Quantum Cognition Notes

Quantum Cognition Notes

Life is complex, it has both real and imaginary parts. (Anonymous)

This page contains drafts of the notes upon which I based my Quantum Tutorials presented at Cognitive Science 2007, 2008, 2009.

"This material is based upon work supported by the National Science Foundation under Grant No. 0817965."

WHAT IS QUANTUM COGNITION, AND HOW CAN IT BE USED TO MODEL BEHAVIOR IN COGNITIVE SCIENCE?

Cognitive scientists face some of the same types of problems that forced physicists to abandon classical dynamics. Their measurements are often incompatible, and the first measurement may disturb a second measurement. Thus only partial information about a complex system can be obtained at any point in time. Combining partial information about a system into a coherent understanding of the entire system is the hallmark of quantum theory. Quantum theory provides a fundamentally different approach to logic, reasoning, and probabilistic inference. For example, quantum logic does not always follow the distributive axiom of Boolean logic; quantum probabilities do not always obey the Kolmogorov law of total probability; quantum reasoning does not always obey the principle of monotonic reasoning. For this tutorial, I will present the basic assumptions of classic versus quantum information processing theories. These basic assumptions will be examined, side by side, in a parallel and elementary manner. Classic theory will emerge as a possibly overly restrictive case of the more general quantum theory. The fundamental implications of these contrasting assumptions for modeling cognition will be examined.

Participants:

This tutorial will introduce participants to an entirely new area and no previous experience or background with quantum theory will be assumed. No background in Physics is required. In fact, except for two simple examples to motivate the introduction, little or no reference to Physics will be made during main part of the tutorial. What is required is an elementary background in classic logic (e.g., conjunction, disjunction), classic probability (e.g., AND/OR rules), and linear algebra (e.g. matrix multiplication). Furthermore, as much as possible within the time frame, the tutorial will attempt to review matrix algebra concepts (e.g., eigenvectors, projection matrices).

Introductory Chapters:

1. Quantum Probability

2. Quantum Dynamics

3. Quantum Computing

Quantum Probability Power Point

Quantum Dynamics Power Point

Papers:

Article on a Quantum Dynamic Model of Decision Making in Journal of Mathematical Psychology

Article on a Quantum Explanation for Irrational Decision Making in Proceedings of the Royal Society B

Article on Categorization and Decision Making in Journal of Mathematical Psychology

Article on Quantum Inference

Article on Quantum probability explanation for probability judgment errors