COMPUTING ANTICIPATORY SYSTEMS: CASYS'05  Seventh International Conference

General Principles for Brain Design
View Description Hide DescriptionThe task of understanding how the brain works has met with only limited success since important design concepts are not as yet incorporated in the analysis. Relevant concepts can be uncovered by studying the powerful methodologies that have evolved in the context of computer programming, raising the question of how the concepts involved there can be realised in neural hardware. Insights can be gained in regard to such issues through the study of the role played by models and representation. These insights lead on to an appreciation of the mechanisms underlying subtle capacities such as those concerned with the use of language. A precise, essentially mathematical account of such capacities is in prospect for the future.

The Dual Incursive System of the Discrete Harmonic Oscillator
View Description Hide DescriptionThis paper deals with the dual incursive system of the discrete harmonic oscillator, in the framework of discrete physics. Its basic premisses are that nature computes incursively, and that this is a consequence of the principle of maximum efficiency. The incursive system is based on two parallel algorithms depending on the order in which the computations are processed. Its incursivity, operationallity, and duality are discussed. We study the system conceptually, analytically, numerically and graphically. We give a number of different formulations of the equations of motion, study the closed form solutions, shifted natural frequency of oscillation. We find the system to be operationally efficient, orbitally stable in phase space, and to possess constants of the motion having the dimensions of energy.

The Superposed Hyperincursive System of the Discrete Harmonic Oscillator
View Description Hide DescriptionIn the preceding paper [1] we showed how the dual incursive system of the discrete harmonic oscillator exhibits orbital stability, and possesses constants related to energy expressions. This paper introduces the concept of structural system bifurcation and we study the superposed hyperincursive system of the discrete harmonic oscillator. The computing algorithm of this superposed hyperincursive system, is a superposition of the two computing algorithms of the dual incursive system of the discrete harmonic oscillator. We study it conceptually, analytically, numerically and graphically. We analyze its difference equations of motion, closed form solutions, energy conservation, orbital stability, and coherence conditions. The new concept of the phase of discretized time for parallel computing algorithms is introduced. We find that the system exhibits orbital stability and admits infinitely many energy conserving solutions. It can be fine tuned in order to conserve the classical expression for the energy. This, to the best of our knowledge, has never been achieved before. This work is one more step in the process of unifying the clockwork universe, the quantum universe and the computing universe, by the discretization of spacetime.

Thermonuclear Fusion Research Progress and the Way to the Reactor
View Description Hide DescriptionThe paper reviews the progress of fusion research and its prospects for electricity generation. It starts with a reminder of the principles of thermonuclear fusion and a brief discussion of its potential role in the future of the world energy production. The reactions allowing energy production by fusion of nuclei in stars and on earth and the conditions required to sustain them are reviewed. At the high temperatures required for fusion (hundred millions kelvins), matter is completely ionized and has reached what is called its 4^{th} state: the plasma state. The possible means to achieve these extreme temperatures is discussed. The remainder of the paper focuses on the most promising of these approaches, magnetic confinement. The operating principles of the presently most efficient machine of this type — the tokamak — is described in some detail. On the road to producing energy with fusion, a number of obstacles have to be overcome. The plasma, a fluid that reacts to electromagnetic forces and carries currents and charges, is a complex medium. Fusion plasma is strongly heated and is therefore a good example of a system far from equilibrium. A wide variety of instabilities can grow in this system and lead to self‐organized structures and spontaneous cycles. Turbulence is generated that degrades the confinement and hinders easy achievement of long lasting hot plasmas. Physicists have learned how to quench turbulence, thereby creating sort of insulating bottles inside the plasma itself to circumvent this problem. The recent history of fusion performance is outlined and the prospect of achieving power generation by fusion in a near future is discussed in the light of the development of the “International Tokamak Experimental Reactor” project ITER.

Cosmological Constant Problem Solution Valid for Both Planck’s and Cosmological Scales
View Description Hide DescriptionThe relation between cosmological constant Λ and the energy density of the vacuum has led to a big problem. Thus, the modern quantum field theories such as QCD, EW and GUTs predicted vary large values for vacuum energy density ρ_{Λ} and its dimensionless form Ω_{Λ,0} at the present time (GUTs: ρ_{Λ}=10^{93} g cm^{−3}, , where h_{0} is a present Hubble parameter). On the other side some cosmologists have preferred that Λ should be close to zero. But, setting Λ to zero is not in accordance with the present observations indicating that Ω_{Λ,0} is in fact of order unity. Now, the main problem is to find out a cancellation mechanism which may cancel at precisely the 123 decimal places. This “cosmological‐constant problem” has been considered in this paper. It is shown that the solution of Λ = f(r) et the Planck’s scale is of order 10^{70} m^{−2} and gives values for ρ_{Λ} and Ω_{Λ,0} exactly equal to predictions of GUTs. On the other side, the same solution of Λ at the cosmological scale is of order 10^{−53} m^{−2} and gives values for Ω_{Λ,0} of order unity. Thus, it seems that the cosmological constant problem is solved.

Further Development of the Mie‐de Broglie Theory of Quantum Gravity and the Implications for the General Theory of Relativity
View Description Hide DescriptionThe Mie‐de Broglie theory of quantum gravity, derived in a previous paper by the author, had a restricted value because it seemed rather disconnected from main stream modern physics, due to the circumstance that both Mie’s and de Broglie’s theories have become “losing” or forgotten theories in the history of physics. But the Mie‐de Broglie QG, incorporating a unification at the level of electrons, atoms and nuclei, is less isolated than it seems. With the use of von Laue’s relativistic tensor dynamics I will connect the Mie‐de Broglie QG to modern physics. A relation derived by Yarman will prove to be a key ingredient. As a result, we claim that one of the basic axioms of General Theory of Relativity, the principle of equivalence, is incompatible with the existence of de Broglie’s wave‐lengths in Quantum Mechanics. So GTR and QM, as based on the wavelength postulate, are non‐unifiable. If we choose de Broglie’s phase harmony as fundamental, a new theory of gravity is needed. The Mie‐Yarman theory of gravity seems to qualify as such.

Why do Quantum Systems Implement Self‐Referential Logic? A Simple Question With a Catastrophic Answer
View Description Hide DescriptionSimple self‐referential algorithms can model the essential logic of quantum systems and the quantum formalism is sufficiently rich to be able to model the output states of self‐referential alogrithms. We identify a key feature of self‐referentiality and show that both quantum mechanics and general relativity exhibit this feature in distinct yet complementary ways. This implies that self‐referentiality must be a foundational principle, but causality protection prohibits it being directly observed. Examining two facets of causality protection we find that quantum mechanics implements one and general relativity the other. The implication is that there can be no mathematically consistent theory for quantum gravity. However we can gain understanding of the constraints imposed on physical law when viewing a noncausal reality as if it were a causal sequence. We derive the 3+1 dimensionality of spacetime and quantum non‐locality and also possible rationale for the U(1) × SU (2) × SU (3) symmetry of the Standard Model. We also identify a number of key open problems.

Structure of Ensemble of Cosmological Models with Dark Energy
View Description Hide DescriptionWe show that all cosmological models which offer the explanation of the present acceleration of the Universe can be represented in terms of a fictitious particle moving in a one‐dimensional potential parameterized by the scale factor or redshift. On the other hand this potential function can be reconstructed from SNIa data. From the potential function we can reconstruct the phase portraits and find that only models which are topologically equivalent to the ΛCDM model seems to be realistic models of the accelerating universe. We define the ensemble of dark energy models as a subspace of planar dynamical systems. We demonstrate that the ensemble can be structuralized by introducing the Sobolev metric. Then we obtain the Banach space structure of the ensemble. We investigate this ensemble in the context of the generic universe.

The Space Structure, Force Fields and Quantum Mechanics
View Description Hide DescriptionIt is proposed that the cosmic digital code consists of 1 and 0 for an attachment space and a detachment space, respectively. The attachment space attaches to an object, while the detachment space detaches from the object. The cosmic digital code relates to the reduction of > 4D space‐time into 4D space‐time and the derivation of the space structure. Through the detachment space, > 4D space‐time is sliced into infinitely many 4D slices surrounding the 4D core attachment space. The space structurally is a partition space, or a lattice space. The lattice space consists of repetitive units of alternative attachment space and detachment space and provides for a coherent wave function and gauge force fields, while the partition space consists of separated continuous phases of attachment space and detachment space providing the space structure for the collapse of wave function and the permanent detachment or attachment of gauge bosons. Thus, the wave function and gauge bosons become pure physical fields. The mechanism for the emergence of the space structure is varying dimension numbers, ensuring the metric for the slicing of > 4D space‐time.

Building the Space‐Time Structure in Theories of Physics
View Description Hide DescriptionWe study how the supposed space‐time structure is built from given space‐time derivative operators, we show that our understanding of the reality is limited by the dimensional closure to 3D due to the cross product and the usual rotation operators which are used in the definition of several space‐time derivative operators and spinors, either in classical or in relativist quantum theories of physics.
We conclude that the physical space might have more than 3 dimensions: If matter spread over a physical space which has more than 3 dimensions, its properties in additional dimensions must be quite different from what we presently know in the usual 3D observations.

A Toy‐World That Satisfies Some Principles of “El Naschie’s E‐Infinity Theory”
View Description Hide DescriptionThe classical view of our external world is revised and its tacit a priori assumptions are confronted with consequences from Mohammed S. El Naschie’s E‐infinity theory. The far‐reaching investigations of El Naschie have demonstrated the necessity of a new unconventional thinking in physics. First we motivate the a priori assumptions of classical mechanics with the requirements of the mathematical formalisms. We explain the difficulties to construct models for a reality which shows the phenomenon of contextualism, like for example quantum mechanics. In a second step we use the principles of Husserl’s phenomenology to deduce a toy world from a contextual understanding of empirical data. In such a toy world one can illustrate the fundamental phenomena from quantum mechanics and ideas from E‐infinity theory. We will use this toy world to demonstrate that the classical a priori assumptions are not necessary and that alternative ways of thinking are possible in physics.

Fermion Interactions and Mass Generation in the Nilpotent Formalism
View Description Hide DescriptionThe relative signs associated with the energy and momentum operators used in representing the nilpotent Dirac state vectors of fermions and antifermions are a direct indication of the interactions to which these particles are subject, and also of the processes by which mass is generated from the vacuum.

The Doubling Theory Corrects the Titius‐Bode Law and Defines the Fine Structure Constant in the Solar System
View Description Hide DescriptionThe fundamental movement of the “doubling theory”, developed in our preceding papers, is applied as a model of the dynamics of the solar system. It is shown that this model justifies and corrects the distances of the planets given by the Titius‐Bode law, and predicts new planets between the Kuiper Belt and the Oort Cloud. Indeed, the empirical Titius‐Bode law defines in an approximate way the distances of the planets to the sun, and becomes totally false for the most distant planets (Neptune and Pluto) and does not include the Oort Cloud and Kuiper Belt. The doubling theory is based on successive embedded finite structures of space‐time domain at different scale levels. The cycle of the doubling movement in the solar system corresponds to 25920 years. It is shown that this cycle defines the fine structure constant.

Object‐Oriented Representations of Formal Theories as Tools for Simulation of Anticipatory Systems
View Description Hide DescriptionThe paper is oriented to application of locally used formal theories as tools for analysis and modeling of anticipatory systems, and especially of nesting anticipation, which takes place e.g. in anticipation during a design of a system that is expected to be anticipatory one. The specialization of theories enables to “tailor” them near to the studied systems and the nesting of theories enables formulating exact theories of systems, the elements of which carry their proper theories. In certain programming languages such theories make easy computer model construction and especially automatic generation of simulation models.

An Anticipatory Extension of Malthusian Model
View Description Hide DescriptionIn this paper, on the base of a new variable — deviation of population from an average value, we propose a new extension of the Malthusian model (see equations (10), (15) and (20)) using differential equations with piecewise constant argument which can be retarded as well as advanced. We study existence of periodic solutions and stability of the equations by method of reduction to discrete equations. Equations (15) and (20) with advanced argument are systems with strong anticipation. Moreover, we obtain a new interpretation of known results for differential equations with piecewise constant argument (6) and (8).

Some Two‐Steps Discrete‐Time Anticipatory Models With ‘Boiling’ Multivaluedness
View Description Hide DescriptionThis paper describes and investigates a class of models and the concept which can make a universal methodological background for difficult social, economic and public systems concerning different spatial and time scales and hierarchical levels. These are nonlinear models of difficult processes with foresight expectations. In the review some existing models with foresight expectations is presented, and the new nonlinear model with the behavior similar to models of neural network is proposed. This model has further differences from the existing one. At first the model is anticipatory, that is passing on two steps ahead, and secondly the nonlinearity in the equations has a piecewise‐linear character, and looks like the activation function of neurons. The condition for multivaludness had been found. Such multivaluedness is a special type of ‘boiling tank’ when the multiplicity had created at the restricted region of space. The suggested concept and principles allow the development of some practical applications of models.

Avoiding Extinction in a Managed Single Species Population Model by Means of Anticipative Control
View Description Hide DescriptionPopulation models with a high intrinsic growth rate that are subject to an Allee effect are known to exhibit chaotic transients which end in a population collapse and consequent extinction. In a managed environment, it might be possible to anticipate this event and affect the outcome by a carefully designed strategy. In this paper, the dynamics of a managed single species are modelled using an Anticipatory System and possible control strategies resulting from this are analysed and evaluated.

Conditions for Fully Autonomous Anticipation
View Description Hide DescriptionAnticipation allows a system to adapt to conditions that have not yet come to be, either externally to the system or internally. Autonomous systems actively control the conditions of their own existence so as to increase their overall viability. This paper will first give minimal necessary and sufficient conditions for autonomous anticipation, followed by a taxonomy of autonomous anticipation. In more complex systems, there can be semi‐autonomous subsystems that can anticipate and adapt on their own. Such subsystems can be integrated into a system’s overall autonomy, typically with greater efficiency due to modularity and specialization of function. However, it is also possible that semi‐autonomous subsystems can act against the viability of the overall system, and have their own functions that conflict with overall system functions.

Probability as Sentence Sets and its Incursive Calculus
View Description Hide DescriptionGiven the events of a same system and their respective probability, this paper gives a method to represent these events with their probabilities as sentence sets that contains all the same atomic sentences with reduction of probability calculus to a sentence set incursive calculus.