Combining Prototypes: Quantal Macrostates & Entanglement

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

2. 1Introduction Reinhard Blutner · Universiteit van Amsterdam · 19th July 2007

3. 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 Reinhard Blutner · Universiteit van Amsterdam · 19th July 2007

4. The systemic approach • 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.“ Reinhard Blutner · Universiteit van Amsterdam · 19th July 2007

5. Arguments Thesis: The emergence of quantal macrostates does not necessarily require the reference to corresponding quantal microstates. • 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 Reinhard Blutner · Universiteit van Amsterdam · 19th July 2007

6. Analogous Structures in Cognition/QT Reinhard Blutner · Universiteit van Amsterdam · 19th July 2007

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

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 apple stone lion Reinhard Blutner · Universiteit van Amsterdam · 19th July 2007

9. 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 • cx(A&B) > cx(B) • In case of "incompatible conjunctions" such as pet fish or striped apple the conjunction effect is greater than in "compatible conjunctions“ (red apple). • cx(A‘ & B) – cx(B') > cx(A & B) – cx(B) (if A invites B but A' does not invite B') Reinhard Blutner · Universiteit van Amsterdam · 19th July 2007

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

11. 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. Reinhard Blutner · Universiteit van Amsterdam · 19th July 2007

12. Construction of simple concepts in QT • Assume that independent instances are modelled byorthonormal base vectors | i   ℋ • Concepts as superposition of instances: |a = iAai| i , with ai2 = 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) Reinhard Blutner · Universiteit van Amsterdam · 19th July 2007

13. 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  Reinhard Blutner · Universiteit van Amsterdam · 19th July 2007

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

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

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

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

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

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

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

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

22. 4Conclusions Reinhard Blutner · Universiteit van Amsterdam · 19th July 2007

23. 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 Reinhard Blutner · Universiteit van Amsterdam · 19th July 2007

24. 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. Reinhard Blutner · Universiteit van Amsterdam · 19th July 2007

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

26. Introverted Extraverted 16 Types 4 3 5 6 NT ST 4 3 5 6 hinking 1 2 8 7 i tuition NF SF ensing 1 2 8 7 eeling Reinhard Blutner · Universiteit van Amsterdam · 19th July 2007

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

28. Reinhard Blutner · Universiteit van Amsterdam · 19th July 2007

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