arXiv subjects

Diederik Aerts

Publications and source records attributed to Diederik Aerts.

At least 73 records · Page 4Linked to original sources

arXiv2015

From Ambiguity Aversion to a Generalized Expected Utility. Modeling Preferences in a Quantum Probabilistic Framework

Ambiguity and ambiguity aversion have been widely studied in decision theory and economics both at a theoretical and an experimental level. After Ellsberg's seminal studies challenging subjective expected utility theory (SEUT), several (mainly normative) approaches have been put forward to reproduce ambiguity aversion and Ellsberg-type preferences. However, Machina and other authors have pointed out some fundamental difficulties of these generalizations of SEUT to cope with some variants of Ellsberg's thought experiments, which has recently been experimentally confirmed. Starting from our quantum modeling approach to human cognition, we develop here a general probabilistic framework to model human decisions under uncertainty. We show that our quantum theoretical model faithfully represents different sets of data collected on both the Ellsberg and the Machina paradox situations, and is flexible enough to describe different subjective attitudes with respect to ambiguity. Our approach opens the way toward a quantum-based generalization of expected utility theory (QEUT), where subjective probabilities depend on the state of the conceptual entity at play and its interaction with the decision-maker, while preferences between acts are determined by the maximization of this 'state-dependent expected utility'.

physics.soc-ph↗

arXiv2015

Beyond-Quantum Modeling of Question Order Effects and Response Replicability in Psychological Measurements

A general tension-reduction (GTR) model was recently considered to derive quantum probabilities as (universal) averages over all possible forms of non-uniform fluctuations, and explain their considerable success in describing experimental situations also outside of the domain of physics, for instance in the ambit of quantum models of cognition and decision. Yet, this result also highlighted the possibility of observing violations of the predictions of the Born rule, in those situations where the averaging would not be large enough, or would be altered because of the combination of multiple measurements. In this article we show that this is indeed the case in typical psychological measurements exhibiting question order effects, by showing that their statistics of outcomes are inherently non-Hilbertian, and require the larger framework of the GTR-model to receive an exact mathematical description. We also consider another unsolved problem of quantum cognition: response replicability. It is has been observed that when question order effects and response replicability occur together, the situation cannot be handled anymore by quantum theory. However, we show that it can be easily and naturally described in the GTR-model. Based on these findings, we motivate the adoption in cognitive science of a hidden-measurements interpretation of the quantum formalism, and of its GTR-model generalization, as the natural interpretational framework explaining the data of psychological measurements on conceptual entities.

cs.AI↗

arXiv2015

A New Fundamental Evidence of Non-Classical Structure in the Combination of Natural Concepts

We recently performed cognitive experiments on conjunctions and negations of two concepts with the aim of investigating the combination problem of concepts. Our experiments confirmed the deviations (conceptual vagueness, underextension, overextension, etc.) from the rules of classical (fuzzy) logic and probability theory observed by several scholars in concept theory, while our data were successfully modeled in a quantum-theoretic framework developed by ourselves. In this paper, we isolate a new, very stable and systematic pattern of violation of classicality that occurs in concept combinations. In addition, the strength and regularity of this non-classical effect leads us to believe that it occurs at a more fundamental level than the deviations observed up to now. It is our opinion that we have identified a deep non-classical mechanism determining not only how concepts are combined but, rather, how they are formed. We show that this effect can be faithfully modeled in a two-sector Fock space structure, and that it can be exactly explained by assuming that human thought is the supersposition of two processes, a 'logical reasoning', guided by 'logic', and a 'conceptual reasoning' guided by 'emergence', and that the latter generally prevails over the former. All these findings provide a new fundamental support to our quantum-theoretic approach to human cognition.

cs.AI↗

arXiv2015

The Extended Bloch Representation of Quantum Mechanics. Explaining Superposition, Interference and Entanglement

The extended Bloch representation of quantum mechanics was recently derived to offer a (hidden-measurement) solution to the measurement problem. In this article we use it to investigate the geometry of superposition and entangled states, explaining the interference effects, and the entanglement correlations, in terms of the different orientations that a state-vector can take within the generalized Bloch sphere. We also introduce a tensorial determination of the generators of SU(N), particularly suitable to describe multipartite systems, from the viewpoint of the sub-entities. We then use it to show that non-product states admit a general description in which the sub-entities can always remain in well-defined states, even when they are entangled. Therefore, the completed version of quantum mechanics provided by the extended Bloch representation, in which the density operators are also representative of pure states, allows to solve not only the well-known measurement problem, but also the lesser-known entanglement problem. This because we no longer need to give up the general physical principle saying that a composite entity exists, and therefore is in a pure state, if and only if its components also exist, and therefore are in well-defined pure states.

quant-ph↗

arXiv2015

Quantum Structure of Negation and Conjunction in Human Thought

We analyse in this paper the data collected in a set of experiments performed on human subjects on the combination of natural concepts. We investigate the mutual influence of conceptual conjunction and negation by measuring the membership weights of a list of exemplars with respect to two concepts, e.g., 'Fruits' and 'Vegetables', and their conjunction 'Fruits And Vegetables', but also their conjunction when one or both concepts are negated, namely, 'Fruits And Not Vegetables', 'Not Fruits And Vegetables' and 'Not Fruits And Not Vegetables'. Our findings sharpen existing analysis on conceptual combinations, revealing systematic and remarkable deviations from classical (fuzzy set) logic and probability theory. And, more important, our results give further considerable evidence to the validity of our quantum-theoretic framework for the combination of two concepts. Indeed, the representation of conceptual negation naturally arises from the general assumptions of our two-sector Fock space model, and this representation faithfully agrees with the collected data. In addition, we find a further significant deviation and a priori unexpected from classicality, which can exactly be explained by assuming that human reasoning is the superposition of an 'emergent reasoning' and a 'logical reasoning', and that these two processes can be successfully represented in a Fock space algebraic structure.

cs.AI↗

arXiv2015

Quantum Structure in Cognition, Origins, Developments, Successes and Expectations

We provide an overview of the results we have attained in the last decade on the identification of quantum structures in cognition and, more specifically, in the formalization and representation of natural concepts. We firstly discuss the quantum foundational reasons that led us to investigate the mechanisms of formation and combination of concepts in human reasoning, starting from the empirically observed deviations from classical logical and probabilistic structures. We then develop our quantum-theoretic perspective in Fock space which allows successful modeling of various sets of cognitive experiments collected by different scientists, including ourselves. In addition, we formulate a unified explanatory hypothesis for the presence of quantum structures in cognitive processes, and discuss our recent discovery of further quantum aspects in concept combinations, namely, 'entanglement' and 'indistinguishability'. We finally illustrate perspectives for future research.

cs.AI↗

arXiv2015

Do Spins Have Directions?

The standard Bloch sphere representation was recently generalized to the 'extended Bloch representation' describing not only systems of arbitrary dimension, but also their measurements. This model solves the measurement problem and is based on the 'hidden-measurement interpretation', according to which the Born rule results from our lack of knowledge about the interaction between measuring apparatus and the measured entity. We present here the extended Bloch model and use it to investigate the nature of quantum spin and its relation to our Euclidean space. We show that spin eigenstates cannot generally be associated with directions in the Euclidean space, but only with generalized directions in the Blochean space, which generally is a space of higher dimension. Hence, spin entities have to be considered as genuine non-spatial entities. We also show, however, that specific vectors can be identified in the Blochean theater that are isomorphic to the Euclidean space directions, and therefore representative of them, and that spin eigenstates always have a predetermined orientation with respect to them. We use the details of our results to put forward a new view of realism, that we call 'multiplex realism', providing a specific framework with which to interpret the human observations and understanding of the component parts of the world. Elements of reality can be represented in different theaters, one being our customary Euclidean space, and another one the quantum realm, revealed to us through our sophisticated experiments, whose elements of reality, in the quantum jargon, are the eigenvalues and eigenstates. Our understanding of the component parts of the world can then be guided by looking for the possible connections, in the form of partial morphisms, between the different representations, which is precisely what we do in this article with regard to spin entities.

quant-ph↗

arXiv2014

Quantum Structure in Cognition and the Foundations of Human Reasoning

Traditional cognitive science rests on a foundation of classical logic and probability theory. This foundation has been seriously challenged by several findings in experimental psychology on human decision making. Meanwhile, the formalism of quantum theory has provided an efficient resource for modeling these classically problematical situations. In this paper, we start from our successful quantum-theoretic approach to the modeling of concept combinations to formulate a unifying explanatory hypothesis. In it, human reasoning is the superposition of two processes -- a conceptual reasoning, whose nature is emergence of new conceptuality, and a logical reasoning, founded on an algebraic calculus of the logical type. In most cognitive processes however, the former reasoning prevails over the latter. In this perspective, the observed deviations from classical logical reasoning should not be interpreted as biases but, rather, as natural expressions of emergence in its deepest form.

cs.AI↗

arXiv2014

The Quantum Nature of Identity in Human Thought: Bose-Einstein Statistics for Conceptual Indistinguishability

Increasing experimental evidence shows that humans combine concepts in a way that violates the rules of classical logic and probability theory. On the other hand, mathematical models inspired by the formalism of quantum theory are in accordance with data on concepts and their combinations. In this paper, we investigate a novel type of concept combination were a number is combined with a noun, e.g., `Eleven Animals. Our aim is to study 'conceptual identity' and the effects of 'indistinguishability' - in the combination 'Eleven Animals', the 'animals' are identical and indistinguishable - on the mechanisms of conceptual combination. We perform experiments on human subjects and find significant evidence of deviation from the predictions of classical statistical theories, more specifically deviations with respect to Maxwell-Boltzmann statistics. This deviation is of the 'same type' of the deviation of quantum mechanical from classical mechanical statistics, due to indistinguishability of microscopic quantum particles, i.e we find convincing evidence of the presence of Bose-Einstein statistics. We also present preliminary promising evidence of this phenomenon in a web-based study.

cs.AI↗

arXiv2014

Many-Measurements or Many-Worlds? A Dialogue

Many advocates of the Everettian interpretation consider that theirs is the only approach to take quantum mechanics really seriously, and that this approach allows to deduce a fantastic scenario for our reality, one that consists of an infinite number of parallel worlds that branch out continuously. In this article, written in dialogue form, we suggest that quantum mechanics can be taken even more seriously, if the 'many-worlds' view is replaced by a 'many-measurements' view. This allows not only to derive the Born rule, thus solving the measurement problem, but also to deduce a one-world 'non-spatial' reality, providing an even more fantastic scenario than that of the multiverse.

quant-ph↗

arXiv2014

The Unreasonable Success of Quantum Probability I: Quantum Measurements as Uniform Fluctuations

We introduce a 'uniform tension-reduction' (UTR) model, which allows to represent the probabilities associated with an arbitrary measurement situation and use it to explain the emergence of quantum probabilities (the Born rule) as 'uniform' fluctuations on this measurement situation. The model exploits the geometry of simplexes to represent the states, in a way that the measurement probabilities can be derived as the 'Lebesgue measure' of suitably defined convex subregions of the simplexes. We consider a very simple and evocative physical realization of the abstract model, using a material point particle which is acted upon by elastic membranes, which by breaking and collapsing produce the different possible outcomes. This easy to visualize mechanical realization allows one to gain considerable insight into the possible hidden structure of an arbitrary measurement process. We also show that the UTR-model can be further generalized into a 'general tension-reduction' (GTR) model, describing conditions of lack of knowledge generated by 'non-uniform' fluctuations. In this ampler framework, particularly suitable to describe experiments in cognitive science, we define and motivate a notion of 'universal measurement', describing the most general possible condition of lack of knowledge in a measurement, emphasizing that the uniform fluctuations characterizing quantum measurements can also be understood as an average over all possible forms of non-uniform fluctuations which can be actualized in a measurement context. This means that the Born rule of quantum mechanics can be understood as a first order approximation of a more general non-uniform theory, thus explaining part of the great success of quantum probability in the description of different domains of reality. This is the first part of a two-part article.

quant-ph↗

arXiv2014

The Unreasonable Success of Quantum Probability II: Quantum Measurements as Universal Measurements

In the first part of this two-part article, we have introduced and analyzed a multidimensional model, called the 'general tension-reduction' (GTR) model, able to describe general quantum-like measurements with an arbitrary number of outcomes, and we have used it as a general theoretical framework to study the most general possible condition of lack of knowledge in a measurement, so defining what we have called a 'universal measurement'. In this second part, we present the formal proof that universal measurements, which are averages over all possible forms of fluctuations, produce the same probabilities as measurements characterized by 'uniform' fluctuations on the measurement situation. Since quantum probabilities can be shown to arise from the presence of such uniform fluctuations, we have proven that they can be interpreted as the probabilities of a first-order non-classical theory, describing situations in which the experimenter lacks complete knowledge about the nature of the interaction between the measuring apparatus and the entity under investigation. This same explanation can be applied -- mutatis mutandis -- to the case of cognitive measurements, made by human subjects on conceptual entities, or in decision processes, although it is not necessarily the case that the structure of the set of states would be in this case strictly Hilbertian. We also show that universal measurements correspond to maximally 'robust' descriptions of indeterministic reproducible experiments, and since quantum measurements can also be shown to be maximally robust, this adds plausibility to their interpretation as universal measurements, and provides a further element of explanation for the great success of the quantum statistics in the description of a large class of phenomena.

quant-ph↗

arXiv2014

Solving the Hard Problem of Bertrand's Paradox

Bertrand's paradox is a famous problem of probability theory, pointing to a possible inconsistency in Laplace's principle of insufficient reason. In this article we show that Bertrand's paradox contains two different problems: an "easy" problem and a "hard" problem. The easy problem can be solved by formulating Bertrand's question in sufficiently precise terms, so allowing for a non ambiguous modelization of the entity subjected to the randomization. We then show that once the easy problem is settled, also the hard problem becomes solvable, provided Laplace's principle of insufficient reason is applied not to the outcomes of the experiment, but to the different possible "ways of selecting" an interaction between the entity under investigation and that producing the randomization. This consists in evaluating a huge average over all possible "ways of selecting" an interaction, which we call a 'universal average'. Following a strategy similar to that used in the definition of the Wiener measure, we calculate such universal average and therefore solve the hard problem of Bertrand's paradox. The link between Bertrand's problem of probability theory and the measurement problem of quantum mechanics is also briefly discussed.

physics.hist-ph↗

arXiv2014

What is Quantum? Unifying Its Micro-Physical and Structural Appearance

We can recognize two modes in which 'quantum appears' in macro domains: (i) a 'micro-physical appearance', where quantum laws are assumed to be universal and they are transferred from the micro to the macro level if suitable 'quantum coherence' conditions (e.g., very low temperatures) are realized, (ii) a 'structural appearance', where no hypothesis is made on the validity of quantum laws at a micro level, while genuine quantum aspects are detected at a structural-modeling level. In this paper, we inquire into the connections between the two appearances. We put forward the explanatory hypothesis that, 'the appearance of quantum in both cases' is due to 'the existence of a specific form of organisation, which has the capacity to cope with random perturbations that would destroy this organisation when not coped with'. We analyse how 'organisation of matter', 'organisation of life', and 'organisation of culture', play this role each in their specific domain of application, point out the importance of evolution in this respect, and put forward how our analysis sheds new light on 'what quantum is'.

physics.hist-ph↗

arXiv2014

Quantum Theory and Human Perception of the Macro-World

We investigate the question of 'why customary macroscopic entities appear to us humans as they do, i.e. as bounded entities occupying space and persisting through time', starting from our knowledge of quantum theory, how it affects the behavior of such customary macroscopic entities, and how it influences our perception of them. For this purpose, we approach the question from three perspectives. Firstly, we look at the situation from the standard quantum angle, more specifically the de Broglie wavelength analysis of the behavior of macroscopic entities, indicate how a problem with spin and identity arises, and illustrate how both play a fundamental role in well-established experimental quantum-macroscopical phenomena, such as Bose-Einstein condensates. Secondly, we analyze how the question is influenced by our result in axiomatic quantum theory, which proves that standard quantum theory is structurally incapable of describing separated entities. Thirdly, we put forward our new 'conceptual quantum interpretation', including a highly detailed reformulation of the question to confront the new insights and views that arise with the foregoing analysis. At the end of the final section, a nuanced answer is given that can be summarized as follows. The specific and very classical perception of human seeing -- light as a geometric theory -- and human touching -- only ruled by Pauli's exclusion principle -- plays a role in our perception of macroscopic entities as ontologically stable entities in space. To ascertain quantum behavior in such macroscopic entities, we will need measuring apparatuses capable of its detection. Future experimental research will have to show if sharp quantum effects -- as they occur in smaller entities -- appear to be ontological aspects of customary macroscopic entities.

physics.hist-ph↗

arXiv2014

Quantum Structure in Competing Lizard Communities

Almost two decades of research on applications of the mathematical formalism of quantum theory as a modeling tool in domains different from the micro-world has given rise to many successful applications in situations related to human behavior and thought, more specifically in cognitive processes of decision-making and the ways concepts are combined into sentences. In this article, we extend this approach to animal behavior, showing that an analysis of an interactive situation involving a mating competition between certain lizard morphs allows to identify a quantum theoretic structure. More in particular, we show that when this lizard competition is analyzed structurally in the light of a compound entity consisting of subentities, the contextuality provided by the presence of an underlying rock-paper-scissors cyclic dynamics leads to a violation of Bell's inequality, which means it is of a non-classical type. We work out an explicit quantum-mechanical representation in Hilbert space for the lizard situation and show that it faithfully models a set of experimental data collected on three throat-colored morphs of a specific lizard species. Furthermore, we investigate the Hilbert space modeling, and show that the states describing the lizard competitions contain entanglement for each one of the considered confrontations of lizards with different competing strategies, which renders it no longer possible to interpret these states of the competing lizards as compositions of states of the individual lizards.

physics.bio-ph↗

arXiv2014

Modeling Concept Combinations in a Quantum-theoretic Framework

We present modeling for conceptual combinations which uses the mathematical formalism of quantum theory. Our model faithfully describes a large amount of experimental data collected by different scholars on concept conjunctions and disjunctions. Furthermore, our approach sheds a new light on long standing drawbacks connected with vagueness, or fuzziness, of concepts, and puts forward a completely novel possible solution to the 'combination problem' in concept theory. Additionally, we introduce an explanation for the occurrence of quantum structures in the mechanisms and dynamics of concepts and, more generally, in cognitive and decision processes, according to which human thought is a well structured superposition of a 'logical thought' and a 'conceptual thought', and the latter usually prevails over the former, at variance with some widespread beliefs

cs.AI↗

arXiv2013

Identifying Quantum Structures in the Ellsberg Paradox

Empirical evidence has confirmed that quantum effects occur frequently also outside the microscopic domain, while quantum structures satisfactorily model various situations in several areas of science, including biological, cognitive and social processes. In this paper, we elaborate a quantum mechanical model which faithfully describes the 'Ellsberg paradox' in economics, showing that the mathematical formalism of quantum mechanics is capable to represent the 'ambiguity' present in this kind of situations, because of the presence of 'contextuality'. Then, we analyze the data collected in a concrete experiment we performed on the Ellsberg paradox and work out a complete representation of them in complex Hilbert space. We prove that the presence of quantum structure is genuine, that is, 'interference' and 'superposition' in a complex Hilbert space are really necessary to describe the conceptual situation presented by Ellsberg. Moreover, our approach sheds light on 'ambiguity laden' decision processes in economics and decision theory, and allows to deal with different Ellsberg-type generalizations, e.g., the 'Machina paradox'.

physics.soc-ph↗