The Thermodynamics of Network Coding, and an Algorithmic Refinement of the Principle of Maximum Entropy

The principle of maximum entropy (Maxent) is often used to obtain prior probability distributions as a method to obtain a Gibbs measure under some restriction giving the probability that a system will be in a certain state compared to the rest of the elements in the distribution. Because classical entropy-based Maxent collapses cases confounding all distinct degrees of randomness and pseudo-randomness, here we take into consideration the generative mechanism of the systems considered in the ensemble to separate objects that may comply with the principle under some restriction and whose entropy is maximal but may be generated recursively from those that are actually algorithmically random offering a refinement to classical Maxent. We take advantage of a causal algorithmic calculus to derive a thermodynamic-like result based on how difficult it is to reprogram a computer code. Using the distinction between computable and algorithmic randomness we quantify the cost in information loss associated with reprogramming. To illustrate this we apply the algorithmic refinement to Maxent on graphs and introduce a Maximal Algorithmic Randomness Preferential Attachment (MARPA) Algorithm, a generalisation over previous approaches. We discuss practical implications of evaluation of network randomness. Our analysis provides insight in that the reprogrammability asymmetry appears to originate from a non-monotonic relationship to algorithmic probability. Our analysis motivates further analysis of the origin and consequences of the aforementioned asymmetries, reprogrammability, and computation.Comment: 30 page

Kolmogorov Complexity, Cosmic Background Radiation and Irreversibility

We discuss the algorithmic information approach to the analysis of the observational data on the Universe. Kolmogorov complexity is proposed as a descriptor of the Cosmic Microwave Background (CMB) radiation maps. An algorithm of computation of the complexity is described, applied, first, to toy models and then, to the data of the Boomerang experiment. The sky maps obtained via the summing of two independent Boomerang channels reveal threshold independent behavior of the mean ellipticity of the anisotropies, thus indicating correlations present in the sky signal and possibly carrying crucial information on the curvature and the non-Friedmannian, i.e. accelerated expansion of the Universe. Similar effect has been detected for COBE-DMR 4 year maps. Finally, as another application of these concepts, we consider the possible link between the CMB properties, curvature of the Universe and arrows of time.Comment: Talk at XXII Solvay Conference on Physics "The Physics of Communication" (Delphi, November 24-29, 2001); the discussion include

A Blueprint for the Hard Problem of Consciousness

A Blueprint for the Hard Problem of Consciousness addresses the fundamental mechanism that allows physical events to transcend into subjective experiences, termed the Hard Problem of Consciousness. Consciousness is made available as the abstract product of self-referent realization of information by strange loops through the levels of processing of the brain. Readers are introduced to the concept of the Hard Problem of Consciousness and related concepts followed by a critical discourse of different theories of consciousness. Next, the author identifies the fundamental flaw of the Integrated Information Theory (IIT) and proposes an alternative that avoids the cryptic intelligent design and panpsychism of the IIT. This author also demonstrates how something can be created out of nothing without resorting to quantum theory, while pointing out neurobiological alternatives to the bottom-up approach of quantum theories of consciousness. The book then delves into the philosophy of qualia in different physiological knowledge networks (spatial, temporal and olfactory, cortical signals, for example) to explain an action-based model consistent with the generational principles of Predictive Coding, which maps prediction and predictive-error signals for perceptual representations supporting integrated goal-directed behaviors. Conscious experiences are considered the outcome of abstractions realized out of map overlays and provided by sustained oscillatory activity. The key feature of this blueprint is that it offers a perspective of the Hard Problem of Consciousness from the point of view of the subject; the experience of ‘being the subject’ is predicted to be the realization of inference inversely mapped out of hidden causes of global integrated actions. The author explains the consistencies of his blueprint with ideas of the Global Neuronal Workspace and the Adaptive Resonance Theory of consciousness as well as with the empirical evidence supporting the Integrated Information Theory. A Blueprint for the Hard Problem of Consciousness offers a unique perspective to readers interested in the scientific philosophy and cognitive neuroscience theory in relation to models of the theory of consciousness

Lorentzian and Euclidean Quantum Gravity - Analytical and Numerical Results

We review some recent attempts to extract information about the nature of quantum gravity, with and without matter, by quantum field theoretical methods. More specifically, we work within a covariant lattice approach where the individual space-time geometries are constructed from fundamental simplicial building blocks, and the path integral over geometries is approximated by summing over a class of piece-wise linear geometries. This method of ``dynamical triangulations'' is very powerful in 2d, where the regularized theory can be solved explicitly, and gives us more insights into the quantum nature of 2d space-time than continuum methods are presently able to provide. It also allows us to establish an explicit relation between the Lorentzian- and Euclidean-signature quantum theories. Analogous regularized gravitational models can be set up in higher dimensions. Some analytic tools exist to study their state sums, but, unlike in 2d, no complete analytic solutions have yet been constructed. However, a great advantage of our approach is the fact that it is well-suited for numerical simulations. In the second part of this review we describe the relevant Monte Carlo techniques, as well as some of the physical results that have been obtained from the simulations of Euclidean gravity. We also explain why the Lorentzian version of dynamical triangulations is a promising candidate for a non-perturbative theory of quantum gravity.Comment: 69 pages, 16 figures, references adde