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10/09/2013 1Ubiquitous Quanta

Lecce, Italy, September 10, 2013

QUANTUM SOCIAL SCIENCE

“Ubiquitous Quanta”. Introduction

QUESTIONSAPPLICATIONS

HISTORY

SANDRO SOZZO

CENTER LEO APOSTEL FOR INTERDISCIPLINARY

STUDIES (CLEA)

FREE UNIVERSITY OF BRUXELLES (VUB)

www.vub.ac.be/clea/vub/people/sozzo

QUESTIONSAPPLICATIONS

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.


macroscopic physics (superfluidity, supercondictivity), up to cosmology.

Quantum teleportation.

Quantum information.

Applications.

Quantum cryptography.

Quantum computation.

QUANTUM THEORY: MYSTERIES

“... I think I can safely say that nobody understands quantum mechanics.”

Richard P. Feynman

Nonobjectivity.Superposition principle, linearity , interference.


Black Lines, December 1913, Vasily

Kandinsky.

Wave-particle duality.

Uncertainty principle.

Entanglement.

Quantum probability.


“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.

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.


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.

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.


Computer science. Finance.

SOME HIGHLIGHTS

First ideas.

Books.


Quantum Interaction workshops. Stanford (2007), Oxford (2008), Saarbrücken (2009), Washington

(2010), Aberdeen (2011), Paris (2012), Leicester (2013), Filzbach (2014).

Media.

Impact factor 2011: 25.056.


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.

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.


(?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.

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

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


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.

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).


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’.

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


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

78

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


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.

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.


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

Guppye

FishGuppyFish

Guppye

PetGuppyPet

PetFish

FishPet

)ˆ,,(),ˆ,,(

)ˆ,1,(),ˆ,1,(

ˆˆ

ˆˆ

1

1

µµ

µµ

→→

→→

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


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.

THE CONJUNCTION OF TWO CONCEPTS

Hampton’s data on concept conjunction (1988a) cannot be modeled within a classical probability theory.


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.

A QUANTUM MODEL FOR THE CONJUNCTION

Let us now illustrate how we model Hampton's (1988a) membership test by using the quantum formalism.


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.


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).

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.


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


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.

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


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)

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.


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.

QUANTUM MODELING OF THE DISJUNCTION

(as for conjunction)


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.

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


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).

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.


THE CHSH INEQUALITY


RESULTS OF THE COGNITIVE TEST

We performed an

experiment with

81 test subjects.

Results.


(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 <

A QUANTUM REPRESENTATION FOR THE

ANIMAL ACTS. OPERATIONAL PART


A QUANTUM REPRESENTATION FOR

THE ANIMAL ACTS. TECHNICAL PART


Entangled state


Entangled measurement

ANALYSIS OF THE RESULTS


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


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.

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 ofInsights.

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.

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


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.

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