COMPUTING ANTICIPATORY SYSTEMS: CASYS'03  Sixth International Conference

Anticipation, Orbital Stability, and Energy Conservation in Discrete Harmonic Oscillators
View Description Hide DescriptionWe make a systematic analysis of the dual incursive model of the discrete harmonic oscillator. We derive its closed form solution, and identify its natural frequency of oscillation. We study its orbital stability, and the conservation of its total energy. We finally propose a superposed model that conserves energy with absolute precision, and exhibits a high degree of orbital stability. Within the conjecture that spacetime is discrete, the above results lead to the conclusion that discretization must be accompanied by anticipation, in order to guarantee orbital stability and energy conservation.

Nonlinear Dynamics, Artificial Cognition and Galactic Export
View Description Hide DescriptionThe field of nonlinear dynamics focuses on function rather than structure. Evolution and brain function are examples. An equation for a brain, described in 1973, is explained. Then, a principle of interactional function change between two coupled equations of this type is described. However, all of this is not done in an abstract manner but in close contact with the meaning of these equations in a biological context. Ethological motivation theory and Batesonian interaction theory are reencountered. So is a fairly unknown finding by van Hooff on the indistinguishability of smile and laughter in a single primate species. Personhood and evil, two human characteristics, are described abstractly. Therapies and the question of whether it is ethically allowed to export benevolence are discussed. The whole dynamic approach is couched in terms of the Cartesian narrative, invented in the 17th century and later called Enlightenment. Whether or not it is true that a “second Enlightenment” is around the corner is the main question raised in the present paper.

The Theory of Scale Relativity: Non‐Differentiable Geometry and Fractal Space‐Time
View Description Hide DescriptionThe aim of the theory of scale relativity is to derive the physical behavior of a non‐differentiable and fractal space‐time and of its geodesics (with which particles are identified), under the constraint of the principle of the relativity of scales. We mainly study in this contribution the effects induced by internal fractal structures on the motion in standard space. We find that the main consequence is the transformation of classical mechanics in a quantum mechanics. The various mathematical quantum tools (complex wave functions, spinors, bi‐spinors) are built as manifestations of the non‐differentiable geometry. Then the Schrödinger, Klein‐Gordon and Dirac equations are successively derived as integrals of the geodesics equation, for more and more profound levels of description. Finally we tentatively suggest a new development of the theory, in which quantum laws would hold also in the scale‐space: in such an approach, one naturally defines a new conservative quantity, named ‘complexergy’, which measures the complexity of a system as regards its internal hierarchy of organization. We also give some examples of applications of these proposals in various sciences, and of their experimental and observational tests.

About Localization in Quantum Mechanics
View Description Hide DescriptionIn quantum mechanics, the three coordinate operators have each the set of real numers as eigen values. The problem of localization of a particle being linked to that of measurement of distance to a given point we can equivalently consider the “square distance operator”. The eigen‐values of the “square distance operator” acting on functions of position are the same as those of the Laplacian (multiplied by a negative constant involving h) acting on functions of momentum (Fourier transforms, involving h, of the function of position). We impose to these functions (as well as to the Fourier transform of the wave function) to vanish outside a compact and on its boundary. Consequently the above Laplacian has a discrete infinite spectrum of strictly positive eigen‐values which are also the eigen‐values of of the “square distance operator”. So their square roots are the observable values of distance with a minimum observable distance. Examples are given.

Symmetry Breaking And The Nilpotent Dirac Equation
View Description Hide DescriptionA multivariate 4‐vector representation for space‐time and a quaternion representation for mass and the electric, strong and weak charges leads to a nilpotent form of the Dirac equation, which packages the entire physical information available about a fermion state. The nilpotent state vector breaks the symmetry between the strong, electric and weak interactions, by associating their respective charges with vector, scalar and pseudoscalar operators, leading directly to the SU (3) × SU (2)_{ L } × U(1) symmetry, and to particle structures and mass‐generating states. In addition, the nilpotent Dirac equation has just three solutions for spherically‐symmetric distance‐dependent potentials, and these correspond once again to those that would be expected for the three interactions: linear for the strong interaction; inverse linear for the electromagnetic; and a harmonic oscillator‐type solution, which can be equated with the dipolar annihilation and creation mechanisms of the weak interaction.

On the Anticipatory Aspects of the Four Interactions: what the Known Classical and Semi‐Classical Solutions Teach us
View Description Hide DescriptionThe four (electro‐magnetic, weak, strong and gravitational) interactions are described by singular Lagrangians and by Dirac‐Bergmann theory of Hamiltonian constraints. As a consequence a subset of the original configuration variables are gauge variables, not determined by the equations of motion. Only at the Hamiltonian level it is possible to separate the gauge variables from the deterministic physical degrees of freedom, the Dirac observables, and to formulate a well posed Cauchy problem for them both in special and general relativity. Then the requirement of causality dictates the choice of retarded solutions at the classical level. However both the problems of the classical theory of the electron, leading to the choice of (retarded + advanced) solutions, and the regularization of quantum field teory, leading to the Feynman propagator, introduce anticipatory aspects. The determination of the relativistic Darwin potential as a semi‐classical approximation to the Lienard‐Wiechert solution for particles with Grassmann‐valued electric charges, regularizing the Coulomb self‐energies, shows that these anticipatory effects live beyond the semi‐classical approximation (tree level) under the form of radiative corrections, at least for the electro‐magnetic interaction.
Talk and “best contribution” at The Sixth International Conference on Computing Anticipatory Systems CASYS’03, Liege August 11–16, 2003.

The Random Graph Pregeometry, Some of its Implications and new Insights in Universe and Time Structures
View Description Hide DescriptionWe expose a conception of the physical universe based on acausal relations between fundamental elements with only a binary property. Relations occur following a stochastic process which describes universe evolution. Separations can be defined by the spinor null‐pole formula to define a possibly scale dependent geometry. The central unknown being the stochastic process, some properties can be inferred from macroscopic evidence, but some alternatives are opened for example to have a time model closer from the physical one accounting for example for the past‐present‐future distinction and the “depth of physical time”. Independent of considerations about the evolution process, some properties of the universe as a matter‐antimatter implied gemellarity automatically arises if the binary fundamental property is identified with charge polarity.

The Cosmological Constant Λ is not Really Constant but the Function of a Gravitational Radius
View Description Hide DescriptionA general line element and a general metric tensor are defined as functions of two parameters α and α′. The related Einstein’s field equations of a gravitational potential field in a vacuum, including parameter Λ, have been derived. The parameters α and α′ are identified in a gravitational field by the solution of the Einstein’s field equations. Parallel with this, it has been find out that the so‐called cosmological constant Λ, is not really constant, but a function of gravitational radius, Λ = f(r). This discovery is very important, among the others, for cosmology. One of the consequences is the new form of the acceleration equation of the universe motion that can be attractive (negative) or repulsive (positive). According to the observations, the repulsive acceleration gives rise to accelerating expansion of the universe at the present time. The obtained solution of the diagonal line element can be applied in a very strong gravitational field. Besides, this solution gives the Ricci scalar equal to zero, R= 0. This is in an agreement with the current observation that our universe is flat.

The Fundamental Limit and Origin of Complexity in Biological Systems: A New Model for the Origin of Life
View Description Hide DescriptionGenerally unicellular prokaryotes are considered the most fundamental form of living system. Many researchers include viruses since they commandeer cellular machinery in their replication; while others insist viruses are merely complex infective proteins. New biological principles are introduced suggesting that even the prion, the infectious protein responsible for transmissible spongiform encephalopathies, qualifies as the most fundamental form of life; and remains in general concordance with the six‐point definition of living systems put forth by Humberto Maturana and his colleagues in their original characterization of living organisms as a class of complex self‐organized autopoietic systems in 1974.

Back to the Future: Anatomy of a System
View Description Hide DescriptionSystem design and implementation targets operation in the future. Success depends on anticipation and timely response. Artificial systems are designed to emulate living organisms, but do they really do that? Does our existing image of a system reflect life? We have dissected widely held organizational concepts and misconceptions to try and establish the essential “anatomy” of a system. This paper reports our conclusions. “A system” implies unity: quantum‐mechanical “systems” are unified by entanglement; Newtonian ones are inescapably fragmented. A Newtonian system is not directly unified: we are inevitably a part of the system: the necessary entanglement is provided by our brains! We conclude that system unification is always through quantum‐mechanical entanglement. Artificial systems can never be both Newtonian and autonomous. Anticipation of future events requires multiply‐scaled models of the environment, created in the past for use in the future. These, must be united through entanglement into a system’s “anatomical” structure, in which anticipative processes unfold. We should not expect artificial systems to successfully emulate anticipatory organisms.

Inertia and Gravitation as Vacuum Effects — the case for Passive Gravitational Mass
View Description Hide DescriptionIt has previously been shown that there is a connection between the vacuum electromagnetic field, or zero‐point electromagnetic field, and the phenomenon of inertia. A general expression was then derived for the vacuum electromagnetic contribution to the inertial mass of an object. Similar contributions are to be expected from the other vacuum field components. Here we show that the case for inertial mass can indeed be extended to passive gravitational mass. As a byproduct of this we also get Newton’s law of universal gravitation. It is furthermore shown why these results are consistent with gravitational theories of the metric kind and in particular with General Relativity. The extension to active gravitational mass, namely, solving the problem of why mass creates a gravitational field, i.e., why it “bends” or changes the curvature of spacetime, remains unsolved.

Resolution of Infinite‐Loop in Hyperincursive and Nonlocal Cellular Automata: Introduction to Slime Mold Computing
View Description Hide DescriptionHow can non‐algorithmic/non‐deterministic computational syntax be computed? “The hyperincursive system” introduced by Dubois is an anticipatory system embracing the contradiction/uncertainty. Although it may provide a novel viewpoint for the understanding of complex systems, conventional digital computers cannot run faithfully as the hyperincursive computational syntax specifies, in a strict sense. Then is it an imaginary story? In this paper we try to argue that it is not. We show that a model of complex systems “Elementary Conflictable Cellular Automata (ECCA)” proposed by Aono and Gunji is embracing the hyperincursivity and the nonlocality. ECCA is based on locality‐only type settings basically as well as other CA models, and/but at the same time, each cell is required to refer to globality‐dominant regularity. Due to this contradictory locality‐globality loop, the time evolution equation specifies that the system reaches the deadlock/infinite‐loop. However, we show that there is a possibility of the resolution of these problems if the computing system has parallel and/but non‐distributed property like an amoeboid organism. This paper is an introduction to “the slime mold computing” that is an attempt to cultivate an unconventional notion of computation.

Material Implementation of Hyperincursive Field on Slime Mold Computer
View Description Hide Description“Elementary Conflictable Cellular Automaton (ECCA)” was introduced by Aono and Gunji as a problematic computational syntax embracing the non‐deterministic/non‐algorithmic property due to its hyperincursivity and nonlocality. Although ECCA’s hyperincursive evolution equation indicates the occurrence of the deadlock/infinite‐loop, we do not consider that this problem declares the fundamental impossibility of implementing ECCA materially. Dubois proposed to call a computing system where uncertainty/contradiction occurs “the hyperincursive field”. In this paper we introduce a material implementation of the hyperincursive field by using plasmodia of the true slime mold Physarum polycephalum. The amoeboid organism is adopted as a computing media of ECCA slime mold computer (ECCA‐SMC) mainly because; it is a parallel non‐distributed system whose locally branched tips (components) can act in parallel with asynchronism and nonlocal correlation. A notable characteristic of ECCA‐SMC is that a cell representing a spatio‐temporal segment of computation is occupied (overlapped) redundantly by multiple spatially adjacent computing operations and by temporally successive computing events. The overlapped time representation may contribute to the progression of discussions on unconventional notions of the time.

Some Remarks on Functional Equations with Advanced‐Delayed Operators
View Description Hide DescriptionThis paper is aimed at proving that several classes of systems, described by functional equations involving operators with advanced‐delayed argument, can oscillate within the class of almost periodic motions. The paper illustrates systems described by convolution equations, both linear and nonlinear, as well as those described by certain classes of functional differential‐difference equations. The concepts of almost periodicity are those due to H. Bohr and V. Stepanov. In most cases the conditions imposed for the existence of almost periodic oscillations are frequential nature (related to the Fourier transform of some data).

The Anticipative Value of Individual and Group Information Feedback on the Decision Process During the Simulation Experiment
View Description Hide DescriptionThis paper presents the influence of individual and group feedback information introduced by the system dynamics model in a multicriteria decision process. The experiment was performed in a controlled environment. The criteria function was explicitly defined in order to increase the level of experimental control. The experiment was conducted under three experimental conditions: a_{1}) determination of strategy on the basis of a subjective judgment of the task, a_{2}) determination of strategy with the application of a system dynamics model without group interaction, and a_{3}) determination of strategy with the application of a formal model with subject interaction supported by group feedback information. 147 subjects, senior university students, participated in the experiment. The hypothesis that model application and group feedback information positively influence the convergence of the decision process and contribute to higher criteria function values was confirmed.

Further Properties of Derived Scalar Strong Anticipatory Systems
View Description Hide DescriptionThe study of self referential anticipatory systems derived from causal systems or recursions has received attention in recent years. This paper builds on and extends previously reported results by investigating what happens to the regular dynamics of a first order system modelled by a recursion when the recursion is replaced by an associated incursion. The effect of this replacement on the stability properties of the fixed points and cycles of the map is examined.

Interactively Open Autonomy Unifies Two Approaches to Function
View Description Hide DescriptionFunctionality is essential to any form of anticipation beyond simple directedness at an end. In the literature on function in biology, there are two distinct approaches. One, the etiological view, places the origin of function in selection, while the other, the organizational view, individuates function by organizational role. Both approaches have well‐known advantages and disadvantages. I propose a reconciliation of the two approaches, based in an interactivist approach to the individuation and stability of organisms. The approach was suggested by Kant in the Critique of Judgment, but since it requires, on his account, the identification a new form of causation, it has not been accessible by analytical techniques. I proceed by construction of the required concept to fit certain design requirements. This construction builds on concepts introduced in my previous four talks to these meetings.

Backward Stochastic Differential Systems and Their Anticipatory Property
View Description Hide DescriptionThis paper concerns with computing anticipatory property of a stochastic system, which is characterized by backward stochastic differential equations (BSDEs) of the Pardoux and Peng type. Since a Pardoux‐Peng solution of a BSDE is required adaptedness to the natural filtration of a standard Brownian motion, it is non‐anticipatory in the sense of stochastic integrals. However, the equation is solved backwardly with a terminal state and the solution will depend on the future state. Hence, a system described by BSDEs completely or partially is a strong computing anticipatory system.

Anticipatory Adaptive Control for a Class of Stochastic Systems With Incomplete Information
View Description Hide DescriptionIn this paper, we deal with a computing anticipatory system that computes its current states in taking into account its past and present states but also its potential future (anticipative) states. We present an adaptive dual control scheme for controlling this system with incomplete information about (parameters) constant components (whose “statistics” are determined via current state of the system) where the control is chosen both to regulate and to elicit information. Thus, the emphasis is on the closed‐loop policy, which has the important property that it can be actively (anticipatory) adaptive, while the open‐loop feedback policy can only be passively (non‐anticipatory) adaptive. Each component is assumed to be a random variable distributed with an underlying probability density function whose parameters are supposed to be changed adaptively on the basis of obtained information about a current state of the system. An explicit solution for the anticipatory adaptive controller is obtained by using the dynamic programming approach, which leads to functional recurrence equations. Illustrative examples are given.

Modeling Connectionist Networks: Categorical, Geometric Aspects (Towards “Homomorphic Learning”)
View Description Hide DescriptionWork in interdisciplinary fields is very interesting and always a great challenge. We present work on applications of mathematical methods to modeling problems arising in the area of artificial neural networks (ANN). We concentrate on modeling network structures that are motivated and based on knowledge about net structures coming from neurophysiology. In past years such insights have been exploited already in computer based ANN‐simulations which are well suited for industrial applications. In the analysis of network structures, considering assemblies of cells (neurons) in biological nets, from a geometric point of view one can indentify and interpret, locally, what is called a geometric configuration. Following notions from algebraic topology, we are speaking about simplicial configurations (e.g. triangular, tetrahedral configurations, etc.). It turns out that category theory, geometry, algebra (group theory), graph theory (more general, net theory) come together, in a natural interdisciplinary way. Simplices are of basic importance.The interpretation of a learning step as a morphism in categorical terms suggests the opening of a systematic theory of learning (we call it “Homomorphic Learning”).