Do We Think and Communicate in Quantum Ways? On the Presence of Quantum Structures in Language

While some of the properties of quantum mechanics are essentially linked to the nature of the microworld, others are connected to fundamental structures of the world at large and could therefore in principle also appear in other domains than the micro-world. The aim of this article is to show the presence of genuine quantum structures in human language. More in particular, we will point out the violation of Bell's inequalities in specific situations encountered in language. The first sections of this article explain why the violation of Bell's inequalities is proof of the presence of genuine quantum structures, and how over the past decades this insight has increasingly made itself felt in the foundations of quantum mechanics research. This article also contains an overview of earlier work of ours discussing the detection of quantum structures in other domains than the micro-world.

[1]  C. Piron,et al.  On the Foundations of Quantum Physics , 1976 .

[2]  E. Knill,et al.  Deterministic quantum teleportation of atomic qubits , 2004, Nature.

[3]  Bernd Kuckert Mathematische Grundlagen der Quantenmechanik , 2005 .

[4]  Thomas K. Landauer,et al.  On the computational basis of learning and cognition: Arguments from LSA , 2002 .

[5]  D. Bohm A SUGGESTED INTERPRETATION OF THE QUANTUM THEORY IN TERMS OF "HIDDEN" VARIABLES. II , 1952 .

[6]  Sven Aerts,et al.  Hidden Measurements from Contextual Axiomatics , 2002 .

[7]  Peter W. Foltz,et al.  Learning Human-like Knowledge by Singular Value Decomposition: A Progress Report , 1997, NIPS.

[8]  Geoffrey E. Hinton Tensor Product Variable Binding and the Representation of Symbolic Structures in Connectionist Systems , 1991 .

[9]  D. A. Edwards The mathematical foundations of quantum mechanics , 1979, Synthese.

[10]  J. Fodor,et al.  Concepts: a potboiler , 1994, Cognition.

[11]  M. F.,et al.  Bibliography , 1985, Experimental Gerontology.

[12]  T. Landauer,et al.  A Solution to Plato's Problem: The Latent Semantic Analysis Theory of Acquisition, Induction, and Representation of Knowledge. , 1997 .

[13]  Stanley P. Gudder,et al.  Hidden Variables in Quantum Mechanics Reconsidered , 1968 .

[14]  Thomas Hofmann,et al.  Probabilistic Latent Semantic Analysis , 1999, UAI.

[15]  F. Sontag,et al.  Wholeness and the Implicate Order , 1983 .

[16]  Richard M. Shiffrin,et al.  1 Semantic Spaces based on Free Association that Predict Memory Performance , 2000 .

[17]  H. S. Allen The Quantum Theory , 1928, Nature.

[18]  Lance J. Rips,et al.  The Current Status of Research on Concept Combination , 1995 .

[19]  J. Hampton Conceptual combination , 2003 .

[20]  Thomas L. Griffiths,et al.  Prediction and Semantic Association , 2002, NIPS.

[21]  R. Nosofsky Exemplars, prototypes, and similarity rules. , 1992 .

[22]  Richard A. Harshman,et al.  Indexing by Latent Semantic Analysis , 1990, J. Am. Soc. Inf. Sci..

[23]  J. Naudts,et al.  Thermostatistics based on Kolmogorov–Nagumo averages: unifying framework for extensive and nonextensive generalizations , 2001, cond-mat/0106324.

[24]  R. Nosofsky Exemplar-Based Accounts of Relations Between Classification, Recognition, and Typicality , 1988 .

[25]  Luigi Accardi,et al.  The Probabilistic Roots of the Quantum Mechanical Paradoxes , 1984 .

[26]  E. Rosch Cognitive Representations of Semantic Categories. , 1975 .

[27]  A. Aspect Bell's inequality test: more ideal than ever , 1999, Nature.

[28]  Diederik Aerts The stuff the world is made of: physics and reality , 1999 .

[29]  F. Schmidt-Kaler,et al.  Deterministic quantum teleportation with atoms , 2004, Nature.

[30]  Edward E. Smith,et al.  Gradedness and conceptual combination , 1982, Cognition.

[31]  On classical models of Spin , 1992, quant-ph/0205010.

[32]  Diederik Aerts,et al.  On the Origin of Probabilities in Quantum Mechanics: Creative and Contextual Aspects , 1999 .

[33]  Diederik Aerts,et al.  A Theory of Concepts and Their Combinations II: A Hilbert Space Representation , 2004 .

[34]  J. Bell On the Problem of Hidden Variables in Quantum Mechanics , 1966 .

[35]  L. Komatsu Recent views of conceptual structure , 1992 .

[36]  Marcelo A. Montemurro,et al.  Beyond the Zipf-Mandelbrot law in quantitative linguistics , 2001, ArXiv.

[37]  Diederik Aerts,et al.  Applications of Quantum Statistics in Psychological Studies of Decision Processes , 1995 .

[38]  Albert Einstein,et al.  Can Quantum-Mechanical Description of Physical Reality Be Considered Complete? , 1935 .

[39]  H. Kamp,et al.  Prototype theory and compositionality , 1995, Cognition.

[40]  Diederik Aerts,et al.  The Hidden-Measurement Formalism: Quantum Mechanics as a Consequence of Fluctuations on the Measurement , 1997 .

[41]  Tony A. Plate,et al.  Holographic Reduced Representation: Distributed Representation for Cognitive Structures , 2003 .

[42]  A. N. Kolmogorov,et al.  Foundations of the theory of probability , 1960 .

[43]  Michael I. Jordan,et al.  Latent Dirichlet Allocation , 2001, J. Mach. Learn. Res..

[44]  S. Peters,et al.  Word Vectors and Quantum Logic Experiments with negation and disjunction , 2003 .

[45]  M. Halliday New trends in conceptual representation: Challenges to Piaget's theory , 1985 .

[46]  Curt Burgess,et al.  Producing high-dimensional semantic spaces from lexical co-occurrence , 1996 .

[47]  Diederik Aerts,et al.  Contextualizing concepts using a mathematical generalization of the quantum formalism , 2002, J. Exp. Theor. Artif. Intell..

[48]  Henry P. Stapp,et al.  The Undivided Universe: An ontological interpretation of Quantum Theory , 1994 .

[49]  Diederik Aerts,et al.  The Violation of Bell Inequalities in the Macroworld , 2000, quant-ph/0007044.

[50]  S. Aerts,et al.  Conditional probabilities with a quantal and a kolmogorovian limit , 1996 .

[51]  H. Erlichson The Einstein-Podolski-Rosen Paradox , 1972, Philosophy of Science.

[52]  Mark W. Altom,et al.  Given versus induced category representations: use of prototype and exemplar information in classification. , 1984, Journal of experimental psychology. Learning, memory, and cognition.

[53]  Diederik Aerts,et al.  A Model with Varying Fluctuations in the Measurement Context , 1997 .

[54]  Jack Sutcliffe,et al.  Concept, Class, And Category In The Tradition Of Aristotle , 1993 .

[55]  Dirk Aerts,et al.  A possible explanation for the probabilities of quantum mechanics , 1986 .

[56]  A. Gleason Measures on the Closed Subspaces of a Hilbert Space , 1957 .

[57]  E. Rosch,et al.  Family resemblances: Studies in the internal structure of categories , 1975, Cognitive Psychology.

[58]  Diederik Aerts,et al.  LETTER TO THE EDITOR: Quantum aspects of semantic analysis and symbolic artificial intelligence , 2003, quant-ph/0309022.

[59]  Edward E. Smith,et al.  On the adequacy of prototype theory as a theory of concepts , 1981, Cognition.

[60]  Diederik Aerts,et al.  The Origin of the Non-Classical Character of the Quantum Probability Model , 1987 .

[61]  Diederik Aerts,et al.  Quantum structures due to fluctuations of the measurement situation , 1993 .

[62]  J. Jauch,et al.  CAN HIDDEN VARIABLES BE EXCLUDED IN QUANTUM MECHANICS , 1963 .

[63]  Diederik Aerts,et al.  A theory of concepts and their combinations I: The structure of the sets of contexts and properties , 2005 .

[64]  Sven Aerts Interactive Probability Models: Inverse Problems on the Sphere , 1998 .

[65]  A. Shimony,et al.  Bell's theorem. Experimental tests and implications , 1978 .

[66]  L. A. Zadeh,et al.  A note on prototype theory and fuzzy sets , 1982, Cognition.

[67]  S. Aerts The Born Rule from a Consistency Requirement on Hidden Measurements in Complex Hilbert Space , 2002 .

[68]  I. Pitowsky Quantum Probability ― Quantum Logic , 1989 .