quantum mind symposium · salzburg 1 reinhard blutner · universiteit van amsterdam · 19th july...

1

Quantum Mind Symposium Salzburg

Reinhard Blutner Universiteit van Amsterdam 19th July 2007

Combining Prototypes

Quantal Macrostatesamp Entanglement

Reinhard BlutnerUniversiteit van Amsterdam

blutneruvanl

2



1 Introduction

3



Reductionist vs Systemic Approaches

Reductionist approaches (Penrose Hameroff hellip) ndash Consciousness is not a consequence of interactions

between neurons in the brain but arises as from microtubules within cells which are much smaller and for which quantum effects could be significant

Systemic approach (present position)ndash There are important structural analogies between

descriptions of the micro-world (as investigated by QT) and descriptions of the cognitive realm

4



Diederik Aerts amp Liane GaborabdquoWhile some of the properties of quantum mechanics are essentially linked to the nature of the microworld others are connected to fundamental structures of the world at large and could therefore in principle also appear in other domains than the micro-worldldquo

Harald Atmanspacher Hans Primas amp Peter beim GrabenbdquoA generalized version of the formal scheme of ordinary quantum theory in which particular features of ordinary quantum theory are not contained should be used in some non-physical contextsldquo

The systemic approach

5



Arguments

Complementary observables can arise in classical dynamic systems with incompatible partitions of the phase space (b Graben amp Atmanspacher)Uncertainty relations in the macroworldndash between bandwidth and duration of electric signalsndash between the Liouville operator and the information

operator in descriptions of a chaotic flow

Thesis The emergence of quantal macrostates does not necessarily require the reference to corresponding quantal microstates

6



Analogous Structures in CognitionQT

Vector space- Superposition (afterimages)- Similarity measure

Hilbert space- Vector addition- Inner product

Concepts- Convex subspaces

Observables- Projection operators

Cognitive Operations Unitary evolution

Instantiation of concepts- Salience centrality typicality

Measurement- Probability measure

Conceptual combinations- Tensor product (Smolensky)

Composite systems- Tensor product

7



2 Combining Prototypes

The Problem

8



Effect of contrast classes

A collie is a dog but a tall collie is not a tall dog

Red nose red flag red beans

Striped applestone lion

9



Conjunction Effect of Typicality

x=guppy is a poorish example of a fish and a poorish example of a pet but its quite a good example of a pet fish ndash cx(AampB) gt cx(B)

In case of incompatible conjunctions such as pet fish or striped apple the conjunction effect is greater than in compatible conjunctionsldquo (red apple) ndash cx(Alsquo amp B) ndash cx(B) gt cx(A amp B) ndash cx(B)

(if A invites B but A does not invite B)

10




in QMT

11



Compositional Semantics and Global Effects

Fregean Formal Semantics is based on the Principal of CompositionalityGlobal effects The meaning of one part can influence the meaning of another part Context as a global (hidden) parameterFrege (1884) took this as an argument against compositionality in Natural LanguageQMT can explain the global contextual effects without giving up compositionality because the different constituents can be entangled

12



Construction of simple concepts in QT

Assume that independent instances are modelled by orthonormal base vectors | i ℋ

Concepts as superposition of instances|a = iA ai | i with ai

2 = P( i | A)

Fact The quantum probability that a concept vector |a collapses into an instance vector | i is then the classical probability P(i | A)

13



Typicality and conjoined conceptsFor conjoind concepts A B perform the following steps

1 Build the corresponding vectors |a and |b

2 Construct the tensor product |a |b

3 Perform the diagonalization operation in order to build an entangled state (|a |b)

4 The typicality of instance i is the quantum probability that the entangled state collapses into (| i | i

vu

ijvu

ij jixjijix

)()(

14



Tensorproduct of Two Vectors

10 objectsConcept Andash Object 1object 10

Concept Bndash Object 10object 1

15



Diagonalization

Unitary operation of diagonalization

It leads to an entangled state |xdiag |a |b

vu

ijvu

ij jixjijix

)()(

16



Conjunction effect

2 4 6 8 10 12 14Instances

005

01

015

02

025

Typicality

striped apple

striped apple

17



Striped apple 2

Form

Texture

Apple

striped

18



Concept combination a geometrical model(Peter Gaumlrdenfors)

19



Red Nose

General Distribution

Red

Color Distribution

NosesConjoined Concept

Red Nose

20



Red and White Beans


Red

Color Distribution

Beans

Color Distribution

Red Beans

21



Red and White Beans

Color Distribution

White Beans

Color Distribution

Beans


White

22



4 Conclusions

23



The emergence of quantal macrostates does not necessarily require the reference to corresponding quantal microstatesA deeper understanding of the mind requires locally Boolean but globally non-Boolean descriptions with their naturally associated holistic correlationsA series of real cognitive puzzles can be solved by using the QM approachndash Combining simple concepts and prototype

structurendash Underdetermination and ambiguityndash The binding problemndash 2 Qbits for CG Jungrsquos theory of personality

24



ReferencesDiederik Aerts amp Liane Gabora (2005) A state-context-property

model of concepts and their combinations Kybernetes 34 151-205

Gottlob Frege (1884) Grundlagen der Arithmetik Eine logisch-mathematische Untersuchung uumlber den Begriff der Zahl W Koebner Breslau

Peter beim Graben amp Harald Atmanspacher Complementarity in classical dynamical systems Foundations of Physics 36 291 ndash 306

Peter Gaumlrdenfors (2000) Conceptual spaces The geometry of thought The MIT Press Cambridge Mass

Daniel N Osherson amp Edward E Smith (1981) On the adequacy of prototype theory as a theory of concepts Cognition 9 35-58

Hans Primas (2007) Non-Boolean descriptions for mind-matter problems Mind amp Matter 5 7ndash44

Jennifer Spenader amp Reinhard Blutner (2006) Compositionality and Systematicity In G Bouma IKraumlmer amp J Zwarts (eds) Cognitive Foundations of Interpretation KNAW Publications Amsterdam

25



Appendix

Two Qbits for CG Jungs psychological types

(joint work with E Hochnadel)

26



16 Types

NT ST

NF

Introverted

Extraverted

SF

3 4 6 5

3 4 6 5

2 1 7 8

2 1 7 8

i

tuiti

on

ensingeeling

hinking

27



A Two Q-bit Theory of Personality

A

R

First Q-bit the fourpsychological functions

Second Q-bit the two attitudes

The two Q-bits are orthogonal (independent)

28



29



Red Flag

Flagness

Redness

FlagRed

2



1 Introduction

3








4






5



Arguments




6













7




The Problem

8







9







10




in QMT

11





12






2 = P( i | A)


13








vu

ijvu

ij jixjijix

)()(

14






15



Diagonalization



vu

ijvu

ij jixjijix

)()(

16



Conjunction effect

2 4 6 8 10 12 14Instances

005

01

015

02

025

Typicality

striped apple

striped apple

17



Striped apple 2

Form

Texture

Apple

striped

18




19



Red Nose


Red

Color Distribution


Red Nose

20



Red and White Beans


Red

Color Distribution

Beans

Color Distribution

Red Beans

21



Red and White Beans

Color Distribution

White Beans

Color Distribution

Beans


White

22



4 Conclusions

23





24











25



Appendix



26



16 Types

NT ST

NF

Introverted

Extraverted

SF

3 4 6 5

3 4 6 5

2 1 7 8

2 1 7 8

i

tuiti

on

ensingeeling

hinking

27




A

R




28



29



Red Flag

Flagness

Redness

FlagRed

3








4






5



Arguments




6













7




The Problem

8







9







10




in QMT

11





12






2 = P( i | A)


13








vu

ijvu

ij jixjijix

)()(

14






15



Diagonalization



vu

ijvu

ij jixjijix

)()(

16



Conjunction effect

2 4 6 8 10 12 14Instances

005

01

015

02

025

Typicality

striped apple

striped apple

17



Striped apple 2

Form

Texture

Apple

striped

18




19



Red Nose


Red

Color Distribution


Red Nose

20



Red and White Beans


Red

Color Distribution

Beans

Color Distribution

Red Beans

21



Red and White Beans

Color Distribution

White Beans

Color Distribution

Beans


White

22



4 Conclusions

23





24











25



Appendix



26



16 Types

NT ST

NF

Introverted

Extraverted

SF

3 4 6 5

3 4 6 5

2 1 7 8

2 1 7 8

i

tuiti

on

ensingeeling

hinking

27




A

R




28



29



Red Flag

Flagness

Redness

FlagRed

4






5



Arguments




6













7




The Problem

8







9







10




in QMT

11





12






2 = P( i | A)


13








vu

ijvu

ij jixjijix

)()(

14






15



Diagonalization



vu

ijvu

ij jixjijix

)()(

16



Conjunction effect

2 4 6 8 10 12 14Instances

005

01

015

02

025

Typicality

striped apple

striped apple

17



Striped apple 2

Form

Texture

Apple

striped

18




19



Red Nose


Red

Color Distribution


Red Nose

20



Red and White Beans


Red

Color Distribution

Beans

Color Distribution

Red Beans

21



Red and White Beans

Color Distribution

White Beans

Color Distribution

Beans


White

22



4 Conclusions

23





24











25



Appendix



26



16 Types

NT ST

NF

Introverted

Extraverted

SF

3 4 6 5

3 4 6 5

2 1 7 8

2 1 7 8

i

tuiti

on

ensingeeling

hinking

27




A

R




28



29



Red Flag

Flagness

Redness

FlagRed

5



Arguments




6













7




The Problem

8







9







10




in QMT

11





12






2 = P( i | A)


13








vu

ijvu

ij jixjijix

)()(

14






15



Diagonalization



vu

ijvu

ij jixjijix

)()(

16



Conjunction effect

2 4 6 8 10 12 14Instances

005

01

015

02

025

Typicality

striped apple

striped apple

17



Striped apple 2

Form

Texture

Apple

striped

18




19



Red Nose


Red

Color Distribution


Red Nose

20



Red and White Beans


Red

Color Distribution

Beans

Color Distribution

Red Beans

21



Red and White Beans

Color Distribution

White Beans

Color Distribution

Beans


White

22



4 Conclusions

23





24











25



Appendix



26



16 Types

NT ST

NF

Introverted

Extraverted

SF

3 4 6 5

3 4 6 5

2 1 7 8

2 1 7 8

i

tuiti

on

ensingeeling

hinking

27




A

R




28



29



Red Flag

Flagness

Redness

FlagRed

6













7




The Problem

8







9







10




in QMT

11





12






2 = P( i | A)


13








vu

ijvu

ij jixjijix

)()(

14






15



Diagonalization



vu

ijvu

ij jixjijix

)()(

16



Conjunction effect

2 4 6 8 10 12 14Instances

005

01

015

02

025

Typicality

striped apple

striped apple

17



Striped apple 2

Form

Texture

Apple

striped

18




19



Red Nose


Red

Color Distribution


Red Nose

20



Red and White Beans


Red

Color Distribution

Beans

Color Distribution

Red Beans

21



Red and White Beans

Color Distribution

White Beans

Color Distribution

Beans


White

22



4 Conclusions

23





24











25



Appendix



26



16 Types

NT ST

NF

Introverted

Extraverted

SF

3 4 6 5

3 4 6 5

2 1 7 8

2 1 7 8

i

tuiti

on

ensingeeling

hinking

27




A

R




28



29



Red Flag

Flagness

Redness

FlagRed

7




The Problem

8







9







10




in QMT

11





12






2 = P( i | A)


13








vu

ijvu

ij jixjijix

)()(

14






15



Diagonalization



vu

ijvu

ij jixjijix

)()(

16



Conjunction effect

2 4 6 8 10 12 14Instances

005

01

015

02

025

Typicality

striped apple

striped apple

17



Striped apple 2

Form

Texture

Apple

striped

18




19



Red Nose


Red

Color Distribution


Red Nose

20



Red and White Beans


Red

Color Distribution

Beans

Color Distribution

Red Beans

21



Red and White Beans

Color Distribution

White Beans

Color Distribution

Beans


White

22



4 Conclusions

23





24











25



Appendix



26



16 Types

NT ST

NF

Introverted

Extraverted

SF

3 4 6 5

3 4 6 5

2 1 7 8

2 1 7 8

i

tuiti

on

ensingeeling

hinking

27




A

R




28



29



Red Flag

Flagness

Redness

FlagRed

8







9







10




in QMT

11





12






2 = P( i | A)


13








vu

ijvu

ij jixjijix

)()(

14






15



Diagonalization



vu

ijvu

ij jixjijix

)()(

16



Conjunction effect

2 4 6 8 10 12 14Instances

005

01

015

02

025

Typicality

striped apple

striped apple

17



Striped apple 2

Form

Texture

Apple

striped

18




19



Red Nose


Red

Color Distribution


Red Nose

20



Red and White Beans


Red

Color Distribution

Beans

Color Distribution

Red Beans

21



Red and White Beans

Color Distribution

White Beans

Color Distribution

Beans


White

22



4 Conclusions

23





24











25



Appendix



26



16 Types

NT ST

NF

Introverted

Extraverted

SF

3 4 6 5

3 4 6 5

2 1 7 8

2 1 7 8

i

tuiti

on

ensingeeling

hinking

27




A

R




28



29



Red Flag

Flagness

Redness

FlagRed

9







10




in QMT

11





12






2 = P( i | A)


13








vu

ijvu

ij jixjijix

)()(

14






15



Diagonalization



vu

ijvu

ij jixjijix

)()(

16



Conjunction effect

2 4 6 8 10 12 14Instances

005

01

015

02

025

Typicality

striped apple

striped apple

17



Striped apple 2

Form

Texture

Apple

striped

18




19



Red Nose


Red

Color Distribution


Red Nose

20



Red and White Beans


Red

Color Distribution

Beans

Color Distribution

Red Beans

21



Red and White Beans

Color Distribution

White Beans

Color Distribution

Beans


White

22



4 Conclusions

23





24











25



Appendix



26



16 Types

NT ST

NF

Introverted

Extraverted

SF

3 4 6 5

3 4 6 5

2 1 7 8

2 1 7 8

i

tuiti

on

ensingeeling

hinking

27




A

R




28



29



Red Flag

Flagness

Redness

FlagRed

10




in QMT

11





12






2 = P( i | A)


13








vu

ijvu

ij jixjijix

)()(

14






15



Diagonalization



vu

ijvu

ij jixjijix

)()(

16



Conjunction effect

2 4 6 8 10 12 14Instances

005

01

015

02

025

Typicality

striped apple

striped apple

17



Striped apple 2

Form

Texture

Apple

striped

18




19



Red Nose


Red

Color Distribution


Red Nose

20



Red and White Beans


Red

Color Distribution

Beans

Color Distribution

Red Beans

21



Red and White Beans

Color Distribution

White Beans

Color Distribution

Beans


White

22



4 Conclusions

23





24











25



Appendix



26



16 Types

NT ST

NF

Introverted

Extraverted

SF

3 4 6 5

3 4 6 5

2 1 7 8

2 1 7 8

i

tuiti

on

ensingeeling

hinking

27




A

R




28



29



Red Flag

Flagness

Redness

FlagRed

11





12






2 = P( i | A)


13








vu

ijvu

ij jixjijix

)()(

14






15



Diagonalization



vu

ijvu

ij jixjijix

)()(

16



Conjunction effect

2 4 6 8 10 12 14Instances

005

01

015

02

025

Typicality

striped apple

striped apple

17



Striped apple 2

Form

Texture

Apple

striped

18




19



Red Nose


Red

Color Distribution


Red Nose

20



Red and White Beans


Red

Color Distribution

Beans

Color Distribution

Red Beans

21



Red and White Beans

Color Distribution

White Beans

Color Distribution

Beans


White

22



4 Conclusions

23





24











25



Appendix



26



16 Types

NT ST

NF

Introverted

Extraverted

SF

3 4 6 5

3 4 6 5

2 1 7 8

2 1 7 8

i

tuiti

on

ensingeeling

hinking

27




A

R




28



29



Red Flag

Flagness

Redness

FlagRed

12






2 = P( i | A)


13








vu

ijvu

ij jixjijix

)()(

14






15



Diagonalization



vu

ijvu

ij jixjijix

)()(

16



Conjunction effect

2 4 6 8 10 12 14Instances

005

01

015

02

025

Typicality

striped apple

striped apple

17



Striped apple 2

Form

Texture

Apple

striped

18




19



Red Nose


Red

Color Distribution


Red Nose

20



Red and White Beans


Red

Color Distribution

Beans

Color Distribution

Red Beans

21



Red and White Beans

Color Distribution

White Beans

Color Distribution

Beans


White

22



4 Conclusions

23





24











25



Appendix



26



16 Types

NT ST

NF

Introverted

Extraverted

SF

3 4 6 5

3 4 6 5

2 1 7 8

2 1 7 8

i

tuiti

on

ensingeeling

hinking

27




A

R




28



29



Red Flag

Flagness

Redness

FlagRed

13








vu

ijvu

ij jixjijix

)()(

14






15



Diagonalization



vu

ijvu

ij jixjijix

)()(

16



Conjunction effect

2 4 6 8 10 12 14Instances

005

01

015

02

025

Typicality

striped apple

striped apple

17



Striped apple 2

Form

Texture

Apple

striped

18




19



Red Nose


Red

Color Distribution


Red Nose

20



Red and White Beans


Red

Color Distribution

Beans

Color Distribution

Red Beans

21



Red and White Beans

Color Distribution

White Beans

Color Distribution

Beans


White

22



4 Conclusions

23





24











25



Appendix



26



16 Types

NT ST

NF

Introverted

Extraverted

SF

3 4 6 5

3 4 6 5

2 1 7 8

2 1 7 8

i

tuiti

on

ensingeeling

hinking

27




A

R




28



29



Red Flag

Flagness

Redness

FlagRed

14






15



Diagonalization



vu

ijvu

ij jixjijix

)()(

16



Conjunction effect

2 4 6 8 10 12 14Instances

005

01

015

02

025

Typicality

striped apple

striped apple

17



Striped apple 2

Form

Texture

Apple

striped

18




19



Red Nose


Red

Color Distribution


Red Nose

20



Red and White Beans


Red

Color Distribution

Beans

Color Distribution

Red Beans

21



Red and White Beans

Color Distribution

White Beans

Color Distribution

Beans


White

22



4 Conclusions

23





24











25



Appendix



26



16 Types

NT ST

NF

Introverted

Extraverted

SF

3 4 6 5

3 4 6 5

2 1 7 8

2 1 7 8

i

tuiti

on

ensingeeling

hinking

27




A

R




28



29



Red Flag

Flagness

Redness

FlagRed

15



Diagonalization



vu

ijvu

ij jixjijix

)()(

16



Conjunction effect

2 4 6 8 10 12 14Instances

005

01

015

02

025

Typicality

striped apple

striped apple

17



Striped apple 2

Form

Texture

Apple

striped

18




19



Red Nose


Red

Color Distribution


Red Nose

20



Red and White Beans


Red

Color Distribution

Beans

Color Distribution

Red Beans

21



Red and White Beans

Color Distribution

White Beans

Color Distribution

Beans


White

22



4 Conclusions

23





24











25



Appendix



26



16 Types

NT ST

NF

Introverted

Extraverted

SF

3 4 6 5

3 4 6 5

2 1 7 8

2 1 7 8

i

tuiti

on

ensingeeling

hinking

27




A

R




28



29



Red Flag

Flagness

Redness

FlagRed

16



Conjunction effect

2 4 6 8 10 12 14Instances

005

01

015

02

025

Typicality

striped apple

striped apple

17



Striped apple 2

Form

Texture

Apple

striped

18




19



Red Nose


Red

Color Distribution


Red Nose

20



Red and White Beans


Red

Color Distribution

Beans

Color Distribution

Red Beans

21



Red and White Beans

Color Distribution

White Beans

Color Distribution

Beans


White

22



4 Conclusions

23





24











25



Appendix



26



16 Types

NT ST

NF

Introverted

Extraverted

SF

3 4 6 5

3 4 6 5

2 1 7 8

2 1 7 8

i

tuiti

on

ensingeeling

hinking

27




A

R




28



29



Red Flag

Flagness

Redness

FlagRed

17



Striped apple 2

Form

Texture

Apple

striped

18




19



Red Nose


Red

Color Distribution


Red Nose

20



Red and White Beans


Red

Color Distribution

Beans

Color Distribution

Red Beans

21



Red and White Beans

Color Distribution

White Beans

Color Distribution

Beans


White

22



4 Conclusions

23





24











25



Appendix



26



16 Types

NT ST

NF

Introverted

Extraverted

SF

3 4 6 5

3 4 6 5

2 1 7 8

2 1 7 8

i

tuiti

on

ensingeeling

hinking

27




A

R




28



29



Red Flag

Flagness

Redness

FlagRed

18




19



Red Nose


Red

Color Distribution


Red Nose

20



Red and White Beans


Red

Color Distribution

Beans

Color Distribution

Red Beans

21



Red and White Beans

Color Distribution

White Beans

Color Distribution

Beans


White

22



4 Conclusions

23





24











25



Appendix



26



16 Types

NT ST

NF

Introverted

Extraverted

SF

3 4 6 5

3 4 6 5

2 1 7 8

2 1 7 8

i

tuiti

on

ensingeeling

hinking

27




A

R




28



29



Red Flag

Flagness

Redness

FlagRed

19



Red Nose


Red

Color Distribution


Red Nose

20



Red and White Beans


Red

Color Distribution

Beans

Color Distribution

Red Beans

21



Red and White Beans

Color Distribution

White Beans

Color Distribution

Beans


White

22



4 Conclusions

23





24











25



Appendix



26



16 Types

NT ST

NF

Introverted

Extraverted

SF

3 4 6 5

3 4 6 5

2 1 7 8

2 1 7 8

i

tuiti

on

ensingeeling

hinking

27




A

R




28



29



Red Flag

Flagness

Redness

FlagRed

20



Red and White Beans


Red

Color Distribution

Beans

Color Distribution

Red Beans

21



Red and White Beans

Color Distribution

White Beans

Color Distribution

Beans


White

22



4 Conclusions

23





24











25



Appendix



26



16 Types

NT ST

NF

Introverted

Extraverted

SF

3 4 6 5

3 4 6 5

2 1 7 8

2 1 7 8

i

tuiti

on

ensingeeling

hinking

27




A

R




28



29



Red Flag

Flagness

Redness

FlagRed

21



Red and White Beans

Color Distribution

White Beans

Color Distribution

Beans


White

22



4 Conclusions

23





24











25



Appendix



26



16 Types

NT ST

NF

Introverted

Extraverted

SF

3 4 6 5

3 4 6 5

2 1 7 8

2 1 7 8

i

tuiti

on

ensingeeling

hinking

27




A

R




28



29



Red Flag

Flagness

Redness

FlagRed

22



4 Conclusions

23





24











25



Appendix



26



16 Types

NT ST

NF

Introverted

Extraverted

SF

3 4 6 5

3 4 6 5

2 1 7 8

2 1 7 8

i

tuiti

on

ensingeeling

hinking

27




A

R




28



29



Red Flag

Flagness

Redness

FlagRed

23





24











25



Appendix



26



16 Types

NT ST

NF

Introverted

Extraverted

SF

3 4 6 5

3 4 6 5

2 1 7 8

2 1 7 8

i

tuiti

on

ensingeeling

hinking

27




A

R




28



29



Red Flag

Flagness

Redness

FlagRed

24











25



Appendix



26



16 Types

NT ST

NF

Introverted

Extraverted

SF

3 4 6 5

3 4 6 5

2 1 7 8

2 1 7 8

i

tuiti

on

ensingeeling

hinking

27




A

R




28



29



Red Flag

Flagness

Redness

FlagRed

25



Appendix



26



16 Types

NT ST

NF

Introverted

Extraverted

SF

3 4 6 5

3 4 6 5

2 1 7 8

2 1 7 8

i

tuiti

on

ensingeeling

hinking

27




A

R




28



29



Red Flag

Flagness

Redness

FlagRed

26



16 Types

NT ST

NF

Introverted

Extraverted

SF

3 4 6 5

3 4 6 5

2 1 7 8

2 1 7 8

i

tuiti

on

ensingeeling

hinking

27




A

R




28



29



Red Flag

Flagness

Redness

FlagRed

27




A

R




28



29



Red Flag

Flagness

Redness

FlagRed

28



29



Red Flag

Flagness

Redness

FlagRed

29



Red Flag

Flagness

Redness

FlagRed

quantum mind symposium · salzburg 1 reinhard blutner · universiteit van amsterdam · 19th july...

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