The Rise of Statistical Thinking, 1820–1900
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The Rise of Statistical Thinking, 1820–1900

Theodore M. Porter

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eBook - ePub

The Rise of Statistical Thinking, 1820–1900

Theodore M. Porter

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An essential work on the origins of statistics The Rise of Statistical Thinking, 1820–1900 explores the history of statistics from the field's origins in the nineteenth century through to the factors that produced the burst of modern statistical innovation in the early twentieth century. Theodore Porter shows that statistics was not developed by mathematicians and then applied to the sciences and social sciences. Rather, the field came into being through the efforts of social scientists, who saw a need for statistical tools in their examination of society. Pioneering statistical physicists and biologists James Clerk Maxwell, Ludwig Boltzmann, and Francis Galton introduced statistical models to the sciences by pointing to analogies between their disciplines and the social sciences. A new preface by the author looks at how the book has remained relevant since its initial publication, and considers the current place of statistics in scientific research.

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“In this life we want nothing but Facts, sir, nothing but Facts.” Thomas Gradgrind
“So many people are employed in situations of trust; so many people, out of so many, will be dishonest. I have heard you talk, a hundred times, of its being a law. How can I help laws?” Tom Gradgrind (Junior)
—CHARLES DICKENS, Hard Times (1854)
Humanity is regarded as a sort of volume of German memoirs, of the kind described by Carlyle, and all it wants … is an index.
—ANONYMOUS, in Meliora (1866)
I can scarcely conceive any more wholesome study for a stern unbending Tory than the examination of statistics, for he cannot fail to recognize the grand irrecusable law, as true in politics as in everything else, that movement must always be progressive and never retrogressive.
—L. L. PRICE (ca. 1883)


The modern periodic census was introduced in the most advanced states of Europe and America around the beginning of the nineteenth century, and spread over much of the world in subsequent years. Records of population, health, and related matters, however, had been collected intermittently in a variety of territories since ancient times. Most often, the chief purpose of this statistical activity has been the promotion of bureaucratic efficiency. Without detailed records, centralized administration is almost inconceivable, and numerical tabulation has long been recognized as an especially convenient form for certain kinds of information. Until about 1800, the growing movement to investigate these numbers in the spirit of the new natural philosophy was likewise justified as a strategy for consolidating and rationalizing state power.
The importance of bureaucratic efficiency was by no means forgotten when political arithmetic gave way to the new social science of statistics at the beginning of the nineteenth century. Increasingly, however, statistical writers became persuaded that society was far more than a passive recipient of legislative initiatives. Always dynamic, often recalcitrant, society evidently possessed considerable autonomy, and had to be understood before the aims of the state could be put into effect. Statistics was for the most part a liberal enterprise, pursued by business and professional men who favored a narrower definition of the function of the state even while working to enlist it in some particular reform. The most fervent advocates of systematic bureaucratic expansion still conceded that the state could act successfully only within the constraints defined by the nature of society.
Hence, statistical authors of the scientific persuasion set themselves to uncover the principles that governed society, both in its present condition and, especially, as a historical object. The concept of “statistical law” was first presented to the world around 1830 as an early result of this search. As a social truth it was propagated widely and refined or disputed by decades of writers. Shortly afterwards, statistical regularity came to be seen as the basis for a new understanding of probability, the frequency interpretation, which facilitated its application to real events in nature as well as society. The idea of statistical regularity was thus of signal importance for the mathematical development of statistics.

Chapter One


The systematic study of social numbers in the spirit of natural philosophy was pioneered during the 1660s, and was known for about a century and a half as political arithmetic. Its purpose, when not confined to the calculation of insurance or annuity rates, was the promotion of sound, well-informed state policy. John Graunt observed in his pathbreaking “Observation upon the Bills of Mortality” of 1662:
That whereas the Art of Governing, and the true Politicks, is how to preserve the Subject in Peace and Plenty; that men study only that part of it which teacheth how to supplant and over-reach one another, and how, not by fair out-running but by tripping up each other’s heels, to win the Prize.
Now, the Foundation or Elements of this honest harmless Policy is to understand the Land, and the Hands of the Territory, to be governed according to all their intrinsick and accidental differences.1
Graunt’s scholarly claims were modest. “I hope,” he began, that readers “will not expect from me, not professing Letters, things demonstrated with the same certainty, wherewith Learned men determine in their Schools; but will take it well, that I should offer at a new thing, and could forbear presuming to meddle where any of the Learned Pens have ever touched before, and that I have taken the pains, and been at the charge of setting out those Tables, whereby all men may both correct my Positions, and raise others of their own.”2 Still, he desired to conduct his inquiry philosophically, and his work was dedicated to Robert Moray, head of the “Knights and Burgesses” that “sit in the Parliament of Nature,”3 as well as to the high official, Lord John Roberts, who might be moved to execute some of its recommendations.
William Petty, who invented the phrase “political arithmetic” and is thought by many to have had a hand in the composition of Graunt’s work, was in full accord with his friend as to the purpose of these studies. Political arithmetic was, in his view, the application of Baconian principles to the art of government. Bacon, he wrote, had drawn “a judicious Parallel … between the Body Natural and Body Politick,” and it was evident “that to practice upon the Politick, without knowing the Symmetry, Fabrick, and Proportion of it, is as casual as the practice of Old-women and Empyricks.”4 Petty sought always to bring “puzling and perplext Matters … to Terms of Number, Weight and Measure,”5 so that official policy might be grounded in an understanding of the land and its inhabitants.
Implicit in the use by political arithmeticians of social numbers was the belief that the wealth and strength of the state depended strongly on the number and character of its subjects. Accordingly, the sovereign was frequently enjoined to take measures to protect the lives or health of his subjects. For example, Petty pointed out that considerable expenditures were required to raise a man or woman to maturity, and he advised the king that money spent to combat the plague could bring higher rewards than the most lucrative of investments, since it would preserve part of the vastly greater sum wrapped up in the lives of those who might otherwise perish. Still, it was the standpoint of the sovereign that was almost always assumed, and the members of society typically appeared as objects that could and should be manipulated at will. Petty’s philosophy appeared sometimes as authoritarian as that of his old master, Thomas Hobbes. In his Treatise of Ireland, Petty proposed that all Irishmen, save a few cowherds, should be forceably transported to England, for since the value of an English life far surpassed that of an Irish one, the wealth of the kingdom would thereby be greatly augmented.6
Petty envisioned political arithmetic as embracing a variety of schemes through which number and calculation could be applied to subjects. The Irish resettlement project, while exceptionally high-handed, was not uncharacteristic methodologically. Another illustration of Petty’s computational rationalism is provided by his calculation of the number of clergy requisite for the English people, based solely on the land area. Petty’s successors made political arithmetic a more sober discipline, closely tied to the empirical collection of population records and especially to the preparation of accurate life tables for the purpose of calculating insurance and annuity rates.
Even so, political arithmetic continued to inspire vigorous controversy, for eighteenth-century mercantilists generally regarded either population size or its rate of growth as the supreme criterion of a prosperous and well-governed country. Thus Montesquieu employed a dubious comparison of ancient and modern populations to affirm the superiority of ancient morals,7 while David Hume observed that, after taking account of climate and geography, “it seems natural to expect that wherever there are most happiness and virtue, and the wisest institutions, there will also be most people.”8 Jean-Jacques Rousseau exalted the enumerator as the preeminent judge of policy: “The government under which … the citizens do most increase and multiply, is infallibly the best. Similarly, the government under which a people diminishes in number and wastes away, is the worst. Experts in calculation! I leave it to you to count, to measure, to compare.”9
Obligingly, the experts in calculation struggled to find a reliable method for measuring population size and deciding if it was expanding or contracting. Rousseau’s infallible guide, however, proved evasive, for census data were nonexistent, birth registers were imperfect, and it was difficult to decide upon a community for which the ratio of total population to annual births would be representative of an entire state. It was more practical to turn the equation around and cite evidence of changes in prosperity or general happiness as proof that the population must be increasing or declining. Accordingly, the social and political determinants of population growth were widely discussed and debated long before Malthus composed his famous essay.10
Similarly, presumed influences on population were routinely invoked to attack customs, creeds, and circumstances of every description. Cities almost always showed a surplus of deaths over births, obviously attributable to the idleness, luxury, and corruption that they nourished, and were the bane of political arithmeticians. Thomas Short called them “Golgothas, or Places of the Waste and Destruction of Mankind, but seldom of their Increase, and often least Prolific. “11 British and German authors rarely failed to castigate the Catholic Church, whose adherence to priestly celibacy was blamed for the alleged depopulation of popish lands. “This superstitious and dangerous tenet,” wrote Robert Wallace, “most justly deserves to be esteemed a doctrine of those devils, who are the seducers and destroyers of mankind, and is very suitable to the views and designs of a church, which has discovered such an enormous ambition, and made such havock of the human race, in order to raise, establish and preserve an usurped and tyrannical power.”12 Alcohol, gaming, promiscuity, and bad air were likewise condemned by the political arithmetician as moralist.
The most ambitious eighteenth-century work on population was Johann Peter Sussmilchüs treatise on the “divine order” in these demographic affairs, which went through four editions between 1740 and 1798 and grew to three thick volumes by the final printing. God’s first commandment was to “be fruitful and multiply” (Genesis 1), Süssmilch wrote, although he conceded that the human institution most conducive to population increase, marriage, was, “not so much a fruit of religion and of Christianity, as a necessary consequence of nature and sound reason. But is it not good, if Christianity confirms, inculcates, and blesses the command of nature?”13 Since this “first, fundamental law of earth” was grounded in human welfare and the prosperity of states, every institution, creed, habit, and law could be judged against one universal standard—did it promote or inhibit the growth of population? Süssmilch undertook to discover the conditions which most encouraged population increase by comparing the available information from a variety of countries, both past and present. He made extensive use of parish records and maintained an extensive correspondence. He also relied heavily on the publications of such writers as Antoine De-parcieux of France; Pehr Wilhelm Wargentin of Sweden; Nicolas Struyck, Willem Kersseboom, and Bernard Nieuwentyt of the Netherlands; and British authors Graunt, Petty, Gregory King, and John Arbuthnot.
Sussmilch’s theology led to a system of ethical and political maxims founded on the same desideratum of maximizing population. A Protestant pastor, he naturally decried alcohol, gambling, prostitution, urban life, priestly celibacy, and s...

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