Survey of Mental Modeling


This is from a 1983 outline for a two semester course on Mental Modeling. It was designed to acquaint people with some analytic tools and models in order to improve their understanding of the psychologic of their experiences. After an overview of mathematical concepts and physical descriptions, the differences between classical and quantum (i.e. non-distributive/irreducible) concepts is discussed.

Examples are primarily from neuropsychological, cognitive, and psychopathological models of mind. Discussions includes possible policy implications of toward issues such as "insanity" as a legal defense, affirmative actions policies, brainwashing, ECT, interpersonal and intragroup relations, and cross-cultural understanding and international cooperation.

Contextual Quotes

"Erst die Theorie entscheidet daržber, was man beobachten kann." ("Only the theory decides what can be observed.") - Albert Einstein.

" ... it can scarcely be ... chance that it was not until the change had been made in the definition of the mental that it became possible to construct a comprehensive and coherent theory of mental life. ..." - Sigmund Freud.

"The general lesson of the role that mathematics has played through the ages in natural philosophy is the recognition that no relationship can be defined without a logical frame and that any apparent disharmony in the description of experiences can be eliminated only by an appropriate widening of the conceptual framework." - Niels Bohr.

Models and Modeling

Epistemological assumptions and agreements; empirical questions and observation sets; interpretive structures, formal structures and rules of correspondence.

Semantics, syntax, and validity as meaning, structure and truth.

Some Topics in Mathematical Methods

Derivatives, infinitesimal differences and slopes; integrals, sums and areas; Taylor's theorem, shift rules, and change (i.e. differences in time).

Coordinate systems, linear dependence and independence, bases, orthogonal function decompositions (e.g. Fourier series and transforms).

Matrices, Gibbs's vectors, linear transformations, and eigenvalues or spectra.

Transformation groups and representation; Lie algebras, generators and structure constants.

Symmetries, invariances, and conservations:

Scalars, vectors, and tensors.

Rotations and isotropy; angular momentum and torque.

Translations, and homogeneity; frequency, spatial frequency, energy, and force.

Symmetric relations, heterarchy and equivalence; antisymmetric relations, partial orderings, hierarchy and equality.

Classical Logics

Relations between sets and subsets - Venn diagrams, truth tables, classical computers, and George Boole's image of mind.

Assumptions of fixed sample spaces; inferences, classical causal structures and determinism in physical formalisms; "compatibility" and Friedrich Ludwig Gottlob Frege's unique partition of experience.

Classical Neural Models

On/Off black box models - McCulloch-Pitts neural nets, Turing automata, von Neumann automata, perceptrons, Boyd's mythology model.

Control models - feedback/forward, Ross Ashby's homeostat, TOTEs, La Violettes's cortical/paleocortical emotional cognitive cycle.

Distributed memory models - Little-Shaw Ising model of memory and hysteresis model of memory; Pribram, DeValois, etc. and Holographic Wave models.

Quantum Logic

Picture logic game - "lattice Hasse diagrams" for iconicly exhibiting structure and ordering relations among constructs; quantum logic and the relation between spaces and subspaces - von Neumann's thesis.

Constructing a logic of empirical questions (yes/no propositions); Stern-Gerlach experiment and non-distributivity; quantum logic as a more general representation, the classical limit; paradoxes as quantum logic.

Elements of quantum measurements - observation and interaction; transformations; irreversible amplification; psycho-physical parallelism (von Neumann) and psychophysical complementarity (Shepard).

Coding ambiguities with non-selecting measurements" - Elie Joseph Cartan's spinors as elementary quantum dichotomies and as building blocks for "internal representations;" Orlovian doubt states; aesthetics, art and humor.

Classical vs. quantum waves and rules for computing probability (Richard P. Feynman, Georg von Bekesy); synaptic summation vs. synaptic spanning; Orlov's wave logic of consciousness.

Quantum logic as a meta-logic (von Weizsacker/Heisenberg); MRI's second order change; George Kelly's personal constructs.

Looking at abstract vs. enumerative class formation, creativity, hypnosis, salesmanship, Buberian transcendence (I-Thou-We); representations of G-d.

Intrapsychic Processes

Freudian primary and secondary process of models of mind and brain - paralogical/paleological processes (von Domarus, Silvano Arieti, G. Klein); discharge vs. inhibition (Sigmund Freud, Karl H. Pribram & Merton Max Gill); repression and negation (Freud and Psychology Today article) and unconscious vs. conscious processes.

Models of schizophrenia: Von Domarus/Arieti/Boyd; double binds; Ignacio Matte Blanco's principle of symmetry; information processing deficits; biochemical; interactional/family; Thomas S. Szasz's "myth".

Non-verbal codings - body language, etc. (Rohrlich, Hall); depth poetry; Bernstein's sinusoid decomposition of motion; motion impletion (Shepard); nei chia and representations in Chinese martial arts, etc.

Toward New Hypotheses of Mind and Consciousness

My own work and attempts at piecing the above together; Class member alternatives; experimental possibilities; policy implications.

Complementary Readings

Methodologies of Interdisciplinary Modelings, David McGoveran, unpublished paper.

The Pleasure of Finding Things Out, Richard P. Feynman, BBC Horizon/PBS Nova

The Image, Kenneth E. Boulding

The Will to Be Human, Silvano Arieti

The Ascent of Man, Jacob Bronowski

Thirty Years That Shook Physics: The Story of Quantum Theory, George Gamow

Mathematics Today, editor Lynn Arthur Steen

The Nature of Scientific Thought, Marshall John Walker

The Structure of Scientific Revolutions, Thomas Kuhn

Introduction to Cybernetics, W. Ross Ashby

The Character of Physical Laws, Richard P. Feynman

The Responsibility of Scientists, Richard P. Feynman

Atomic Theory and the Description of Nature, Niels Bohr

Language and Reality in Modern Physics, Werner Karl Heisenberg