The observation is so unerringly reproducible, it justly earns the appellation, law. Appropriately, we call 1.1 SD the fundamental constant of sociology. Table 1 illustrates.

Urban migration in the twentieth century
    When John and Mack Rust invented the first reliable cotton picking machine in 1936, they could not have imagined the sociological impact it was to have. Perfected in the 1940s, the machine could pick as much as fifty men at one-eighth the cost. It gradually replaced Southern, mostly black field hands. Out of work, they turned northward to earn a living. Three-quarters of the 6.5 million blacks who migrated north between 1910 and 1970 left the South after the cotton picking machine came into widespread use. Jim Crow may have started the great migration, but it was the emergence of this new technology that fueled it.

    Black migrants settled mostly in Northern and Midwestern cities where they found work in low-skilled jobs. Barred from most residential areas, their neighborhoods hardened into overcrowded crime-plagued ghettos. Whites, facing an inhospitable intrusion into their lives, began a migration of their own to more remote parts of the city and eventually to the suburbs.

    With the passage of civil rights legislation in 1964, new residential opportunities opened for blacks. They began their own urban exodus, following whites to the suburbs. By the end of the twentieth century, most whites with the means to leave the central city had already done so. Black flight, however, was alive and well. Starting from near zero in 1960, by 1990 32 percent of metro-area blacks lived in suburbia, 39 percent by 2000.

    But escape from the inner city is a highly selective enterprise. It is an option open mostly to the right half of the bell curve. Consequently, urban flight creates a cognitive discontinuity where the city meets the suburbs. Left behind in the city is a human residue wanting in human capital. Unemployment, welfare dependency, drug addiction, coarseness and incivility are its hallmarks, low IQ its nub. Below we characterize the discontinuity, closely estimating mean IQs of inner-city and suburban dwellers, black and white.

Methodology
    In December 2000, La Griffe du Lion introduced the method of thresholds. Designed to assess group differences in "fuzzy," i.e., poorly-defined, variables like aggressiveness, criminality and sex drive, the method works as well for precisely defined variables like IQ. Though the calculations are performed analytically (Appendix A) we will take a graphical walk-through to reveal their underpinnings as we assess the mean IQ of African Americans in Maryland.

    The method of thresholds employs surrogate variables. Here, we use MSPAP test scores as a stand-in for IQ. Input is the proportion of each of two groups that attains a "satisfactory" score, i.e., reaches the threshold. (MSPAP pass rates are reported at two levels of performance, "satisfactory" and "excellent." )

    Over nine years and roughly half a million test scores, 58.8% of white and 19.1% of black 8th graders passed at the satisfactory level. Figure 1 shows the white test score distribution, assumed Gaussian. (See Appendix B for a justification of the use of Gaussian functions.) The distribution is normalized to make the area under the curve unity. The passing score is marked on the score axis (abscissa) as "satisfactory pass." It is placed to make the area under the curve to the right of it (shaded in the figure) equal to 0.588, the white passing fraction.

    Next we locate the black distribution on the same axes (Figure 2). This is accomplished by shifting the (white) distribution left until the area under the curve to the right of the passing score equals the black passing fraction, 0.191. The mean difference is the distance separating the two curves, measured here to be 1.1 SD.

    Conversion to IQ units is straightforward. Customarily, the mean IQ of non-Hispanic whites is set to 100, with a standard deviation of 15. A gap of 1.1 SD then corresponds to a mean black IQ in Maryland of 83.5, i.e., 100 - (1.1)(15).

    The method of thresholds, as illustrated above, yields a statewide black-white cognitive gap of 1.1 SD, in agreement with the fundamental law. To dispel any suspicion of fortuity, we divided the data into nine independent parts corresponding to the nine administrations of the test between 1993 and 2001. Each year's data was analyzed separately. Table 2 shows the result of this computation. The average of the nine values was 1.106 SD with a standard error of 0.045, ruling out fortuity.

Effects of urban flight on IQ distribution
    Maryland's big city, Baltimore, saw its population peak just short of a million in 1950. It has been declining for nearly half a century, 17% in the last twenty years alone. Today it numbers about 651,000. White flight followed by black has drained the city of inhabitants. As its population dwindled, Baltimore like many other Northern and Midwestern cities without significant recent foreign immigration became blacker. Today, Baltimore is 65% African American, and 32% non-Hispanic white.

    Baltimoreans who fled the city moved mostly to neighboring Baltimore County. The County, which surrounds the city, is the first stop on the way out. Thirty years ago Baltimore County was lily white. Today, African Americans are 17 percent of its 726,000 inhabitants. And they keep coming.

    Table 3 illustrates the effect that urban flight has had on IQ distribution. We computed mean differences between Maryland's non-Hispanic white population and each of four local groups: inner-city and suburban blacks and whites. From these, we computed mean IQs, assigning a value of 100 to Maryland's non-Hispanic white population with a standard deviation of 15. (Affluent whites and blacks inside the city are not represented in these data. They neither live in slums nor send their kids to public schools.)

Conclusions
    Baltimore is typical of many Midwestern and Northern cities, whose demographics were forever changed by the great black migration of the twentieth century. Not unexpectedly we found a cognitive discontinuity at the city line. Surprising, however, was its magnitude. Whereas suburban mean IQs (86 for blacks, 99 for whites) conform more or less to national norms, city IQs are dreadfully low. With a mean IQ of 76, inner-city blacks fall about 0.6 SD below the African American average nationally. More than a third have death-penalty immunity on grounds of mental retardation. The inner-city white mean of 86 is nearly a full standard deviation below the national white average. By this measure, whites fared worse than blacks. Both groups are seriously deficient in human capital. Neither is very employable. To compound matters, we almost certainly have overstated urban IQs. City residents constitute a low-IQ group extracted from a more cognitively representative population. Their kids, whose test scores we analyzed, should have regressed toward their racial means, i.e., toward higher IQs. That is, inner city kids are smarter than their parents. Accordingly, our estimates of inner-city IQs are best regarded as upper bounds to adult values.

    IQ hardens early in life, locking in the urban deficit. With few prospects for improvement, cities must look elsewhere for amelioration. While we all are aware of the advantages that accrue to the brightest among us, we also know that other qualities carry with them inestimable benefits. Traits like honesty, reliability, perseverance and self-discipline, when cultivated contribute to employability and to a more productive life in general. Indeed, for low-skilled jobs these latter qualities are more important than intellect. Unfortunately, casual observation finds such virtues also wanting.

    Finally, we note that a problem cannot be solved until it is defined. This we have done. But where we see cognitive inadequacy, some will find only abject, hopeless misery. As for our efforts, we can be certain of only one thing -- vilification. It could drive a man to pseudonymity

    The fraction, f_B, of B's who reach or surpass λ is:

where Δ is the mean difference, <x_A> - <x_B>.

    Equation A.2 is conveniently transformed as follows:

    From the known fractions, f_A and f_B , both the mean difference, Δ, and threshold, λ, may be obtained by simultaneous solution of (A.1) and (A.3). Reader Ken Hirsch shows how, using Gaussian distribution functions, this may be simply accomplished with a spreadsheet. (Appendix B justifies the use of Gaussians in the analysis of MSPAP data.)

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