Human Accomplishment by Charles Murray

Author:Charles Murray
Language: eng
Format: epub
Publisher: HarperCollins
Published: 2003-07-20T16:00:00+00:00

MEASURING THE RATE OF ACCOMPLISHMENT

Population can be “taken into account” in two ways. One is to enter population as a variable in a regression equation, a method that will be used subsequently. But the simpler and more familiar way is to calculate a ratio, using population as the denominator. The crime rate, unemployment rate, birth rate, and per capita earnings are familiar examples of such ratios. They are just one form of the widespread, everyday use of rates—miles per hour, calories per serving, bushels per acre, batting average, and interest rate.

Using the same method, I now give you the unweighted accomplishment rate, consisting of the number of significant figures per 10 million population. For example, France in the period 1850–1870 saw the appearance of 54 significant figures among a population that at the beginning of that period stood at about 35.7 million. The accomplishment rate is therefore 15.1.[2]

To get a sense of how the rate has varied over time, it is also useful to create a weighted accomplishment rate that incorporates information conveyed by the index scores. Instead of computing the rate by counting each significant figure equally, I add up the index scores and use them as the numerator. To continue with the example of France in 1850–70, the index scores of the 54 significant figures add up to 697. This use of summed index scores produces a weighted accomplishment rate of 195.2.

For the arts and philosophy inventories, these two measures of the accomplishment rate are the basis for tracking rises and declines across the centuries. The scientific inventories have counts of events as well as people, giving a third perspective: the number of significant events per 10 million. France from 1850–70 numbered 40 events in the scientific inventories combined, yielding an event rate of 11.2.

The pages that follow show timelines for each of the inventories.[3] The lines represent a moving average over three decades, meaning that each significant figure is counted for the decade in which he turned 40 plus the decade on either side.

Because I want to show how the alternative measures of the rate track with each other, I converted all the rates into what are known as standard scores. The computation and uses of standard scores are discussed in Appendix1. To recapitulate, standard scores always have a mean of 0 and a standard deviation of 1. Except when noted, the scale in the timelines that follow runs from +3 to –3 standard deviations. Three standard deviations above or below a mean represents the top tenth of the top centile in a normal distribution. Because it is the shape of the moving average that conveys the important information, not the specific values (the specific values, like the mean, are sensitive to the choice of time span),[4] I have labeled the top and bottom of the scale simply “Very high” and “Very low.”

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