On Quantum Models of the Human Mind

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<ul><li><p>Topics in Cognitive Science 6 (2014) 98103Copyright 2013 Cognitive Science Society, Inc. All rights reserved.ISSN:1756-8757 print / 1756-8765 onlineDOI: 10.1111/tops.12064</p><p>On Quantum Models of the Human Mind</p><p>Hongbin Wang, Yanlong Sun</p><p>School of Biomedical Informatics, The University of Texas Health Science Center at Houston</p><p>Received 30 December 2012; received in revised form 21 February 2013; accepted 1 March 2013</p><p>Abstract</p><p>Recent years have witnessed rapidly increasing interests in developing quantum theoretical</p><p>models of human cognition. Quantum mechanisms have been taken seriously to describe how the</p><p>mind reasons and decides. Papers in this special issue report the newest results in the field. Here</p><p>we discuss why the two levels of commitment, treating the human brain as a quantum computer</p><p>and merely adopting abstract quantum probability principles to model human cognition, should be</p><p>integrated. We speculate that quantum cognition models gain greater modeling power due to a</p><p>richer representation scheme.</p><p>Keywords: Cognitive modeling; Quantum cognition; Quantum computation; Quantum probabilitytheory; Knowledge representation; Order effect</p><p>German philosopher Arthur Schopenhauer sees three stages in the revelation of any</p><p>truth: First, it is ridiculed. Second, it is violently opposed. Third, it is accepted as self-</p><p>evident. In the case of quantum cognition, an emerging field that advocates using quan-</p><p>tum theory to explain the human mind, depending on your perspectives (i.e., how the</p><p>wave function collapses, or more precisely, which subspace in your mental Hilbert space</p><p>you choose to project your mental vector to), different assessments can be given. To a</p><p>certain extent, however, we think that confused is probably a more fitting description</p><p>of peoples perception to the field. Here, the best footnote may be the critical comment</p><p>made by Stephen Hawking on Roger Penroses quantum theoretical approach to human</p><p>consciousness: His argument seemed to be that consciousness is a mystery and quantum</p><p>gravity is another mystery so they must be related (Penrose, 1997, p. 171). It is in this</p><p>context that we applaud this special issue of topiCS on quantum cognition. The targetpapers showcase some of the newest results in using quantum theory to build models of</p><p>Correspondence should be sent to Hongbin Wang, School of Biomedical Informatics, The University of</p><p>Texas Health Science Center at Houston, 7000 Fannin Suite 600, Houston, TX 77030. E-mail: hongbin.</p><p>wang@uth.tmc.edu</p></li><li><p>human cognition. More important, they stimulate people to ponder some of the funda-</p><p>mental questions in cognitive modeling.</p><p>Different versions of quantum cognition</p><p>Quantum theory, the brain child of a few of the greatest minds in the early 20th cen-</p><p>tury, offers a very accurate description of how the physical world works. For example,</p><p>quantum field theory, the combination of quantum mechanics and the special theory of</p><p>relativity, is known to be accurate to about one part in 1011 (Penrose, 2005). Although</p><p>the idea that quantum theory may also offer a credible description to metaphysical aspects</p><p>of reality goes back to as early as the dawn age of the theory (e.g., Schrodinger, 1944/</p><p>1958), using quantum theory to seriously tackle issues related to the human mind is a</p><p>more recent development (for recent reviews, see Aaronson, 2013; Busemeyer &amp; Bruza,</p><p>2012; Hameroff, 2012; Koch &amp; Hepp, 2006). By seriously we mean those efforts that</p><p>literally, rather than philosophically/metaphorically, believe in quantum theory as the road</p><p>to mental reality and hold that the human mind results from quantum computation. There</p><p>is a difference, however, in terms of the degree of seriousness. We see at least two levels</p><p>of commitment. The strong claim, represented by, among others, the PenroseHamerofftheory of orchestrated objective reduction (Orch OR) to human consciousness (Hamer-</p><p>off, 1998, 2007; Penrose, 1997), argues that the human brain is a quantum computer and</p><p>that quantum computations occur in the brain materially and literally. More important, it</p><p>is exactly this kind of quantum computations in the brain that leads to the mind in gen-</p><p>eral and consciousness in particular. Much effort has been taken to pinpoint how quantum</p><p>computations are carried out neurophysically, for example, through entangled microtu-</p><p>bules in neurons connected and synchronized by gap junctions. When entanglement col-</p><p>lapses by orchestrated objective reduction, a fundamental effect of quantum gravity,</p><p>consciousness arises. Recently, this Orch OR state reduction is linked to the gamma band</p><p>EEG signal in the brain (~40 Hz), suggesting a ~25-ms rhythm of conscious progression(Hameroff, 2012).</p><p>On the other hand, there is a weak claim, which is the one taken by the editors and</p><p>many authors in this special issue. In the call for commentaries, it was claimed that this</p><p>special issue is not interested in physics, and neither does the work presented claim the</p><p>brain is a quantum computer. Rather, our approach applies abstract, mathematical prin-</p><p>ciples of quantum theory to inquiries in cognitive science (Wang, Busemeyer, Atmansp-</p><p>acher, &amp; Pothos, 2013, p. 3).</p><p>It is not clear, however, to what extent that one can clearly treat the two levels of com-</p><p>mitment completely separate and still proclaim a complete theory of human cognition. In</p><p>a seminal analysis on cognitive theory development, John Anderson suggests that any</p><p>credible cognitive theories have to pass two tests, discovery and uniqueness (Anderson,</p><p>1993). The discovery test has to do with how a theory is found and identified among</p><p>often many potential candidates, and the uniqueness test deals with how to demonstrate</p><p>and prove the discovered theory is a right one. One of the important criteria underlying</p><p>H. Wang, Y. Sun / Topics in Cognitive Science 6 (2014) 99</p></li><li><p>the uniqueness test is the demonstration of biological realism and implementation. With-</p><p>out such a demonstration, a theory is no more than a principled framework and is there-</p><p>fore often incomplete and unfalsifiable.</p><p>Similar criticisms exist for the classical probabilistic (CP) approach to human cognition</p><p>(Bowers &amp; Davis, 2012; McClelland et al., 2010), which the current quantum probability</p><p>(QP)-based approach is compared to (as well as contrasted with). In a recent Sciencereview, Tenenbaum and colleagues justify the Bayesian approach to modeling cognition</p><p>and suggest that the claim human minds learn and reason according to Bayesian princi-</p><p>ples is not a claim that the mind can implement any Bayesian inference (Tenenbaum,</p><p>Kemp, Griffiths, &amp; Goodman, 2011, p. 1280). However, in the end of the article, they</p><p>recognize the issue of pushing Bayesian models down through the algorithmic and imple-</p><p>mentation levels in neural circuits as one of the key open questions and acknowledge that</p><p>the project of reverse-engineering the mind must unfold over multiple levels of analysis</p><p>(p. 1284). From this perspective, the QP approach is advantageous over the CP approach</p><p>in providing a more complete theory of the human mind given its closer link to physics</p><p>and biology. A unified set of quantum mechanisms such as superposition, entanglement,</p><p>decoherence, and interference may therefore be used to describe both physical and psy-</p><p>chological realities.</p><p>We would like to point out another interesting yet related observation concerning the</p><p>difference between the CP and QP approaches to modeling cognition. In justifying the</p><p>appeal of the Bayesian approach, Tenenbaum and colleagues further delimit its scope and</p><p>notice that only those inductive computations that the mind is designed to perform well,</p><p>where biology has had time and cause to engineer effective and efficient mechanisms, are</p><p>likely to be understood in Bayesian terms (p. 1280). They claim that this is why the</p><p>Bayesian approach enjoys great successes in modeling rapid, intuitive, low-level, and</p><p>unconscious processes, but notoriously fails in various high-level and explicit judgment</p><p>and decision-making tasks (e.g., biases and heuristics). It is interesting to note that it is</p><p>in these explicit judgment and decision-making tasks that the QP models excel. The QP</p><p>model of the conjunction fallacy in the Linda problem is not only elegant but also</p><p>insightful (Busemeyer &amp; Bruza, 2012; Wang et al., 2013). Similar examples, as demon-</p><p>strated by papers in this special issue, include the order effect (Wang &amp; Busemeyer,</p><p>2013) and vagueness judgment (Blutner, Pothos, &amp; Bruza, 2013). Then, it is quite puz-</p><p>zling how the QP theory enjoys most success in modeling these naturally not effective</p><p>and efficient tasks, whereas the CP models justifiably give them up as the mind is not</p><p>designed to perform them well.</p><p>New insights for decoding the human mind</p><p>The puzzle may be related to a deeper issue, which is, compared with other general</p><p>theories of human cognition, such as connectionist models and symbolic rule-based</p><p>systems, what new insights about the workings of the human mind does the quantum</p><p>theoretical approach bring about? To be fair, the quantum approach has a lot to offer. As</p><p>100 H. Wang, Y. Sun / Topics in Cognitive Science 6 (2014)</p></li><li><p>demonstrated by the results presented in this special issue, quantum theoretical models</p><p>have a huge potential to build insightful models of human cognition in a wide range of</p><p>task domains. One may wonder, besides those fancy concepts such as superposition,</p><p>entanglement, decoherence, and complementarity, what is the magic?</p><p>We would like to argue that one such magic has to do with knowledge representation.</p><p>By representing mental states as vectors in a mental vector space (Hilbert space) and</p><p>mental operations as vector projections, the quantum cognition approach offers a more</p><p>powerful representational scheme, and therefore allows rich semantics and structures for</p><p>encoding the stuff of thought (Pinker, 2007). Comparisons can be made, for example,</p><p>to knowledge representation in ACT-R, a cognitive architecture (Anderson &amp; Lebiere,</p><p>1998; Anderson et al., 2004). In ACT-R, declarative knowledge is represented by chunks,</p><p>linked in a semantic map fashion; and procedural knowledge is represented by a (unstruc-</p><p>tured) set of production rules. Therefore, in the case of the Linda problem, feminist</p><p>and bank teller are two chunks which may or may not be directly associated. However,</p><p>in the QP model (Wang et al., 2013), feminist and bank teller are represented as</p><p>incompatible events, and as a consequence, become subspaces with a nonorthogonalangle. By setting the angle to be 45, the model then demonstrates how the conjunctionfallacy follows naturally from this representational scheme.</p><p>A similar treatment is used to explain the disjunction fallacy (Blutner et al., 2013),</p><p>manifested by the situation where a student would purchase a Hawaiian vacation package</p><p>no matter if he has passed an exam (to celebrate) or he has failed (to console), but would</p><p>decide to hold on the purchase decision if he does not know the exam result. The QP</p><p>model shows that an angle of 115 between purchasing the vacation and passing theexam induces the interference effect that fits the empirical data (p. 31).</p><p>It is possible that such additional dimensions, induced naturally by the vector space repre-</p><p>sentation, lead to a larger expression power and richer semantics. This argument is supported</p><p>by another observation. Note that both CP and QP theories involve quantifying uncertainty</p><p>by assigning probabilities. CP theory starts with the sample space, which is a set of all pos-sible outcomes of an experiment. By defining a probability mass function f that maps from to [0,1] a probability function can then be defined on events, which are subsets of . It hasbeen shown that by defining a new basic probability assignment function m, which mapsfrom the power set of to [0,1], one can extend a probability function to a belief function(Shafer, 1976). A belief function uses two numbers, rather than one (the probability), to</p><p>quantify the uncertainty, and therefore allows simultaneous representation of belief (evi-</p><p>dence that supports the event) and plausibility (evidence that fails to support not the event).</p><p>We have shown previously how a similar richer representation allows us to model the order</p><p>effect in judgment and decision making (Wang, Johnson, &amp; Zhang, 2006). In that treatment,</p><p>we represent the uncertainty about a hypothesis with two numbers: a traditional probability</p><p>value (Bayesian or Frequentist) and a confidence value. The latter is a function of the amount</p><p>of evidence the probability value is based on, and therefore summarizing the degree of confi-</p><p>dence one has on the associated probability value. With this scheme, in the light of new evi-</p><p>dence, belief revision is determined not only by the probability values but also by the</p><p>confidence values (e.g., a probability with a high confidence value is hard to be changed</p><p>H. Wang, Y. Sun / Topics in Cognitive Science 6 (2014) 101</p></li><li><p>much). With the addition of this confidence dimension, we show that the order effect appears</p><p>and disappears depending on different levels of experience, which fits human data well. It is</p><p>clear that QP theory also induces additional representational structures, as the basic space</p><p>now becomes a Hilbert vector space and states are now represented by combination of</p><p>events, weighted by complex numbers. The human mind is by no means simple, but it is no</p><p>surprise that a richer expression scheme comes with a greater modeling power.</p><p>Acknowledgments</p><p>The work is partially supported by the Office of Naval Research (ONR) grant number</p><p>N00014-08-1-0042, and Intelligence Advanced Research Projects Activity (IARPA) via</p><p>Department of the Interior (DOI) contract number D10PC20021.</p><p>References</p><p>Aaronson, S. (2013). Quantum computing since Democritus. New York: Cambridge University Press.Anderson, J. R. (1993). Rules of the mind. Hillsdale, NJ: Lawrence Erlbaum Associates.Anderson, J. R., Bothell, D., Byrne, M. D., Douglass, S., Lebiere, C., &amp; Qin, Y. (2004). An integrated theory</p><p>of the mind. Psychological Review, 111(4), 10361060.Anderson, J. R., &amp; Lebiere, C. (1998). The atomic components of thought. Hillsdale, NJ: Lawrence Erlbaum</p><p>Press.</p><p>Blutner, R., Pothos, E. M., &amp; Bruza, P. (2013). A quantum probability perspective on boderline vagueness.</p><p>Topics in Cognitive Science, 5(4), 711736.Bowers, J. S., &amp; Davis, C. J. (2012). Bayesian just-so stories in psychology and neuroscience. Psychological</p><p>Bulletin, 138(3), 389414.Busemeyer, J. R., &amp; Bruza, P. D. (2012). Quantum models of cognition and decision. New York: Cambridge</p><p>University Press.</p><p>Hameroff, S. R. (1998). Quantum computation in brain microtubules? The Penrose-Hameroff Orch OR</p><p>model of consciousness. Philosophical Transactions of the Royal Society, London Series A, 356, 18691896.</p><p>Hameroff, S. R. (2007). The brain is both neurocomputer and quantum computer. Cognitive Science, 31(6),10351045.</p><p>Hameroff, S. R. (2012). How quantum brain biology can rescue conscious free will. Frontiers in IntegrativeNeuroscience, 6, 93....</p></li></ul>