August 31, 2004

A Calculating People, Patricia Cline Cohen

Subtitle: The Spread of Numeracy in Early America

The spread of numeracy is reasonably interesting if you're interested in economic history, or in how skills travel between "rote skills" and trade schools, and "knowledge" and liberal schooling. Reckoning was a practical, even embarrassingly practical, skill for hundreds of years of the rise of commerce; the first colonialists weren't especially numerate, since the Puritans believed in theological studies instead, and the tobacco planters were above such petty things. (I overstate.)

Some people found argument by number irresistible as soon as it was imaginable, though; for instance, the Virginia Company got into a long brangle over how many of its colonists had died, and of what. Also, of course, the rise of the organized state and of mercantilism paid for surveying, muster-lists, etc. Reckoning became a strength of the state. Around this time the rhetorical claim that women couldn't do arithmetic was swept under the rug in the interest of hiring math teachers out of a cheap labor supply.

My favorite chapter is on the Census of 1840, though, and most of that is about an error in the census, probably exacerbated by difficult form design, which followed a decade of brangling in the courts and had results that probably lasted through Jim Crow.

The most controversial "finding" was that the black population of the North appeared to be beset with epidemic rates of insanity, which suggested to some that "science," as revealed by tables of figures, had proved freedom to be detrimental to blacks.

By 1840 physicists had learned that you can't carry out chains of calculations on bad data and get good results; but most number-enthusiasts apparently started with the belief that a number, however arrived at, had more credibility than words. Sir William Petty, for instance, was more precise than accurate.

What was measured by the 1840 census was already skewed by interest. The age groups for blacks and whites were different, possibly to preclude comparing mortality. Insanity was to be measured to judge outlay for the support of dependents, employment was measured in more categories than the 1820 census had needed, the president wanted to know about military pensioners, education and literacy took up another several columns.

Each schedule contained seventy-four columns, with headings in microscopic type printed across the tops of two pages.

It would be only mildly interesting if a complex form had produced randomly untrustworthy data; but this one probably invited a particular error. Because the error was pleasant to racists, it became a popular claim even though it was inconsistent with the rest of the data in the same census, and was often explicitly disprovable.

So Jarvis checked for internal consistency and was mortified to find that many of the towns reported to harbor insane blacks in fact had no black population at all! A study of the printed statistics of other northern states turned up the same pattern...
...individual assistant marshals had indeed entered digits in the columns for "insane and idiot" blacks in families where there were no blacks.

This Jarvis, who was a member of both the American Statistical Association and of the Massachusetts Medical Society, worked out with his colleagues that it was common in the North for "insane or idiot" white family members to be listed in the column for black family members. The Census had already gone through a conflict, or even scandal, over who had the right to print it; and the printer Weaver made an excellent front for the political interest, i.e. John C. Calhoun, who wanted to use the results. Much I'm-rubber-you're-glue was printed, and I would guess that most of the country was already tired of the whole issue. Jarvis got no traction.

Cohen consulted the manuscript returns on microfilm, and has a theory as to why the error was systematic:

Suppose, then, that a certain number of senile whites were considered idiots in the common parlance but not insane; suppose that some fraction of them were entered in the column for insane and idiot blacks merely because the word "idiot" was not prominent in the section for whites, while the word "colored" was not prominent in the section for blacks. It stands to reason, then, that a series of ratios comparing insane blacks to the total black population would exhibit an interesting gradient from North to South and from East to West, because there was an excess of elderly people in the East and a deficiency of black people—the denominator of the ratio—in the North. In regions with large black populations, such as the South, the small numbers of errors recording senile whites would fade into insignificance.

Parallells to ballot design and climate data crunching are an exercise for the reader.

Genealogists use census data, so if you're willing to pay a modest sum, you can buy online access to images (of the microfilms of?) the census returns. Where the data is available as a database, I haven't found the categories relevant to this error listed at all. It looks as though many large libraries have the censuses in microfilm, at least the local censuses; but I admit I'm probably not going to hunt down an actual image of an inconsistent return, having failed to find one online.

ISBN: 0226112845

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