arXiv subjects

Diederik Aerts

Publications and source records attributed to Diederik Aerts.

At least 37 records · Page 2Linked to original sources

arXiv2021

Entanglement in Cognition violating Bell Inequalities Beyond Cirel'son's Bound

We present the results of two tests where a sample of human participants were asked to make judgements about the conceptual combinations {\it The Animal Acts} and {\it The Animal eats the Food}. Both tests significantly violate the Clauser-Horne-Shimony-Holt version of Bell inequalities (`CHSH inequality'), thus exhibiting manifestly non-classical behaviour due to the meaning connection between the individual concepts that are combined. We then apply a quantum-theoretic framework which we developed for any Bell-type situation and represent empirical data in complex Hilbert space. We show that the observed violations of the CHSH inequality can be explained as a consequence of a strong form of `quantum entanglement' between the component conceptual entities in which both the state and measurements are entangled. We finally observe that a quantum model in Hilbert space can be elaborated in these Bell-type situations even when the CHSH violation exceeds the known `Cirel'son bound', in contrast to a widespread belief. These findings confirm and strengthen the results we recently obtained in a variety of cognitive tests and document and image retrieval operations on the same conceptual combinations.

q-bio.NC↗

arXiv2020

Are Bell-tests only about local incompatibility?

The view exists that Bell-tests would only be about local incompatibility of quantum observables and that quantum non-locality would be an unnecessary concept in physics. In this note, we emphasize that it is not incompatibility at the local level that is important for the violation of Bell-CHSH inequality, but incompatibility at the non-local level of the joint measurements. Hence, non-locality remains a necessary concept to properly interpret the outcomes of certain joint quantum measurements.

quant-ph↗

arXiv2020

When Bertlmann wears no socks. Common causes induced by measurements as an explanation for quantum correlations

It is well known that correlations produced by common causes in the past cannot violate Bell's inequalities. This was emphasized by Bell in his celebrated example of Bertlmann's socks. However, if common causes are induced by the very measurement process i.e., actualized at each run of a joint measurement, in a way that depends on the type of joint measurement that is being executed (hence, the common causes are contextually actualized), the resulting correlations are able to violate Bell's inequalities, thus providing a simple and general explanation for the origin of quantum correlations. We illustrate this mechanism by revisiting Bertlmann's socks example. In doing so, we also emphasize that Bell's inequalities, in their essence, are about demarcating 'non-induced by measurements' (non-contextual) from 'induced by measurements' (contextual) common causes, where the latter would operate at a non-spatial level of our physical reality, when the jointly measured entangled entities are microscopic in nature.

quant-ph↗

arXiv2019

Quantum Structure in Cognition: Human Language as a Boson Gas of Entangled Words

We model a piece of text of human language telling a story by means of the quantum structure describing a Bose gas in a state close to a Bose-Einstein condensate near absolute zero temperature. For this we introduce energy levels for the words (concepts) used in the story and we also introduce the new notion of 'cogniton' as the quantum of human thought. Words (concepts) are then cognitons in different energy states as it is the case for photons in different energy states, or states of different radiative frequency, when the considered boson gas is that of the quanta of the electromagnetic field. We show that Bose-Einstein statistics delivers a very good model for these pieces of texts telling stories, both for short stories and for long stories of the size of novels. We analyze an unexpected connection with Zipf's law in human language, the Zipf ranking relating to the energy levels of the words, and the Bose-Einstein graph coinciding with the Zipf graph. We investigate the issue of 'identity and indistinguishability' from this new perspective and conjecture that the way one can easily understand how two of 'the same concepts' are 'absolutely identical and indistinguishable' in human language is also the way in which quantum particles are absolutely identical and indistinguishable in physical reality, providing in this way new evidence for our conceptuality interpretation of quantum theory.

q-bio.NC↗

arXiv2019

Measuring Conceptual Entanglement in Collections of Documents

Conceptual entanglement is a crucial phenomenon in quantum cognition because it implies that classical probabilities cannot model non--compositional conceptual phenomena. While several psychological experiments have been developed to test conceptual entanglement, this has not been explored in the context of Natural Language Processing. In this paper, we apply the hypothesis that words of a document are traces of the concepts that a person has in mind when writing the document. Therefore, if these concepts are entangled, we should be able to observe traces of their entanglement in the documents. In particular, we test conceptual entanglement by contrasting language simulations with results obtained from a text corpus. Our analysis indicates that conceptual entanglement is strongly linked to the way in which language is structured. We discuss the implications of this finding in the context of conceptual modeling and of Natural Language Processing.

cs.CL↗

arXiv2019

Violation of the Bell-CHSH inequality and marginal laws in a single-entity Bell-test experiment

We describe a simple experimental setting where joint measurements performed on a single (classical or quantum) entity can violate both the Bell-CHSH inequality and the marginal laws (also called no-signaling conditions). Once emitted by a source, the entity propagates within the space of Alice's and Bob's detection screens, with the measurements' outcomes corresponding to the entity being absorbed or not absorbed in a given time interval. The violation of the marginal laws results from the fact that the choice of the screen on the side of Alice affects the detection probability on the side of Bob, and vice versa, and we show that for certain screen choices the Bell-CHSH inequality can be violated up to its mathematical maximum. Our analysis provides a clarification of the mechanisms that could be at play when the Bell-CHSH inequality and marginal laws are violated in entangled bipartite systems, which would not primarily depend on the presence of a bipartite structure but on the fact that the latter can manifest as an undivided whole.

quant-ph↗

arXiv2019

Distilling the Essence of an Evolutionary Process and Implications for a Formal Description of Culture

It has been proposed that, since the origin of life and the ensuing evolution of biological species, a second evolutionary process has appeared on our planet. It is the evolution of culture-e.g., ideas, beliefs, and artifacts. Does culture evolve in the same genuine sense as biological life? And if so, does it evolve through natural selection, or by some other means? Why does no other species remotely approach the degree of cultural complexity of humans? These questions lie at the foundation of who we are and what makes our lives meaningful. Although much research has been done on how selective pressures operating at the biological level affect cognition and culture, little research has focused on culture as an evolutionary process in its own right. Like biological forms, cultural forms-ideas, attitudes, artifacts, mannerisms, etc.-incrementally adapt to the constraints and affordances of their environment through descent with modification. In some respects culture appears to be Darwinian, i.e., a process of differential replication and selection amongst randomly generated variants. This suggests that knowledge of biological evolution can be put to use to gain insight into culture. However, attempts to apply Darwinian theory to culture have not yielded the kind of unifying framework for the social sciences that it provided for the biological sciences, largely because of the nonrandom manner in which the mind-the hub of cultural change-generates and assimilates novelty. This paper investigates how and when humans became capable of supporting culture, and what previously held it back, focusing on how we attained the creative powers we now possess. To invent in the strategic, intuitive manner characteristic of humans requires a cognitive architecture that supports the capacity to spontaneously adapt concepts to new circumstances and merge them together to conceptualize new situations.

q-bio.PE↗

arXiv2019

A Cross-disciplinary Framework for the Description of Contextually Mediated Change

We present a mathematical framework (referred to as Context-driven Actualization of Potential, or CAP) for describing how entities change over time under the influence of a context. The approach facilitates comparison of change of state of entities studied in different disciplines. Processes are seen to differ according to the degree of nondeterminism, and the degree to which they are sensitive to, internalize, and depend upon a particular context. Our analysis suggests that the dynamical evolution of a quantum entity described by the Schrodinger equation is not fundamentally different from change provoked by a measurement often referred to as collapse, but a limiting case, with only one way to collapse. The biological transition to coded replication is seen as a means of preserving structure in the fact of context-driven change, and sextual replication as a means of increasing potentiality thus enhancing diversity through interaction with context. The framework sheds light on concepts like selection and fitness, reveals how exceptional Darwinian evolution is as a means of 'change of state', and clarifies in what sense culture, and the creative process underlying it, are Darwinian.

physics.gen-ph↗

arXiv2019

Quantum entanglement in physical and cognitive systems: a conceptual analysis and a general representation

We provide a general description of the phenomenon of entanglement in bipartite systems, as it manifests in micro and macro physical systems, as well as in human cognitive processes. We do so by observing that when genuine coincidence measurements are considered, the violation of the 'marginal laws', in addition to the Bell-CHSH inequality, is also to be expected. The situation can be described in the quantum formalism by considering the presence of entanglement not only at the level of the states, but also at the level of the measurements. However, at the "local'" level of a specific joint measurement, a description where entanglement is only incorporated in the state remains always possible, by adopting a fine-tuned tensor product representation. But contextual tensor product representations should only be considered when there are good reasons to describe the outcome-states as (non-entangled) product states. This will not in general be true, hence, the entangement resource will have to generally be allocated both in the states and in the measurements. In view of the numerous violations of the marginal laws observed in physics' laboratories, it remains unclear to date if entanglement in micro-physical systems is to be understood only as an 'entanglement of the states', or also as an 'entanglement of the measurements'. But even if measurements would also be entangled, the corresponding violation of the marginal laws (no-signaling conditions) would not for this imply that a superluminal communication would be possible.

q-bio.NC↗

arXiv2019

Quantum-theoretic Modeling in Computer Science A complex Hilbert space model for entangled concepts in corpuses of documents

We work out a quantum-theoretic model in complex Hilbert space of a recently performed test on co-occurrencies of two concepts and their combination in retrieval processes on specific corpuses of documents. The test violated the Clauser-Horne-Shimony-Holt version of the Bell inequalities ('CHSH inequality'), thus indicating the presence of entanglement between the combined concepts. We make use of a recently elaborated 'entanglement scheme' and represent the collected data in the tensor product of Hilbert spaces of the individual concepts, showing that the identified violation is due to the occurrence of a strong form of entanglement, involving both states and measurements and reflecting the meaning connection between the component concepts. These results provide a significant confirmation of the presence of quantum structures in corpuses of documents, like it is the case for the entanglement identified in human cognition.

cs.CL↗

arXiv2018

Quantum Theory Methods as a Possible Alternative for the Double-Blind Gold Standard of Evidence-Based Medicine: Outlining a New Research Program

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.

q-bio.NC↗

arXiv2018

Modeling Meaning Associated with Documental Entities: Introducing the Brussels Quantum Approach

We show that the Brussels operational-realistic approach to quantum physics and quantum cognition offers a fundamental strategy for modeling the meaning associated with collections of documental entities. To do so, we take the World Wide Web as a paradigmatic example and emphasize the importance of distinguishing the Web, made of printed documents, from a more abstract meaning entity, which we call the Quantum Web, or QWeb, where the former is considered to be the collection of traces that can be left by the latter, in specific measurements, similarly to how a non-spatial quantum entity, like an electron, can leave localized traces of impact on a detection screen. The double-slit experiment is extensively used to illustrate the rationale of the modeling, which is guided by how physicists constructed quantum theory to describe the behavior of the microscopic entities. We also emphasize that the superposition principle and the associated interference effects are not sufficient to model all experimental probabilistic data, like those obtained by counting the relative number of documents containing certain words and co-occurrences of words. For this, additional effects, like context effects, must also be taken into consideration.

cs.IR↗

arXiv2018

Modeling Human Decision-making: An Overview of the Brussels Quantum Approach

We present the fundamentals of the quantum theoretical approach we have developed in the last decade to model cognitive phenomena that resisted modeling by means of classical logical and probabilistic structures, like Boolean, Kolmogorovian and, more generally, set theoretical structures. We firstly sketch the operational-realistic foundations of conceptual entities, i.e. concepts, conceptual combinations, propositions, decision-making entities, etc. Then, we briefly illustrate the application of the quantum formalism in Hilbert space to represent combinations of natural concepts, discussing its success in modeling a wide range of empirical data on concepts and their conjunction, disjunction and negation. Next, we naturally extend the quantum theoretical approach to model some long-standing `fallacies of human reasoning', namely, the `conjunction fallacy' and the `disjunction effect'. Finally, we put forward an explanatory hypothesis according to which human reasoning is a defined superposition of `emergent reasoning' and `logical reasoning', where the former generally prevails over the latter. The quantum theoretical approach explains human fallacies as the consequence of genuine quantum structures in human reasoning, i.e. `contextuality', `emergence', `entanglement', `interference' and `superposition'. As such, it is alternative to the Kahneman-Tversky research programme, which instead aims to explain human fallacies in terms of `individual heuristics and biases'.

q-bio.NC↗

arXiv2018

From Quantum Axiomatics to Quantum Conceptuality

Since its inception, many physicists have seen in quantum mechanics the possibility, if not the necessity, of bringing cognitive aspects into the play, which were instead absent, or unnoticed, in the previous classical theories. In this article, we outline the path that led us to support the hypothesis that our physical reality is fundamentally conceptual-like and cognitivistic-like. However, contrary to the 'abstract ego hypothesis' introduced by John von Neumann and further explored, in more recent times, by Henry Stapp, our approach does not rely on the measurement problem as expressing a possible 'gap in physical causation', which would point to a reality lying beyond the mind-matter distinction. On the contrary, in our approach the measurement problem is considered to be essentially solved, at least for what concerns the origin of quantum probabilities, which we have reasons to believe they would be epistemic. Our conclusion that conceptuality and cognition would be an integral part of all physical processes comes instead from the observation of the striking similarities between the non-spatial behavior of the quantum micro-physical entities and that of the human concepts. This gave birth to a new interpretation of quantum mechanics, called the 'conceptualistic interpretation', currently under investigation within our group in Brussels.

quant-ph↗

arXiv2018

Simple fractal calculus from fractal arithmetic

Non-Newtonian calculus that starts with elementary non-Diophantine arithmetic operations of a Burgin type is applicable to all fractals whose cardinality is continuum. The resulting definitions of derivatives and integrals are simpler from what one finds in the more traditional literature of the subject, and they often work in the cases where the standard methods fail. As an illustration, we perform a Fourier transform of a real-valued function with Sierpiński-set domain. The resulting formalism is as simple as the usual undergraduate calculus.

math.GN↗

arXiv2018

Quantum cognition goes beyond-quantum: modeling the collective participant in psychological measurements

In psychological measurements, two levels should be distinguished: the 'individual level', relative to the different participants in a given cognitive situation, and the 'collective level', relative to the overall statistics of their outcomes, which we propose to associate with a notion of 'collective participant'. When the distinction between these two levels is properly formalized, it reveals why the modeling of the collective participant generally requires beyond-quantum - non-Bornian - probabilistic models, when sequential measurements at the individual level are considered, and this though a pure quantum description remains valid for single measurement situations.

q-bio.NC↗

arXiv2018

Towards a Quantum World Wide Web

We elaborate a quantum model for the meaning associated with corpora of written documents, like the pages forming the World Wide Web. To that end, we are guided by how physicists constructed quantum theory for microscopic entities, which unlike classical objects cannot be fully represented in our spatial theater. We suggest that a similar construction needs to be carried out by linguists and computational scientists, to capture the full meaning carried by collections of documental entities. More precisely, we show how to associate a quantum-like 'entity of meaning' to a 'language entity formed by printed documents', considering the latter as the collection of traces that are left by the former, in specific results of search actions that we describe as measurements. In other words, we offer a perspective where a collection of documents, like the Web, is described as the space of manifestation of a more complex entity - the QWeb - which is the object of our modeling, drawing its inspiration from previous studies on operational-realistic approaches to quantum physics and quantum modeling of human cognition and decision-making. We emphasize that a consistent QWeb model needs to account for the observed correlations between words appearing in printed documents, e.g., co-occurrences, as the latter would depend on the 'meaning connections' existing between the concepts that are associated with these words. In that respect, we show that both 'context and interference (quantum) effects' are required to explain the probabilities calculated by counting the relative number of documents containing certain words and co-ocurrrences of words.

cs.AI↗

arXiv2017

On the Conceptuality Interpretation of Quantum and Relativity Theories

How can we explain the strange behavior of quantum and relativistic entities? Why do they behave in ways that defy our intuition about how physical entities should behave, considering our ordinary experience of the world around us? In this article, we address these questions by showing that the comportment of quantum and relativistic entities is not that strange after all, if we only consider what their nature might possibly be: not an objectual one, but a conceptual one. This not in the sense that quantum and relativistic entities would be human concepts, but in the sense that they would share with the latter a same conceptual nature, similarly to how electromagnetic and sound waves, although very different entities, can share a same undulatory nature. When this hypothesis is adopted, i.e., when a 'conceptuality interpretation' about the deep nature of physical entities is taken seriously, many of the interpretational difficulties disappear and our physical world is back making sense, though our view of it becomes radically different from what our classical prejudice made us believe in the first place.

physics.hist-ph↗