Abstract

In this study, a model is constructed in which the formation of new synaptic contacts and the tuning of synaptic weights are mediated by quantum nonlocal interactions. The interaction between biologically important molecules in the brain can be the basis of the quantum metalanguage, which controls the behavior of humans and animals. The dynamics of biologically important molecules must include their topological properties. Thus the work of the brain can only be consistently described using quantum mechanics.

1. Introduction

The act of thinking is one of the most heavily researched phenomena in science, but despite this, the mechanisms of thinking remain largely unclear. One of the key unresolved issues is the unclear relationship between thinking and the brain. This issue has been discussed repeatedly since the very emergence of science. In particular, in recent decades, a number of authors have advanced the assumptions regarding the role of quantum mechanics in brain function and thinking. Another important issue is understanding the origin of new knowledge. For example, in Melkikh, 2014a; Melkikh et al., 2018, the existence of innate behavioral programs based on quantum processes has been proposed as a mechanism of this process. Thus, the processes of thinking and the work of the brain can, to a greater or lesser degree, have a quantum nature.

We can distinguish three significant motivations for the application of quantum mechanics to the processes of thinking and brain function.

One of the first motivations is the set of ideas of Penrose and Hamcroff (Penrose, 1989; Hameroff, 1994, 2003, Hameroff, Penrose, 2014), who suggested that mental processes are associated with the collapse of the wave function, which is caused by the effects of gravity. In this case, non-computability plays an important role in the processes of thinking. According to the author (Penrose, 1994), the ability to understand cannot be formalized within a particular set of rules. The author comes to the conclusion that for the establishment of mathematical truth, mathematicians do not apply justified algorithms. According to the author (Penrose, 1994), this applies not only to mathematics but also to thinking in general. At present, this trend continues to develop (see, for example, Craddock ct al., 2015, 2017).

Another important application of quantum mechanics to cognitive sciences is decision making. This field is actively developing and includes many researchers (see, for example, Bagarello et al., 2017; Basieva et al., 2017; Khrennikov, 1999, 2010a, 2010b, 2011, Aerts et al., 2011, 2013, Dzhafarov and Kujala (2012); Pothos and Busemeyer, 2013). The main motivation in this field is to solve, with the help of quantum mechanics, paradoxes in decision-making. Such paradoxes, for example, include the Eisberg paradox, a violation of the sure-thing principle, among others. In the authors' opinion, it is quantum mechanics that makes it possible to explain the decision making in situations that classical probability theory cannot explain. The most important property of quantum probabilities is that in addition to the usual classical probabilities, they contain interference terms related to the wave character of quantum particles.

The third motivation can be attributed to the fact that the brain itself, on the basis of which thinking is realized, functions as a fundamentally quantum system. Studies (Melkikh, 2014b; Melkikh and Meijer, 2018) have shown that neural behavior is contradictory at the molecular level. This is reflected in the fact that the accuracy of protein-ligand and protein-protein biochemical reactions, protein and DNA (RNA) folding, cannot be explained by the presence of short-range potentials between biologically important molecules. In this case, the entangled (in the classical sense) and inoperable states of macro- molecules should be realized with an overwhelming probability. This phenomenon, in particular, will lead to inefficient substance transport both inside neurons and through neural membranes. Taken together (formulated by the authors as a generalized Levinthal’s paradox), these findings requires a revision to our understanding of the mechanisms of the cellular function at the molecular level. To solve the paradox, the authors propose a quantum model of intermolecular interactions. The most significant point of this model is the long-range interaction, which ensures the efficient operation of intracellular molecular machines. In this instance, the motivation for using quantum mechanics is based on the fact that classical mechanics cannot in principle provide such an interaction.

This paper is devoted to the development of ideas regarding the quantum basis of cell function (including neurons), previously expressed in the papers (Melkikh, 2014a, b, Melkikh and Meijer, 2018). In particular, the topological aspect of quantum effects in neural function will be considered, providing a basis for thinking to be understood.

2. Quantum effects in neural function. Does non-computability impact the brain's work?

Before discussion quantum effects in the brain, consider the definitions of some of the most important concepts.

Thinking is the most common property of a human to reflect the surrounding reality. Thinking is closely related to the work of the brain, but this connection is largely unclear. At present, forms of thinking that arc not related to the work of the brain are not known, but on the other hand, it is not possible to localize in the brain the molecular structure with which thinking is connected directly. The distinctive feature of thinking is the property to receive knowledge about such objects, properties and relations of the surrounding world, which cannot be directly perceived.

Knowledge is an image of the surrounding reality, expressed in the form of concepts. In a narrower sense, knowledge is information about the surrounding world, which may be more or less true. However, the mechanism for acquiring new knowledge remains largely unclear.

Part of the thinking process is understanding. The most important property of understanding is that after understanding the actions of a human (the intellectual system) become more adequate than before. Understanding is closely related to recognition of the environmental. The recognition procedure in the most general form includes a comparison of the image obtained by the receptors with a certain standard. As a result, there may be two possible options: either the image coincides with the standard (corresponds to it) or not.

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Biosystems 176 (2019) 32-40

DOI: 10.1016/j.biosystems.2018.12.007