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  Though there is a vast psychological literature on intelligence, it contains surprisingly few
insights into the foundational questions which interest us here: what is intelligence, and how can it, practically or theoretically, be quantified? The problem is that, as Robert Sternberg has observed, theories of intelligence are not all theories of the same thing. Rather, they tend to be theories of different aspects of intelligence. To make matters worse, the theorists who propose these theories rarely make it clear just what aspects of intelligence their theories embrace (1987, p.141).

   The psychology of intelligence has dwelled on the context-specific and the easily measurable.
But transcending the bounds of particular contexts is what intelligence is all about; and there is no reason to expect this ability to be easy to gauge.

    The confusion may be traced back to the turn of the century. First, Galton (1883) analyzed
intelligence as a combination of various psychophysical abilities, everything from strength of
grip to reaction time. And then, not too much later, Binet and Simon (1916) proposed that
intelligence is a matter of problem solving, logical reasoning and spatial judgement. Binet’s
approach was of more immediate practical use — it led to the I.Q. test, which is fairly good at
predicting certain aspects of behavior; e.g. at predicting which children are capable of benefiting from schooling. But aspects of Galton’s theory have recently been revived (Carroll, 1976; Jensen, 1982). It is now clear that mental speed is closely connected with intelligence; and some modern psychologists (Hunt, 1978; Jensen, 1979) have advocated studying intelligence in terms of quantities such as speed of lexical access. Now it is recognized that the ideas of Galton and Binet, though at first glance contradictory, are on most important points complementary: they refer to different aspects of intelligence.

  Just as modern psychology has integrated the ideas of Galton and Binet, Sternberg’s "triarchic
theory" proposes to synthesize several apparently contradictory currents in the contemporary
psychology of intelligence. It seeks to understand the interconnections between: 1) the structures and processesunderlying intelligent behavior, 2) the application of these structures to the problem of attaining goals in the external world, and 3) the role of experience in molding intelligence and its application. Sternberg’s triarchic theory is useful here, not because its details are particularly similar to those of the mathematical theory to be presented below, but rather because it provides a convenient context for relating this abstract mathematics with contemporary psychological research. The triarchic theory begins with mainstream psychology and arrives at the somewhat radical hypothesis that, although intelligence can be defined only relative to a certain context, there are certain universal structures underlying all intelligent behavior.

STRUCTURES AND PROCESSES
  In the triarchic theory, the structures and processes underlying intelligence are divided into
three different categories: metacomponents, performance components, and knowledge-
acquisition components. From the point of view of internal structure, intelligence is understood
as a problem-solving activity which is allocated specific problems from some external source.
   Metacomponents have to do with the high-level management of problem-solving: deciding on
the nature of the problem with which one is confronted, selecting a problem-solving strategy,
selecting a mental representation of the problem, allocating mental resources to the solution of
the problem, monitoring problem-solving progress, and so on. Studies show that all of these
factors are essential to intelligent performance at practical tasks (MacLeod, Hunt and Mathews,
1978; Kosslyn, 1980; Hunt and Lansman, 1982).

   Metacomponents direct the search for solutions; but they do not actually provide answers to
problems. The mental structures which do this are called performance components. These are of
less philosophical interest than metacomponents, because the human mind probably contains
thousands of different special-case problem-solving algorithms, and there is no reason to suppose that every intelligent entity must employ the same ones. Most likely, the essential thing is to have a very wide array of performance components with varying degrees of specialization.

   For example, consider a standard analogy problem: "lawyer is to client as doctor is to a)
patient b) medicine". Solving this problem is a routine exercise in induction. Given three entities W, X and Y:
1) the memory is searched for two entities W and X,
2) a relation R(W,X) between the two entities is inferred from            the memory,
3) the memory is searched for some Z so that R(Y,Z) holds

This process is a performance component, to be considered in much more detail in the following
chapter. It is not "low-level" in the physiological sense; it requires the coordination of three
difficult tasks: locating entities in memorybased on names, inference of relations between
entities, and locating entities in memory based on abstract properties. But it is clearly on a lower level than the metacomponents mentioned above.

   Neisser (1983), among others, believes that the number of performance components is
essentially unlimited, with new performance components being generated for every new context.
In this point of view, it is futile to attempt to list the five or ten or one hundred most important problem solving algorithms; the important thing is to understand how the mind generates new algorithms. There is certainly some truth to this view. However, it may be argued that there are some relatively high-level performance components which are of universal significance — for instance, the three forms of analogy to be discussed in the following chapter. These general algorithms may be used on their own, or in connection with the more specific procedures in which Neisser, Hunt (1980), Jensen (1980) and others are interested.
   This brings us to the knowledge acquisition components of intelligence: those structures and
processes by which performance components and metacomponents are learned. For example,
three essential knowledge acquisition components are: sifting out relevant from irrelevant
information, detecting significant coincidences (Barlow, 1985), and fusing various bits of
information into a coherent model of a situation. These three abilities will be considered in detail in later chapters.

   The importance of effective knowledge acquisition for intelligence is obvious. The ability to
speed-read will help one perform "intelligently" on an I.Q. test; and the ability to immediately
detect anomalous features of the physical environment will help one perform intelligently as a
detective. One might argue that factors such as this do not really affect intelligence, but only the ability to put intelligence to practical use. However, intelligence which is not used at all cannot be measured; it is hard to see how it could even be studied theoretically. The mathematical theory of intelligence to be given below provides a partial way around this dilemma by admitting that one part of a mind can be intelligent with respect to another part of the mind even if it displays no intelligent behavior with respect to the external environment.

INTELLIGENCE AND EXPERIENCE
 The experiential approach to intelligence begins with the idea that most behavior is "scripted"
(Schank and Abelson, 1977). Most actions are executed according to unconscious routine; and
strict adherence to routine, though certainly the intelligent thing to do in many circumstances,
can hardly be called the essence of intelligence. It would rather seem that the core of intelligence is to be found in the learning of new scripts or routines.

    For instance, one might focus on the rate at which newly learned scripts are "automatized".
The faster a behavior is made automatic, the faster the mind will be free to focus on learning
other things. Or one could study the ability todeal with novel situations, for which no script yet exists. Insight, the ability to synthesize appropriate new metacomponents, performance
components and even knowledge acquisition components, is essential to intelligence. It has been
extensively studied under the label "fluid intelligence" (Snow and Lohman, 1984).

  The relevance of insight to tests such as the I.Q. test is a controversial matter (Sternberg,
1985). It would seem that most I.Q. test problems involve a fixed set of high-level
metacomponents, as well as a fixed set of performance components: analogical, spatial and
logical reasoning procedures. In other words, in order to do well on an I.Q. test, one must know
how to manage one’s mind in such a way as to solve puzzles fast, and one must also have a
mastery of a certain array of specialized problem-solving skills. However, in this example one
sees that the dichotomy between metacomponents and performance components is rather coarse.
It would seem that, to do well on an I.Q. test, one has to have a great deal of insight on an
intermediate plane: on a level between that of specific problem-solving methods and that of
overall management strategies. One must have a mastery of appropriate high-level and low-level
scripts, and an ability to improvise intermediate-level behavior.

INTELLIGENCE AND CONTEXT
    One may look at intelligence as an array of structures and processes directed toward the
solution of specific, externally given problems. One may understand intelligence as the learning
of new structures and processes. Or — third in Sternberg’s triarchy — one may hypothesize that
intelligent thought is directed toward one or more of three behavioral goals: adaptation to
an environment, shaping of an environment, or selection of an environment. These three
goals may be viewed as the functions toward which intelligence is directed: Intelligence is not
aimless or random mental activity that happens to involve certain components of information
processing at certain levels of experience. Rather, it is purposefully directed toward the pursuit of these three global goals, all of which have more specific and concrete instantiations in people’s lives. (1987, p.158)

This contextual approach to intelligence has the advantage that it is not biased toward any
particular culture or species.

   For instance, Cole, Gay and Sharp (1971) asked adult Kpelle tribesmen to sort twenty familiar
objects, putting each object in a group with those objects that "belonged" with it. Western adults tend to sort by commonality of attributes: e.g. knives, forks and spoons together. But Western children tend to sort by function: e.g. a knife together with an orange. The Kpelle sorted like Western children — but the punchline is, when asked to sort the way a stupid person would, they sorted like Western adults. According to their culture, what we consider intelligent is stupid; and vice versa. By asking how well a personhas adapted to their environment, rather than how well a person does a certain task, one can to some extent overcome such cultural biases.

 Sternberg distinguishes adaptation to an environment from shaping an environment and
selecting an environment. In the general framework to be presented below, these three abilities
will be synthesized under one definition. These technicalities aside, however, there is a serious problem with defining intelligence as adaptation. The problem is that the cockroach is very well adapted to its environment — probably better adapted than we are. Therefore, the fact that an entity is well adapted to its environment does not imply that it is intelligent. It is true that different cultures may value different qualities, but the fact that a certain culture values physical strength over the ability to reason logically does not imply that physical strength is a valid measure of intelligence.

   Sternberg dismisses this objection by postulating that the components of intelligence are manifested at different levels of experience with tasks and in situations of varying degrees of contextual relevance to a person’s life. The components of intelligence are… universal to intelligence: thus, the components that contribute to intelligence in one culture do so in all other cultures as well. Moreover, the importance of dealing with novelty and automatization of information processing to intelligence are… universal. But the
manifestations of these components in experience are… relative to cultural contexts (1987, p.
168).
This is a powerful statement, very similar to one of the hypotheses of this book: that there is a universal structure of intelligence. However, psychology brings us only this far. Its conceptual tools are not adequate for the problem of characterizing this structure in a general, rigorous way.

Kaynak: A New Mathematical Model of Mind
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