The tables to which the German university statisticians objected were, or could be, instruments of political arithmetic. In England and Sweden, debate about the use of statistics centered explicitly on the program of quantitative social and economic analysis that descended from the work of William Petty and his contemporaries at the end of the 17th century.
William Petty was held in high esteem in circles populated by the likes of Robert Boyle, John Wallis, Samuel Hartlib, and Thomas Hobbes. Considered by Samuel Pepys "the most rational man that I ever heard speak with a tongue," Petty fit in well with the successful men of science who met in the Invisible College and the Royal Society. He dreamed of a perfectly rational society, a social edifice as stable and unassailable as a mathematical theorem. Each element had to be weighed, measured, and evaluated before it could be incorporated into this rational system. Petty made the point explicitly: "The Method I take. . .is not very usual; for instead of using only comparative and superlative Words, and intellectual Arguments, I have taken the course. . .to express myself in Terms of Number, Weight or Measure ; to use only Arguments of Sense, and to consider only such Causes, as have visible Foundations in Nature; leaving those that depend upon the mutable Minds, Opinions, Appetites, and Passions of particular Men."
Petty aimed at a science that used quantitative methods (counting and measuring) to isolate, describe, and analyze the elements that created a society's prosperity. Available observations of population, land, and resources—all in numerical form—were used in the calculation of values of other, as yet unknown, resources.
To reduce Petty himself to arithmetic, or rather geometry, his program lay at the intersection of inspiration of Baconian empiricism and Newtonian natural philosophy. He called for the assembly of individual measurements (of, for example, birth and mortality rates, work capacity, output, consumption, and fertility) to form a valid picture of a general reality. In practice, however, he often relied on estimates and averages; and his columns of numbers necessarily remained isolated from one another since correcting principles analogous to the law of gravity eluded him. Petty and his successors Gregory King and Charles D'Avenant framed a general program of social analysis based on computations and systematic collection of facts: "He who will pretend to Compute, must draw his Conclusions from many Premises; he must not argue from single Instances, but from a thorough view of many Particulars; and that Body of Political Arithmetick, which is to frame Schemes reduceable to Practise, must be compos'd of a great variety of Members."
The strong political context of political arithmetic may be discovered in a fight in Parliament over a proposal to provide it with one of its basic instruments. In 1753 advocates of a coherent program of social statistics, among them the mathematician James Dodson, called for a general census. But the census bill fell victim to strong opposition fed by fears of an expanding government. Five years later Parliament rejected a similar proposal for mandatory registration of births, marriages, and deaths. Prosperity appeared better served by capital, industry, and steam power than by the calculations of a power-hungry central government. Parliament thereby denied to proponents of political arithmetic both the means of collecting
data—the census and the registration of vital statistics—and the function intended by Petty and his contemporaries—that of a political instrument of scientific legitimacy.
That, of course, did not prevent private groups from compiling vital statistics for their political purposes. Republicans and religious dissenters picked up political arithmetic and wielded it to combat the "faithful guardians of the state" and reduce their authority. These advocates of local power counted local conditions as more significant than national aggregations of class, rank, and occupation. A good example is Richard Price's statistical studies of national debt and local prosperity based on data privately collected. Another is development of the work of John Graunt and Edmund Halley on the mathematical analysis of life expectancy. Graunt had demonstrated the utility of vital statistics for establishing the laws of demography; Halley's studies (published in 1693) of mortality lists from the city of Breslau had shown that generally valid calculations of life expectancy could be based on mathematical analysis of available, incomplete data on births and deaths. As a basis for calculating insurance premiums and annuities, quantitative data thus offered real practical value. By the second half of the 18th century, both governments and private investors recognized insurance ventures as a promising prospect. Price saw annuity societies, if guided by mathematicians, as a solution to England's economic ills.
While republicans and dissenters in England reserved political arithmetic for their own purposes and rejected its use as a tool of central government policy, Swedish officials sought a socioeconomic
strategy based on social measurement that might replace the capital and manpower the country had lost during long years of war. To remedy these ills, members of the Swedish parliament followed orthodox mercantilist lines based on the conception that population is the best measure of a nation's real riches. "A plenitude of poor people is a country's greatest wealth." In the mercantilist analysis a surplus of people meant a surplus of need, which would inspire economic initiative, industry, and cultivation of land. A Swedish economist of the time wrote, borrowing a line from D'Avenant, "It may be better for the people to suffer a shortage of land than for the land to suffer a shortage of people." The line symbolized a tie: in 18th-century Sweden, the old English idea of political arithmetic would enjoy political support, the notice of the Royal Academy of Sciences, an institutional platform in the parliament, and enthusiastic public backing. The key role of quantitative analysis in the Swedish debate on ways and means to national prosperity can be traced in pamphlets and programmes; in the Transactions of the Royal Academy of Sciences; in parish surveys, state memoranda, and confidential parliamentary reports.
In accord with the proposition that people attracted industry, rather than the reverse, colonization projects of all kinds, resettlement projects, and measures to stimulate population growth abounded in Sweden beginning in the 1730s. So, too, did optimism about the rate at which the population of Sweden might increase. Some fortune tellers saw a doubling in the space of twenty years. In the long run, the population of Sweden (which then included Finland) might reach ten, twenty, even thirty million inhabitants. (The actual population figures in the mid-18th century, not disclosed at the time, were closer to two million.) The mainstream of public
discussion overflowed with optimistic calculations from leading social theorists, and from reports submitted to the Riksdag by the Office of Tables.
How could these calculators arrive at such preposterous figures? In part, the optimism derived from conceptions of Sweden's great natural resources inherited from the patriotic historiography of the preceding century. In the years when Sweden was emerging as a great power, the country of the north was often depicted as the vagina gentium , the land chosen by the sons of Noah for its natural riches.
Mercantilism reinforced this patriotic tradition in a land of unexploited natural resources. "No man dares keep any land unusable and unfruitful, now and in the future, once he has seen the new ideas that can spring from ingenuity when spurred by need in a populous country," proclaimed the director of the Land Survey Board in 1758. In Sweden, all agreed, the good Lord had "let abundance drip from His footsteps." He had also arranged for an advantageous climate. The cold protected Sweden's populace from infectious diseases and made them "merry, lively, and manly." Snow on the ground prevented the evaporation of nutritious substances; once it melted, rotting leaves and needles gave way to rich humus soil. The woods teemed with useful game ("if anyone would seriously try to domesticate our elk, they might well become our camels"); lakes and rivers overflowed with salmon and other splendid fish, pearl-filled mollusks, oysters, and lobsters. Nonetheless, God's handiwork could be improved upon. "If wildernesses and wastes are cultivated, a whole new land can be created, even more fruitful, milder in climate, more pleasant in every way, rich and able to support and feed millions more people than today."
The language and the imagery were as rich as Sweden herself. But how to measure and master these natural resources? Political arithmetic offered a key to calculating Sweden's potential and devising a new strategy for growth and prosperity. For three decades, from 1740 to 1770, intense public debate would focus on the interpretation and application of political arithmetic. Three varieties of Swedish statistics emerged in these years: utopian, practical, and descriptive.