Topics in Cognitive Science 6 (2014) 63–66 Copyright © 2013 Cognitive Science Society, Inc. All rights reserved. ISSN:1756-8757 print / 1756-8765 online DOI: 10.1111/tops.12067
Comments on Episodic Superposition of Memory States Ariane Lambert-Mogiliansky Paris School of Economics Received 6 February 2013; received in revised form 28 February 2013; accepted 8 March 2013
Abstract This article develops a commentary to Charles Brainerd, Zheng Wang and Valerie F. Reyna’s article entitled “Superposition of episodic memories: Overdistribution and quantum models” published in a special number of topiCS 2013 devoted to quantum modelling in cognitive sciences. Keywords: Superposition; Interference; Quantum indeterminacy
To many people it may appear unmotivated or artificial to turn to quantum mechanics (QM) when investigating human behavioral and perceptual phenomena. However, the founders of QM, including Bohr and Heisenberg, early recognized the similarities between the two fields. In particular, Bohr was influenced by the psychology and philosophy of knowledge of Harald H€ offding. The similarity stems from the fact that in both fields the object of investigation cannot (always) be separated from the process of investigation. In the words of Bohr: “we face the impossibility of a sharp separation between the behavior of atomic object and the interaction with the measuring instruments which serves to define the condition under which the phenomena appear.” In psychology, investigating a person’s emotional or perceptual state affects the state of the person. In social sciences “revealing” one’s preferences in a choice can affect those preferences. According to Kahnemann, “There is a growing body of evidence that supports an alternative conception according to which preferences are often constructed—not merely revealed—in the elicitation process. These constructions are contingent on the framing of the problem, the method of elicitation, and the context of the choice.” Quantum mechanics and in particular its mathematical formalism was developed to respond to that epistemological challenge: How can we study a system that changes as we try to learn about it? Introducing (quantum) indeterminacy in social sciences, psychology, and perception has shown itself very fruitful to explain a wide variety of behavioral and perceptual phenomena ranging from quantum zeno effect in visual perception Atmanspasher et al. 2004 Correspondence should be sent to Ariane Lambert-Mogiliansky, Paris School of Economics, 48 Boulevard Jourdan 75014 Paris, France. E-mail: [email protected]
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to cognitive dissonance, preferences reversal, the inverse fallacy, or the disjunction effect (Atmanspasher et al., 2004; Busemeyer, 2007; Busemeyer & Lambert-Mogiliansky, 2009; Busemeyer et al., 2006, 2008; Danilov & Lambert-Mogiliansky, 2008b, 2009; Franco, 2008; Lambert-Mogiliansky, 2009, 2010; Mura, 2005; Wang et al., 2013). I would like to stress that the stake is beyond just having a model that fits the experimental data. A quantum model of the human mind opens for deeply new perspectives on human mind and human behavior. First, it invites one to consider a holistic model of the mind: The mind cannot be fully decomposed in its simplest parts, but larger composed parts truly function as integrated systems. Second, it implies that the human mind is constantly evolving in response to its interaction with the outside world and with its inner work (e.g., introspection). Thus, it gives us a model of a mind that is intrinsically contextual and plastic—it is not endowed with determinate characteristics in isolation, but comes into being (as a system endowed with characteristics) in interaction with its environment (see Lambert-Mogiliansky and Busemeyer, 2012). In this context, the issue of episodic superposition is a very interesting one and appears most suitable for a quantum explanation. My view is that the quantum model should not be viewed as a substitute for the Over Distribution (OD) theory, but rather as a formalized take of the same approach. Indeed, I shall argue that the OD theory suggests that the verbatim and gist are alternative (complementary in the sense of Bohr) representations of the state of memory and that a quantum model in that spirit can be formulated. I have some reservations with respect to the quantum model (QEM) that is being proposed in the article by Charles Brainerd, Zheng Wang, and Valerie F. Reyna. It is constructed in close comparison with the two-slit experiment which shows a pattern of interference effects when both slits are open. As far as I understand, this became a puzzle only when it could be shown for a single electron. Otherwise it simply suggests a classical wave interpretation. Because we cannot single out a memory particle a “memorion,” I believe that a quantum model closer to the Stern–Gerlach experiment which demonstrates superposition by considering the outcome of a sequence of incompatible measurements may be more adapted. In particular, it would allow for an interpretation of the verbatim and gist memory representation as complementary rather than substitute or independent. I would suggest to model verbatim and gist memory as two incompatible properties of memory. They would correspond to alternative representations of the memory state which are complementary in Bohr meaning like the spin under different angles. The eigenstates within each representation are mutually exclusive, but the eigenstates of the gist representation are not exclusive of the eigenstates entering the verbatim representation. As a consequence, one would not put both verbatim and gist features as mutually exclusive basis vectors that span the memory space as done by the authors in equation 7. Instead, I suggest that they are correlated in the sense that they correspond to alternative bases of the same memory space, which appears more in line with the idea that the two traces run in parallel. In the proposed QEM, the probes are direct measurements of the state as formulated. The assumption is that the probe that asks “is it presented in list 1(or 2 or 3)?” projects on a subspace spanned by two eigenvectors list 1(or 2 or 3) and gist. As far as I can see,
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such a model is equivalent to a classical one where we do not know where the state is and we have coarse measurement to learn about it. Consider the following alternative. The probes or questions may be coarse measurements of either representation (gist or verbatim). Or they may be neither true verbatim nor gist measurements. They may be yet another kind of measurement which does not commute with either a gist or a verbatim measurement or with both. The presence of sub (or super) additive probabilities then reflects interferences effects due to the fact that when putting say a verbatim (or gist or third type) question, indeterminacy with respect to the gist (or verbatim) measurement has not been resolved, leaving room for interference. This seems to correspond to the description of the OD theory given in the article “On conjoint recognition test, test cues provoke retrieval of verbatim and gist trace, …, with the two types of trace leading to the same response under some instruction but to different responses under other instructions” (p. 10). Thus, the probes T, R, or TUR are not viewed as analogies with the slits, but rather as the possible results on the landing distribution on the detector. The analog of the slits would be true verbatim (gist) questions which are not put to the agent (leaving indeterminacy in those respects). We do not know through which slit the “memorion” passes. It is the absence of screening (i.e., we do not check through which slit it passed) that generates super (sub) additivity in the responses to the probes analog of interferences observed on the detector. Such a quantum model would allow for an interpretation of episodic superposition that is richer in the sense that it generates interferences from the Bohr complementarity of the two representations. It also appeals for another kind of test experiment in the spirit of Stern–Gerlach experiment. The value of an approach with non-commuting operators is to make a clear distinction between orthogonal (mutually exclusive) features and features belonging to incompatible perspectives (not mutually exclusive). The huge contribution of quantum mechanics is precisely to allow us to deal with non-orthogonal yet atomic states (complete characterization of the system). In the classical model all atomic states are orthogonal. Of course, the classical model allows for non-orthogonal properties but then they are compatible and can be combined to produce a more complete characterization of the system. The quantum model in the article could be clarified in this respect. If list and gist features are incompatible, they cannot be outcomes of one and the same measurement and if they are compatible (a classical model) there cannot be any quantum interference effect because that is the signature of incompatibility. The proposed alternative approach with non-commuting operators also gives a precise meaning to ambiguity in terms of indeterminacy, that is, coexistence of orthogonal features in the mind before a measurement is made. On the other side, the very existence of incompatible perspectives (e.g., verbatim and gist, like two overlapping alternatives) on the same memory state has rich implications in terms of the dynamics of the mind: First, when you ask a verbatim question from a state of indeterminacy, this affects the system and it affects the expected response with respect to gist questions. Second, the interference effects that we talk about in QM cannot be dissociated from the notion and the formalization of incompatible measurements (as projectors on alternative basis of the same
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state space). I know of no other fundamental measurement theory that accounts for interference effects. Those interference effects are the key to quantum probabilities. The QEM could be modified to give a better account for the emergence of interference effects. Concluding, I would like to emphasize that I believe that quantum modeling in psychological and perceptual analysis has a great potential. A definitive advantage of perceptual phenomena is that we are more likely to deal with simple phenomena as compared with, for example, social behavioral phenomena. That allows performing experiments which are true tests of the theory. They represent crucial contributions for establishing the quantum paradigm in the analysis of the human mind and human behavior. References Atmanspacher, H., Filk, T., & Romer, R. (2004). Quantum Zeno features of bistable perception. Biological Cybernetics, 90, 33–40. Brainerd, C., Wang, Z., & Reyna, V. (2013). Superposition of episodic memories: Overdistribution and quantum models. Topics in Cognitive Science, 5(4), 773–99. Busemeyer, J. R. (2007). Quantum information processing explanation for interaction between inferences and decisions. Proceedings of the Quantum Interaction Symposium. Busemeyer, J., & Lambert-Mogiliansky, A. (2009). An exploration of type indeterminacy in strategic decision-making. Quantum Interaction, Springer LNAI 5494, 113–128. Busemeyer, J., & Lambert-Mogiliansky, A. (2012). Quantum indeterminacy in dynamic decision making. Games, LNCS 7620, 102–114. Busemeyer, J. R., Santuy, E., & Lambert-Mogiliansky, A. (2008). Distinguishing quantum and markov models of human decision making. Proceedings of the Quantum Interaction Symposium, 68–75. Busemeyer, J. R., Wang, Z., & Townsend, J. T. (2006). Quantum dynamics of human decision-making. Journal of Mathematical Psychology, 50, 220–241. Danilov, V. I., & Lambert-Mogiliansky, A. (2008a). Measurable systems and behavioral sciences. Mathematical Social Sciences, 55, 315–340. Danilov, V. I., & Lambert-Mogiliansky, A. (2009). Expected utility under non-classical uncertainty. Theory and Decision, 2010/68, 25–47. Franco, R. (2008). The inverse fallacy and quantum formalism. Proceedings of the Quantum Interaction Symposium, 2008, 94–98. La Mura, P. (2005). Correlated equilibria of classical strategies with quantum signals. International Journal of Quantum Information, 3, 183–188. Lambert-Mogiliansky, A. (2010). Endogenous preferences in games with type-indeterminate players (pp. 70– 77). Menlo Park, CA: AAAI Press. Lambert-Mogiliansky, A. (2012) The emergence and instability of individual identity. Quantum Interaction 2012, 102–114. Lambert-Mogiliansky, A., Zamir, S., & Zwirn, H. (2009). Type indeterminacy—A model of the KT (Khaneman Tversky)-man. Journal of Mathematical Psychology, 53(5), 349–361. Wang, Z., Busemeyer, J. R., Atmanspacher, H., & Pothos, E. (2013). The potential of using quantum theory to build models of cognition. Topics in Cognitive Science, 5(4), 672–88.
Comments on Episodic Superposition of Memory States Ariane Lambert-Mogiliansky Paris School of Economics Received 6 February 2013; received in revised form 28 February 2013; accepted 8 March 2013
Abstract This article develops a commentary to Charles Brainerd, Zheng Wang and Valerie F. Reyna’s article entitled “Superposition of episodic memories: Overdistribution and quantum models” published in a special number of topiCS 2013 devoted to quantum modelling in cognitive sciences. Keywords: Superposition; Interference; Quantum indeterminacy
To many people it may appear unmotivated or artificial to turn to quantum mechanics (QM) when investigating human behavioral and perceptual phenomena. However, the founders of QM, including Bohr and Heisenberg, early recognized the similarities between the two fields. In particular, Bohr was influenced by the psychology and philosophy of knowledge of Harald H€ offding. The similarity stems from the fact that in both fields the object of investigation cannot (always) be separated from the process of investigation. In the words of Bohr: “we face the impossibility of a sharp separation between the behavior of atomic object and the interaction with the measuring instruments which serves to define the condition under which the phenomena appear.” In psychology, investigating a person’s emotional or perceptual state affects the state of the person. In social sciences “revealing” one’s preferences in a choice can affect those preferences. According to Kahnemann, “There is a growing body of evidence that supports an alternative conception according to which preferences are often constructed—not merely revealed—in the elicitation process. These constructions are contingent on the framing of the problem, the method of elicitation, and the context of the choice.” Quantum mechanics and in particular its mathematical formalism was developed to respond to that epistemological challenge: How can we study a system that changes as we try to learn about it? Introducing (quantum) indeterminacy in social sciences, psychology, and perception has shown itself very fruitful to explain a wide variety of behavioral and perceptual phenomena ranging from quantum zeno effect in visual perception Atmanspasher et al. 2004 Correspondence should be sent to Ariane Lambert-Mogiliansky, Paris School of Economics, 48 Boulevard Jourdan 75014 Paris, France. E-mail: [email protected]
64
A. Lambert-Mogiliansky / Topics in Cognitive Science 6 (2014)
to cognitive dissonance, preferences reversal, the inverse fallacy, or the disjunction effect (Atmanspasher et al., 2004; Busemeyer, 2007; Busemeyer & Lambert-Mogiliansky, 2009; Busemeyer et al., 2006, 2008; Danilov & Lambert-Mogiliansky, 2008b, 2009; Franco, 2008; Lambert-Mogiliansky, 2009, 2010; Mura, 2005; Wang et al., 2013). I would like to stress that the stake is beyond just having a model that fits the experimental data. A quantum model of the human mind opens for deeply new perspectives on human mind and human behavior. First, it invites one to consider a holistic model of the mind: The mind cannot be fully decomposed in its simplest parts, but larger composed parts truly function as integrated systems. Second, it implies that the human mind is constantly evolving in response to its interaction with the outside world and with its inner work (e.g., introspection). Thus, it gives us a model of a mind that is intrinsically contextual and plastic—it is not endowed with determinate characteristics in isolation, but comes into being (as a system endowed with characteristics) in interaction with its environment (see Lambert-Mogiliansky and Busemeyer, 2012). In this context, the issue of episodic superposition is a very interesting one and appears most suitable for a quantum explanation. My view is that the quantum model should not be viewed as a substitute for the Over Distribution (OD) theory, but rather as a formalized take of the same approach. Indeed, I shall argue that the OD theory suggests that the verbatim and gist are alternative (complementary in the sense of Bohr) representations of the state of memory and that a quantum model in that spirit can be formulated. I have some reservations with respect to the quantum model (QEM) that is being proposed in the article by Charles Brainerd, Zheng Wang, and Valerie F. Reyna. It is constructed in close comparison with the two-slit experiment which shows a pattern of interference effects when both slits are open. As far as I understand, this became a puzzle only when it could be shown for a single electron. Otherwise it simply suggests a classical wave interpretation. Because we cannot single out a memory particle a “memorion,” I believe that a quantum model closer to the Stern–Gerlach experiment which demonstrates superposition by considering the outcome of a sequence of incompatible measurements may be more adapted. In particular, it would allow for an interpretation of the verbatim and gist memory representation as complementary rather than substitute or independent. I would suggest to model verbatim and gist memory as two incompatible properties of memory. They would correspond to alternative representations of the memory state which are complementary in Bohr meaning like the spin under different angles. The eigenstates within each representation are mutually exclusive, but the eigenstates of the gist representation are not exclusive of the eigenstates entering the verbatim representation. As a consequence, one would not put both verbatim and gist features as mutually exclusive basis vectors that span the memory space as done by the authors in equation 7. Instead, I suggest that they are correlated in the sense that they correspond to alternative bases of the same memory space, which appears more in line with the idea that the two traces run in parallel. In the proposed QEM, the probes are direct measurements of the state as formulated. The assumption is that the probe that asks “is it presented in list 1(or 2 or 3)?” projects on a subspace spanned by two eigenvectors list 1(or 2 or 3) and gist. As far as I can see,
A. Lambert-Mogiliansky / Topics in Cognitive Science 6 (2014)
65
such a model is equivalent to a classical one where we do not know where the state is and we have coarse measurement to learn about it. Consider the following alternative. The probes or questions may be coarse measurements of either representation (gist or verbatim). Or they may be neither true verbatim nor gist measurements. They may be yet another kind of measurement which does not commute with either a gist or a verbatim measurement or with both. The presence of sub (or super) additive probabilities then reflects interferences effects due to the fact that when putting say a verbatim (or gist or third type) question, indeterminacy with respect to the gist (or verbatim) measurement has not been resolved, leaving room for interference. This seems to correspond to the description of the OD theory given in the article “On conjoint recognition test, test cues provoke retrieval of verbatim and gist trace, …, with the two types of trace leading to the same response under some instruction but to different responses under other instructions” (p. 10). Thus, the probes T, R, or TUR are not viewed as analogies with the slits, but rather as the possible results on the landing distribution on the detector. The analog of the slits would be true verbatim (gist) questions which are not put to the agent (leaving indeterminacy in those respects). We do not know through which slit the “memorion” passes. It is the absence of screening (i.e., we do not check through which slit it passed) that generates super (sub) additivity in the responses to the probes analog of interferences observed on the detector. Such a quantum model would allow for an interpretation of episodic superposition that is richer in the sense that it generates interferences from the Bohr complementarity of the two representations. It also appeals for another kind of test experiment in the spirit of Stern–Gerlach experiment. The value of an approach with non-commuting operators is to make a clear distinction between orthogonal (mutually exclusive) features and features belonging to incompatible perspectives (not mutually exclusive). The huge contribution of quantum mechanics is precisely to allow us to deal with non-orthogonal yet atomic states (complete characterization of the system). In the classical model all atomic states are orthogonal. Of course, the classical model allows for non-orthogonal properties but then they are compatible and can be combined to produce a more complete characterization of the system. The quantum model in the article could be clarified in this respect. If list and gist features are incompatible, they cannot be outcomes of one and the same measurement and if they are compatible (a classical model) there cannot be any quantum interference effect because that is the signature of incompatibility. The proposed alternative approach with non-commuting operators also gives a precise meaning to ambiguity in terms of indeterminacy, that is, coexistence of orthogonal features in the mind before a measurement is made. On the other side, the very existence of incompatible perspectives (e.g., verbatim and gist, like two overlapping alternatives) on the same memory state has rich implications in terms of the dynamics of the mind: First, when you ask a verbatim question from a state of indeterminacy, this affects the system and it affects the expected response with respect to gist questions. Second, the interference effects that we talk about in QM cannot be dissociated from the notion and the formalization of incompatible measurements (as projectors on alternative basis of the same
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state space). I know of no other fundamental measurement theory that accounts for interference effects. Those interference effects are the key to quantum probabilities. The QEM could be modified to give a better account for the emergence of interference effects. Concluding, I would like to emphasize that I believe that quantum modeling in psychological and perceptual analysis has a great potential. A definitive advantage of perceptual phenomena is that we are more likely to deal with simple phenomena as compared with, for example, social behavioral phenomena. That allows performing experiments which are true tests of the theory. They represent crucial contributions for establishing the quantum paradigm in the analysis of the human mind and human behavior. References Atmanspacher, H., Filk, T., & Romer, R. (2004). Quantum Zeno features of bistable perception. Biological Cybernetics, 90, 33–40. Brainerd, C., Wang, Z., & Reyna, V. (2013). Superposition of episodic memories: Overdistribution and quantum models. Topics in Cognitive Science, 5(4), 773–99. Busemeyer, J. R. (2007). Quantum information processing explanation for interaction between inferences and decisions. Proceedings of the Quantum Interaction Symposium. Busemeyer, J., & Lambert-Mogiliansky, A. (2009). An exploration of type indeterminacy in strategic decision-making. Quantum Interaction, Springer LNAI 5494, 113–128. Busemeyer, J., & Lambert-Mogiliansky, A. (2012). Quantum indeterminacy in dynamic decision making. Games, LNCS 7620, 102–114. Busemeyer, J. R., Santuy, E., & Lambert-Mogiliansky, A. (2008). Distinguishing quantum and markov models of human decision making. Proceedings of the Quantum Interaction Symposium, 68–75. Busemeyer, J. R., Wang, Z., & Townsend, J. T. (2006). Quantum dynamics of human decision-making. Journal of Mathematical Psychology, 50, 220–241. Danilov, V. I., & Lambert-Mogiliansky, A. (2008a). Measurable systems and behavioral sciences. Mathematical Social Sciences, 55, 315–340. Danilov, V. I., & Lambert-Mogiliansky, A. (2009). Expected utility under non-classical uncertainty. Theory and Decision, 2010/68, 25–47. Franco, R. (2008). The inverse fallacy and quantum formalism. Proceedings of the Quantum Interaction Symposium, 2008, 94–98. La Mura, P. (2005). Correlated equilibria of classical strategies with quantum signals. International Journal of Quantum Information, 3, 183–188. Lambert-Mogiliansky, A. (2010). Endogenous preferences in games with type-indeterminate players (pp. 70– 77). Menlo Park, CA: AAAI Press. Lambert-Mogiliansky, A. (2012) The emergence and instability of individual identity. Quantum Interaction 2012, 102–114. Lambert-Mogiliansky, A., Zamir, S., & Zwirn, H. (2009). Type indeterminacy—A model of the KT (Khaneman Tversky)-man. Journal of Mathematical Psychology, 53(5), 349–361. Wang, Z., Busemeyer, J. R., Atmanspacher, H., & Pothos, E. (2013). The potential of using quantum theory to build models of cognition. Topics in Cognitive Science, 5(4), 672–88.
