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Psychological and social systems provide us with a natural domain for the study of anticipations because these systems are based on and operate in terms of intentionality. Psychological systems can be expected to contain a model of themselves and their environments; social systems can be strongly anticipatory and therefore co-construct their environments, for example, in techno-economic (co-)evolutions. Using Dubois’ hyper-incursive and incursive formulations of the logistic equation, these two types of systems and their couplings can be simulated. In addition to their structural coupling, psychological and social systems are also coupled by providing meaning reflexively to each other’s meaning-processing. Luhmann’s distinctions among (1) interactions between intentions at the micro-level, (2) organization at the meso-level, and (3) self-organization of the fluxes of meaningful communication at the global level can be modeled and simulated using three hyper-incursive equations. The global level of self-organizing interactions among fluxes of communication is retained at the meso-level of organization. In a knowledge-based economy, these two levels of anticipatory structuration can be expected to propel each other at the supra-individual level. [ABSTRACT FROM AUTHOR]

This 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. © 2006 American Institute of Physics [ABSTRACT FROM AUTHOR]

In biological systems, the capacity of anticipation—that is, entertaining a model of the system within the system—can be considered as naturally given. Human languages enable psychological systems to construct and exchange mental models of themselves and their environments reflexively, that is, provide meaning to the events. At the level of the social system expectations can further be codified. When these codifications are functionally differentiated—like between market mechanisms and scientific research programs—the potential asynchronicity in the update among the subsystems provides room for a second anticipatory mechanism at the level of the transversal information exchange among differently codified meaning-processing subsystems. Interactions between the two different anticipatory mechanisms (the transversal one and the one along the time axis in each subsystem) may lead to co-evolutions and stabilization of expectations along trajectories. The wider horizon of knowledgeable expectations can be expected to meta-stabilize and also globalize a previously stabilized configuration of expectations against the axis of time. While stabilization can be considered as consequences of interaction and aggregation among incursive formulations of the logistic equation, globalization can be modeled using the hyperincursive formulation of this equation. The knowledge-based subdynamic at the global level which thus emerges, enables historical agents to inform the reconstruction of previous states and to co-construct future states of the social system, for example, in a techno-economic co-evolution. © 2006 American Institute of Physics [ABSTRACT FROM AUTHOR]

We 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. © 2004 American Institute of Physics [ABSTRACT FROM AUTHOR]

The 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. © 2004 American Institute of Physics [ABSTRACT FROM AUTHOR]