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- Harald Atmanspacher (2006). Consciousness: A Mathematical Treatment of the Global Neuronal Workspace Model. Acta Biotheoretica 54 (2).
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We apply Baars' Global Workspace model of consciousness to inattentional blindness, using the groupoid network method of Stewart et al. to explore modular structures defined by information measures associated with cognitive process. Internal cross-talk breaks the fundamental groupoid symmetry, and, if sufficiently strong, creates, in a highly punctuated manner, a linked, shifting, giant component which instantiates the global workspace of consciousness. Embedding, exterior, information sources act as an external field which breaks the groupoid symmetry in a somewhat different manner, definng the slowly-acting contexts of Baars' theory and providing topological constraints on the manifestations of consciousness. This analysis significantly extends recent mathematical treatments of the global workspace, and identifies a shifting, topologically-determined syntactical and grammatical 'bottleneck' as a tunable rate distortion manifold which constrains what sensory or other signals can be brought to conscious attention, typically in a punctuated manner. Sensations outside the limits of that filter's syntactic 'bandpass' have lower probability of detection, regardless of their structure, accounting for generalized forms of inattentional blindness.
Network theory provides an alternative to the renormalization and phase transition methods used in Wallace's (2005a) treatment of Baars' Global Workspace model. Like the earlier study, the new analysis produces the workplace itself, the tunable threshold of consciousness, and the essential role for embedding contexts, in an explicitly analytic 'necessary conditions' manner which suffers neither the mereological fallacy inherent to brain-only theories nor the sufficiency indeterminacy of neural network or agent-based simulations. This suggests that the new approach, and the earlier, represent different analytically solvable limits in a broad continuum of possible models, analogous to the differences between bond and site percolation or between the two and many-body limits of classical mechanics. The development significantly extends the theoretical foundations for an empirical general cognitive model (GCM) based on the Shannon-McMillan Theorem. Patterned after the general linear model which reflects the Central Limit Theorem, the proposed technique should be both useful for the reduction of expermiental data on consciousness and in the design of devices with capacities which may transcend those of conventional machines and provide new perspectives on the varieties of biological consciousness.
Theorists are converging from quite different quarters on a version of the global neuronal workspace model of consciousness, but there are residual confusions to be dissolved. In particular, theorists must resist the temptation to see global accessibility as the cause of consciousness (as if consciousness were some other, further condition); rather, it is consciousness. A useful metaphor for keeping this elusive idea in focus is that consciousness is rather like fame in the brain. It is not a privileged medium of representation, or an added property some states have; it is the very mutual accessibility that gives some informational states the powers that come with a subject's consciousness of that information. Like fame, consciousness is not a momentary condition, or a purely dispositional state, but rather a matter of actual influence over time. Theorists who take on the task of accounting for the aftermath that is critical for consciousness often appear to be leaving out the Subject of consciousness, when in fact they are providing an analysis of the Subject, a necessary component in any serious theory of consciousness.
The asymptotic limit theorems of information theory permit a concise formulation of Bernard Baars' global workspace/global broadcast picture of consciousness, focusing on how networks of unconscious cognitive modules are driven by the classic 'no free lunch' argument into shifting, tunable, alliances having variable thresholds for signal detection. The model directly accounts for the punctuated characteristics of many conscious phenomena, and derives the inherent necessity of inattentional blindness and related effects.
Baars (1988, 1997) has proposed a psychological theory of consciousness, called global workspace theory. The present study describes a software agent implementation of that theory, called ''Conscious'' Mattie (CMattie). CMattie operates in a clerical domain from within a UNIX operating system, sending messages and interpreting messages in natural language that organize seminars at a university. CMattie fleshes out global workspace theory with a detailed computational model that integrates contemporary architectures in cognitive science and artificial intelligence. Baars (1997) lists the psychological ''facts that any complete theory of consciousness must explain'' in his appendix to In the Theater of Consciousness; global workspace theory was designed to explain these ''facts.'' The present article discusses how the design of CMattie accounts for these facts and thereby the extent to which it implements global workspace theory.
This paper explores a remarkable convergence of ideas and evidence, previously presented in separate places by its authors. That convergence has now become so persuasive that we believe we are working within substantially the same broad framework. Taylor's mathematical papers on neuronal systems involved in consciousness dovetail well with work by Newman and Baars on the thalamocortical system, suggesting a brain mechanism much like the global workspace architecture developed by Baars (see references below). This architecture is relational, in the sense that it continuously mediates the interaction of input with memory. While our approaches overlap in a number of ways, each of us tends to focus on different areas of detail. What is most striking, and we believe significant, is the extent of consensus, which we believe to be consistent with other contemporary approaches by Weiskrantz, Gray, Crick and Koch, Edelman, Gazzaniga, Newell and colleagues, Posner, Baddeley, and a number of others. We suggest that cognitive neuroscience is moving toward a shared understanding of consciousness in the brain.
Dehaene and Naccache, Dennett and Jack and Shallice “see convergence coming from many different quarters on a version of the neuronal global workspace model†(Dennett, p. 1). (Boldface references are to papers in this volume.) On the contrary, even within this volume, there are commitments to very different perspectives on consciousness. And these differing perspectives are based on tacit differences in philosophical starting places that should be made explicit.  Indeed, it is not clear that different uses of “consciousness†and “awareness†in this volume can be taken to refer to the same phenomenon. More specifically, I think there are three different concepts of consciousness in play in this issue. The global workspace model makes much more sense on one of these than on the others.
Adapting Dretske's approach on the necessary conditions for mental process, we apply a communication theory analysis of interacting cognitive biological and social modules to the global neuronal workspace, the emerging standard model for consciousness. Using an obvious canonical homology with statistical physics, the method, when iterated, generates a fluctuating dynamic threshold recognizably similar to phase transition in a physical system, but constrained to a manifold/atlas structure analogous to a tunable retina. The resulting 'General Cognitive Model' can be extended in a straightforward manner to include the effects of psychosocial stress, culture, or other cognitive modules which constitute a structured, embedding hierarchy of contextual constraints acting at a slower rate than neuronal function itself. This produces a 'biopsychosociocultural' treatment of consciousness that, while otherwise remarkably similar to the standard development, meets compelling philosophical and other objections to brain-only descriptions.
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