view, by the mean of a theory written with Bennequin that derives and extends information theory within algebraic topology. Information structures, that accounts for statistical dependencies within n-body interacting systems are interpreted a la Leibniz within a monadic-panpsychic framework where consciousness is information and physical, and arise from collective interactions. The electrodynamic intrinsic nature of consciousness, sustained by an analogical code, is illustrated by standard neuroscience and psychophysic results. It accounts for the diversity of the learning mechanisms, including adaptive and homeostatic processes on multiple scales, and details their expression within information theory. The axiomatization and logic of cognition are rooted in measure theory expressed within a topos intrinsic probabilistic constructive logic, allowing to express the information of mathematical formula as a Gödel code. Information topology provides a synthesis of the main models of consciousness (integrated information, global neuronal workspace, free energy principle) within a formal Gestalt theory, an expression of information structures and patterns in correspondence with Galois cohomology and symmetries. We give several examples of the application of information topology to standard recognition challenges in AI- machine learning. Filmed at the Models of Consciousness conference, University of Oxford, September 2019.

One in a series of talks from the 2019 Models of Consciousness conference. Paul Baird Université de Bretagne Atlantique I will present a mathematical model which encapsulates 3D perception from planar 2D data: to a combinatorial graph, we associate its "geometric spectrum"; eigenstates then correspond to local realizations of the graph in Euclidean 3-space as "invariant" frameworks. In this way geometry emerges from the structure, rather than being imposed upon it. One may attempt to construct a model universe based on such structures, in which state realization enacts change; change being synonymous with time, which at an elementary level, we hypothesize, is the realization of temporal states. A coherent time should then emerge from a "survival of the fittest" principle. Conscious entities might then be considered as systems which possess "higher order universality", that is, which process potential information (rather than hard information) such as a "potential" 3D cube, to enact their own change.

One in a series of talks from the 2019 Models of Consciousness conference. Mauro D’Ariano Dipartimento di Fisica, Università degli Studi di Pavia I will explore the possibility of drawing definite theoretical assertions about “awareness”, including possible experimental falsification. Awareness will be regarded as a manifestation of a special kind of “information”, and, as such, formalised as an operational probabilistic theory (OPT) [1]. Awareness would correspond to “the feeling of the process” experienced by the OPT-systems involved in the process. As a kind of information “awareness” is special in being “private”. Assuming that such privacy is an in-principle one implies a number of interesting consequences. For example, according to a theorem about information privacy in OPTs [2], investigation will be restricted to OPTs that are essentially non classical, among which the most relevant instance is the quantum theory. After presenting the OPT framework, assessing its methodological robustness in separating objective from theoretical elements, and examining postulates guaranteeing experimental control and falsifiability, I will compare postulates of relevant OPTs, and provide mathematical definitions of notions as holism, causality, complementarity, purification, and information privacy. Finally, I will explore the hypothesis of “awareness as quantum coherence”, providing a list of motivations and consequences, and discussing the possibility of experimental tests in cognitive sciences, including the evaluation of the number of qubits involved in the awareness, the existence of complementary observables, and violations of local-realism bounds. [1] G. M. D’Ariano, G. Chiribella, and P. Perinotti, “Quantum Theory from First Principles: An Informational Approach” (Cambridge University Press 2017) [2] G. M. D’Ariano, P. Perinotti, A. Tosini, “Information and disturbance in operational probabilistic theories”, unpublished Filmed at the Models of Consciousness conference, University of Oxford, September 2019.

One in a series of talks from the 2019 Models of Consciousness conference. Anita Mehta Leverhulme Visiting Professor, University of Oxford Short- and long-term memories are distinguished by their forgettability. Most of what we perceive and store is lost rather quickly to noise, as new sensations replace older ones, while some memories last for as long as we live. Synaptic dynamics is key to the process of memory storage; in this talk I will discuss a few approaches we have taken to this problem, culminating in a model of synaptic networks containing both cooperative and competitive dynamics. It turns out that the competition between synapses is key to the natural emergence of long-term memory in this model, as in reality. Filmed at the Models of Consciousness conference, University of Oxford, September 2019.

One in a series of talks from the 2019 Models of Consciousness conference. Ramón Guevara Erra Integrative Neuroscience and Cognition Center (UMR 8002), CNRS and Université Paris Descartes, Paris, France It has been argued that consciousness could be an emergent property of large neuronal networks, associated to the integration of information in the brain. However, it is not yet clear how is consciousness related to the complexity of functional brain networks. Based on a statistical mechanics approach, we sought to identify features of brain organization that are optimal for sensory processing, and that may guide the emergence of consciousness, by analyzing neurophysiological recordings in conscious and unconscious states. We find a surprisingly simple result: Normal wakeful states are characterized by the greatest number of possible configurations of interactions between brain networks, representing highest entropy values. Therefore, the information content is larger in the network associated to conscious states, suggesting that consciousness could be the result of an optimization of information processing. These findings help to guide in a more formal sense inquiry into how consciousness arises from the organization of matter. Filmed at the Models of Consciousness conference, University of Oxford, September 2019.

One in a series of talks from the 2019 Models of Consciousness conference. Michael Silberstein Department of Philosophy, Elizabethtown College; Department of Philosophy, University of Maryland We discuss the implications for the determinateness and intersubjective consistency of conscious experience in two gedanken experiments from quantum mechanics (QM). In particular, we discuss Wigner's friend and the delayed choice quantum eraser experiment with a twist. These are both cases (experiments) where quantum phenomena, or at least allegedly possible quantum phenomena/experiments, and the content/ecacy of conscious experience seem to bear on one another. We discuss why these two cases raise concerns for the determinateness and intersubjective consistency of conscious experience. We outline a 4D-global constraint-based approach to explanation in general and for QM in particular that resolves any such concerns without having to invoke metaphysical quietism (as with pragmatic accounts of QM), objective collapse mechanisms or subjective collapse. In short, we provide an account of QM free from any concerns associated with either the standard formalism or relative-state formalism, an account that yields a single 4D block universe with determinate and intersubjectively consistent conscious experience for all conscious agents. Essentially the mystery in both experiments is caused by a dynamical/causal view of QM, e.g., time-evolved states in Hilbert space, and as we show this mystery can be avoided by a spatiotemporal, constraint-based view of QM, e.g., path integral calculation of probability amplitudes using future boundary conditions. What will become clear is that rather than furiously seeking some way to make dubious deep connections between quantum physics and conscious experience, the kinds of 4D adynamical global constraints that are fundamental to both classical and quantum physics and the relationship between them, also constrain conscious experience. That is, physics properly understood, already is psychology. Filmed at the Models of Consciousness conference, University of Oxford, September 2019.

One in a series of talks from the 2019 Models of Consciousness conference. Yakov Kremnitzer Mathematical Institute, University of Oxford In this talk I will explore how quantum collapse models can be a key to understanding awareness. I will explain the mathematical structure of quantum collapse models and give an example where collapse is caused by a quantum version of integrated information (this is joint with Andre Ranchin). I will then look at the possibility of understanding awareness from collapse models and how this could be used to model consciousness as an emergent phenomenon (joint work in progress with Johannes Kleiner). Filmed at the Models of Consciousness conference, University of Oxford, September 2019.

One in a series of talks from the 2019 Models of Consciousness conference. Adrian Kent Department of Applied Mathematics and Theoretical Physics, University of Cambridge The scientific consensus is that, although many important details remain to be elaborated, Darwinian evolution can be understood in principle as a consequence of known physical laws. As William James first pointed out, the development of human consciousness, and in particular the fact that it appears to have evolutionarily advantageous features, are hard to explain within a purely materialist Darwinian theory, according to which we would function equally well in the world if we were unconscious zombies or if pleasure and pain qualia were inverted. However, it is difficult to find attractive alternatives that have any more explanatory power. In this talk I describe toy models that are intended to illuminate the space of possibilities and the difficulties. Filmed at the Models of Consciousness conference, University of Oxford, September 2019.

One in a series of talks from the 2019 Models of Consciousness conference. Ian Durham Saint Anselm College Most discussions around the nature of free will center on whether or not it exists or can exist. Lost in this argument is the fact that we at least perceive that free will exists, whether or not it actually does. This is an important distinction. If we take an operational view of perceived free will, we can construct meaningful measures for analyzing ensembles of possible choices. I present such a formal model here that is based on statistical emergence and that gives concrete, formal measures of free choices and free will. Filmed at the Models of Consciousness conference, University of Oxford, September 2019.

One in a series of talks from the 2019 Models of Consciousness conference. Peter Lloyd School of Computing, University of Kent There has been a recent resurgence of interest in mental monism as a theory of consciousness (Goldschmidt & Pearce 2017, Chalmers 2017, 2018), and Lloyd (2006, 2019) has defended a form of Berkeleyanism that aligns with Pearce (2014) and Schrödinger’s (1958) “physical construct”. Unlike theories that take the conscious mind to supervene on the brain, mental monism faces the burden of constructing ab initio the structure and dynamics of the conscious mind without any physical substrate to fall back on. Little work has been done on modelling the constituents of the mind at this fundamental level, under the tenets of mental monism. Energy, which is the driver of the physical world, has no counterpart in the mental world, which operates informatically instead. An automata-theoretic approach to modelling the conscious mind within mental monism is therefore a natural choice to explore. The model is constrained by (a) the mind’s interaction with other minds including the background consciousness, an interaction that must be mapped onto quantum mechanical measurement in the physical construct; and (b) the basic features of a mind such as individuation, privacy, mental space, psychological embodiment, attention, memory. What do these constraints imply for any substrate-free automata-theoretic model of consciousness? Filmed at the Models of Consciousness conference, University of Oxford, September 2019.

One in a series of talks from the 2019 Models of Consciousness conference. Tim Palmer Department of Physics, University of Oxford This talk is in two parts. In the first part, I suggest that creativity arises from a close synergy between two modes of neuronal operation (corresponding to Kahnemann’s Systems 1 and 2) where in the first, the limited amount of available energy to the brain is spread across large numbers of active neuronal networks, making them susceptible to noise; and in the second, available energy is focussed on smaller subset of active networks, making them operate more deterministically. In the second part, I define consciousness in terms of an ability to perceive an object as independent of its surroundings. This implies an ability to perceive counterfactual worlds where objects are perturbed relative to their surroundings. I argue that such perception may require quantum theoretic processes to be operating in the brain, since the very formulation of quantum theory (whether in convention or unconventional interpretations) involves the primacy of states of alternate worlds - alive and dead cats and so on. I argue that the brain’s reliance on such quantum processes may have arisen because they are more energy efficient than corresponding classical processes, and give some examples to justify this. Overall, I argue that human creativity and consciousness may have arisen from the brain’s evolution to become an organ of exceptional energy efficiency. Filmed at the Models of Consciousness conference, University of Oxford, September 2019.

One in a series of talks from the 2019 Models of Consciousness conference. Jonathan Mason Mathematical Institute, University of Oxford Over recent decades several complementary mathematical theories of consciousness have been put forward including Karl Friston’s Free Energy Principle and Giulio Tononi’s Integrated Information Theory. In contrast to these, in this talk I present the theory of Expected Float Entropy minimisation (EFE minimisation) which is an attempt to explain how the brain defines the content of consciousness up to relationship isomorphism and has been around since 2012. EFE involves a version of conditional Shannon Entropy parameterised by relationships. For systems with bias due to learning, such as various cortical regions, certain choices for the relationship parameters are isolated since giving much lower EFE values than others and, hence, the system defines relationships. It is proposed that, in the context of all these relationships, a brain state acquires meaning in the form of the relational content of the associated experience. In its simplest form involving only “primary relationships” EFE minimisation can also be considered as a generalisation of the initial topology (i.e. weak topology). For us the family of functions involved are the typical (probable) system states, the common domain of these functions is the set of system nodes (e.g. neurons, tuples of neurons or larger structures) and the common codomain is the set of node states. In the case of the initial topology a topology is already assumed on the common codomain and the initial topology is then the coarsest topology on the common domain for which the functions are continuous. In our case no structure is assumed on either the domain or codomain. Instead EFE minimisation simultaneously finds structures (for us weighted graphs, but topologies could in principle be used) on both the domain and codomain such that the functions are close (in some suitable sense) to being continuous whilst avoiding trivial solutions (such as the two element trivial topology) for which arbitrary improbable functions (system states) would also be continuous. Thus we find the primary relational structures that the system itself defines. In this context objects (visual and auditory) are present and EFE then extends to secondary relationships between such objects by involving correlation for example. To aid application of the theory, computationally cheaper surrogates for EFE are being developed. Filmed at the Models of Consciousness conference, University of Oxford, September 2019.

One in a series of talks from the 2019 Models of Consciousness conference. Aaron Sloman School of Computer Science, University of Birmingham, UK Most recent discussions of consciousness focus on a tiny subset of loosely characterized examples of human consciousness, ignoring evolutionary origins and transitions, the diversity of human and non-human phenomena, the variety of functions of consciousness, including consciousness of: possibilities for change, constraints on those possibilities, and implications of the possibilities and constraints -- together enabling extraordinary spatial competences in many species (e.g. portia spiders, squirrels, crows, apes) and, in humans, mathematical consciousness of spatial possibilities/impossibilities/necessities, discussed by Immanuel Kant (1781). (James Gibson missed important details.) These are products of evolution's repeated discovery and use, in evolved construction-kits, of increasingly complex types of mathematical structure with constrained possibilities, used to specify new species with increasingly complex needs and behaviours, using lower-level impossibilities (constraints) to support higher level possibilities and necessities, employing new biological mechanisms that require more sophisticated information-based control. Such transitions produce new layers of control requirements: including acquisition and use of nutrients and other resources, reproductive processes, physical and informational development in individual organisms, and recognition and use of possibilities for action and their consequences by individuals, using layered mixtures of possibilities and constraints in the environment, over varying spatial and temporal scales (e.g. sand-castles to cranes and cathedrals). I'll try to show how all this relates to aspects of mathematical consciousness noticed by Kant, essential for creative science and engineering as well as everyday actions, and also involved in spatial cognition used in ancient mathematical discoveries. In contrast, mechanisms using statistical evidence to derive probabilities cannot explain these achievements, and modern logic (unavailable to ancient mathematicians, and non-human species) lacks powerful heuristic features of spatial mathematical reasoning. New models of computation may be required, e.g. sub-neural chemistry-based computation with its mixture of discreteness and continuity (see recent work by Seth Grant). Filmed at the Models of Consciousness conference, University of Oxford, September 2019.

One in a series of talks from the 2019 Models of Consciousness conference. Pedro Resende Técnico Lisboa I present a mathematical definition of qualia from which a toy model of consciousness is derived, partly as an attempt to provide a mathematical formulation of the theory of qualia and concepts put forward by C.I. Lewis in 1929. This formulation is guided by the identification of basic principles that convey abstract aspects of the behavior of physical devices that “detect” qualia, such as brains of animals seem to do. The ensuing notion of space of qualia consists of a topological space Q equipped with additional algebraic structure that yields a notion of subjective time and makes Q a so-called stably Gelfand quantale. This leads to interesting conceptual consequences. For instance, “stable observers” emerge naturally and relate closely to the perception of space, which here, contrary to time, is not a primitive notion; and logical versions of quantum superposition and complementarity are obtained. Indeed a mathematical relation exists to quantum theory via operator algebras, due to which a space of qualia can also be regarded as an algebraic and topological model of quantum measurements. Filmed at the Models of Consciousness conference, University of Oxford, September 2019.

One in a series of talks from the 2019 Models of Consciousness conference. Peter Grindrod (joint research with Christopher Lester) Mathematical Institute, University of Oxford We seek to model the human cortex with 1B to 10B neurones arranged in a directed and highly modular network (a network of networks); with the tightly coupled modules (each containing 10,000 neurones or so) representing the cortical “columns”. Each neurone has an excitable and refectory dynamic and the neurone-to-neurone connections incur individual time delays. Thus the whole is a massive set of modular delay-differential equations (expensive to solve on a binary computer, but easily implemented within 1.5kg of neural wet- ware). Our early work has shown why evolution has resulted in such a design to ensure optimal use of the limited space and energy available. Indeed we can show that if the time delays were all integers rather than reals then much of the potential behaviour (dynamical degrees of freedom) would be lost. Simulating a 1B neurone directed graph produces its own big data challenge. We focus on the inner life of these complex dynamical system, and show that the dynamical responses to external stimuli result in distinct, latent (internal), dynamic “states" or modes. These inner subjective and private states govern the immediate dynamical responses to further incoming stimuli. Hence they are candidates for internal “feelings”. So, what is it like to be a human? A human brain must also possess such inertial dynamical states, and a human brain can experience being within them: they are natural and necessary byproducts of the system's architecture and dynamics, and they suggest that the "hard problem of consciousness” is mainly explicable, and can be anticipated, in terms of network science and dynamical systems theory. The numerical simulation at such large scales requires a special computing platform, such as SpiNNaker (at the University of Manchester). We will set out the methodology to be deployed in (i) defining such complex systems; (ii) in simulating the spiking behaviour being passed around when such a system is subject to various stimuli; and (iii) the post processing - reverse engineering - of the whole system performance, to demonstrate that internal states/modes exist. We cannot reverse engineer a real human brain at the neurone-to- neurone level, but we can do so for such ambitious simulations. Filmed at the Models of Consciousness conference, University of Oxford, September 2019.

One in a series of talks from the 2019 Models of Consciousness conference. Camilo Miguel Signorelli Department of Computer Science, University of Oxford Empirical evidence regarding neural studies of consciousness and conscious perception is mainly unknown in fields such as physics and mathematics, or sometimes even misunderstood by many scientists inside the own field of consciousness research. A critical survey of these experiments reveals different aspects and dynamical features among distinct processes related to the conscious phenomenon. These features and distinctions need to be incorporated in any attempt of modelling consciousness and the study of mathematical structures of consciousness. Therefore, part of that evidence is first reviewed to later generate a preliminary multi-layer model called Consciousness interaction, suitable for further mathematical generalization. In this “prototype” of theory, biological and cellular principles together with mathematical structures are fundamental ingredients and important complement for current physical descriptions such as dynamical systems, emergent, and sub-emergent properties. One advantage of the mentioned approach is the potential of reducing the apparent number of theories of consciousness to a few models, without the need for a single experiment. Moreover, new insights and empirical predictions are expected after this theoretical exercise, eventually producing a list of few experimental tests to verify or falsify current and future models of consciousness. Filmed at the Models of Consciousness conference, University of Oxford, September 2019.

One in a series of talks from the 2019 Models of Consciousness conference. Sean Tull Department of Computer Science, University of Oxford Integrated Information Theory (IIT), developed by Giulio Tononi and collaborators, has emerged as one of the leading scientific theories of consciousness. At the heart of IIT is an algorithm which, based on the level of integration of the internal causal relationships of a physical system in a given state, claims to determine the intensity and quality of its conscious experience. However, IIT is known to possess several technical problems, and is only applicable to simple classical physical systems. To be treated as fundamental, it should ideally be extended to more general physical theories. In this work, we investigate the formal structure of IIT, and define a notion of generalised integrated information theory in order to address these problems. Formally such a theory specifies a mapping from a given theory of physics to one of conscious experience, each satisfying minimal conditions needed for the IIT algorithm. In particular we show how a generalisation of IIT may be constructed from any suitable physical process theory, as described mathematically by a symmetric monoidal category. Specialising to classical processes yields IIT as usually defined, while restricting to quantum processes yields the recently proposed Quantum IIT of Zanardi et al. as a special case. Filmed at the Models of Consciousness conference, University of Oxford, September 2019.

One in a series of talks from the 2019 Models of Consciousness conference. Stuart Hameroff Center for Consciousness Studies, University of Arizona, Tucson, Arizona The Penrose-Hameroff ‘Orchestrated objective reduction’ (‘Orch OR’) theory suggests consciousness arises from ‘orchestrated’ quantum superpositioned oscillations in microtubules inside brain neurons. These evolve to reach threshold for Penrose ‘objective reduction’ (‘OR’) by E=h/t (E is the gravitational self-energy of the superposition/separation, h is the Planck-Dirac constant, and at the time at which Orch OR occurs) to give moments of conscious experience. Sequences, interference and resonance of entangled moments govern neurophysiology and provide our ‘stream’ of consciousness. Anesthetic gases selectively block consciousness, sparing non-conscious brain activities, binding by quantum coupling with aromatic amino acid rings inside brain proteins. Genomic, proteomic and optogenetic evidence indicate the microtubule protein tubulin as the site of anesthetic action. We (Craddock et al, Scientific Reports 7,9877, 2017) modelled couplings among all 86 aromatic amino acid rings in tubulin, and found a spectrum of terahertz (‘THz’) quantum oscillations including a common mode peak at 613 THz. Simulated presence of 8 different anesthetics each abolished the peak, and dampened the spectrum proportional to anesthetic potency. Non-anesthetic gases which bind in the same regions, but do not cause anesthesia, did not abolish or dampen the THz activity. Orch OR is better supported experimentally than any other theory of consciousness. Filmed at the Models of Consciousness conference, University of Oxford, September 2019.

One in a series of talks from the 2019 Models of Consciousness conference. Sir Roger Penrose Mathematical Institute, University of Oxford A common scientific view is that the actions of a human brain could, in principle, be simulated by appropriate computation, and even that it may not be too far into the future before computers become so powerful that they will be able to exceed the mental capabilities of any human being. However, by using examples from chess and mathematics, I argue, that the quality of conscious understanding is something essentially distinct from computation. Nevertheless, I maintain that the action of a conscious brain is the product of physical laws, whence consciousness itself must result from physical processes of some kind. Yet physical actions, over a huge range, can be simulated very precisely by computational techniques, as is exemplified by the LIGO gravitational wave detectors confirming precise calculations, within Einstein’s general relativity theory, of signals from black-hole encounters in distant galaxies. Despite this, I argue that there is a profound gap in our understanding of how Einstein’s theory affects quantum systems, and that there is reason to believe that the events termed “collapse of the wave-function” take place objectively (gravitational OR), in a way that defies computation, yet should be observable in certain experiments. It is argued that each such event is accompanied by a moment of “proto-consciousness”, and that actual consciousness is the result of vast numbers of such events, orchestrated in an appropriate way so as to provide an actual conscious experience (Orch-OR). Filmed at the Models of Consciousness conference, University of Oxford, September 2019.

One in a series of talks from the 2019 Models of Consciousness conference. Xerxes Arsiwalla Institute for Bioengineering of Catalonia Barcelona, Spain Theories of consciousness such as Integrated Information Theory (IIT) and its various approximations are grounded on intrinsic information and causal dynamics. However, what seems to be missing or at least is not explicitly addressed in this framework is the role of meaning. One could argue that conscious experience not only generates information, but also meaning. We postulate that meaning associated to experience is intrinsically generated, is compositional, specific and integrated. How can this be formalized within the context of IIT? Here we propose a framework for computing the compositional meaning of the maximally irreducible conceptual structure or Q-shape in IIT. A Q-shape is a set of concepts and their relations. To compute the meaning of a Q-shape we apply the category theoretic formulation of Distributional Semantics, used in natural language processing. This assigns to every concept in the Q-shape, a distributional meaning and a grammatical type. By consistency, concepts with very high phi (core concepts) will be the most pertinent for the experience at that specific instance. The distributional meaning of each core concept depends on its relations to all other concepts in the Q- shape and can be computed using a vector space spanned by a basis of concepts as is done in Distributional Semantics. The grammatical types associated to core concepts are constrained by their relations to other core concepts. Furthermore, a pre-group algebra imposes ordering of grammatical types. We then show how the sub-network of core concepts in the Q-shape can be identified with a category theoretic process diagram. The compositional meaning of this process diagram is computed within a monoidal category and yields the meaning associated to the experience. We demonstrate this computation with a simple toy model. Finally, we comment on how meaning imposes phenomenologically relevant constraints to any information-based theory of consciousness. Filmed at the Models of Consciousness conference, University of Oxford, September 2019.

One in a series of talks from the 2019 Models of Consciousness conference. Adam Barrett Sackler Centre for Consciousness Science, University of Sussex, UK Integrated Information Theory (IIT) has gained a lot of attention for potentially explaining, fundamentally, what is the physical substrate of consciousness. The foundational concepts behind IIT were extremely innovative, and it has been very exciting to see certain predictions being upheld in experiments. However, many problems have been uncovered with the mathematical formulae that IIT proposes for measuring consciousness exactly. This has led to fragmentation amongst consciousness researchers, between those who accept IIT, and those who reject IIT. In this talk, I make the case for a `weak’ form of IIT as a pillar of a future theory of consciousness, and summarise some of the problems with `strong’ IIT. Weak IIT maintains that neural correlates of consciousness must reflect two key aspects of phenomenology. First, that each conscious moment is extremely informative (it is one of a vast repertoire of possible experiences). Second, that each conscious experience is integrated (it is experienced as a coherent whole). I review some of the empirical evidence for this, in the form of greater diversity and connectivity in observed neural dynamics from conscious versus unconscious humans. I then discuss how the Phi measure of integrated information is not well-defined, and not unique given the axioms of IIT, and hence that the current version of strong IIT should be rejected. I conclude with some discussion on possible ways forward. Filmed at the Models of Consciousness conference, University of Oxford, September 2019.

One in a series of talks from the 2019 Models of Consciousness conference. Johannes Kleiner, Institute for Theoretical Physics, Leibniz University of Hannover. The goal of this talk is to discuss the mathematical basis of models of consciousness, most notably the question of which mathematical structure one is to use to describe experience in any formal theory. This question is inextricably linked with the conceptual basis of models of consciousness. After briefly reviewing the various choices made in existing models, I explain how a systematic answer to this question can be constructed based on a further development of the concepts introduced by Thomas Nagel and David Chalmers. If time permits, I will outline how this leads to a full mathematical framework for models of consciousness. Filmed at the Models of Consciousness conference, University of Oxford, September 2019 - https://models-of-consciousness.org/