1. Quantum Mind Symposium · Salzburg 1 Reinhard Blutner · Universiteit van Amsterdam · 19th July 2007 Combining Prototypes: Quantal Macrostates & Entanglement Reinhard Blutner Universiteit van Amsterdam blutner@uva.nl

2. Quantum Mind Symposium · Salzburg 2 Reinhard Blutner · Universiteit van Amsterdam · 19th July 2007 1 Introduction

3. Quantum Mind Symposium · Salzburg 3 Reinhard Blutner · Universiteit van Amsterdam · 19th July 2007 Reductionist vs. Systemic Approaches Reductionist approaches (Penrose, Hameroff, …) –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) –There are important structural analogies between descriptions of the micro-world (as investigated by QT) and descriptions of the cognitive realm

4. Quantum Mind Symposium · Salzburg 4 Reinhard Blutner · Universiteit van Amsterdam · 19th July 2007 Diederik Aerts & Liane Gabora „While 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-world.“ Harald Atmanspacher, Hans Primas, & Peter beim Graben „A 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 contexts.“ The systemic approach

5. Quantum Mind Symposium · Salzburg 5 Reinhard Blutner · Universiteit van Amsterdam · 19th July 2007 Arguments Complementary observables can arise in classical dynamic systems with incompatible partitions of the phase space (b. Graben & Atmanspacher) Uncertainty relations in the macroworld –between bandwidth and duration of electric signals –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. Quantum Mind Symposium · Salzburg 6 Reinhard Blutner · Universiteit van Amsterdam · 19th July 2007 Analogous Structures in Cognition/QT Vector space - Superposition (afterimages!) - Similarity measure Hilbert space - Vector addition - Inner product Concepts - Convex subspaces Observables - Projection operators Cognitive OperationsUnitary evolution Instantiation of concepts - Salience, centrality, typicality Measurement - Probability measure Conceptual combinations - Tensor product (Smolensky) Composite systems - Tensor product

7. Quantum Mind Symposium · Salzburg 7 Reinhard Blutner · Universiteit van Amsterdam · 19th July 2007 2 Combining Prototypes: The Problem

8. Quantum Mind Symposium · Salzburg 8 Reinhard Blutner · Universiteit van Amsterdam · 19th July 2007 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 apple stone lion

9. Quantum Mind Symposium · Salzburg 9 Reinhard Blutner · Universiteit van Amsterdam · 19th July 2007 Conjunction Effect of Typicality x=guppy is a poorish example of a fish, and a poorish example of a pet, but it's quite a good example of a pet fish –c x (A&B) > c x (B) In case of "incompatible conjunctions" such as pet fish or striped apple the conjunction effect is greater than in "compatible conjunctions“ (red apple). –c x (A‘ & B) – c x (B') > c x (A & B) – c x (B) (if A invites B but A' does not invite B')

10. Quantum Mind Symposium · Salzburg 10 Reinhard Blutner · Universiteit van Amsterdam · 19th July 2007 3 Combining Prototypes in QMT

11. Quantum Mind Symposium · Salzburg 11 Reinhard Blutner · Universiteit van Amsterdam · 19th July 2007 Compositional Semantics and Global Effects Fregean Formal Semantics is based on the Principal of Compositionality Global effects: The meaning of one part can influence the meaning of another part. Context as a global (hidden) parameter Frege (1884) took this as an argument against compositionality in Natural Language QMT can explain the global contextual effects without giving up compositionality because the different constituents can be entangled.

12. Quantum Mind Symposium · Salzburg 12 Reinhard Blutner · Universiteit van Amsterdam · 19th July 2007 Construction of simple concepts in QT Assume that independent instances are modelled by orthonormal base vectors | i   ℋ Concepts as superposition of instances: |a  =  i  A a i | i , with a i 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. Quantum Mind Symposium · Salzburg 13 Reinhard Blutner · Universiteit van Amsterdam · 19th July 2007 Typicality and conjoined concepts For conjoind concepts A  B perform the following steps:  Build the corresponding vectors |a  and |b   Construct the tensor product |a   |b   Perform the diagonalization operation in order to build an entangled state  (|a   |b  )  The typicality of instance i is the quantum probability that the entangled state collapses into (| i   | i 

14. Quantum Mind Symposium · Salzburg 14 Reinhard Blutner · Universiteit van Amsterdam · 19th July 2007 Tensorproduct of Two Vectors 10 objects Concept A: –Object 1  object 10 Concept B: –Object 10  object 1

15. Quantum Mind Symposium · Salzburg 15 Reinhard Blutner · Universiteit van Amsterdam · 19th July 2007 Diagonalization Unitary operation of diagonalization It leads to an entangled state |x diag   |a   |b 

16. Quantum Mind Symposium · Salzburg 16 Reinhard Blutner · Universiteit van Amsterdam · 19th July 2007 Conjunction effect striped apple striped apple

17. Quantum Mind Symposium · Salzburg 17 Reinhard Blutner · Universiteit van Amsterdam · 19th July 2007 Striped apple 2 Form Texture Apple striped

18. Quantum Mind Symposium · Salzburg 18 Reinhard Blutner · Universiteit van Amsterdam · 19th July 2007 Concept combination: a geometrical model (Peter Gärdenfors)

19. Quantum Mind Symposium · Salzburg 19 Reinhard Blutner · Universiteit van Amsterdam · 19th July 2007 Red Nose General Distribution Red Color Distribution Noses Conjoined Concept Red Nose

20. Quantum Mind Symposium · Salzburg 20 Reinhard Blutner · Universiteit van Amsterdam · 19th July 2007 Red and White Beans General Distribution Red Color Distribution Beans Color Distribution Red Beans

21. Quantum Mind Symposium · Salzburg 21 Reinhard Blutner · Universiteit van Amsterdam · 19th July 2007 Red and White Beans Color Distribution White Beans Color Distribution Beans General Distribution White

22. Quantum Mind Symposium · Salzburg 22 Reinhard Blutner · Universiteit van Amsterdam · 19th July 2007 4 Conclusions

23. Quantum Mind Symposium · Salzburg 23 Reinhard Blutner · Universiteit van Amsterdam · 19th July 2007 The emergence of quantal macrostates does not necessarily require the reference to corresponding quantal microstates A deeper understanding of the mind requires locally Boolean but globally non-Boolean descriptions with their naturally associated holistic correlations A series of real cognitive puzzles can be solved by using the QM approach –Combining simple concepts and prototype structure –Underdetermination and ambiguity –The binding problem –2 Qbits for C.G. Jung’s theory of personality

24. Quantum Mind Symposium · Salzburg 24 Reinhard Blutner · Universiteit van Amsterdam · 19th July 2007 References Diederik Aerts & 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 über den Begriff der Zahl. W. Koebner, Breslau. Peter beim Graben & Harald Atmanspacher. Complementarity in classical dynamical systems. Foundations of Physics 36, 291 – 306. Peter Gärdenfors (2000). Conceptual spaces: The geometry of thought. The MIT Press, Cambridge, Mass. Daniel N. Osherson & 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 & Matter 5, 7–44. Jennifer Spenader & Reinhard Blutner (2006). Compositionality and Systematicity. In G. Bouma, I.Krämer & J. Zwarts (eds.), Cognitive Foundations of Interpretation. KNAW Publications, Amsterdam.

25. Quantum Mind Symposium · Salzburg 25 Reinhard Blutner · Universiteit van Amsterdam · 19th July 2007 Appendix Two Qbits for C.G. Jung's psychological types (joint work with E. Hochnadel)

26. Quantum Mind Symposium · Salzburg 26 Reinhard Blutner · Universiteit van Amsterdam · 19th July 2007 16 Types NTST NF Introverted Extraverted SF 3 4 6 5 3 4 6 5 2 1 7 8 2 1 7 8 i t u i t i on ensingensing eeling hinking

27. Quantum Mind Symposium · Salzburg 27 Reinhard Blutner · Universiteit van Amsterdam · 19th July 2007 A Two Q-bit Theory of Personality A R First Q-bit: the four psychological functions Second Q-bit: the two attitudes The two Q-bits are orthogonal (independent)

28. Quantum Mind Symposium · Salzburg 28 Reinhard Blutner · Universiteit van Amsterdam · 19th July 2007

29. Quantum Mind Symposium · Salzburg 29 Reinhard Blutner · Universiteit van Amsterdam · 19th July 2007 Red Flag Flagness Redness Flag Red