Hidden information and regularities of information dynamics I

Vladimir S. Lerner 13603 Marina Pointe Drive, C‐608, Marina Del Rey, CA 90292, USA, [email protected] Abstract This presentation’s Part 3 studies the evolutionary information processes and regularities of evolution dynamics, evaluated by an entropy functional (EF) of a random field (modeled by a diffusion information process) and an informational path functional (IPF) on trajectories of the related dynamic process (Lerner 2012). The integral information measure on the process’ trajectories accumulates and encodes inner connections and dependencies between the information states, and contains more information than a sum of Shannon’s entropies, which measures and encodes each process’s states separately. Cutting off the process’ measured information under action of impulse controls (Lerner 2012a), extracts and reveals hidden information, covering the states’ correlations in a multi-dimensional random process, and implements the EF-IPF minimax variation principle (VP). The approach models an information observer (Lerner 2012b)-as an extractor of such information, which is able to convert the collected information of the random process in the information dynamic process and organize it in the hierarchical information network (IN), Part2 (Lerner, 2012c). The IN’s highest level of the structural hierarchy, measured by a maximal quantity and quality of the accumulated cooperative information, evaluates the observer’s intelligence level, associated with its ability to recognize and build such structure of a meaningful hidden information. The considered evolution of optimal extraction, assembling, cooperation, and organization of this information in the IN, satisfying the VP, creates the phenomena of an evolving observer’s intelligence. The requirements of preserving the evolutionary hierarchy impose the restrictions that limit the observer’s intelligence level in the IN. The cooperative information geometry, evolving under observations, limits the size and volumes of a particular observer. Part 3. The Evolutionary Regularities of Informational Dynamics Introduction The studied evolution includes both progressive improvement of existing information systems with their extensive development and creation of more advanced systems, having enhanced evolutional properties, organized it in the hierarchical information network (IN), Part 2 (Lerner, 2012b), which concentrates all measured information. Information, as a logarithmic comparative measure of the compared states (events), in an observed process ought to measure its states’ inner connections, integrating them through all process. The integral information measure on the controlled Markov diffusion process’ trajectories (Part 1) accumulates and encodes inner connections and dependencies between the information states, and contains more information than a sum of Shannon’s entropies, which measures and encodes each process’s states separately.