Three papers by diederick Aerts.(adsbygoogle = window.adsbygoogle || []).push({});

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http://arxiv.org/abs/1212.0107

On the Foundations of the Theory of Evolution

Diederik Aerts, Stan Bundervoet, Marek Czachor, Bart D'Hooghe, Liane Gabora, Philip Polk, Sandro Sozzo

(Submitted on 1 Dec 2012)

Darwinism conceives evolution as a consequence of random variation and natural selection, hence it is based on a materialistic, i.e. matter-based, view of science inspired by classical physics. But matter in itself is considered a very complex notion in modern physics. More specifically, at a microscopic level, matter and energy are no longer retained within their simple form, and quantum mechanical models are proposed wherein potential form is considered in addition to actual form. In this paper we propose an alternative to standard Neodarwinian evolution theory. We suggest that the starting point of evolution theory cannot be limited to actual variation whereupon is selected, but to variation in the potential of entities according to the context. We therefore develop a formalism, referred to as Context driven Actualization of Potential (CAP), which handles potentiality and describes the evolution of entities as an actualization of potential through a reiterated interaction with the context. As in quantum mechanics, lack of knowledge of the entity, its context, or the interaction between context and entity leads to different forms of indeterminism in relation to the state of the entity. This indeterminism generates a non-Kolmogorovian distribution of probabilities that is different from the classical distribution of chance described by Darwinian evolution theory, which stems from a 'actuality focused', i.e. materialistic, view of nature. We also present a quantum evolution game that highlights the main differences arising from our new perspective and shows that it is more fundamental to consider evolution in general, and biological evolution in specific, as a process of actualization of potential induced by context, for which its material reduction is only a special case.

http://arxiv.org/abs/1212.0104

Potentiality States: Quantum versus Classical Emergence

Diederik Aerts, Bart D'Hooghe

(Submitted on 1 Dec 2012)

We identify emergence with the existence of states of potentiality related to relevant physical quantities. We introduce the concept of 'potentiality state' operationally and show how it reduces to 'superposition state' when standard quantum mechanics can be applied. We consider several examples to illustrate our approach, and define the potentiality states giving rise to emergence in each example. We prove that Bell inequalities are violated by the potentiality states in the examples, which, taking into account Pitowsky's theorem, experimentally indicates the presence of quantum structure in emergence. In the first example emergence arises because of the many ways water can be subdivided into different vessels. In the second example, we put forward a full quantum description of the Liar paradox situation, and identify the potentiality states, which in this case turn out to be superposition states. In the example of the soccer team, we show the difference between classical emergence as stable dynamical pattern and emergence defined by a potentiality state, and show how Bell inequalities can be violated in the case of highly contextual experiments.

http://arxiv.org/abs/1212.0109

Quantum Probabilistic Structures in Competing Lizard Communities

Diederik Aerts, Marek Czachor, Maciej Kuna, Barry Sinervo, Sandro Sozzo

(Submitted on 1 Dec 2012)

Almost two decades of research on the use of the mathematical formalism of quantum theory as a modeling tool for entities and their dynamics in domains different from the micro-world has now firmly shown the systematic appearance of quantum structures in aspects of human behavior and thought, such as in cognitive processes of decision-making, and in the way concepts are combined into sentences. In this paper, we extend this insight to animal behavior showing that a quantum probabilistic structure models the mating competition of three side-blotched lizard morphs. We analyze a set of experimental data collected from 1990 to 2011 on these morphs, whose territorial behavior follows a cyclic rock-paper-scissors (RPS) dynamics. Consequently we prove that a single classical Kolmogorovian space does not exist for the lizard's dynamics, and elaborate an explicit quantum description in Hilbert space faithfully modeling the gathered data. This result is relevant for population dynamics as a whole, since many systems, e.g. the so called plankton paradox situation, are believed to contain elements of cyclic competition.

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# Three papers

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