Disciplinary Matrices in Cybernetics and Systems Science

 

In the postscript to the 1970 edition of The Structure of Scientific Revolutions (University of Chicago Press) Thomas Kuhn proposed, without attempting to be exhaustive, that a scientific theory or a "disciplinary matrix" consists of symbolic generalizations, beliefs or models, values, and exemplars. Subsequent work at The George Washington University has indicated that two additional categories are useful: guiding questions and techniques. To clarify what these terms mean, below are a few examples from other fields and from cybernetics.

(1) "Symbolic generalizations" are sometimes found already in symbolic form: F=MA or I = V/R. Others are ordinarily express in words: Elements combine in constatn proportion by wieght. Action equals reaction. In cybernetics the equations for uncertainty and redundancy from shannon's information theory are examples of generalizations in symbolic form. Ashby's definitions of the law of requisite variety (The variety in a regulator must be equal to or greater than the variety in the system being regulated) and the principle of self-organization (Every isolated, determinate, dynamic system obeying unchanging laws will develop organisms that are adapted to their environments) are examples of generalizations expressed in words.

(2) "Beliefs or models" supply the group with preferred or permissible analogies and metaphors. For example, heat is the kinetic energy of the constituent parts of bodies; an electric circuit may be regarded as a steady state hydrodynamic system; and the molecules of a gas behave like tiny elastic billiard balls in random motion. In cybernetics one often hears that the brain can be thought of as a biological computer or that the human body is homeostatic mechanism.

(3) "Values" are particularly important when the members of a community must choose between incompatible ways of practicing their discipline. Probably the most deeply held values concern predictions. They should be accurate. Quantitative predictions are preferable to qualitative ones. There are also values to be used in judging whole theories. They must, first and foremost, permit puzzle formulation and solution, where possible they should be simple, self-consistent and plausible, compatible, that is, with other theories currently developed. Other sorts of values exist as well-for example, science should (or need not) be socially useful. Reservations expressed following the publication of Wiener's book Cybernetics led to the emphasis within the field on "The human use of human beings."

(4) "Exemplars" are the concrete problem solutions that students encounter from the start of their scientific education, whether in laboratories, on examinations, or at the ends of chapters in scientific texts. Exemplars show scientists how their job is to be done. In physics exemplars include the inclined plane, the conical pendulum, an the Keplerian orbits. In cybernetics, the thermostat is an exemplar for negative feedback. Von Foerster's gedanken experiment, The Magnetic Cubes in a Box, is an exemplar of new properties emerging as a result of self-organization. Ashby's Automatic self-Strategizer is an exemplar of a mechanism that learns even thought it blindly runs down to equilibrium.

(5) A "guiding question" is the principal concern or scientific interest that motivates the development of a theory. Warren McCulloch said that one question, formulated early in his career, had guided all his subsequent research, "What is a number that a man may know it and a man that he may know a number?" Ross Ashby asked, "What is the origin of adaptive behavior?" and, more specifically, "Can a mechanical chess player outplay its designer?" Heinz Von Foerster has been preoccupied with understanding the nature of an observer.

(6) "Techniques" are the methods an author uses to persuade the reader to his point of view. Techniques can be mathematical or verbal. They include statistical analysis, laboratory experiments with animals, large scale social experiments, tape-recorded interview, survey research, gedanken experiments, scenarios, anecdotes, historical examples, the recounting of internal subjective experience, criticism of previous writings, or philosophical speculation. In cybernetics two favored techniques have been mathematical proofs and computer simulation.