Topics in Cognitive Science 6 (2014) 104–107 Copyright © 2013 Cognitive Science Society, Inc. All rights reserved. ISSN:1756-8757 print / 1756-8765 online DOI: 10.1111/tops.12079
Toward a Physical Theory of Quantum Cognition Taiki Takahashi Department of Behavioral Science, Center for Experimental Research in Social Sciences, Hokkaido University Received 25 December 2012; accepted 15 February 2013
Abstract Recently, mathematical models based on quantum formalism have been developed in cognitive science. The target articles in this special issue of Topics in Cognitive Science clearly illustrate how quantum theoretical formalism can account for various aspects of human judgment and decision making in a quantitatively and mathematically rigorous manner. In this commentary, we show how future studies in quantum cognition and decision making should be developed to establish theoretical foundations based on physical theory, by introducing Taketani’s three-stage theory of the development of science. Also, implications for neuroeconomics (another rapidly evolving approach to human judgment and decision making) are discussed. Keywords: Quantum decision theory; Psychophysics; Biophysics; Neuroeconomics
Introduction To account for (and quantitatively model) anomalies in human judgment and decision making, mathematical frameworks of quantum theory have recently been utilized and developed (Busemeyer, Wang, & Townsend, 2006; Busemeyer, Pothos, Trueblood, & Franco, 2013; Cheon & Takahashi, 2010, 2012; Conte et al., 2009; Yukalov & Sornette, 2010). Because quantum theory is a generalization of classical (physical) theory based on classical probability theory and local realism, quantum decision and cognition theories have successfully modeled the anomalies in human judgment and decision making. In this special issue, borderline vagueness (Blutner, Pothos, & Bruza, 2013); question order effect (Wang & Busemeyer, 2013); episodic superposition of human memory (Brainerd, Wang, & Reyna, 2013); temporal dynamics of bistable perception (Atmanspacher & Filk, Correspondence should be sent to Taiki Takahashi, Laboratory of Social Psychology, Department of Behavioral Science, Faculty of Letters, Hokkaido University, N.10, W.7, Kita-ku, Sapporo, 060-0810, Japan. E-mail: [email protected]
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2013); contextuality, interference, entanglement, and emergence in human thought (Aerts, Gabora, & Sozzo, 2013); and cooperative and competitive human decision processes (Fuss and Navarro, 2013) have been quantum modeled. In terms of experimental psychology, Wang and Busemeyer’s quantum theory of order effect may be quite ubiquitously useful because almost all types of psychological experiments include sequential (i.e., ordered) measurements of human choices/answers to questionnaires. In this commentary article, I ask three questions. First, what is the main advantage of quantum formalism in cognitive science? Second, what is the next step toward a physical theory of quantum theory of human decision and cognition? Finally, what are potential implications of quantum decision theory for other scientific disciplines such as neuroeconomics? To answer these interesting questions, I will first introduce the theoretical physicist and philosopher Mitsuo Taketani’s three-stage theory of scientific revolutions (Taketani, 1968) and the philosopher Hubert Dreyfus’s criticism on cognitive science (Dreyfus, 1965, 1972). I will finally address how quantum theoretic approaches may answer Dreyfus’s criticism. After seeing revolutions in physics (e.g., theory of relativity and quantum theory) in the early 20th century, the theoretical physicist Mitsuo Taketani (a coworker of Nobel laureates Hideki Yukawa and Shin-itiro Tomonaga) proposed a three-stage theory of scientific revolutions. According to the theory, a process of human scientific understanding of objects follows the three stages (processes): phenomenological, substantialistic, and essentialistic. In the phenomenological stage, scientists observe and model phenomena which require explanations as they are. Next, in the substantialistic stage, scientists investigate the structure of the objects mediating the phenomena. Finally, in the essentialistic stage, scientists discover the fundamental and general principles and rules governing the objects which are structured to produce the initially observed anomalous phenomena. In the history of classical mechanics, Tycho Brahe’s precise descriptions of heavenly bodies’ motions correspond to the phenomenological stage. Johannes Kepler’s three laws of motions of heavenly bodies correspond to the substantialistic stage. Isaac Newton’s three laws of motions including an equation of motion are examples of the products of the essentialistic stage. In this way, according to Taketani’s theory, we should first model the phenomenon in a quantitatively precise manner (corresponding to quantum formalism of human mind). Next, we should explore the structure of objects mediating the phenomena (corresponding to investigations into neural and biophysical mechanisms underlying quantum cognition). Finally, we should find how the objects are governed by physical laws at the microscopic levels (corresponding to the biophysical theory of neural computation exhibiting quantum-like information processing). Let us now return to cognitive science. A long time ago, the philosopher Hubert Dreyfus criticized cognitive science in that human mind is totally different from (classical) information processing performed on digital computers (Dreyfus, 1965, 1973). For instance, he pointed out that, unlike information processing on digital computers, human judgment and decision is highly context-dependent, which cannot be captured by the utilization of (classical) information theory. Hubert Dreyfus claimed that we should
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model human mind at more microscopic levels which may be less context dependent, in comparison to the level of mind (i.e., cognition and decision). However, according to Taketani’s theory, we cannot proceed to establish a good scientific theory at more microscopic levels (i.e., substantialistic theory) without experiencing the phenomenological stage, although Dreyfus’s advice indicates that we should skip the phenomenological stage. As work in this issue suggests, quantum formalism may help us to model contextdependent aspects of human mind because quantum theory in physics per se has contextuality (see Aerts et al., 2013). Therefore, by utilizing quantum theory of decision and cognition, we will be able to model human mind at the phenomenological level, which is necessary (according to Taketani’s theory) for further development of scientific exploration of human mind at deeper levels. This may be one of the advantages of quantum formalism of human mind in terms of cognitive science. Next, we consider the future directions of quantum theory-based cognitive science. As stated above, after establishing phenomenological theory, we can proceed to explore substantialistic theory of quantum decision and cognition. This exploration may correspond to investigations into neural foundations underlying quantum cognition and decision making. Several possible neural mechanisms have already been proposed: neuronal oscillators (Acacio de Barros, 2012) and neural population coding of psychological intensity (Takahashi & Cheon, 2012). It is to be noted that more possible mechanisms should be explored in both theoretical and experimental manners. In any case, the investigation at the substantialistic stage into quantum cognition and decision may require sophisticated neurobiological tools such as optogenetics and knock-out animals, as well as more conventional tools such as electrophysiology and neuroimaging. Studies at this stage might have resemblance to cognitive neuroscience, which could be coined as cognitive neuroscience of quantum cognition. Furthermore, we will eventually need to establish biophysical theory of quantum cognition and decision (at the essentialistic stage). Whether the theory at this stage requires quantum physics (similar to quantum biophysics of photosynthesis) or not is an open question at present. We now discuss implications for other scientific disciplines of the quantum-formalized theories of cognition and decision. It is interesting to take an example of neuroeconomics (Glimcher, 2010) because it is also a recently developed branch of decision science. In neuroeconomics (Takahashi, 2009), it is typical to utilize mathematical frameworks in behavioral economics to interpret neural correlates of human decision making. However, mathematical objects in behavioral economics are highly context dependent. For instance, in human intertemporal choice, psychological time differs in waiting for gain and loss (Han & Takahashi, 2012). These types of context dependency in behavioral economics could be modeled with quantum formalism. Furthermore, social preference has been one of the major topics in neuroeconomics. A recent theoretical study by Takahashi (2012) demonstrated that interference effect in emotion can account for the violation of surething principle in the prisoner’s dilemma game. Therefore, future studies in quantum decision should extend the quantum-like effect into psychological quantities other than probability (e.g., emotion) to model anomalies in time, risk, and social preferences which are of neuroeconomic interest.
T. Takahashi / Topics in Cognitive Science 6 (2014)
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References Acacio de Barros, J. (2012). Quantum-like model of behavioral response computation using neural oscillators. Biosystems, 110, 171–182. Aerts, D., Gabora, L., & Sozzo, S. (2013). Concepts and their dynamics: A quantum-theoretic modeling of human thought. Topics in Cognitive Science, 5(4), 737–772. Atmanspacher, H., & Filk, T. (2013). The Necker-Zeno model for bistable perception. Topics of Cognitive Science, 5(4), 800–817. Blutner, R., Pothos, E. M., & Bruza, P. (2013). A quantum probability perspective on borderline vagueness. Topics in Cognitive Science, 5(4), 711–736. Brainerd, C. J., Wang, Z., & Reyna, V. F. (2013). Superposition of episodic memories: Overdistribution and quantum models. Topics in Cognitive Science, 5(4), 773–799. Busemeyer, J. R., Pothos, E., Trueblood, J., & Franco, R. (2013). A quantum theoretical explanation for probability judgment “errors.” Psychological Review, 118, 193–218. Busemeyer, J. R., Wang, Z., & Townsend, J. T. (2006). Quantum dynamics of human decision-making. Journal of Mathematical Psychology, 50, 220–241 Cheon, T., & Takahashi, T. (2010). Interference and inequality in quantum decision theory. Physics Letters A, 375, 100–104. Cheon, T., & Takahashi, T. (2012). Quantum phenomenology of conjunction fallacy. Journal Physical Society of Japan, 81, 104801–104806. Conte, E., Khrennikov, A. Y., Todarello, O., Federici, A., Mendolicchio, L., & Zbilut, J. P. (2009). Mental states follow quantum mechanics during perception and cognition of ambiguous figures. Open Systems and Information Dynamics, 16, 1–17. Dreyfus, H. (1965) Alchemy and artificial intelligence. Available at http://www.rand.org/pubs/papers/P3244. html Dreyfus, H. (1972) What computers can’t do: The limits of artificial intelligence. Cambridge, MA: MIT Press. Fuss, I. G., & Navarro, D. J. (2013). Open parallel cooperative and competitive decision processes: A potential provenance for quantum probability decision models. Topics in Cognitive Science, 5(4), 818– 843. Glimcher, PW. (2010). Foundations of neuroeconomic analysis. New York: Oxford University Press. Han, R., & Takahashi, T. (2012). Psychophysics of valuation and time perception in temporal discounting of gain and loss. Physica A, 391, 6568–6576. Takahashi, T. (2009). Theoretical frameworks for neuroeconomics of intertemporal choice. Journal of Neuroscience, Psychology, and Economics, 2(2), 75–90. Takahashi, T. (2012). Emotion interference solves social dilemma. Theoretical Economics Letters, 2(5), 446– 449. Takahashi, T., & Cheon, T. (2012). A nonlinear neural population coding theory of quantum cognition and decision making. World Journal of Neuroscience, 2, 183–186. Taketani, M. (1968) The problem of dialectics. Keiso-shobo (in Japanese). Tokyo: Keiso-Shobo. Wang, Z., & Busemeyer, J. R. (2013). A quantum question order model supported by empirical tests of an a priori and precise prediction. Topics in Cognitive Science, 5(4), 689–710. Yukalov, V., & Sornette, D. (2010). Decision theory with prospect interference and entanglement. Theory and Decision, 70, 283–328.
Toward a Physical Theory of Quantum Cognition Taiki Takahashi Department of Behavioral Science, Center for Experimental Research in Social Sciences, Hokkaido University Received 25 December 2012; accepted 15 February 2013
Abstract Recently, mathematical models based on quantum formalism have been developed in cognitive science. The target articles in this special issue of Topics in Cognitive Science clearly illustrate how quantum theoretical formalism can account for various aspects of human judgment and decision making in a quantitatively and mathematically rigorous manner. In this commentary, we show how future studies in quantum cognition and decision making should be developed to establish theoretical foundations based on physical theory, by introducing Taketani’s three-stage theory of the development of science. Also, implications for neuroeconomics (another rapidly evolving approach to human judgment and decision making) are discussed. Keywords: Quantum decision theory; Psychophysics; Biophysics; Neuroeconomics
Introduction To account for (and quantitatively model) anomalies in human judgment and decision making, mathematical frameworks of quantum theory have recently been utilized and developed (Busemeyer, Wang, & Townsend, 2006; Busemeyer, Pothos, Trueblood, & Franco, 2013; Cheon & Takahashi, 2010, 2012; Conte et al., 2009; Yukalov & Sornette, 2010). Because quantum theory is a generalization of classical (physical) theory based on classical probability theory and local realism, quantum decision and cognition theories have successfully modeled the anomalies in human judgment and decision making. In this special issue, borderline vagueness (Blutner, Pothos, & Bruza, 2013); question order effect (Wang & Busemeyer, 2013); episodic superposition of human memory (Brainerd, Wang, & Reyna, 2013); temporal dynamics of bistable perception (Atmanspacher & Filk, Correspondence should be sent to Taiki Takahashi, Laboratory of Social Psychology, Department of Behavioral Science, Faculty of Letters, Hokkaido University, N.10, W.7, Kita-ku, Sapporo, 060-0810, Japan. E-mail: [email protected]
T. Takahashi / Topics in Cognitive Science 6 (2014)
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2013); contextuality, interference, entanglement, and emergence in human thought (Aerts, Gabora, & Sozzo, 2013); and cooperative and competitive human decision processes (Fuss and Navarro, 2013) have been quantum modeled. In terms of experimental psychology, Wang and Busemeyer’s quantum theory of order effect may be quite ubiquitously useful because almost all types of psychological experiments include sequential (i.e., ordered) measurements of human choices/answers to questionnaires. In this commentary article, I ask three questions. First, what is the main advantage of quantum formalism in cognitive science? Second, what is the next step toward a physical theory of quantum theory of human decision and cognition? Finally, what are potential implications of quantum decision theory for other scientific disciplines such as neuroeconomics? To answer these interesting questions, I will first introduce the theoretical physicist and philosopher Mitsuo Taketani’s three-stage theory of scientific revolutions (Taketani, 1968) and the philosopher Hubert Dreyfus’s criticism on cognitive science (Dreyfus, 1965, 1972). I will finally address how quantum theoretic approaches may answer Dreyfus’s criticism. After seeing revolutions in physics (e.g., theory of relativity and quantum theory) in the early 20th century, the theoretical physicist Mitsuo Taketani (a coworker of Nobel laureates Hideki Yukawa and Shin-itiro Tomonaga) proposed a three-stage theory of scientific revolutions. According to the theory, a process of human scientific understanding of objects follows the three stages (processes): phenomenological, substantialistic, and essentialistic. In the phenomenological stage, scientists observe and model phenomena which require explanations as they are. Next, in the substantialistic stage, scientists investigate the structure of the objects mediating the phenomena. Finally, in the essentialistic stage, scientists discover the fundamental and general principles and rules governing the objects which are structured to produce the initially observed anomalous phenomena. In the history of classical mechanics, Tycho Brahe’s precise descriptions of heavenly bodies’ motions correspond to the phenomenological stage. Johannes Kepler’s three laws of motions of heavenly bodies correspond to the substantialistic stage. Isaac Newton’s three laws of motions including an equation of motion are examples of the products of the essentialistic stage. In this way, according to Taketani’s theory, we should first model the phenomenon in a quantitatively precise manner (corresponding to quantum formalism of human mind). Next, we should explore the structure of objects mediating the phenomena (corresponding to investigations into neural and biophysical mechanisms underlying quantum cognition). Finally, we should find how the objects are governed by physical laws at the microscopic levels (corresponding to the biophysical theory of neural computation exhibiting quantum-like information processing). Let us now return to cognitive science. A long time ago, the philosopher Hubert Dreyfus criticized cognitive science in that human mind is totally different from (classical) information processing performed on digital computers (Dreyfus, 1965, 1973). For instance, he pointed out that, unlike information processing on digital computers, human judgment and decision is highly context-dependent, which cannot be captured by the utilization of (classical) information theory. Hubert Dreyfus claimed that we should
106
T. Takahashi / Topics in Cognitive Science 6 (2014)
model human mind at more microscopic levels which may be less context dependent, in comparison to the level of mind (i.e., cognition and decision). However, according to Taketani’s theory, we cannot proceed to establish a good scientific theory at more microscopic levels (i.e., substantialistic theory) without experiencing the phenomenological stage, although Dreyfus’s advice indicates that we should skip the phenomenological stage. As work in this issue suggests, quantum formalism may help us to model contextdependent aspects of human mind because quantum theory in physics per se has contextuality (see Aerts et al., 2013). Therefore, by utilizing quantum theory of decision and cognition, we will be able to model human mind at the phenomenological level, which is necessary (according to Taketani’s theory) for further development of scientific exploration of human mind at deeper levels. This may be one of the advantages of quantum formalism of human mind in terms of cognitive science. Next, we consider the future directions of quantum theory-based cognitive science. As stated above, after establishing phenomenological theory, we can proceed to explore substantialistic theory of quantum decision and cognition. This exploration may correspond to investigations into neural foundations underlying quantum cognition and decision making. Several possible neural mechanisms have already been proposed: neuronal oscillators (Acacio de Barros, 2012) and neural population coding of psychological intensity (Takahashi & Cheon, 2012). It is to be noted that more possible mechanisms should be explored in both theoretical and experimental manners. In any case, the investigation at the substantialistic stage into quantum cognition and decision may require sophisticated neurobiological tools such as optogenetics and knock-out animals, as well as more conventional tools such as electrophysiology and neuroimaging. Studies at this stage might have resemblance to cognitive neuroscience, which could be coined as cognitive neuroscience of quantum cognition. Furthermore, we will eventually need to establish biophysical theory of quantum cognition and decision (at the essentialistic stage). Whether the theory at this stage requires quantum physics (similar to quantum biophysics of photosynthesis) or not is an open question at present. We now discuss implications for other scientific disciplines of the quantum-formalized theories of cognition and decision. It is interesting to take an example of neuroeconomics (Glimcher, 2010) because it is also a recently developed branch of decision science. In neuroeconomics (Takahashi, 2009), it is typical to utilize mathematical frameworks in behavioral economics to interpret neural correlates of human decision making. However, mathematical objects in behavioral economics are highly context dependent. For instance, in human intertemporal choice, psychological time differs in waiting for gain and loss (Han & Takahashi, 2012). These types of context dependency in behavioral economics could be modeled with quantum formalism. Furthermore, social preference has been one of the major topics in neuroeconomics. A recent theoretical study by Takahashi (2012) demonstrated that interference effect in emotion can account for the violation of surething principle in the prisoner’s dilemma game. Therefore, future studies in quantum decision should extend the quantum-like effect into psychological quantities other than probability (e.g., emotion) to model anomalies in time, risk, and social preferences which are of neuroeconomic interest.
T. Takahashi / Topics in Cognitive Science 6 (2014)
107
References Acacio de Barros, J. (2012). Quantum-like model of behavioral response computation using neural oscillators. Biosystems, 110, 171–182. Aerts, D., Gabora, L., & Sozzo, S. (2013). Concepts and their dynamics: A quantum-theoretic modeling of human thought. Topics in Cognitive Science, 5(4), 737–772. Atmanspacher, H., & Filk, T. (2013). The Necker-Zeno model for bistable perception. Topics of Cognitive Science, 5(4), 800–817. Blutner, R., Pothos, E. M., & Bruza, P. (2013). A quantum probability perspective on borderline vagueness. Topics in Cognitive Science, 5(4), 711–736. Brainerd, C. J., Wang, Z., & Reyna, V. F. (2013). Superposition of episodic memories: Overdistribution and quantum models. Topics in Cognitive Science, 5(4), 773–799. Busemeyer, J. R., Pothos, E., Trueblood, J., & Franco, R. (2013). A quantum theoretical explanation for probability judgment “errors.” Psychological Review, 118, 193–218. Busemeyer, J. R., Wang, Z., & Townsend, J. T. (2006). Quantum dynamics of human decision-making. Journal of Mathematical Psychology, 50, 220–241 Cheon, T., & Takahashi, T. (2010). Interference and inequality in quantum decision theory. Physics Letters A, 375, 100–104. Cheon, T., & Takahashi, T. (2012). Quantum phenomenology of conjunction fallacy. Journal Physical Society of Japan, 81, 104801–104806. Conte, E., Khrennikov, A. Y., Todarello, O., Federici, A., Mendolicchio, L., & Zbilut, J. P. (2009). Mental states follow quantum mechanics during perception and cognition of ambiguous figures. Open Systems and Information Dynamics, 16, 1–17. Dreyfus, H. (1965) Alchemy and artificial intelligence. Available at http://www.rand.org/pubs/papers/P3244. html Dreyfus, H. (1972) What computers can’t do: The limits of artificial intelligence. Cambridge, MA: MIT Press. Fuss, I. G., & Navarro, D. J. (2013). Open parallel cooperative and competitive decision processes: A potential provenance for quantum probability decision models. Topics in Cognitive Science, 5(4), 818– 843. Glimcher, PW. (2010). Foundations of neuroeconomic analysis. New York: Oxford University Press. Han, R., & Takahashi, T. (2012). Psychophysics of valuation and time perception in temporal discounting of gain and loss. Physica A, 391, 6568–6576. Takahashi, T. (2009). Theoretical frameworks for neuroeconomics of intertemporal choice. Journal of Neuroscience, Psychology, and Economics, 2(2), 75–90. Takahashi, T. (2012). Emotion interference solves social dilemma. Theoretical Economics Letters, 2(5), 446– 449. Takahashi, T., & Cheon, T. (2012). A nonlinear neural population coding theory of quantum cognition and decision making. World Journal of Neuroscience, 2, 183–186. Taketani, M. (1968) The problem of dialectics. Keiso-shobo (in Japanese). Tokyo: Keiso-Shobo. Wang, Z., & Busemeyer, J. R. (2013). A quantum question order model supported by empirical tests of an a priori and precise prediction. Topics in Cognitive Science, 5(4), 689–710. Yukalov, V., & Sornette, D. (2010). Decision theory with prospect interference and entanglement. Theory and Decision, 70, 283–328.
