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Introduction to the Special Issue on Quantum Cognition Gabora, Liane Oct 31, 2009

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 1 Bruza, P., Busemeyer, J., & Gabora, L. (2009). Introduction to the special issue on quantum cognition. Journal of Mathematical Psychology, 53, 303-305.    Introduction to the Special Issue on Quantum Cognition  Peter Bruza, Jerome Busemeyer, and Liane Gabora  The subject of this special issue is quantum models of cognition. At first sight it may seem bizarre, even ridiculous, to draw a connection between quantum mechanics, a highly successful theory usually understood as modeling sub-atomic phenomena, and cognitive science. However, a growing number of researchers are looking to quantum theory to circumvent stubborn problems within their own fields. This is also true within cognitive science and related areas, hence this special issue.  Justification Given the nascent state of this field, some words of justification are warranted. The researchers just mentioned are not concerned with modeling physical phenomena, but instead turn to quantum theory as a fresh conceptual framework in which to consider problems, as well as a source of alternative formal tools. With less than perfect accuracy, there are two aspects of quantum theory which open the door to addressing problems in a totally new light (see Barros & Suppes on this issue). The first is known as “contextuality”. Even within quantum theory, contextuality is a subtle notion to grasp. However, one way to understand it is in terms of interference. When quantum systems are in superposed states, they can interfere. Interference has an expression within the underlying probabilistic apparatus, which is not to be found within the “classical” probabilistic framework.  The second aspect is “quantum entanglement”. Entanglement is a bizarre phenomenon in which seemingly separated quantum systems behave as one. Entanglement has led to ongoing philosophical debate about the nature of reality, and was at the heart of a famous debate between Neils Bohr and Albert Einstein. Erwin Schrödinger, one of the founding fathers of quantum theory wrote in 1935, “I would not call [entanglement] one but rather the characteristic trait of quantum mechanics, the one that enforces its entire departure from classical lines of thought.” In quantum physics, the term “non-locality” is often mentioned in conjunction with entanglement, meaning that performing a measurement on one system directly and instantaneously affects the state another system, even when such systems are separated. The key move made by researchers exploiting notions of entanglement outside of physics is to view it as a promising means to model non-separability of cognitive states. Several phenomena in psychology that have stubbornly resisted traditional modeling techniques are showing promise with a new modeling approach inspired by the formalisms of quantum mechanics. Before going into any details about this new approach, let us look at a couple of these phenomena: Decision making – When people are given a chance to play a particular gamble twice, if they think they won the first play, or alternatively if they think they lost the first play, then the majority chooses to play again on the second round. Given these preferences, they should also play the second round even if they don’t think about the outcome of the first round. Yet people do just the opposite in the latter case (Tversky & Shafir, 1992). This finding violates the law of total probability, yet it can be explained as a quantum interference effect in a manner similar to  2 the explanation for the results from two-hole experiments in physics (Pothos & Busemeyer, 2009).   The Contextual Nature of Concepts and their Combinations –When quantum entities become entangled, they form a new entity with properties different from either constituent, and one cannot manipulate one constituent without simultaneously affecting the other. The mathematics of entanglement has been used to model the nonmonotonic relations observed among concepts when they are combined to form a new concepts such as STONE LION (Gabora & Aerts, 2005).  The Legacy and Contents of this Special Issue Quantum theory was originally invented by physicists to explain findings that seemed paradoxical from a standard physical view point. Later Von Neumann (1932) provided an axiomatic foundation for quantum theory, and by doing so, he discovered that it implied a new type of logic and probability theory. Consequently, there are now two general theories for assigning probabilities to events: classical (Kolmogorov, 1933) and quantum (von Neumann, 1933). Classic probability theory defines events as subsets of a universal set, which obey all the laws of Boolean algebra. Quantum theory defines events as subspaces of a Hilbert space, which obey all the laws of Boolean algebra except the distributive axiom. Following from the distributive axiom, classic probability theory adheres to one of its most important theorems, the law of total probability. In contrast, because quantum logic does not have to obey the distributive law, quantum probabilities do not have to obey the law of total probability. Based on a Hilbert space representation, quantum probabilities are required to obey two other laws: reciprocity and double stochasticity. Classic probability theory is not based on a Hilbert space representation, and so it does not have to obey the latter two laws. Thus there is a substantial disagreement between the two probability theories, and which theory is best is an empirical question. There is a short, but significant history of applying the formalisms of quantum theory to topics in psychology. Initially, actual quantum physics was used to model the brain and explain consciousness (Hameroff, 1994, 1998; Hameroff & Penrose, 1996; Jibu et al., 1994; Pribram, 1991; Penrose, 1993). An influential web-based course on quantum consciousness was hosted by the University of Arizona in Tucson, as well as series of international conferences on the topic. At about the same time, ideas for applying quantum formalisms to cognition appeared (Aerts & Aerts, 1994; Atmanspacher, 1992; Bordley, 1998; Khrennikov, 1999;  Turvey & Shaw, 1995). Shortly afterwards, there appeared some more detailed efforts (Atmanspacher, Spilk, & Romer, 2004; Bruza & Cole, 2005; Busemeyer, Wang, & Townsend, 2006; Gabora & Aerts, 2002; Ivancevic, & Aidman, 2007; van Rijsbergen, 2004; Widdows, 2003). However, it wasn’t until the first Quantum Interaction workshop at Stanford in 2007 organized by Peter Bruza, William Lawless, C. J. van Rijsbergen, and Don Sofge as part of the AAAI Spring Symposium that a community began to emerge. This first workshop was followed by workshops at Oxford (England) in 2008, Vaexjo (Sweeden) in 2008, and Saarbruken (Germany) in 2009. Tutorials also were presented annually beginning in 2008 until present at the meeting of the Cognitive Science Society.  The papers in this issue are highly interdisciplinary; their authors are based in psychology, mathematics, physics, and computer science. Several of them are speculative, as perhaps should be the case when a field is very new. Within this special issue, interference is being exploited by a number of researchers, for example, in relation to new models of human judgment and decision making (Busemeyer, Wang, & Lampert-Mogiliansky, Franco, LaMura, Narens, Khrennikov & Haven, Lampert-Mogiliansky, Zamir, & Zwirn). Entanglement is being explored for word  3 associates in human memory (Bruza, Kitto, Nelson and McEvoy), modeling words as non-separable in concept combinations, and in relation to emergent concepts (Aerts, Czachor, de Moor & Aerts) and emergent worldviews (Gabora and Aerts). We believe these papers pave the way for a very promising new direction of psychological investigation.    REFERENCES Aerts, D. & Aerts, S. (1994). Applications of quantum statistics in psychological studies   of decision processes. Foundations of Science, 1, 85-97. Atmanspacher, H. (1992). Categoreal and acategoreal representation of knowledge. Cognitive Systems, 3, 259-288. Atmanspacher, H., Filk, T., & Romer, H. (2004). Quantum Zeno features of bistable   perception. Biological Cybernetics, 90, 33-40. Bordley, R. F. (1998). Quantum mechanical and human violations of compound probability principles: Toward a generalized Heisenberg uncertainty principle.  Operations Research, 46, 923-926. Bruza, P. D., Lawless, W., van Rijsbergen, C.J., & Sofge, D., Editors. (2007). Proceedings of the AAAI Spring Symposium on Quantum Interaction, March 27-29. Stanford University, 2007. AAAI Press. Bruza, P. D., Lawless, W., van Rijsbergen, C.J., & Sofge, D., Editors. (2008). Quantum interaction: Proceedings of the Second Quantum Interaction Symposium.  London: College Publications.  Bruza, P.D., Sofge, D., Lawless, W., Van Risjbergen, K., & Klusch, M., Editors. (2009). Proceedings of the Third Quantum Interaction Symposium.  Lecture Notes in Artificial Intelligence, vol. 5494, Springer. Bruza, P.D. & Cole, R.J. (2005). Quantum logic of semantic space: An exploratory investigation of context effects in practical reasoning In S. Artemov, H. Barringer, A. S. d'Avila Garcez, L.C. Lamb, J. Woods (eds.) We Will Show Them: Essays in Honour of Dov Gabbay. College Publications. Gabora, L. & Aerts, D. (2002). Contextualizing concepts using a mathematical generalization of the quantum formalism. Journal of Experimental and Theoretical Artificial Intelligence, 14(4), 327-358. Busemeyer, J. R., Wang, Z., & Townsend, J. T. (2006). Quantum dynamics of human  decision making. Journal of Mathematical Psychology, 50 (3), 220-241. Hameroff S.R. (1998). Quantum computation in brain microtubules? The Penrose-Hameroff "Orch OR" model of consciousness. Philosophical Transactions Royal Society London, (A)356, 1869-1896. Hameroff, SR. (1994). Quantum coherence in microtubules: A neural basis for emergent consciousness? Journal of Consciousness Studies, 1(1), 91-118. Hameroff S.R., Penrose R.  (1995). Orchestrated reduction of quantum coherence in brain microtubules: a model for consciousness? Neural Network World, 5, 793-804. Ivancevic, V. and Aidman, E. (2007). Life space foam: a medium for motivational and cognitive dynamics. Physica A, 382, 616-630. Jibu M, Hagan S, Pribram K, Hameroff SR, Yasue K (1994). Quantum optical coherence in cytoskeletal microtubules: implications for brain function. BioSystems, 32, 195-209. Kolmogorov, A. N. (1933). Foundations of the Theory of Probability. Chelsea Publishing Co., New York.  Khrennikov, A. Y. (1999). Classical and quantum mechanics on information spaces with  4  applications to cognitive, psychological, social, and anomalous phenomena.  Foundations of Physics, 29, 1065-1098. Pothos, E. M. & Busemeyer, J. R. (2009). A quantum probability model explanation for violations of ‘rational’ decision theory. Proceedings of the Royal Society, B. Pribram, K. H. (1991). Brain and perception: Holonomy and structure in figural  processing. NJ: Erlbaum.  Pribram, K. H. (1993). Rethinking neural networks: Quantum fields and biological data. Hillsdale, N. J: Earlbaum.  Turvey, M. T. & Shaw, R. E. (1995). Toward an ecological physics and a physical psychology.  In R. Solso and D. Massaro (Eds.), The science of the mind: 2001 and beyond. (pp. 144-169). Oxford: Oxford University Press. Tversky, A., & Shafir, E. (1992). The disjunction effect in choice under uncertainty. Psychological Science, 3, 305-309. Von Neumann, J. (1932). Mathematical Foundations of Quantum Theory. Princeton, NJ: Princeton University Press. Widdows, D. & Peters, S. (2003). Word Vectors and Quantum Logic: Experiments with negation and disjunction. Eighth Mathematics of Language Conference, 141-154.  

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