on quantum models of the human mind
TRANSCRIPT
Topics in Cognitive Science 6 (2014) 98–103Copyright © 2013 Cognitive Science Society, Inc. All rights reserved.ISSN:1756-8757 print / 1756-8765 onlineDOI: 10.1111/tops.12064
On Quantum Models of the Human Mind
Hongbin Wang, Yanlong Sun
School of Biomedical Informatics, The University of Texas Health Science Center at Houston
Received 30 December 2012; received in revised form 21 February 2013; accepted 1 March 2013
Abstract
Recent years have witnessed rapidly increasing interests in developing quantum theoretical
models of human cognition. Quantum mechanisms have been taken seriously to describe how the
mind reasons and decides. Papers in this special issue report the newest results in the field. Here
we discuss why the two levels of commitment, treating the human brain as a quantum computer
and merely adopting abstract quantum probability principles to model human cognition, should be
integrated. We speculate that quantum cognition models gain greater modeling power due to a
richer representation scheme.
Keywords: Cognitive modeling; Quantum cognition; Quantum computation; Quantum probability
theory; Knowledge representation; Order effect
German philosopher Arthur Schopenhauer sees three stages in the revelation of any
truth: First, it is ridiculed. Second, it is violently opposed. Third, it is accepted as self-
evident. In the case of quantum cognition, an emerging field that advocates using quan-
tum theory to explain the human mind, depending on your perspectives (i.e., how the
wave function collapses, or more precisely, which subspace in your mental Hilbert space
you choose to project your mental vector to), different assessments can be given. To a
certain extent, however, we think that “confused” is probably a more fitting description
of people’s perception to the field. Here, the best footnote may be the critical comment
made by Stephen Hawking on Roger Penrose’s quantum theoretical approach to human
consciousness: “His argument seemed to be that consciousness is a mystery and quantum
gravity is another mystery so they must be related” (Penrose, 1997, p. 171). It is in this
context that we applaud this special issue of topiCS on quantum cognition. The target
papers showcase some of the newest results in using quantum theory to build models of
Correspondence should be sent to Hongbin Wang, School of Biomedical Informatics, The University of
Texas Health Science Center at Houston, 7000 Fannin Suite 600, Houston, TX 77030. E-mail: hongbin.
human cognition. More important, they stimulate people to ponder some of the funda-
mental questions in cognitive modeling.
Different versions of quantum cognition
Quantum theory, the brain child of a few of the greatest minds in the early 20th cen-
tury, offers a very accurate description of how the physical world works. For example,
quantum field theory, the combination of quantum mechanics and the special theory of
relativity, is known to be accurate to about one part in 1011 (Penrose, 2005). Although
the idea that quantum theory may also offer a credible description to metaphysical aspects
of reality goes back to as early as the dawn age of the theory (e.g., Schrodinger, 1944/
1958), using quantum theory to seriously tackle issues related to the human mind is a
more recent development (for recent reviews, see Aaronson, 2013; Busemeyer & Bruza,
2012; Hameroff, 2012; Koch & Hepp, 2006). By “seriously” we mean those efforts that
literally, rather than philosophically/metaphorically, believe in quantum theory as the road
to mental reality and hold that the human mind results from quantum computation. There
is a difference, however, in terms of the degree of seriousness. We see at least two levels
of commitment. The strong claim, represented by, among others, the Penrose–Hameroff
theory of “orchestrated objective reduction (Orch OR)” to human consciousness (Hamer-
off, 1998, 2007; Penrose, 1997), argues that the human brain is a quantum computer and
that quantum computations occur in the brain materially and literally. More important, it
is exactly this kind of quantum computations in the brain that leads to the mind in gen-
eral and consciousness in particular. Much effort has been taken to pinpoint how quantum
computations are carried out neurophysically, for example, through entangled microtu-
bules in neurons connected and synchronized by gap junctions. When entanglement col-
lapses by “orchestrated objective reduction,” a fundamental effect of quantum gravity,
consciousness arises. Recently, this Orch OR state reduction is linked to the gamma band
EEG signal in the brain (~40 Hz), suggesting a ~25-ms rhythm of conscious progression
(Hameroff, 2012).
On the other hand, there is a weak claim, which is the one taken by the editors and
many authors in this special issue. In the call for commentaries, it was claimed that “this
special issue is not interested in physics, and neither does the work presented claim the
brain is a quantum computer.” Rather, “our approach applies abstract, mathematical prin-
ciples of quantum theory to inquiries in cognitive science” (Wang, Busemeyer, Atmansp-
acher, & Pothos, 2013, p. 3).
It is not clear, however, to what extent that one can clearly treat the two levels of com-
mitment completely separate and still proclaim a complete theory of human cognition. In
a seminal analysis on cognitive theory development, John Anderson suggests that any
credible cognitive theories have to pass two tests, discovery and uniqueness (Anderson,
1993). The discovery test has to do with how a theory is found and identified among
often many potential candidates, and the uniqueness test deals with how to demonstrate
and prove the discovered theory is a right one. One of the important criteria underlying
H. Wang, Y. Sun / Topics in Cognitive Science 6 (2014) 99
the uniqueness test is the demonstration of biological realism and implementation. With-
out such a demonstration, a theory is no more than a principled framework and is there-
fore often incomplete and unfalsifiable.
Similar criticisms exist for the classical probabilistic (CP) approach to human cognition
(Bowers & Davis, 2012; McClelland et al., 2010), which the current quantum probability
(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
and suggest that “the claim human minds learn and reason according to Bayesian princi-
ples is not a claim that the mind can implement any Bayesian inference” (Tenenbaum,
Kemp, Griffiths, & Goodman, 2011, p. 1280). However, in the end of the article, they
recognize the issue of pushing Bayesian models down through the algorithmic and imple-
mentation levels in neural circuits as one of the key open questions and acknowledge that
“the project of reverse-engineering the mind must unfold over multiple levels of analysis”
(p. 1284). From this perspective, the QP approach is advantageous over the CP approach
in providing a more complete theory of the human mind given its closer link to physics
and biology. A unified set of quantum mechanisms such as superposition, entanglement,
decoherence, and interference may therefore be used to describe both physical and psy-
chological realities.
We would like to point out another interesting yet related observation concerning the
difference between the CP and QP approaches to modeling cognition. In justifying the
appeal of the Bayesian approach, Tenenbaum and colleagues further delimit its scope and
notice that “only those inductive computations that the mind is designed to perform well,
where biology has had time and cause to engineer effective and efficient mechanisms, are
likely to be understood in Bayesian terms” (p. 1280). They claim that this is why the
Bayesian approach enjoys great successes in modeling rapid, intuitive, low-level, and
unconscious processes, but notoriously fails in various high-level and explicit judgment
and decision-making tasks (e.g., “biases and heuristics”). It is interesting to note that it is
in these explicit judgment and decision-making tasks that the QP models excel. The QP
model of the conjunction fallacy in the Linda problem is not only elegant but also
insightful (Busemeyer & Bruza, 2012; Wang et al., 2013). Similar examples, as demon-
strated by papers in this special issue, include the order effect (Wang & Busemeyer,
2013) and vagueness judgment (Blutner, Pothos, & Bruza, 2013). Then, it is quite puz-
zling how the QP theory enjoys most success in modeling these naturally not “effective
and efficient” tasks, whereas the CP models justifiably give them up as the mind is not
“designed to perform them well.”
New insights for decoding the human mind
The puzzle may be related to a deeper issue, which is, compared with other general
theories of human cognition, such as connectionist models and symbolic rule-based
systems, what new insights about the workings of the human mind does the quantum
theoretical approach bring about? To be fair, the quantum approach has a lot to offer. As
100 H. Wang, Y. Sun / Topics in Cognitive Science 6 (2014)
demonstrated by the results presented in this special issue, quantum theoretical models
have a huge potential to build insightful models of human cognition in a wide range of
task domains. One may wonder, besides those fancy concepts such as superposition,
entanglement, decoherence, and complementarity, what is the magic?
We would like to argue that one such magic has to do with knowledge representation.
By representing mental states as vectors in a mental vector space (Hilbert space) and
mental operations as vector projections, the quantum cognition approach offers a more
powerful representational scheme, and therefore allows rich semantics and structures for
encoding “the stuff” of thought (Pinker, 2007). Comparisons can be made, for example,
to knowledge representation in ACT-R, a cognitive architecture (Anderson & Lebiere,
1998; Anderson et al., 2004). In ACT-R, declarative knowledge is represented by chunks,
linked in a semantic map fashion; and procedural knowledge is represented by a (unstruc-
tured) set of production rules. Therefore, in the case of the Linda problem, “feminist”
and “bank teller” are two chunks which may or may not be directly associated. However,
in the QP model (Wang et al., 2013), “feminist” and “bank teller” are represented as
incompatible events, and as a consequence, become subspaces with a nonorthogonal
angle. By setting the angle to be 45�, the model then demonstrates how the conjunction
fallacy follows naturally from this representational scheme.
A similar treatment is used to explain the disjunction fallacy (Blutner et al., 2013),
manifested by the situation where a student would purchase a Hawaiian vacation package
no matter if he has passed an exam (to celebrate) or he has failed (to console), but would
decide to hold on the purchase decision if he does not know the exam result. The QP
model shows that an angle of 115� between purchasing the vacation and passing the
exam induces the interference effect that fits the empirical data (p. 31).
It is possible that such additional dimensions, induced naturally by the vector space repre-
sentation, lead to a larger expression power and richer semantics. This argument is supported
by another observation. Note that both CP and QP theories involve quantifying uncertainty
by assigning probabilities. CP theory starts with the sample spaceΘ, which is a set of all pos-
sible outcomes of an experiment. By defining a probability mass function f that maps from Θto [0,1] a probability function can then be defined on events, which are subsets of Θ. It has
been shown that by defining a new basic probability assignment function m, which maps
from the power set of Θ 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
quantify the uncertainty, and therefore allows simultaneous representation of belief (evi-
dence that supports the event) and plausibility (evidence that fails to support “not the event”).
We have shown previously how a similar richer representation allows us to model the order
effect in judgment and decision making (Wang, Johnson, & Zhang, 2006). In that treatment,
we represent the uncertainty about a hypothesis with two numbers: a traditional probability
value (Bayesian or Frequentist) and a confidence value. The latter is a function of the amount
of evidence the probability value is based on, and therefore summarizing the degree of confi-
dence one has on the associated probability value. With this scheme, in the light of new evi-
dence, belief revision is determined not only by the probability values but also by the
confidence values (e.g., a probability with a high confidence value is hard to be changed
H. Wang, Y. Sun / Topics in Cognitive Science 6 (2014) 101
much). With the addition of this confidence dimension, we show that the order effect appears
and disappears depending on different levels of experience, which fits human data well. It is
clear that QP theory also induces additional representational structures, as the basic space
now becomes a Hilbert vector space and states are now represented by combination of
events, weighted by complex numbers. The human mind is by no means simple, but it is no
surprise that a richer expression scheme comes with a greater modeling power.
Acknowledgments
The work is partially supported by the Office of Naval Research (ONR) grant number
N00014-08-1-0042, and Intelligence Advanced Research Projects Activity (IARPA) via
Department of the Interior (DOI) contract number D10PC20021.
References
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., & Qin, Y. (2004). An integrated theory
of the mind. Psychological Review, 111(4), 1036–1060.Anderson, J. R., & Lebiere, C. (1998). The atomic components of thought. Hillsdale, NJ: Lawrence Erlbaum
Press.
Blutner, R., Pothos, E. M., & Bruza, P. (2013). A quantum probability perspective on boderline vagueness.
Topics in Cognitive Science, 5(4), 711–736.Bowers, J. S., & Davis, C. J. (2012). Bayesian just-so stories in psychology and neuroscience. Psychological
Bulletin, 138(3), 389–414.Busemeyer, J. R., & Bruza, P. D. (2012). Quantum models of cognition and decision. New York: Cambridge
University Press.
Hameroff, S. R. (1998). Quantum computation in brain microtubules? The Penrose-Hameroff ‘Orch OR’
model of consciousness. Philosophical Transactions of the Royal Society, London Series A, 356, 1869–1896.
Hameroff, S. R. (2007). The brain is both neurocomputer and quantum computer. Cognitive Science, 31(6),1035–1045.
Hameroff, S. R. (2012). How quantum brain biology can rescue conscious free will. Frontiers in IntegrativeNeuroscience, 6, 93.
Koch, C., & Hepp, K. (2006). Quantum mechanics in the brain. Nature, 440, 611–612.McClelland, J. L., Botvinick, M. M., Noelle, D. C., Plaut, D. C., Rogers, T. T., Seidenberg, M. S., Smith,
L. B. (2010). Letting structure emerge: Connectionist and dynamical systems approaches to cognition.
Trends in Cognitive Sciences, 14(8), 348–356.Penrose, R. (1997). The large, the small and the human mind. New York: Cambridge University Press.
Penrose, R. (2005). The road to reality: A complete guide to the laws of the university. New York: Random
House.
Pinker, S. (2007). The stuff of thought: Language as a window into human nature. Cambridge, MA: MIT
press.
Schrodinger, E. (1944/1958). What is life? and mind and matter. New York: Cambridge University Press.
Shafer, G. (1976). A mathematical theory of evidence. Princeton, NJ: Princeton University Press.
102 H. Wang, Y. Sun / Topics in Cognitive Science 6 (2014)
Tenenbaum, J. B., Kemp, C., Griffiths, T. L., & Goodman, N. D. (2011). How to grow a mind: Statistics,
structure, and abstraction. Science, 331, 1279–1285.Wang, Z., & Busemeyer, J. R. (2013). A quantum question oder model supported by empirical tests of an A
Priori and precise prediction. Topics in Cognitive Science, 5(4), 689–710.Wang, Z., Busemeyer, J. R., Atmanspacher, H., & Pothos, E. M. (2013). The potential of using quantum
theory to build models of cognition. Topics in Cognitive Science, 5(4), 672–688.Wang, H., Johnson, T. R., & Zhang, J. (2006). The order effect in human abductive reasoning: An empirical
and computational study. Journal of Experimental and Theoretical Artificial Intelligence, 18(2), 215–247.
H. Wang, Y. Sun / Topics in Cognitive Science 6 (2014) 103