2. Lecce, Italy, September 10, 2013
QUANTUM SOCIAL SCIENCE
“Ubiquitous Quanta”. Introduction
QUESTIONS
APPLICATIONS
HISTORY
SANDRO SOZZO
CENTER LEO APOSTEL FOR INTERDISCIPLINARY
STUDIES (CLEA)
FREE UNIVERSITY OF BRUXELLES (VUB)
www.vub.ac.be/clea/vub/people/sozzo
QUESTIONS
APPLICATIONS
3. QUANTUM THEORY: SUCCESS, APPLICATIONS
Quantum theory is one of the building blocks of modern physics because of its unmatched
predictive success and its impact on our conception of the physical world and our
everyday life. Quantum theory brought in conceptual novelties and marked the departure
from ordinary intuition and common sense on which classical physics rest.
Quantum theory applies at any conceivable scale, from elementary
particles to nuclei, from atoms and molecules to condensed matter and
macroscopic physics (superfluidity, supercondictivity), up to cosmology.
10/09/2013 3Ubiquitous Quanta
macroscopic physics (superfluidity, supercondictivity), up to cosmology.
Quantum teleportation.
Quantum information.
Applications.
Quantum cryptography.
Quantum computation.
4. QUANTUM THEORY: MYSTERIES
“... I think I can safely say that nobody understands quantum mechanics.”
Richard P. Feynman
Nonobjectivity.
Superposition principle, linearity , interference.
10/09/2013 4Ubiquitous Quanta
Black Lines, December 1913, Vasily
Kandinsky.
Wave-particle duality.
Uncertainty principle.
5. Entanglement.
Quantum probability.
10/09/2013 5Ubiquitous Quanta
“It is a fundamental quantum doctrine that a
measurement does not reveal, in general, a preexisting
value of the measured property. On the contrary, the
outcome of a measurement is brought into being by the
act of measurement itself, a joint manifestation of the
state of the probed system and the probing apparatus.”
N. David Mermin
Quantum probability.
Contextuality.
6. The structural differences
between classical and quantum
theory, e.g., classical and
quantum probability, have been
understood.
FOUNDATIONS OF QUANTUM THEORY
Non-commutative algebra of quantum observables.
Non-Kolmogorovian quantum probability.
Non-Boolean quantum logic.
10/09/2013 6Ubiquitous Quanta
Detection of genuine quantum aspects (interference, superposition,
emergence, entanglement, incompatibility) in macroscopic physical
systems and, more generally, outside the microscopic world.
The identification of quantum structures outside the microscopic domain of quantum
physics and the employment of the mathematical formalisms of quantum theory to
model experimental data in social science is now a well established research field.
7. Results have been obtained
in the modeling of cognitive
and decision processes. Decision theory.
Computer science.
Animal behavior.
Behavioral economics.
QUANTUM COGNITION
Concept theory.
Finance.
10/09/2013 7Ubiquitous Quanta
Computer science. Finance.
8. SOME HIGHLIGHTS
First ideas.
Books.
10/09/2013 8Ubiquitous Quanta
Quantum Interaction workshops. Stanford (2007), Oxford (2008), Saarbrücken (2009), Washington
(2010), Aberdeen (2011), Paris (2012), Leicester (2013), Filzbach (2014).
Media.
9. Impact factor 2011: 25.056.
10/09/2013 9Ubiquitous Quanta
The Brussels team (S. Sozzo, D. Aerts, J. Broekaert and T. Veloz) has recently received
a prestigious Outstanding Scholarly Contribution Award by the International Institute
for Advanced Studies in Systems Research and Cybernetics for his research on “The
Quantum Challenge in Concept Theory and Natural Language Processing”.
The 5-year project G.0234.08 “Development of a contextual non-classical (quantum
physics based) theory for financial option pricing and for modeling a socio-economic
system”, co-promoters D. Aerts and E. Haven, was funded by the FWO (Fonds
Wetenschappelijk Onderzoek, Vlaanderen) for fundamental research in Economics.
10. QUESTIONS AND FUTURE DEVELOPMENTS
(?) Why the quantum-mechanical formalisms are so efficient in these domains?
(??) Can we infer anything on the existence of microscopic quantum processes in
the human brain? Quantum consciousness?
(???) Is this really “quantum”?
(?V) What about alternative classical explanations? Do they exist?
The mathematical formalisms of quantum theory provide a
successful modeling in cognitive and decision processes and, more
generally, outside the microscopic world of quantum physics.
Questions.
Results.
10/09/2013 10Ubiquitous Quanta
(?V) What about alternative classical explanations? Do they exist?
Applications.
Simulation of mental processes,
artificial intelligence, robotics.
Economics and finance. Black-Scholes model
of option pricing, random walk hypothesis.
Nontrivial quantum effects in biological systems.
Semantic analysis, information retrieval, world wide web search.
11. Lecce, Italy, September 10, 2013
THE QUANTUM CHALLENGE IN CONCEPT THEORY
AND NATURAL LANGUAGE PROCESSING
“Ubiquitous Quanta”. Introducing quantum
models in cognitive and economic sciences
SANDRO SOZZO
CENTER LEO APOSTEL FOR INTERDISCIPLINARY
STUDIES (CLEA)
FREE UNIVERSITY OF BRUXELLES (VUB)
www.vub.ac.be/clea/vub/people/sozzo
AND NATURAL LANGUAGE PROCESSING
12. THE COMBINATION PROBLEM
To understand the structure and dynamics of
human concepts, how concepts combine to form
sentences, and how meaning is expressed by such
combinations, is one of the age-old challenges of
scientists studying the human mind.
Progress in many fields (psychology,
linguistics, AI, cognitive science)
depends crucially on it.
Major scientific issues (text analysis,
IR, human-computer interaction)
rely on a deeper understanding of
10/09/2013 12Ubiquitous Quanta
Much effort has been devoted to these matters, but very few substantial results have been obtained.
However, models of concepts making use of the mathematical formalisms of
quantum theory have been substantially more successful than classical approaches
at modeling data generated in studies on combinations of two concepts.
rely on a deeper understanding of
how concepts combine.
13. QUANTUM MODELING OF CONCEPTS
We explain how the quantum effects of superposition, interference, emergence and contextuality
give rise to a modeling of the overextension and the underextension of membership weights of
We put forward a quantum-theoretic modeling of how concepts combine, and identify the specific
quantum aspects that contribute to the successful modeling of the extensive collection of
experimental data for the conjunction and the disjunction of two concepts (Hampton 1988a,b).
10/09/2013 13Ubiquitous Quanta
give rise to a modeling of the overextension and the underextension of membership weights of
exemplars with respect to the conjunction and the disjunction of concepts.
We identify an experimental violation of Bell’s inequalities for a specific concept combination, and
elaborate a quantum representation for it, thus proving the entanglement of such combinations.
We show how a more sophisticated Fock space modeling reveals human thought as a
superposition of ‘quantum logical thought’ and ‘quantum emergent thought’.
14. Classical view. All instances of a concept
share a common set of necessary and
sufficient defining properties.Wittgenstein (1953). The meaning
of concepts depends on the
contexts in which they are used.
Rosch (1973). Concepts
exhibit graded typicality.
Following Rosch, a probabilistic or
DIFFICULTIES OF EXISTING CONCEPT THEORIES
Traditional (fuzzy set) approaches. A
concept is a container of instantiations.
1
2
4
3
10/09/2013 14Ubiquitous Quanta
Following Rosch, a probabilistic or
fuzzy set approach was tried.
Osherson & Smith (1981). People rate Guppy neither
as a typical Pet nor as a typical Fish, but they rate it
as a highly typical Pet-Fish (guppy effect).
Hampton (1988a,b). The membership weight of an exemplar of a conjunction
(disjunction) of concepts is higher (lower) than the membership weights of this exemplar
for one or both of the constituent concepts (overextension, underextension).
The guppy effect defies the
fuzzy set modeling of typicality
with respect to conjunction.
5
6
7
8
15. The Brussels group followed the axiomatic and operational approaches to quantum
theory, identifying situations in the macro world, i.e. not necessarily situations of
quantum particles in the micro world, which revealed quantum structures.
A concept is considered as an entity in a specific state, and
not, as in the classical view, as a container of instantiations.
NOVELTIES OF THE BRUSSELS APPROACH
10/09/2013 15Ubiquitous Quanta
not, as in the classical view, as a container of instantiations.
A context is a factor that influences the concept, and changes its state,
and is formed by conceptual landscapes surrounding the concept.
Exemplars of concepts are regarded as different states of the concept.
Typicality is an observable quantity, with different values for different states of the concept.
16. THE GUPPY EFFECT IN SCoP
The guppy effect is explained in the SCoP formalism by
considering the conjunction Pet-Fish as Pet in the context
Fish or Fish in the context Pet. A state pGuppy of Pet (Fish)
has a low typicality in absence of context, while it scores
a high typicality under the context eFish (ePet).
A SCoP formalism was worked out to model any kind of
entity in terms of states, contexts and properties.
10/09/2013 16Ubiquitous Quanta
We built an explicit quantum
representation in a complex
Hilbert space of the experimental
data on the concepts Pet, Fish and
their conjunction Pet-Fish.
highpeppep
lowpppp
pppp
pppp
FishPetGuppyPetFishGuppy
FishFishGuppyPetPetGuppy
Guppy
e
FishGuppyFish
Guppy
e
PetGuppyPet
PetFish
FishPet
)ˆ,,(),ˆ,,(
)ˆ,1,(),ˆ,1,(
ˆˆ
ˆˆ
1
1
µµ
µµ
→→
→→
17. WHY A QUANTUM FORMALISM IS SO EFFICIENT?
When a subject is asked to estimate the membership (or
the typicality) of an exemplar with respect to one (or
more concepts), contextual influence (of a cognitive type)
and a transition from potential to actual occur in which an
outcome is actualized from a set of possible outcomes.
Uncertainty and potentiality are modeled in quantum probability theory in a very
different way than their modeling in classical Kolmogorovian probability theory.
In a quantum measurement
process, the measurement context
actualizes one possible outcome
and provokes an indeterministic
change of state of the microscopic
10/09/2013 17Ubiquitous Quanta
outcome is actualized from a set of possible outcomes.
change of state of the microscopic
quantum particle that is measured.
Both quantum and conceptual entities are realms of genuine
potentialities, not of lack of knowledge of actualities.
At variance with classical Kolmogorovian probability, quantum probability enables
coping with this kind of contextuality and pure potentiality, also taking into account
interference effects through the use of complex numbers.
18. THE CONJUNCTION OF TWO CONCEPTS
Hampton’s data on concept conjunction (1988a) cannot be modeled within a classical probability theory.
10/09/2013 18Ubiquitous Quanta
µMint(Food)=0.87
µMint(Plant)=0.81
µMint(Food and Plant)=0.9
This violation suggests that a quantum
effect could occur in this case.
19. A QUANTUM MODEL FOR THE CONJUNCTION
Let us now illustrate how we model Hampton's (1988a) membership test by using the quantum formalism.
10/09/2013 19Ubiquitous Quanta
20. A CONSTRUCTION IN THE HILBERT SPACE CCCC3
In classical probability, one would expect µ(A)µ(B). Thus, m=1
and n=0 reproduce the `classical probability' situation.
10/09/2013 20Ubiquitous Quanta
To construct a solution for Mint, we take m2=0.3 and n2=0.7, hence β=50.21°. We can
see that complex numbers play an essential role. This is the root of the interference,
hence the deep reason that µMint(Food and Plant) ≥ µMint(Food), µMint(Plant).
21. HAMPTON’S DATA FOR DISJUNCTION
An important role is played by the abundance of exemplars with overextension in case of
conjunction, and with underextension in case of disjunction, except for the pair Fruits and
Vegetables, where disjunction gives rise to overextension too, and in a very strong way.
10/09/2013 21Ubiquitous Quanta
22. Participants estimated Mushroom to be a much stronger
member of Fruits or Vegetables than of Fruits and Vegetables
apart, which defies even the wildest interpretation of a
classical logical structure for the disjunction.
THE DISJUNCTION OF TWO CONCEPTS
µMushroom(Fruit)=0
µMushroom(Vegetable)=0.5
µMushroom(Fruit or Vegetable)=0.9
10/09/2013 22Ubiquitous Quanta
For several other exemplars, the answers of a substantial number of participants have
invariably given rise to a behavior that is highly strange from the point of view of classical logic.
23. Our explanation for this highly non-classical logic behavior is that the participants
considered the exemplars listed above to be characteristic of the newly emerging
concept Fruits or Vegetables, as a concept specially attractive for exemplars `tending to
raise doubts as to whether they are fruits or vegetables'. A clear example is Tomato,
where µTomato(Fruit)=0.7, µTomato(Vegetable)=0.7, µTomato(Fruit or Vegetable)=1, because
many indeed will doubt whether Tomato is a fruit or a vegetable.
EMERGENCE OF NEW CONCEPTS
10/09/2013 23Ubiquitous Quanta
The dominant dynamics of reasoning is emergence, while classical logical reasoning is only
secondary, which can be explained by modeling concept combinations in Fock space (Aerts, 2009a).
Fock space is the direct sum of two complex Hilbert spaces, denoted by Sector 1 and Sector 2.
In Sector 1, pure interference is modeled. Sector 2 is a tensor product Hilbert space, and here
the combination is modeled such that a probabilistic version of classical logic, i.e. quantum
logic, appears as a modeling of a situation with two identical exemplars.
F=H⊕(H⊗H)
24. TWO MODES OF THOUGHT IN FOCK SPACE
In Sector 1, `quantum emergent thought‘
occurs which consists in reflecting whether
Tomato is a member of the new concept
In Sector 2, two identical exemplars of
Tomato are considered. One is confronted
with Fruits and the other one with
Vegetables. If both (one of these)
Example. Consider Tomato, for Fruits or Vegetables.
10/09/2013 24Ubiquitous Quanta
Tomato is a member of the new concept
Fruits or Vegetables. This is a completely
different dynamics of thought than
`quantum logical thought', i.e. the quantum
probabilistic version of classical logical
thought.
Our modeling of human reasoning is situated in the whole of Fock space, hence human
reasoning is a superposition of `emergent reasoning' and `logical reasoning‘ in our approach.
Vegetables. If both (one of these)
confrontations lead(s) to acknowledgement
of membership, the conjunction (disjunction)
is satisfied. We can recognize the calculus of
classical logic in this dynamics, except that
things are probabilistic or fuzzy.
25. QUANTUM MODELING OF THE DISJUNCTION
(as for conjunction)
10/09/2013 25Ubiquitous Quanta
Comparing the correlations of the
Hampton (1988a,b) data with (i)
the average, (ii) the maximum, (iii)
the minimum, we find that, for
the conjunction (disjunction), the
correlations for each of the pairs
with the average are substantially
higher than those with the
minimum (maximum).
This concludes our argumentation for the
presence in human thought of a superposition
of a dominant dynamics of emergent thought
and a secondary dynamics of logical thought.
26. The effects identified in concept research have their counterparts in other domains of cognitive science.
NON-CLASSICAL EFFECTS IN DECISION
THEORY AND ECONOMICS
There is a whole set of findings in
decision theory that entail effects of a
very similar nature, e.g., the disjunction
In behavioral economics, similar effects have
been found that point to a deviation from
classical logical thinking when human decisions
10/09/2013 26Ubiquitous Quanta
The tendency was to consider these deviations from classicality as fallacies, or as effects.
We have shown that what has been called a fallacy, an effect or a deviation, is a consequence of the
dominant dynamics and its nature is emergence, while what has been considered as a default to
deviate from, namely classical logical reasoning, is a consequence of a secondary form of dynamics.
very similar nature, e.g., the disjunction
effect and the conjunction fallacy.
classical logical thinking when human decisions
are at stake (Allais and Ellsberg paradoxes).
27. ENTANGLEMENT IN CONCEPT
COMBINATION: THE ANIMAL ACTS
We have recently performed a cognitive test on The Animal Acts which violated Bell's inequalities.
We have also worked out a quantum representation in C2 ⊗C2 which fits the collected data and
reveals entanglement between Animal and Acts. And, more, it showed a `stronger form of
entanglement' involving not only entangled states but also entangled measurements.
10/09/2013 27Ubiquitous Quanta
29. RESULTS OF THE COGNITIVE TEST
We performed an
experiment with
81 test subjects.
Results.
10/09/2013 29Ubiquitous Quanta
(i) The probabilities corresponding to coincidence measurements cannot be factorized.
(ii) The CHSH inequality is violated within the Tsirelson bound.
(iii) The marginal distribution law is never satisfied. 224197.2 <
34. CONCLUSIONS
We illustrated our quantum modeling approach by providing a description of the
overextension for conjunctions of concepts measured by Hampton (1988a) as an effect
of quantum interference. We pointed out the essential role of complex numbers.
Several findings in concept research (graded nature of exemplars, guppy effect, over- and
under-extension of membership weights) led us to recognize the need for quantum modeling.
The concept combination The Animal Acts, empirically violated Bell’s inequalities, thus
10/09/2013 34Ubiquitous Quanta
The concept combination The Animal Acts, empirically violated Bell’s inequalities, thus
revealing the presence of entanglement in conceptual combinations.
Superposition and interference were studied in the disjunction Fruits or Vegetables, showing that
quantum interference patterns appear whenever one considers suitable exemplars of this disjunction.
Emergence occurs in conceptual processes. We put forward the explanatory hypothesis that human
thought is the quantum superposition of `quantum emergent thought' and `classical logical thought',
and that our quantum modeling approach applied in Fock space enables this general modeling.
35. INSIGHTS AND FUTURE RESEARCH
Identification of quantum structures, e.g., entanglement, in cognitive and
decision processes and, more generally, in macroscopic entities.
Human mind works as a system which
is closer to a quantum computer than
The resources of quantum computation
can be implemented in other types of
Insights.
25/08/2013 35Quantum modeling scheme for
entanglement
is closer to a quantum computer than
it is to a classical computer.
can be implemented in other types of
realizations than microscopic quantum
entities and qubits.
Elaboration of macroscopic devices
which perform quantum algorithms,
thus simulating quantum computers.
The problems connected with
the control of microscopic
entities is avoided.
Insights.
36. i. D. Aerts, L. Gabora (2005a,b), “A Theory of Concepts and Their Combinations I & II”, Kybernetes 34,
pp. 167-191; 192-221.
ii. D. Aerts (2009), “Quantum Structure in Cognition”, J. Math. Psychol. 53, pp. 314-348.
iii. D. Aerts, S. Sozzo (2011), “Quantum Structure in Cognition: Why and How Concepts Are
Entangled”, Quantum Interaction 2011, LNCS 7052, pp. 116-127, Berlin: Springer.
iv. D. Aerts, J. Broekaert, L. Gabora, S. Sozzo (2013), “Quantum Structure and Human Thought”,
Behav. Br. Sci. 36, pp. 274-276.
v. D. Aerts, L. Gabora, S. Sozzo (2013), “How Concepts Combine: A Quantum Theoretic Modeling of
Human Thought”, ArXiv: 1206.1069, in print.
MAIN REFERENCES
10/09/2013 36Ubiquitous Quanta
Human Thought”, ArXiv: 1206.1069, in print.
vi. D. Aerts, S. Sozzo (2013), “Quantum Entanglement in Concept Combinations”, Int. J. Theor. Phys.,
15 pp., ArXiv: 1302.3831v1 [cs.Ai], accepted for publication.
vii. D. Aerts, J. Broekaert, S. Sozzo, T. Veloz, “The Quantum Challenge in Concept Theory and Natural
Language Processing”, Int. J. IIAS Sys. Res. Cyb. 13 (1), pp. 13-17.
