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Attempts to apply the apparatus of quantum mechanics to cognition and language have met, understandably, with a degree of scepticism within the disciplines concerned, but they nevertheless have the potential for opening exciting new perspectives. In this article, I address the question as to what it is exactly about these attempts that has drawn such attention – both positive and negative – in recent years. I shall argue for distinguishing those aspects of quantum cognition that do warrant serious consideration by cognitive psychologists and linguists irrespective of the exact nature of its relationship to classical quantum mechanics. The key lies in the important role played by analogy in both disciplines.

Are our everyday judgments about the world around us normative? Decades of research in the judgment and decision-making literature suggest the answer is no. If people's judgments do not follow normative rules, then what rules if any do they follow? Quantum probability theory is a promising new approach to modeling human behavior that is at odds with normative, classical rules. One key advantage of using quantum theory is that it explains multiple types of judgment errors using the same basic machinery, unifying what have previously been thought of as disparate phenomena. In this article, we test predictions from quantum theory related to the co-occurrence of two classic judgment phenomena, order effects and conjunction fallacies, using judgments about real-world events (related to the U.S. presidential primaries). We also show that our data obeys two a priori and parameter free constraints derived from quantum theory. Further, we examine two factors that moderate the effects, cognitive thinking style (as measured by the Cognitive Reflection Test) and political ideology.

Our interest focusses on the idea, that consciousness is a powerful acting entity. Up to now there does not exist a scientific concept for this idea. This is not due to problems within the field of psychology or brain research, but rather in resisting theories of modern physics. That is, why we have to search for a solution in the field of physics. A solution can be found in a new understanding of the basics of physical theory. That could be given by abstract and absolute quantum bits of information (AQI bits). To avoid the popular misunderstanding of “information” as “meaningful” it was necessary to find a new word for the free-of-meaning AQI bits: the AQI bits establish a quantum pre-structure termed “Protyposis” (Greek: “pre-formation”), out of which real objects can be formed, starting from energetical and material elementary particles. The Protyposis AQI bits provide a pre-structure for all entities in natural sciences. They are the basic entities, whereof the physical nature of the brain, on the one hand, and the mental nature of consciousness, on the other hand, were formed during the cosmological and the following biological evolution. A deeper understanding of quantum structures may help to overcome the resistance against quantum theory in the field of brain research and consciousness. The key for an understanding is the concept of Protyposis, which means an abstract quantum information free of any definite meaning. With the AQI bits of the Protyposis, both, massless and massive quantum particles can be constructed. Even quantum information with special meanings, in example grammatically formulated thoughts, eventually could be explained. As long as the fundamental basis of quantum theory is misunderstood as being formed by a manifold of some small objects like atoms, quarks, or strings, the problem of understanding consciousness has no solution. If instead we understand quantum theory as based on truly simple quantum structures, there would be no longer fundamental problems for an understanding of consciousness.

Alexander Wendt’s Quantum Mind and Social Science reopens the question of the relevance of quantum mechanics to the social sciences. In response, I argue that due to “quantum decoherence,” the macr...

The aim of this paper is to explore the ways in which Axiomatic Reconstructions of Quantum Theory in terms of Information-Theoretic principles (ARQITs) can contribute to explaining and understanding quantum phenomena, as well as to study their explanatory limitations. This is achieved in part by offering an account of the kind of explanation that axiomatic reconstructions of quantum theory provide, and re-evaluating the epistemic status of the program in light of this explanation. As illustrative cases studies, I take Clifton's, Bub's and Halvorson's characterization theorem and Popescu's and Rohrlich's toy models, and their explanatory contribution with respect to quantum non-locality. On the one hand, I argue that ARQITs can aspire to provide genuine explanations of (some aspects of) quantum non-locality. On the other hand, I argue that such explanations cannot rule out a mechanical quantum theory.

In the mid-1990s it was proposed that quantum effects in proteins known as microtubules play a role in the nature of consciousness. The theory was largely dismissed due to the fact that quantum effects were thought unlikely to occur in biological systems, which are warm and wet and subject to decoherence. However, the development of quantum biology now suggests otherwise. Quantum effects have been implicated in photosynthesis, a process fundamental to life on earth. They are also possibly at play in other biological processes such as avian migration and olfaction. The microtubule mechanism of quantum consciousness has been joined by other theories of quantum cognition. It has been proposed that general anaesthetic, which switches off consciousness, does this through quantum means, measured by changes in electron spin. The tunnelling hypothesis developed in the context of olfaction has been applied to the action of neurotransmitters. A recent theory outlines how quantum entanglement between phosphorus nuclei might influence the firing of neurons. These, and other theories, have contributed to a growing field of research that investigates whether quantum effects might contribute to neural processing. This review aims to investigate the current state of this research and how fully the theory is supported by convincing experimental evidence. It also aims to clarify the biological sites of these proposed quantum effects and how progress made in the wider field of quantum biology might be relevant to the specific case of the brain., The following article will be submitted to AVS Quantum Science

We motivate the possibility of using notions and methods derived from quantum physics, and more specifically from the research field known as 'quantum cognition', to optimally model different situations in the field of medicine, its decision-making processes and ensuing practices, particularly in relation to chronic and rare diseases. This also as a way to devise alternative approaches to the generally adopted double-blind gold standard., 9 pages, no figures

This paper proposes that cognitive humour can be modelled using the mathematical framework of quantum theory, suggesting that a Quantum Theory of Humour (QTH) is a viable approach. We begin with brief overviews of both research on humour, and the generalized quantum framework. We show how the bisociation of incongruous frames or word meanings in jokes can be modelled as a linear superposition of a set of basis states, or possible interpretations, in a complex Hilbert space. The choice of possible interpretations depends on the context provided by the set-up versus the punchline of a joke. We apply QTH first to a verbal pun, and then consider how this might be extended to frame blending in cartoons. An initial study of 85 participant responses to 35 jokes (and a number of variants) suggests that there is reason to believe that a quantum approach to the modelling of cognitive humour is a viable new avenue of research for the field of quantum cognition.

In this paper we review the general framework of operational probabilistic theories (OPT), along with the six axioms from which quantum theory can be derived. We argue that the OPT framework along with a relaxed version of five of the axioms, define a general information theory. We close the paper with considerations about the role of the observer in an OPT, and the interpretation of the von Neumann postulate and the Schrodinger-cat paradox.

In physics, at the beginning of the twentieth century it was recognized that some experiments could not be explained by the conventional classical mechanics, but the same could be explained by the newly discovered quantum theory. It resulted in a new mechanics called quantum mechanics that revolutionized scientific and technological developments. Again, at the beginning of the twenty-first century, it is being recognized that some experiments related to the human decision-making processes could not be explained by the conventional classical decision theory but the same could be explained by the models based on quantum mechanics. It is now recognized that we need quantum mechanics in psychology as well as in economics and finance. In this paper we attempt to advance and explain the present understanding of applicability of quantum mechanics to the human decision-making processes. Using the postulates analogous to the postulates of quantum mechanics, we show the derivation of the quantum interference equation to illustrate the quantum approach. The explanation of disjunction effect experiments of Tversky and Shafir (Tversky A, Shafir E (1992) The disjunction effect in choice under uncertainty. Psych. Sci. 3(5):305–309) has been chosen to demonstrate the necessity of a quantum model. Further, to suggest the possibility of application of the quantum theory to the business-related decisions, some terms such as price operator, state of mind of the acquiring firm, etc., are introduced and discussed in context of the merger/acquisition of business firms. The possibility of the development in areas such as quantum finance, quantum management, application of quantum mechanics to the human dynamics related to healthcare management, etc., is also indicated.

The thesis of this paper is that Information, Cognition and a Principle of Existence are intrinsically structured in the quantum model of reality. We reach such evidence by using the Clifford algebra. We analyze quantization in some traditional cases of quantum mechanics and, in particular in quantum harmonic oscillator, orbital angular momentum and hydrogen atom. The results are confirmed analyzing human cognition behavior that evidences a very consistent agreement with the basic quantum mechanical foundations.

Quantum mechanics and violation ofthe sure-thing principle: the use of probability interference andother concepts

The problem of mind and consciousness cannot be treated as an object of science without much difficulty. Inevitably there is the self-contradiction that the work itself in science and thinking is an object of thought. In this meaning, we need to get back to the fundamental problem of how the world is perceived. The fundamental concept of quantum theory includes essentially unsolved problems such as the observation problem. In this paper, we begin to consider this fundamental problem in quantum theory and discuss the possibility of a description of mind in terms of quantum theory.

Common observations of the unpredictability of human behavior and the influence of one question on the answer to another suggest social science experiments are probabilistic and may be mutually incompatible with one another, characteristics attributed to quantum mechanics (as distinguished from classical mechanics). This paper examines this superficial similarity in depth using the Foulis-Randall Operational Statistics language. In contradistinction to physics, social science deals with complex, open systems for which the set of possible experiments is unknowable and outcome interference is a graded phenomenon resulting from the ways the human brain processes information. It is concluded that social science is, in some ways, "less classical" than quantum mechanics, but that generalized "quantum" structures may provide appropriate descriptions of social science experiments. Specific challenges to extending "quantum" structures to social science are identified., Comment: Talk presented at QS2002 Vienna, July 2002

Understanding the role of causality in quantum theory is a growing research direction in quantum information and the foundations of quantum theory. One particular area is to understand generalizations of quantum theory where there is an indefinite causal order between various operations. Building on recent work developing the process matrix formalism, Araújo et al (2015 New J. Phys. 17 [http://dx.doi.org/10.1088/1367-2630/17/10/102001] 102001 ) give formal tools to analyse how causally indefinite processes can be by drawing inspiration from entanglement theory. This approach draws together concepts in quantum information with more speculative ideas in the foundations of quantum theory.

I present a partially historical discussion of the basis of the quantum theory in nonmathematical terms using human knowledge and consciousness as an underlying theme. I show that the philosophical position in both classical and quantum theory is the experimental and mathematical philosophy of Isaac Newton. Because almost all the systems we deal with are multicomponent, we must consider the limitations and openness imposed by thermodynamics on our claims in both classical and quantum treatments. Here the reality of measurement stands in the way of any simple picture but also provides the basis for considerations of free will. Particular care is taken with the concepts of quantum measurement, entanglement, and decoherence because of their importance in the discussion.

I respond to Carl Helrich's criticism of my proposition that the emergence of complex order in the universe is from Virtual State Actualization (VSA). The question is discussed as to whether quantum theory is able to afford any kind of quantum ontology or whether it merely allows an epistemological view. I point out that, even though many contradictory interpretations of quantum theory are currently possible, the concept of VSA is based on molecular properties that are so simple and factual that they are beyond interpretation. Helrich's appeal for caution in proceeding from physical reality to Divine Reality is wholeheartedly supported and a detailed discussion is given.

In this paper we present a neural oscillator model of stimulus response theory that exhibits quantum-like behavior. We then show that without adding any additional assumptions, a quantum model constructed to fit observable pairwise correlations has no predictive power over the unknown triple moment, obtainable through the activation of multiple oscillators. We compare this with the results obtained in reference (de Barros, J.A.: Decision making for inconsistent expert judgments using negative probabilities. In: Quantum Interaction, Lecture Notes in Computer Science. Springer Verlag, Berlin (2014)), where a criteria of rationality gives optimal ranges for the triple moment.

We use the system of p-adic numbers for the description of information processes. Basic objects of our models are so-called transformers of information, basic processes are information processes and statistics are information statistics (thus we present a model of information reality). The classical and quantum mechanical formalisms on information p-adic spaces are developed. It seems that classical and quantum mechanical models on p-adic information spaces can be applied for the investigation of flows of information in cognitive and social systems, since a p-adic metric gives a quite natural description of the ability to form associations.

Quantum cognition research applies abstract, mathematical principles of quantum theory to inquiries in cognitive science. It differs fundamentally from alternative speculations about quantum brain processes. This topic presents new developments within this research program. In the introduction to this topic, we try to answer three questions: Why apply quantum concepts to human cognition? How is quantum cognitive modeling different from traditional cognitive modeling? What cognitive processes have been modeled using a quantum account? In addition, a brief introduction to quantum probability theory and a concrete example is provided to illustrate how a quantum cognitive model can be developed to explain paradoxical empirical findings in psychological literature.

The article explores some of the basic findings of quantum physics and information theory and their possible usefulness in offering new vistas for understanding psychoanalysis and the patient-analyst interchange. Technical terms are explained and placed in context, and examples of applying quantum models to clinical experience are offered. Given the complexity of the findings of quantum mechanics and information theory, the article aims only to introduce some of the major concepts from these disciplines. Within this framework the article also briefly addresses the question of mind as well as the problematic of reducing the experience of consciousness to neurological brain functioning.

The thesis of this paper is that Information, Cognition and a Principle of Existence are intrinsically structured in the quantum model of reality. There is an intrinsic “factor of knowledge” that supports its structure. We reach such evidence by using the Clifford algebra. In detail we analyze quantization in some traditional cases of interest in quantum mechanics and, in particular, in quantum harmonic oscillator, orbital angular momentum and hydrogen atom. We adopt the basic von Neumann results that projection operators represent logical statements and we demonstrated that are intrinsically structured in the cases of quantization that are taken in consideration. NeuroQuantology | March 2013 | Volume 11 | Issue 1| Page 34-46

Why should you be interested in quantum theory applied to Cognition and decision? Perhaps you are a physicist who is curious whether or not quantum principles can be applied outside of physics. In fact, that is one purpose of this book. Perhaps you are a cognitive scientist who is interested in representing concepts by vectors in a multidimensional feature space. This is essentially the way quantum theory works too. Perhaps you are a decision scientist who is trying to understand how people make decisions under uncertainty. Quantum theory could provide some interesting new answers. Generally speaking, quantum theory is a new theory for constructing probabilistic and dynamic systems , and in this book we apply this new theory to topics in cognition and decision. Later in this chapter we will give some specific examples, but let us step back at this point and try to understand the more general principles that support a quantum approach to cognition and decision. Six reasons for a quantum approach to cognition and decision Quantum physics is arguably the most successful scientific theoretical achievement that humans have ever created. It was created to explain puzzling findings that were impossible to understand using the older classical physical theory, and it achieved this by introducing an entirely new set of revolutionary principles. The older classical physical theory is now seen as a special case of the more general quantum theory. In the process of creating quantum mechanics, physicists also created a new theory of probabilistic and dynamic systems that is more general than the previous classic theory (Pitowski, 1989).

What can you learn about quantum theory in one chapter without knowing any physics? A complete presentation of quantum theory requires an entire textbook, but our goal for this chapter is to provide only the essential elements of the theory that we feel are relevant for modelling behavioral phenomena. Just like classical probability theory, quantum theory is based on a small set of axioms used to assign probabilities to events. This chapter is limited to what is called the structural principles of quantum theory, whereas Chapter 8 will set out the dynamic principles. For simplicity, only finite state systems will be described, although quantum theory can also be applied to continuous state systems. Even though this book is limited to finite dimensions, the number of dimensions can be arbitrarily large. For finite state systems, the structural part of quantum theory is expressed in the formalism of linear algebra (for continuous state systems, it is expressed in the formalism of functional analysis). Consequently, a brief tutorial of linear algebra is presented along with our elementary introduction to quantum theory. Various notations are used to describe linear algebra, depending on the application field. Physicists like to use Dirac notation, invented by one of the founders of quantum theory, Paul Dirac (Dirac, 1958). Although the Dirac notation will be unfamiliar to many cognitive scientists, we will still use it as it is a succinct notation for expressing linear algebra. It helps the reader to see relations that are more difficult to identify using other formalisms.

This article is interdisciplinary. It aims to show that we are able, on the basis of discrete quantum mechanics(DQM), to build mathematical models not only for quantum evolution processes but also for processes of mindsystems and, particularly, for their interaction. Thus, the solution of the mind/brain problem that Eccles hasproposed in his theory of exocytosis is treated by giving it a mathematical form. The key assumption is thatquantum systems interact through vector interferences. Eccles’ theory is enlarged and made more exact using adiscrete quantum mechanical model for the perception. This is also applied to the gestalt structuring process; inparticular, the process concerning the gestalt forming of certain reversible (ambiguous) figures is analyzed andthe model compared to empirical data.

This paper summarizes the experience of the V¨ axj¨o series of conferences the longest series of conferenceson foundations of quantum mechanics. One of the main lessons of this series is that the present state ofdevelopment of quantum theory does not exclude a possibility to elaborate a local realistic interpretation. Oneof such interpretations, the V¨ axj¨o interpretaion, combines realism and co ntextuality. And it became recognizedworldwide.Keywords: Epistemology of quantum mechanics, the V¨ axj¨o series of conferences, foundations of quantummechanics, local realistic interpretation, V¨ axj¨o interpretaion, contextuality, information interpretation 1. INTRODUCTION This paper is full of my reminiscences of meetings in V¨ axj¨o and debates on foundations of quantum mechanicswhich took place during these meetings. The V¨ axj¨o series of conferences played an important role in elabo-ration of the epistemology of modern quantum mechanics, the epistemology of quantum physics enlighted byquantum information theory. During the last 12 years a few hundred of leading experts in quantum founda-tions, probability, information, and philosophy of science have been participated in this conference series. Oneof the main lessons of this remarkable series is huge diversity of opinions on foundations of quantum theoryand its epistemology. After all we can “rmly declare that the common viewpoint that the community of peopleinterested in quantum foundations can be split into orthodox Copenhagenists who believe in completeness ofquantum mechanics (and impossibility to go beyond it) and they form the main part of the community and asmall group of outsiders who dream of the comeback of old fashioned Laplacian determinism does not match thereal situation. In the process of debates and discussion s it became completely clear t hat the group of orthodoxCopenhagenistsŽ is very diverse. The d egrees of their beliefs in completeness of quantum mechanics vary essen-tially. Many of brightest Copenhagenists have elaborated original ideas on possibilities to go beyond quantum to create more general theories of micro-phenomena.On the other hand, the majority of people who does not believe in Bohrs claim on completeness of quantummechancs do not at all dream of the recovery of Laplacian determinism of particles. A variety of novel approchesgoing beyond the quantum mathematical model have been elaborated, including various classical “eld-type mod-els, e.g., papers

We present a new approach to the foundations of quantum theory and information theory which is based on the algebraic approach to integration, information geometry, and maximum relative entropy methods. It enables us to deal with conceptual and mathematical problems of quantum theory without any appeal to Hilbert space framework and without frequentist or subjective interpretation of probability.

Experiments in cognitive science and decision theory show that the ways in which people combine concepts and make decisions cannot be described by classical logic and probability theory. This has serious implications for applied disciplines such as information retrieval, artificial intelligence and robotics. Inspired by a mathematical formalism that generalizes quantum mechanics the authors have constructed a contextual framework for both concept representation and decision making, together with quantum models that are in strong alignment with experimental data. The results can be interpreted by assuming the existence in human thought of a double-layered structure, a 'classical logical thought' and a 'quantum conceptual thought', the latter being responsible of the above paradoxes and nonclassical effects. The presence of a quantum structure in cognition is relevant, for it shows that quantum mechanics provides not only a useful modeling tool for experimental data but also supplies a structural model for human and artificial thought processes. This approach has strong connections with theories formalizing meaning, such as semantic analysis, and has also a deep impact on computer science, information retrieval and artificial intelligence. More specifically, the links with information retrieval are discussed in this paper., Comment: 9 pages

My discussion is articulated under the neurological as well as the psychological profile. I insist in particular on the view that mental events arise in analogy with quantum probability fields. I review some results obtained on quantum cognition discussing in detail those that we obtained on quantum interference in mental states during perception-cognition in ambiguous figures. Frequently, I use the approach to quantum mechanics by Clifford algebra. I insist in particular on two recent results. The first is the justification that I obtain of the von Neumann postulate on quantum measurement and the second relates my Clifford demonstration on the logical origins of quantum mechanics and thus on the arising feature that quantum mechanics relates conceptual entities. The whole discussion aims me to support the conclusion that we think in a quantum probabilistic manner.

A generalisation of the concepts utility and information value is given for the non-commutative case. In particular, states and utility operators are considered in dual linear spaces equipped with pre-orders, generated by a wedge of utility operators. It is shown that solutions to the information value problem give rise to an isotone Galois connection between the pre-ordered spaces. A particular form of this connection depends on the choice of a functional representing information resource. The properties of information resource are discussed from the point of information value theory, and an example is presented that generalises several known forms of classical and quantum information. Potential areas of application of information value in cognitive science, biology and quantum theory are discussed.

In physics, at the beginning of the twentieth century it was recognized that some experiments could not be explained by the conventional classical mechanics but the same could be explained by the newly discovered quantum theory. It resulted into a new mechanics called quantum mechanics that revolutionized the scientific and technological developments. Again at the beginning of the twenty-first century, it is being recognized that some experiments related with the human decision making processes could not be explained by the conventional classical decision theory but the same could be explained by the models based on quantum mechanics. It is now recognized that we need quantum mechanics in psychology as well as in economics and finance. In this paper we attempt to advance and explain the present understanding of applicability of quantum mechanics to the human decision making processes. Using the postulates analogous to the postulates of quantum mechanics, we show the derivation of the quantum interference equation to illustrate the quantum approach. The explanation of disjunction effect experiments of Tversky and Shafir (1992) has been chosen to demonstrate the necessity of a quantum model. Further to suggest the possibility of application of the quantum theory to the business related decisions, some terms such as price operator, state of mind of the acquiring firm, etc. are introduced and discussed in context of the merger/acquisition of business firms. The possibility of the development in the areas such as quantum finance, quantum management, application of quantum mechanics to the human dynamics related with health care management, etc. is also indicated.