Quantum Mind Symposium Salzburg Combining Prototypes Quantal Macrostates

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

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

Quantum Mind Symposium · Salzburg 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 3 Reinhard Blutner · Universiteit van Amsterdam · 19 th July 2007

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

Quantum Mind Symposium · Salzburg 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 5 Reinhard Blutner · Universiteit van Amsterdam · 19 th July 2007

Quantum Mind Symposium · Salzburg Analogous Structures in Cognition/QT 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 6 Reinhard Blutner · Universiteit van Amsterdam · 19 th July 2007

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

Quantum Mind Symposium · Salzburg 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 8 Reinhard Blutner · Universiteit van Amsterdam · 19 th July 2007

Quantum Mind Symposium · Salzburg 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') 9 Reinhard Blutner · Universiteit van Amsterdam · 19 th July 2007

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

Quantum Mind Symposium · Salzburg 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. 11 Reinhard Blutner · Universiteit van Amsterdam · 19 th July 2007

Quantum Mind Symposium · Salzburg 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 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) 12 Reinhard Blutner · Universiteit van Amsterdam · 19 th July 2007

Quantum Mind Symposium · Salzburg Typicality and conjoined concepts For 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 13 Reinhard Blutner · Universiteit van Amsterdam · 19 th July 2007

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

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

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

Quantum Mind Symposium · Salzburg Striped apple 2 str d e ip Apple Form Texture 17 Reinhard Blutner · Universiteit van Amsterdam · 19 th July 2007

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

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

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

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

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

Quantum Mind Symposium · Salzburg 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 23 Reinhard Blutner · Universiteit van Amsterdam · 19 th July 2007

Quantum Mind Symposium · Salzburg 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. 24 Reinhard Blutner · Universiteit van Amsterdam · 19 th July 2007

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

Quantum Mind Symposium · Salzburg 16 Types 4 3 NT Introverted Extraverted ST 4 3 5 6 hinking 1 2 NF 2 7 8 SF 1 7 8 i t u i t i on e n s i eeling n g 26 Reinhard Blutner · Universiteit van Amsterdam · 19 th July 2007

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