COMPUTING ANTICIPATORY SYSTEMS: CASYS ‘09: Ninth International Conference on Computing Anticipatory Systems

Adaptive Language Games with Robots
View Description Hide DescriptionThis paper surveys recent research into language evolution using computer simulations and robotic experiments. This field has made tremendous progress in the past decade going from simple simulations of lexicon formation with animallike cybernetic robots to sophisticated grammatical experiments with humanoid robots.

Introduction to the Natural Anticipator and the Artificial Anticipator
View Description Hide DescriptionThis short communication deals with the introduction of the concept of anticipator, which is one who anticipates, in the framework of computing anticipatory systems. The definition of anticipation deals with the concept of program. Indeed, the word program, comes from “pro‐gram” meaning “to write before” by anticipation, and means a plan for the programming of a mechanism, or a sequence of coded instructions that can be inserted into a mechanism, or a sequence of coded instructions, as genes or behavioural responses, that is part of an organism. Any natural or artificial programs are thus related to anticipatory rewriting systems, as shown in this paper. All the cells in the body, and the neurons in the brain, are programmed by the anticipatory genetic code, DNA, in a low‐level language with four signs. The programs in computers are also computing anticipatory systems. It will be shown, at one hand, that the genetic code DNA is a natural anticipator. As demonstrated by Nobel laureate McClintock [8], genomes are programmed. The fundamental program deals with the DNA genetic code. The properties of the DNA consist in self‐replication and self‐modification. The self‐replicating process leads to reproduction of the species, while the self‐modifying process leads to new species or evolution and adaptation in existing ones. The genetic code DNA keeps its instructions in memory in the DNA coding molecule. The genetic code DNA is a rewriting system, from DNA coding to DNA template molecule. The DNA template molecule is a rewriting system to the Messenger RNA molecule. The information is not destroyed during the execution of the rewriting program. On the other hand, it will be demonstrated that Turing machine is an artificial anticipator. The Turing machine is a rewriting system. The head reads and writes, modifying the content of the tape. The information is destroyed during the execution of the program. This is an irreversible process. The input data are lost.

Anticipatory Systems via Anticipatory Behavior
View Description Hide DescriptionAlthough cybernetics and systems research have included references to biological phenomena from their very inception, their technical and conceptual wherewithal remains rooted in engineering and the physical and formal sciences. The methodological consequences of this make themselves increasingly felt as biological systems come under closer scrutiny, when the brain becomes the be‐all‐and‐end‐all of human cognition, or when individual and social behavior comes up for analysis. In the absence of prior empirical research, the application of a straight‐jacketed modus operandi across the board can easily result in conceptual confusion. When the truly functional nature of the phenomena under discussion is not sharply differentiated from our constructional activities, our notational devices may well determine how we conceptualize the object of study instead of the other way around; witness, e.g., the growing literature on “observed” and “observing” systems. A mechanistic outlook fosters the continued treatment of organism and environment as disjoint domains, e.g., when cognition is treated in bucolic ignorance of conative factors without which there would be no cognition or any other behavior to speak of Elucidation of the specific variables, processes, and parameters involved in different fields is needed, if we are to achieve an effective treatment of the automaticity/self‐regulation continuum and capture the synergism that emerges from the environment‐organism interactivity. It is this interactivity that defines the boundaries of the system, self‐regulating or otherwise. Clearly, there is need for deep foundational thinking and much of it revolves around language in the human case. Models are verbal constructions or the product of verbal constructions. Anticipatory systems seem like a good place to begin.

Recycling the Independent Field Approximation Argument in the Far Field
View Description Hide DescriptionThe thermodynamic entropy production and the variational functional for diffusion of one species of particles from a flat membrane to an irregular membrane is studied in detail. The computations for the Laplacian field are realized with a special superconvergent overrelaxation algorithm which is of a very high precision. The possible irregular geometries examined in this work are all non‐scaling geometries, all variants of an initial fractal generator. The calculations are realized for distances of the two membranes higher than the bump of the geometric irregularity, a case which we call here “the Far Field”. The basic conclusion arising for this study is that the active zone approximation is always valid with a good precision.

Dynamical Logic Driven by Classified Inferences Including Abduction
View Description Hide DescriptionWe propose a dynamical model of formal logic which realizes a representation of logical inferences, deduction and induction. In addition, it also represents abduction which is classified by Peirce as the third inference following deduction and induction. The three types of inference are represented as transformations of a directed graph. The state of a relation between objects of the model fluctuates between the collective and the distinctive. In addition, the location of the relation in the sequence of the relation influences its state.

Implication of Abduction: Complexity without Organized Interaction
View Description Hide DescriptionAbduction, which is articulated by C.S. Peirce, is one of the forms of inference. Abduction has been researched not only in philosophy but also in artificial intelligence and information science. Finlay and Dix’s representation of abduction (1996) has almost the same meaning which is given by Peirce. On the other hand, Sawa and Gunji (2010) express three types of inference as operations of arrows on a simple triangular diagram.
In the present paper, we show that Sawa‐Gunji’s representation of abduction is consistent with Finlay‐Dix’s one, and synthesize the two representations. Both parameter estimation and abduction occupy a similar position on the synthesized representation, but they are not completely corresponding. We present “incomplete” parameter estimation as a sort of “simulated abduction”, since abduction has an intrinsic incompleteness, which means that abduction is formally equivalent to “the logical fallacy affirming the consequent”. In other words, a numerical aspect of abduction (i.e. the simulated abduction) is formalized as incomplete parameter estimation. The concept of simulated abduction is applied to parameter estimation of auto‐regressive models, and the effects of it is investigated. As a result of the numerical analyses, the distribution of the incompletely estimated parameter shows a power law of the slop ‐2 in the tail, although conventionally estimated parameter is normally distributed. The power law of the incompletely estimated parameter is based on the structure of ratio distribution. In other words, this result shows that the power law can arise when system observers premise a linearity of input and output data which are too small to estimate the system structure. We call the premise of the system observers “linearity bias”.
As an example of the cause of power law distributions, self‐organized criticality (SOC) has been known. These distributions are based on the mechanisms of the systems themselves, which have some organized interaction between their elements. On the other hand, power law distribution which is derived from the incomplete parameter estimation and the linearity bias is not based on a mechanism of system itself but on relationship between data on the system and observer of the data. Consequently, our research suggests that complexity expressed by a power law distribution can be derived from the incomplete parameter estimation which is a numerical aspect of abduction and is different from SOC mechanisms.

A Statistical Framework for Noise Separation in Dynamic Models of Intracellular Networks
View Description Hide DescriptionWe use a discrete‐time Markov process modeling approach to describe the stochastic dynamics of intracellular networks and focus on the inverse problem of network inference using experimental data. In addition to the intrinsic noise of the system, data are corrupted by measurement errors. Thus, the model describes two superimposed stochastic processes with different variances. We introduce a statistical framework for the separation of these two processes via analyzing the marginal likelihood function and apply this concept to small network examples.

On the Dynamics of an Incursion Describing the Interactions between Functionally Differentiated Subsystems of a Discrete‐time Anticipatory System
View Description Hide DescriptionDubois coined the term incursion, for an inclusive or implicit recursion, to describe a discrete‐time anticipatory system which computes its future states by reference to its future states as well as its current and past states. In this paper, we look at a model which has been proposed in the context of a social system which has functionally differentiated subsystems. The model is derived from a discrete‐time compartmental SIS epidemic model. We analyse a low order instance of the model both in its form as a recursion with no anticipatory capacity, and also as an incursion with associated anticipatory capacity. The properties of the incursion are compared and contrasted with those of the underlying recursion.

Reactively and Anticipatory Behaving Agents for Artificial Life Simulations
View Description Hide DescriptionReactive behavior is still considered and the exact opposite for the anticipatory one. Despite the advances on the field of anticipation there are little thoughts on relation with the reactive behavior, the similarities and where the boundary is. In this article we will present our viewpoint and we will try to show that reactive and anticipatory behavior can be combined. This is the basic ground of our unified theory for anticipatory behavior architecture. We still miss such compact theory, which would integrate multiple aspects of anticipation. My multi‐level anticipatory behavior approach is based on the current understanding of anticipation from both the artificial intelligence and biology point of view. As part of the explanation we will also elaborate on the topic of weak and strong artificial life. Anticipation is not matter of a single mechanism in a living organism. It was noted already that it happens on many different levels even in the very simple creatures. What we consider to be important for our work and what is our original though is that it happens even without voluntary control. We believe that this is novelty though for the anticipation theory. Naturally research of anticipation was in the beginning of this decade focused on the anticipatory principles bringing advances on the field itself. This allowed us to build on those, look at them from higher perspective, and use not one but multiple levels of anticipation in a creature design. This presents second original though and that is composition of the agent architecture that has anticipation built in almost every function. In this article we will focus only on first two levels within the 8‐factor anticipation framework. We will introduce them as defined categories of anticipation and describe them from theory and implementation algorithm point of view. We will also present an experiment conducted, however this experiment serves more as explanatory example. These first two levels may seem trivial, but growing interest in implicit anticipation and reactive anticipation in last two years suggest that this is worthwhile topic. The simplicity of them is intentional to demonstrate our way of thinking and understanding of the topic. The comparison with other results is possible only when these levels are integrated into the complex architecture, as will be shown below that can also act as standalone.

The Schwarzschild Proton
View Description Hide DescriptionWe review our model of a proton that obeys the Schwarzschild condition. We find that only a very small percentage of the vacuum fluctuations available within a proton volume need be cohered and converted to mass‐energy in order for the proton to meet the Schwarzschild condition. This proportion is equivalent to that between gravitation and the strong force where gravitation is thought to be to weaker than the strong force. Gravitational attraction between two contiguous Schwarzschild protons can accommodate both nucleon and quark confinement. We calculate that two contiguous Schwarzschild protons would rotate at c and have a period of and a frequency of which is characteristic of the strong force interaction time and a close approximation of the gamma emission typically associated with nuclear decay. We include a scaling law and find that the Schwarzschild proton data point lies near the least squares trend line for organized matter. Using a semi‐classical model, we find that a proton charge orbiting at a proton radius at c generates a good approximation to the measured anomalous magnetic moment.

Torsion Fields, Propagating Singularities, Nilpotence, Quantum Jumps and the Eikonal Equations
View Description Hide DescriptionWe establish a geometrical theory in terms of torsion fields and their singularities of quantum jumps and of the propagation of wave‐front singularities described by the eikonal equation of geometrical optics basic to Fock’s theory of gravitation and General Relativity. The latter equations correspond to the wavefront propagation for the Maxwell and Einstein equations. We discuss the genesis of spacetime in terms of these singularities and torsion fields. We introduce the class of solutions of the wave propagation (defined in terms of the metric geometry) and the eikonal equations. The lagrangian functional for quantum jumps defined in terms of the quantum potential is introduced. We give a formula that characterizes the quantum jumps in terms of an extension of the argument principle in complex analysis. We show that the wave propagation in terms of the metric geometry under a change of gauge has a natural expression as a wave propagation in terms of the laplacians associated to a torsion geometry of the Cartan‐Weyl type which has an additional interaction first‐order torsion term. In this geometry there is a differential one‐form trace‐torsion term given by the logarithmic differential of (monochromatic) waves. It is shown that quantum jumps are associated with the Cartan‐Weyl geometry, through a torsion potential given by the logarithmic differential of the composition of an analytic function ‐or alternatively a twice differentiable function‐ with a monochromatic wave function. In particular, if follows that monochromatic wave functions generate torsion. The node sets of monochromatic functions are shown to be the locus for quantum jumps. In the case of the metric being Minkowski or positive‐definite, the generalized laplacians corresponding to this torsion geometry, are generators of Brownian motions in which the torsion describes the drift of the Brownian processes. We show that this torsion potential and its singularities due to the nodes of the monochromatic wave functions, gives rise to an Aharonov‐Bohm effect. We briefly indicate the role of quantum jumps in establishing a global time and space coordinates in semiclassical General Relativity. We indicate some relations between the present approach to the geometry of quantum jumps, and the problem of topographical representation in visual perception, the Klein bottle, quantum physics and holography.

Discrete Harmonic Oscillator: A Short Compendium of Formulas
View Description Hide DescriptionSince 2002, we have, in seven papers, studied the problem of the discrete harmonic oscillator, analytically, numerically, and graphically, and made progress on a number of fronts. We identified the natural frequency of oscillation of the dual incursive oscillators, studied the system bifurcation generated by incursive discretization, and the frequency dependent correlation between the resulting incursive oscillators. We also studied the synchronization of the discretizing time interval with the frequency of oscillation. From this analysis there emerged a nonlinear (or more precisely bilinear) formalism that is perfectly stable at all time scales, and fully conserves the total energy of the system. The formalism is applicable to the discrete harmonic oscillator specifically, and to discrete Hamiltonian systems in general. In retrospect the important themes and crucial steps can more easily be identified, and this is the purpose of this short note. In it we give, in a unified notation, a short compendium of the key formulas. This summary can serve as a guide for navigating through the seven papers, as well as a practical concise manual for using the formalism.

Time‐Symmetric Discretization of The Harmonic Oscillator
View Description Hide DescriptionWe explicitly and analytically demonstrate that simple time‐symmetric discretization of the harmonic oscillator (used as a simple model of a discrete dynamical system), leads to discrete equations of motion whose solutions are perfectly stable at all time scales, and whose energy is exactly conserved. This result is important for both fundamental discrete physics, as well as for numerical analysis and simulation.

Discrete Harmonic Oscillator: Evolution of Notation and Cumulative Erratum
View Description Hide DescriptionAs the project on the discrete harmonic oscillator advanced, the notation evolved in parallel with our understanding of the problem, and it became progressively clear that a change of notation concerning the natural angular frequency of oscillation of the system, and related parameters, was required in order to conform to the spirit of the physics being developed. Specifically the notation needed to reflect the fact that the discrete harmonic oscillator is the more general entity, with the continuous harmonic oscillator being a special (and to some extent unrealistic) limiting case corresponding to where Δt is the discretizing time interval. Furthermore, as the discrete nature of time (and eventually space), incursion (anticipation), system bifurcation, hyperincursion, frequency dependent correlation, and synchronization, where progressively integrated into the fabric of the discretizing algorithm, a new discrete, perfectly stable and energy conserving, formalism emerged, and with it evolved, in parallel, the expression for the total energy. In this short note we will focus on the evolution, throughout the project, of the notation for frequency, and the expression for the discrete total energy. We also provide a cumulative erratum for the seven papers in the project so far, as well as a table summarizing the evolution of the notation for the angular frequency and related parameters.

Gibbs Paradox as Property of Observation, Proof of II. Principle of Thermodynamics
View Description Hide DescriptionOur way to deal with the given topic is a connection of both the mathematical definitions of information entropies and their mutual relations within a system of stochastic quantities especially with thermodynamic entropies defined on an isolated system in which a realization of our (repeatable) observation is performed [it is a (cyclic) transformation of heat energy of an observed, measured system].
We use the information description to analyze Gibbs paradox reasoning it as a property of such observation, measuring of an (equilibrium) thermodynamic system.
We state a logical proof of the II. P.T. as a derivation of relations among the entropies of a system of stochastic variables, realized physically, and, the Equivalence Principle of the I., II. and III. Principle of Thermodynamics is formulated.

Generalized Relativistic Hamiltonian in an Alpha Field
View Description Hide DescriptionAn alpha field is a potential field that can be presented by two dimensionless field parameters α and α′. To this category belong, among the others, electromagnetic and gravitational potential fields. The field parameters α and α′ should satisfy the field equations of the related potential field in each concrete case. The problem is to derive the generalized relativistic Hamiltonian that can be applied to an alpha field. Starting with variation principle and with the generalized line element a linear Dirac’s like relativistic Hamiltonian has been derived as the function of the field parameters α and α′. The comparison of the coefficients of that Hamiltonian with the coefficients of the well known Dirac’s Hamiltonian helps to understand their physical sense. The derived linear Dirac’s like relativistic Hamiltonian has been applied to an electromagnetic and to a gravitational field. The application to a gravitational field leads to the gravitomagnetic phenomena on the natural way, without any a priory assumption. The nonlinear relativistic Hamiltonian for an alpha field has also been derived starting with the linear one and using quadratic operation. Both Hamiltonians can be applied to the Special and General Relativity, as well as, to the multipotential alpha fields.

Founding Gravitation in 4D Euclidean Space‐Time Geometry
View Description Hide DescriptionThe Euclidean interpretation of special relativity which has been suggested by the author is a formulation of special relativity in ordinary 4D Euclidean space‐time geometry. The natural and geometrically intuitive generalization of this view involves variations of the speed of light (depending on location and direction) and a Euclidean principle of general covariance. In this article, a gravitation model by Jan Broekaert, which implements a view of relativity theory in the spirit of Lorentz and Poincaré, is reconstructed and shown to fulfill the principles of the Euclidean approach after an appropriate reinterpretation.

The Grammatical Universe and the Laws of Thermodynamics and Quantum Entanglement
View Description Hide DescriptionThe universal nilpotent computational rewrite system (UNCRS) is shown to formalize an irreversible process of evolution in conformity with the First, Second and Third Laws of Thermodynamics, in terms of a single algebraic creation operator which delivers the whole quantum mechanical language apparatus, where k , i , j are quaternions units and E, p, m are energy, momentum and rest mass. This nilpotent evolution describes ‘a dynamic zero totality universe’ in terms of its fermion states (each of which, by Pauli exclusion, is unique and nonzero), where, together with their boson interactions, these define physics at the fundamental level. (The UNCRS implies that the inseparability of objects and fields in the quantum universe is based on the fact that the only valid mathematical representations are all automorphisms of the universe itself, and that this is the mathematical meaning of quantum entanglement. It thus appears that the nilpotent fermion states are in fact what is called the splitting field in Quantum Mechanics of the Galois group which leads to the roots of the corresponding algebraic equation, and concerns in this case the alternating group of even permutations which are themselves automorphisms). In the nilpotent evolutionary process: (i) the Quantum Carnot Engine (QCE) extended model of thermodynamic irreversibility, consisting of a single heat bath of an ensemble of Standard Model elementary particles, retains a small amount of quantum coherence / entanglement, so as to constitute new emergent fermion states of matter, and (ii) the metric ensures the First Law of the conservation of energy operates at each nilpotent stage, so that (iii) prior to each creation (and implied corresponding annihilation / conserve operation), E and m can be postulated to constitute dark energy and matter respectively. It says that the natural language form of the rewrite grammar of the evolution consists of the well known precepts of the Laws of Thermodynamics, formalized by the UNCRS regress, so as to become (as UNCRS rewrites already published at CASYS), firstly the Quantum Laws of Physics in the form of the generalized Dirac equation and later at higher stages of QCE ensemble complexity, the Laws of Life in the form of Nature’s (DNA / RNA genetic) Code and then subsequently those of Intelligence and Consciousness (Nature’s Rules).

Fractals, Coherence and Brain Dynamics
View Description Hide DescriptionI show that the self‐similarity property of deterministic fractals provides a direct connection with the space of the entire analytical functions. Fractals are thus described in terms of coherent states in the Fock‐Bargmann representation. Conversely, my discussion also provides insights on the geometrical properties of coherent states: it allows to recognize, in some specific sense, fractal properties of coherent states. In particular, the relation is exhibited between fractals and q‐deformed coherent states. The connection with the squeezed coherent states is also displayed. In this connection, the non‐commutative geometry arising from the fractal relation with squeezed coherent states is discussed and the fractal spectral properties are identified. I also briefly discuss the description of neuro‐phenomenological data in terms of squeezed coherent states provided by the dissipative model of brain and consider the fact that laboratory observations have shown evidence that self‐similarity characterizes the brain background activity. This suggests that a connection can be established between brain dynamics and the fractal self‐similarity properties on the basis of the relation discussed in this report between fractals and squeezed coherent states. Finally, I do not consider in this paper the so‐called random fractals, namely those fractals obtained by randomization processes introduced in their iterative generation. Since self‐similarity is still a characterizing property in many of such random fractals, my conjecture is that also in such cases there must exist a connection with the coherent state algebraic structure. In condensed matter physics, in many cases the generation by the microscopic dynamics of some kind of coherent states is involved in the process of the emergence of mesoscopic/macroscopic patterns. The discussion presented in this paper suggests that also fractal generation may provide an example of emergence of global features, namely long range correlation at mesoscopic/macroscopic level, from microscopic local deformation processes. In view of the wide spectrum of application of both, fractal studies and coherent state physics, spanning from solid state physics to laser physics, quantum optics, complex dynamical systems and biological systems, the results presented in the present report may lead to interesting practical developments in many research sectors.