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Developmental Review xxx (2004) xxxxxx
On the law of intelligence
Koerner Center for Emeritus Faculty, Yale University, New Haven, CT 06520-8368, USA
Received 21 November 2003; revised 26 March 2004
The law of intelligence is presented in test independent form. Mental abilities, physical
brain size, and infant motor capacity follow the same law of growth from birth to adolescence.
Mental growth is independent of race, SES or the Flynn effect. The vitality of the mental age
scale calls for a reexamination of Wechslers deviation IQ. This paper builds on Yens methodof standardized differences (1986). The main theoretical advance here is to put development
back into intelligence testing and to show a universality among different measures of the
growth of the human nervous system.
2004 Elsevier Inc. All rights reserved.
This paper suggests a new theoretical structure for psychoeducational measure-ment and uses it to derive a scale of growth of mental ability. Over the years, many
researchers sought the law of intelligence, the growth curve of mental ability, a
goal to be addressed by this paper (Bloom, 1964; Bock, 1983; Gesell, 1928; Heinis,
1924; Jensen, 1973; Keats, 1982; Thorndike, Bregman, Cobb, & Woodward, 1927;
Thurstone, 1925, 1928; Thurstone & Ackerson, 1929; and many others).
Remarks on natural laws
We consider quantitative relations in physics and psychophysics, fields that are
sometimes emulated by mental testers.
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2 W. Lichten / Developmental Review xxx (2004) xxxxxx
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A pound of meat is a pound of meat. It weighs the same on the butchers scaleswhether by itself or if added to another piece of meat. The scale divisions are uniform
in meaning over the entire range of measurement. Similarly, an inch is the same any-where on a yardstick. Likewise 1 s has a simple, well defined and measurable mean-
ing at any place or time. Thus the basic units of physics, mass, length, and time, and
the laws based on them, are measured on uniform, well-standardized scales.
Psychophysical scales measure the relation between subjective sensations (such
as loudness, pitch, and brightness) and objective physical correlates (sound inten-
sity, frequency, and light intensity). The scales of psychophysics purport to be uni-
form. For example, one asks an observer to vary the intensity of one sound until it
seems half as loud as a second sound. This way, one can set up a loudness scalewhich has equal divisions. (Licklider, 1951; Stevens, 1951, 1975; Stevens & Davis,
1938; Woodworth & Schlosberg, 1954). An example of a psychophysical law is that
of WeberFechner, that the sensation of pitch or loudness of a sound, brightness
of a light, etc., is proportional to the logarithm of the corresponding physical var-
iable. (For a sampling of the many discussions of this law and alternatives, see En-
gen, 1971; Luce, Bush, & Galanter, 1963; Luce & Krumhansl, 1988; Luce &
Suppes, 2002; Stevens, 1975; Suppes & Zinnes, 1963; Thurlow, 1971; Woodworth
& Schlosberg, 1954.)
Is a law of intelligence possible?
Quantitative physical and psychophysical laws hinge on measurement scales. Canwe set up a law of intelligence by merely following the examples of physics and psy-
chophysics? Unfortunately the matter is not so simple. As Jensen (1993, p. 141) put
it, There are no existing tests that could render such statements as the following at
all meaningful: A person gains half of his adult level of mental ability by the age offive. The rationale underlying this statement is the impossibility of comparing di-rectly the growth of intelligence at different ages.
For example, infants are in Piagets sensorimotor stage:
. . .during the first year. . .intelligence, strictly speaking, is not yet observed.
(Piaget & Inhelder, 1969, p. 9)
On the other hand, adults are in a formal operational stage. Comparing the two
would be a case of apples and oranges.
The earliest intelligence measurements were expressed on a mental age (MA) scale
(Binet & Simon, 1916). On Binets scale, test scores advanced by even amounts eachyear. But almost all subsequent mental tests showed a quite different growth pattern.Terman and Merrill (1937) noted MA was a very uneven scale, with rapid mental
growth among infants and young children and near stasis in late adolescence. Thus
neither the MA scale nor its grade level achievement twin can answer Jensens rhe-torical question. Yet both are quite useful and are still widely used in the clinical,
W. Lichten / Developmental Review xxx (2004) xxxxxx 3
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developmental, and educational literature. In Terman and Merrills words (1937, p.25)
The expression of a test result in terms of age norms is simple and unambiguous, resting
upon no statistical assumptions. A test so scaled does not pretend to measure intelligence
as linear distance is measured by the equal units of a foot-rule, but tells us merely that
the ability of a given subject corresponds to the average ability of children of such and such
It was a pity that the MA scale was dropped from IQ testing. This paper will usethe MA scale to derive the law of intelligence. For further discussion of MA, see the
later section IQ and Mental Age Scales.
Layzer (1972, p. 276) pointed out a related difficulty with IQ, as a measure of de-
viation of intelligence from the average at a given age: IQ does not measure an in-
dividual phenotypic character like height or weight; it is a measure of the rank order
or relative standing of test scores in a given population. (See also Jensen, 1993.) To
illustrate his point, consider this question. Which step in intelligence is the greater:
from 100 to 130 or from 70 to 100 IQ points? 130 and 100 might be the differencebetween a research medical doctor and a butcher. On the other hand, 10070 is
the gap between average and mentally retarded, which under a recent Supreme Court
decision can be the difference between life and death (Atkins vs Virginia, 2002;
Greenhouse, 2002). Both intervals represent 30 points, but how can you compare
the two? Thus it is again an apples and oranges problem to equate units at different
points on existing mental ability scales.
Although we may not yet say what a mental growth scale is, we can certainly say
what it is not. Mental ability is not like a pound of meat; it cannot be put on a scalewhere each interval is exactly equal to every other one in meaning and in size. If it
were that simple, the problem of finding the law of intelligence would be solved and
there would be no need for this paper. We now turn to the measurements which can
be the basis of such a law.
The measurement of mental ability (IQ, achievement, etc.)
Without a simple, linear scale, how can we deal quantitatively with intelligence? In
the words of Jensen (1969, pp. 56)
Intelligence, like electricity, is easier to measure than to define. And if the measurements
bear some systematic relationship to other data, it means we can make meaningful state-
ments about the phenomenon we are measuring. There is no point in arguing the question
to which there is no answer, the question of what intelligence really is. The best we can do is
to obtain measurements of certain kinds of behavior and look at their relationship to other
phenomena and see if these relationships make any kind of sense and order.
Luce and Krumhansl (1988) pointed out that the situation is similar to the early
days of the study of heat. Nobody knew exactly what temperature was. The basis of
the concept was subjective feeling of hot and cold. It took centuries for the develop-
ment of the laws of thermodynamics before temperature was really understood. Nev-
ertheless, pioneers went about constructing thermometers based on expansion of
4 W. Lichten / Developmental Review xxx (2004) xxxxxx
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liquids. They marked their instruments at two standard temperatures and divided it
into equal steps. For example, Fahrenheits scale had its zero at a mixture of ice andsalt and its 96 at body temperature.
A simple way to compare scales is to match mid points. For example, consider
thermometers with standard temperatures at 0 and 100 F. The scale midpoints forgas thermometers differ from each other by only few thousandths of a degree. The
midpoint of the mercury scale differs from gas thermometers by 0.1 F and from al-cohol by 1 F. The excellent agreement among most thermometric materials meansthat thermometer scales are independent of the material used.
Water is an exception. It would make a poor thermometer. It would read 81.3 Fat the midpoint of the 32100 F scale (66 F). The reason for this gross discrepancyis the non-linear expansion of water.
If one were to plot temperature from almost any scale against another, the plotwould be a straight line. This linear agreement among scales made it reasonable
to use any one to define temperature. Such scales preceded and agree with the
now well understood laws of thermodynamics.
Note that we cannot