Jonito Aerts Arguëlles

Diederik Aerts, Jonito Aerts Arguëlles

For two decades, the formalism of quantum mechanics has been successfully used to describe human decision processes, situations of heuristic reasoning, and the contextuality of concepts and their combinations. The phenomenon of 'categorical perception' has put us on track to find a possible deeper cause of the presence of this quantum structure in human cognition. Thus, we show that in an archetype of human perception consisting of the reconciliation of a bottom up stimulus with a top down cognitive expectation pattern, there arises the typical warping of categorical perception, where groups of stimuli clump together to form quanta, which move away from each other and lead to a discretization of a dimension. The individual concepts, which are these quanta, can be modeled by a quantum prototype theory with the square of the absolute value of a corresponding Schrödinger wave function as the fuzzy prototype structure, and the superposition of two such wave functions accounts for the interference pattern that occurs when these concepts are combined. Using a simple quantum measurement model, we analyze this archetype of human perception, provide an overview of the experimental evidence base for categorical perception with the phenomenon of warping leading to quantization, and illustrate our analyses with two examples worked out in detail.

Diederik Aerts, Jonito Aerts Arguëlles, Lester Beltran et al.

Inspired by foundational studies in classical and quantum physics, and by information retrieval studies in quantum information theory, we prove that the notions of 'energy' and 'entropy' can be consistently introduced in human language and, more generally, in human culture. More explicitly, if energy is attributed to words according to their frequency of appearance in a text, then the ensuing energy levels are distributed non-classically, namely, they obey Bose-Einstein, rather than Maxwell-Boltzmann, statistics, as a consequence of the genuinely 'quantum indistinguishability' of the words that appear in the text. Secondly, the 'quantum entanglement' due to the way meaning is carried by a text reduces the (von Neumann) entropy of the words that appear in the text, a behaviour which cannot be explained within classical (thermodynamic or information) entropy. We claim here that this 'quantum-type behaviour is valid in general in human language', namely, any text is conceptually more concrete than the words composing it, which entails that the entropy of the overall text decreases. In addition, we provide examples taken from cognition, where quantization of energy appears in categorical perception, and from culture, where entities collaborate, thus 'entangle', to decrease overall entropy. We use these findings to propose the development of a new 'non-classical thermodynamic theory' for human cognition, which also covers broad parts of human culture and its artefacts and bridges concepts with quantum physics entities.

Diederik Aerts, Jonito Aerts Arguëlles, Lester Beltran et al.

We present a theoretical and empirical investigation of the statistical behaviour of the words in a text produced by human language. To this aim, we analyse the word distribution of various texts of Italian language selected from a specific literary corpus. We firstly generalise a theoretical framework elaborated by ourselves to identify 'quantum mechanical statistics' in large-size texts. Then, we show that, in all analysed texts, words distribute according to 'Bose--Einstein statistics' and show significant deviations from 'Maxwell--Boltzmann statistics'. Next, we introduce an effect of 'word randomization' which instead indicates that the difference between the two statistical models is not as pronounced as in the original cases. These results confirm the empirical patterns obtained in texts of English language and strongly indicate that identical words tend to 'clump together' as a consequence of their meaning, which can be explained as an effect of 'quantum entanglement' produced through a phenomenon of 'contextual updating'. More, word randomization can be seen as the linguistic-conceptual equivalent of an increase of temperature which destroys 'coherence' and makes classical statistics prevail over quantum statistics. Some insights into the origin of quantum statistics in physics are finally provided.

Jonito Aerts Arguëlles

We show that colors are light quanta for human visual perception in a similar way as photons are light quanta for physical measurements of light waves. Our result relies on the identification in the quantum measurement process itself of the warping mechanism which is characteristic of human perception. This warping mechanism makes stimuli classified into the same category perceived as more similar, while stimuli classified into different m categories are perceived as more different. In the quantum measurement process, the warping takes place between the pure states, which play the role played for human perception by the stimuli, and the density states after decoherence, which play the role played for human perception by the percepts. We use the natural metric for pure states, namely the normalized Fubini Study metric to measure distances between pure states, and the natural metric for density states, namely the normalized trace-class metric, to measure distances between density states. We then show that when pure states lie within a well-defined region surrounding an eigenstate, the quantum measurement, namely the process of decoherence, contracts the distance between these pure states, while the reverse happens for pure states lying in a well-defined region between two eigenstates, for which the quantum measurement causes a dilation. We elaborate as an example the situation of a two-dimensional quantum measurement described by the Bloch model and apply it to the situation of two colors 'Light' and 'Dark'. We argue that this analogy of warping, on the one hand in human perception and on the other hand in the quantum measurement process, makes colors to be quanta of light for human vision.

Jonito Aerts Arguelles

We analyse the way in which the principle that 'the whole is greater than the sum of its parts' manifests itself with phenomena of visual perception. For this investigation we use insights and techniques coming from quantum cognition, and more specifically we are inspired by the correspondence of this principle with the phenomenon of the conjunction effect in human cognition. We identify entities of meaning within artefacts of visual perception and rely on how such entities are modelled for corpuses of texts such as the webpages of the World-Wide Web for our study of how they appear in phenomena of visual perception. We identify concretely the conjunction effect in visual artefacts and analyse its structure in the example of a photograph. We also analyse quantum entanglement between different aspects of meaning in artefacts of visual perception. We confirm its presence by showing that well elected experiments on images retrieved accordingly by Google Images give rise to probabilities and expectation values violating the Clauser Horne Shimony Holt version of Bell's inequalities. We point out how this approach can lead to a mathematical description of the meaning content of a visual artefact such as a photograph.

Diederik Aerts, Jonito Aerts Arguelles, Lester Beltran et al.

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.