In this book we develop various mathematical models of information dynamics, I -dynamics (including the process of thinking), based on methods of classical and quantum physics. The main aim of our investigations is to describe mathematically the phenomenon of consciousness. We would like to realize a kind of Newton-Descartes program (corrected by the lessons of statistical and quantum mechanics) for information processes. Starting from the ideas of Newton and Descartes, in physics there was developed an adequate description of the dynamics of material systems. We would like to develop an analogous mathematical formalism for information and, in particular, mental processes. At the beginning of the 21st century it is clear that it would be impossible to create a deterministic model for general information processes. A deterministic model has to be completed by a corresponding statistical model of information flows and, in particular, flows of minds. It might be that such an information statistical model should have a quantum-like structure.

Computers are essential for the functioning of our society. Despite the incredible power of existing computers, computing technology is progressing beyond today’s conventional models. Quantum Computing (QC) is surfacing as a promising disruptive technology. QC is built on the principles of quantum mechanics. QC can run algorithms that are not trivial to run on digital computers. QC systems are being developed for the discovery of new materials and drugs and improved methods for encoding information for secure communication over the Internet. Unprecedented new uses for this technology are bound to emerge from ongoing research. The development of conventional digital computing technology for the arts and humanities has been progressing in tandem with the evolution of computers since the 1950s. Today, computers are absolutely essential for the arts and humanities. Therefore, future developments in QC are most likely to impact on the way in which artists will create and perform, and how research in the humanities will be conducted. This book presents a comprehensive collection of chapters by pioneers of emerging interdisciplinary research at the crossroads of quantum computing, and the arts and humanities, from philosophy and social sciences to visual arts and music. Prof. Eduardo Reck Miranda is a composer and a professor in Computer Music at Plymouth University, UK, where he is a director of the Interdisciplinary Centre for Computer Music Research (ICCMR). His previous publications include the Springer titles Handbook of Artificial Intelligence for Music, Guide to Unconventional Computing for Music, Guide to Brain-Computer Music Interfacing and Guide to Computing for Expressive Music Performance.

Much of our understanding of human thinking is based on probabilistic models. This innovative book by Jerome R. Busemeyer and Peter D. Bruza argues that, actually, the underlying mathematical structures from quantum theory provide a much better account of human thinking than traditional models. They introduce the foundations for modeling probabilistic-dynamic systems using two aspects of quantum theory. The first, 'contextuality', is a way to understand interference effects found with inferences and decisions under conditions of uncertainty. The second, 'quantum entanglement', allows cognitive phenomena to be modeled in non-reductionist ways. Employing these principles drawn from quantum theory allows us to view human cognition and decision in a totally new light. Introducing the basic principles in an easy-to-follow way, this book does not assume a physics background or a quantum brain and comes complete with a tutorial and fully worked-out applications in important areas of cognition and decision.

This book describes state-of-the-art economic ideas and how these ideas can be (and are) used to make economic decision (in particular, to optimally allocate assets) and to gauge the results of different economic decisions (in particular, by using optimal transport methods). Special emphasis is paid to machine learning techniques (including deep learning) and to different aspects of quantum econometrics—when quantum physics and quantum computing models are techniques are applied to study economic phenomena. Applications range from more traditional economic areas to more non-traditional topics such as economic aspects of tourism, cryptocurrencies, telecommunication infrastructure, and pandemic. This book helps student to learn new techniques, practitioners to become better knowledgeable of the state-of-the-art econometric techniques, and researchers to further develop these important research directions

The recent years have been characterized by stormy social protests throughout the world. These protests have some commonalities, but at the same time, their sociopolitical, psychological, and economic contexts differ essentially. An important class of such protests is known as color revolutions. The analysis of these events in social and political literature is characterized by huge diversity of opinions. We remark that the sociopolitical perturbations under consideration are characterized by the cascade dynamics leading to the exponential amplification of coherent social actions. In quantum physics, such exponential and coherent amplification is the basic feature of laser’s functioning. (“Laser” is acronym for light amplification by stimulated emission of radiation). In this book we explore the theory of laser to model aforementioned waves of social protests, from color revolutions to Brexit and Trump’s election. We call such social processes Stimulated Amplification of Social Actions (SASA), but to keep closer to the analogy with physics we merely operate with the term “social laser.”

This book presents interdisciplinary research in the science of Human Cognition through mathematical and computational modeling and simulation. Featuring new approaches developed by leading experts in the field of cognitive science, it highlights the relevance and depth of this important area of social sciences and its expanding reach into the biological, physical, computational and mathematical sciences. This contributed volume compiles the most recent advancements and cutting-edge applications of cognitive modeling, employing a genuinely multidisciplinary approach to simulate thinking, memory, and decision-making. The topics covered encompass a wide range of subjects, such as Agent-based Modeling in psychological research, the Nyayasutra proof pattern, the utilization of the Pheromone Trail Algorithm for modeling Analog Memory, the theory and practical applications of Social Laser Theory, addressing the challenges of probabilistic learning in brain and behavior models, adopting a Physicalistic perspective to understand the emergence of cognition and computation, an in-depth analysis of the conjunction fallacy as a factual occurrence, exploring quantum modeling and causality in physics and its extensions, examining compositional vector semantics within spiking neural networks, delving into the realms of Optimality, Prototypes, and Bilingualism, and finally, investigating the intricate dimensionality of color perception. Given its scope and approach, the book will benefit researchers and students of computational social sciences, mathematics and its applications, quantum physics.

This book deals with applications of quantum mechanical techniques to areas outside of quantum mechanics, so-called quantum-like modeling. Research in this area has grown over the last 15 years. But even already more than 50 years ago, the interaction between Physics Nobelist Pauli and the psychologist Carl Jung in the 1950’s on seeking to find analogous uses of the complementarity principle from quantum mechanics in psychology needs noting. This book does NOT want to advance that society is quantum mechanical! The macroscopic world is manifestly not quantum mechanical. But this rules not out that one can use concepts and the mathematical apparatus from quantum physics in a macroscopic environment. A mainstay ingredient of quantum mechanics, is ‘quantum probability’ and this tool has been proven to be useful in the mathematical modelling of decision making. In the most basic experiment of quantum physics, the double slit experiment, it is known (from the works of A. Khrennikov) that the law of total probability is violated. It is now well documented that several decision making paradoxes in psychology and economics (such as the Ellsberg paradox) do exhibit this violation of the law of total probability. When data is collected with experiments which test ‘non-rational’ decision making behaviour, one can observe that such data often exhibits a complex non-commutative structure, which may be even more complex than if one considers the structure allied to the basic two slit experiment. The community exploring quantum-like models has tried to address how quantum probability can help in better explaining those paradoxes. Research has now been published in very high standing journals on resolving some of the paradoxes with the mathematics of quantum physics. The aim of this book is to collect the contributions of world’s leading experts in quantum like modeling in decision making, psychology, cognition, economics, and finance.