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the fearful role played by mental deficiency in the production of vice, crime, and delinquency (p. 9). Terman also saw the potential for using intelligence tests with adults for determining vocational fitness, but, again, he emphasized employing a psychologist...to weed out the unfit or to determine the minimum intelligence quotient necessary for success in each leading occupation (p. 17). Perhaps because of this emphasis on the assessment of children or concern with the lower end of the intelligence distribution, Terman (1916) did not use a rigorous methodology for constructing his adult-level tasks. Tests below the 14-year level were administered to a fairly representative sample of about 1,000 children and early adolescents. To extend the scale above that level, data were obtained from 30 businessmen, 50 high school students, 150 adolescent delinquents, and 150 migrating unemployed men. Based on a frequency distribution of the mental ages of a mere 62 adults (the 30 businessmen and 32 of the high school students above age 16), Terman partitioned the graph into the following MA categories: 13 15 (inferior adults), 15 17 (average adults), and above 17 (superior adults).

(17.7)

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seven or fewer years of schooling. Thus, the very highly educated adults scored 2.2 SD higher than relatively uneducated adults on Vocabulary and 1.5 SD higher on Block Design. These data show that relatively uneducated people perform poorly on both school-related and school-unrelated tasks, and that both types of tests are substantially related to formal education. As indicated, however, highly educated adults have a greater advantage on crystallized than on fluid tasks (i.e., on Information or Vocabulary than on Block Design). Data from the Fels Longitudinal Study (McCall, 1977) reveal that childhood IQs correlate about .50 ( .10) with both adult educational and occupational attainment, stabilizing at that relatively high level at ages 7 to 8 for males and females. The strong relationship between IQ and formal education should not obscure the considerable variability of IQs earned by individuals with the same educational attainment. Fluctuations in WAIS-R IQ by education level were shown by Reynolds et al. (1987), and are presented in Table 4.5. These results indicate that each level of educational attainment is accompanied by a wide range of Full Scale IQs. For example, individuals with some college education have a higher mean IQ by about 11 points than those with some high school, but their IQ ranges are fairly similar: 76 139 for those with 13 15 years of schooling compared to 59 146 for those with 9 11 years of schooling.

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From the physical interpretation of m(x) as a magnetic moment density, it is reasonable that the above can be expressed as a spatial integral over some function of m(x). The integrand is then the Landau free energy. But why do we choose to hold fix m (x), instead of any other variable, while performing the microscopic average The underlying assumption is that the order parameter is slow to come to thermal equilibrium, long after all other degrees of freedom have become thermalized. In this sense, it is similar to the macroscopic variables of hydrodynamics. To have a completely macroscopic theory, the cutoff A must somehow disappear from final physical answers. Since 1/A is of microscopic scale, the obvious thing to do is to take the limit A ~ 00. That cannot be done in a straightforward manner, however, because it produces divergences in the free energy, (except in the mean-field approximation discussed later.) The correct procedure for taking such a limit involves "renormalization," a scheme originally invented to circumvent divergences of a similar nature in quantum electrodynamics. This will be the subject of discussion in 18. That the inspiration for renormalization came from quantum electrodynamics was not accidental. The Landau theory for d = 4 is equivalent to a relativistic quantum field theory. * More precisely, the partition function with a spatially varying external field H(x) corresponds to the generating functional for the" vacuum Green's functions" of a relativistic quantum field theory in the presence of an external source H( x). Thus the theory has practical application for d = 1,2,3,4:

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