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Ternality Theory


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'Imparity' defined

Choosing which state of affairs to prefer or aim for is both logically and psychologically distinct from being able to discriminate one state of affairs from another. Ternality Theory is about that difference. Being able to discriminate whether or not a cup of coffee has sugar in it is different from whether or not you prefer to have sugar in your coffee, and it is a mistake to think of them as both being subsumed under the concept of information.

The logical distinction

Basically, information is measured as the ratio of the posterior to the prior probability of the occurrence of an event chosen from a repertoire. Within that conceptual framework, all the events in the repertoire are equal, in the respect that the process is one of purely describing which events are coming from the source, without any kind of intervention to affect or change their probabilities. This is so even if their prior probabilities are not equal.

The word 'imparity' means lack of equality. Without imparity, all the events in the repertoire are equally preferred or aimed for. Imparity will be added if some events in the repertoire are preferred, hoped for, chosen, or aimed for—as compared to others (Stewart,1989).

Figure button   'Imparity' defined

If an agent system is controlling, managing, governing, designing or adapting a patient system then, at any moment of time, some events in the communication between them must be preferred to others in some way. The process is no longer one of pure description; the events are evaluated according to some criterion, and the communication involves intervention by the agent system, with the aim of changing the probabilities of the events in the repertoire—or of some complex assemblies of those events.

The psychological distinction

Psychologically, we are all well aware that the ability to discriminate and the ability to prefer are distinct. For example, in a test of musical ability, if phrase A is played, followed by B and C, it is possible to judge which of the phrases B or C is the same as A. It is also separately possible to judge which of the phrases, B or C, is the better phrase, musically speaking. However, these two tasks do not ask for the same ability; most people find the second harder than the first, and some people cannot do the second at all.

Another example would be if we are given the task of choosing a new wallpaper for our walls. The repertoire is a swatch of possible patterns. We can probably discriminate the difference between these papers without difficulty, and probably would not find two patterns which look so similar to us that we have difficulty in telling them apart. In other words, we find the discrimination task easy. However, it is still quite possible that we would then find it very difficult to choose which of the papers we want put on the walls by the decorator.

Finding a formula

In all such examples, if it is possible to settle upon some descriptive aspects of the members of the repertoire which reliably affect the eventual choice, then it may be possible to cut down the number of items among which the purely evaluative choice has to be made. We could, for example, decide that the wallpaper will have to be blue, to match the carpet, and this would enable us to eliminate from consideration all the papers in the swatch which are not blue. Technically speaking, what we are saying is that the distinction between a discriminative task and an evaluative one often depends on whether some formula can be found to state the imparity as a function of a differentia.


It is well-known to cyberneticians that the ability to discriminate is quantitatively governed by a Law of Requisite Variety (Ashby,1956); but there is an analogous law which governs the second ability—to evaluate and chose—and also that our common experience in such situations is that the fatigue which eventually sets in is of two distinct kinds. After an afternoon of trying to decide between wallpapers, it becomes difficult to say which we prefer. The ability to choose is worn out for the day, even though we may still be perfectly capable of reliably distinguishing one pattern from another (Stewart,1989).

These two examples are chosen from cases where the imparity is aesthetic, but the same discontinuity between information and imparity exists with any dimension of evaluation, preference, or choice.

A dimensional scheme

It is obviously desirable for cybernetics to develop its own dimensional scheme within which the various kinds of evaluation can be placed. However, in the meantime, there exists a considerable body of work by philosophers and psychologists, which will serve the purpose. Perhaps the most useful contribution is the scheme suggested by Eduard Spranger (Spranger,1922), which has been used for psychological tests of values in people (Allport & Vernon,1931).

Figure button   Spranger's dimensions of value

This scheme uses the six dimensions of Theoretical, Economic, Aesthetic, Social, Political and Religious. While there is much to criticise in this well-worn scheme—for example it is often said that there ought to be an algedonic dimension—it is remarkably helpful in practical cybernetic analysis of dimensions of imparity, and will serve us well to be going on with. It can readily be shown that the discontinuity between information and imparity, which occurs in the case of aesthetic evaluations, also occurs in all the other dimensions of evaluation.



© Copyright D J Stewart 1987, 1998, 2003. All rights reserved.