Hacking 1990
Hacking, Ian. The Taming of Chance. Cambridge University Press, 1990.
During the nineteenth century it became possible to see that the world might be regular and yet not subject to universal laws of nature. A space was cleared for chance.
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Something else was pervasive and every- body came to know about it: the enumeration of people and their habits. Society became statistical.
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A new type of law came into being, analogous to the laws of nature, but pertaining to people. These new laws were expressed in terms of probability. They carried with them the conno- tations of normalcy and of deviations from the norm.
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1 By the end of the century chance had attained the respectability of a Victorian valet, ready to be the loyal servant of the natural, biological and social sciences.
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Such social and personal laws were to be a matter of probabilities, of chances. Statistical in nature, these laws were nonetheless inexorable; they could even be self-regulating. People are normal if they conform to the central tendency of such laws, while those at the extremes are pathological.
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Few of us fancy being pathological, so 'most of us' try to make ourselves normal, which in turn affects what is normal. Atoms have no such inclinations. The human sciences display a feedback effect not to be found in physics.
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The transformations that I shall describe are closely connected with an event so all-embracing that we seldom pause to notice it: an avalanche of printed numbers. The nation-states classified, counted and tabulated their subjects anew.
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Behind it lay new
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3 technologies for classifying and enumerating, and new bureaucracies with the authority and continuity to deploy the technology.
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Determinism was subverted by laws of chance. To believe there were such laws one needed law-like statistical regularities in large populations. How else could a civilization hooked on universal causality get the idea of some alternative kind of law of nature or social behaviour? Games of chance furnished initial illustrations of chance processes, as did birth and mortality data. Those became an object of mathematical scrutiny in the seventeenth century. Without them we would not have anything much like our modern idea of probability.
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Statistical laws that look like brute, irreducible facts were first found in human affairs, but they could be noticed only after social phenomena had been enumerated, tabulated and made public. That role was well served by the avalanche of printed numbers at the start of the nineteenth century.
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Statistical laws were found in social data in the West, where libertarian, individualistic and atomistic conceptions of the person and the state were rampant. This did not happen in the East, where collectivist and holistic attitudes were more prevalent. Thus the transformations that I describe are to be understood only within a larger context of what an individual is, and of what a society lS.
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This obsession with the chances of danger, and with treatments for changing the odds, descends directly from the forgotten annals of nineteenth century information and control.
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Only around 1840 did the practice of measurement become fully established. In due course measuring became the only experimental thing to do.
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The avalanche of numbers, the erosion of determinism, and the invention of normalcy are embedded in the grander topics of the Industrial Revolution.
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Despite various discernible precursors and anticipa- tions, our idea of probability came into being only around 1660, and the great spurt of statistical thinking did not occur until the nineteenth century.
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Most professionals now believe that representative sampling gives more accurate information about a population than an exhaustive census. This was unthinkable during most of the nineteenth century. 7The very thought of being representative has had to come into being.
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A noncommittal account of what I am attempting might be: an epistemological study of the social and behavioural sciences, with consequences for the concept of causality in the natural sciences.
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Transformations in concepts and in styles of reasoning are the product of countless trickles rather than the intervention of single individuals.
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Peirce positively asserted that the world is irreducibly chancy. The apparently universal laws that are the glory of the natural sciences are a by-product of the workings of chance.
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This is not to say that the erosion of determinism had nothing to do with life. It had everything to do with life: living people. Not living people regarded as vital organic unities, but rather regarded as social atoms subject to social laws. These laws turn out to be statistical in character.
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They could be seen as statistical only when there were, literally, statistics. There could be statistics only when people wanted to count themselves and had the means to do so.
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First I shall take up the counting that existed during the lifespan of Hume and Kant. It was largely of two kinds: secret and official, or public but amateur.
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England was the homeland of insurance for shipping and trade. It originated many other sorts of provisions guarding against contingencies of life or illness, yet its numerical data were a free enterprise hodge-podge of genius and bumbledom.
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Graunt and the English began the public use of statistics. Peoples of the Italian peninsula and elsewhere had promulgated the modern notion of the state. But it was German thinkers and statesmen who brought to full consciousness the idea that the nation-state is essentially characterized by its statistics, and therefore demands a statistical office in order to define itself and its power.
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He formulated this idea of a central statistical office about 1685, a few years after William Petty had made the same recommendation for England. 4Leibniz saw a central office as serving the different branches of administration: military, civil, mining, fo…
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In 1719 an abortive enumeration of the entire state was attempted. Various systems of reporting were experi- mented with, and an initial summary of results was issued on 3 March 1723. By 1730 people were officially sorted into the following nine cate- gories: landlords, goodwives, male and female children; then household members classified as journeymen, farmhands, servants, youths and maids.
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What might the numbers reveal to enemies? A decree of 2 January 1733 forbade publication of the population list. It became a state secret.
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If there is a contrast in point of official statistics between the eighteenth and nineteenth centuries, it is that the former feared to reveal while the latter loved to publish.
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Most designations of minority groups were local and haphazard, the exception being Jews. They show up in the tables in 1745, and, at that time, not as a religious group. Soon there was to be a completely separate and regular enumeration of all Jewish households. Complete tables, known as the General-]udentabellen or Provinzial-]udenfamilie-Listen, became a routine part of Prussian numbers in J769.
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A great landowner and a public man, caught up in the vibrant movement for agricultural reform in Scotland, he had been convinced in Europe that facts and numbers were the handmaiden of progress. Nothing was known of his country: he would change that. 1799 saw the completion of the 21-volume Statistical Account of Scotland that he had started directly after the European tour, 1788.
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The British kept people separate from stuff. Vital statistics in the south were prepared by the Registrar-General for England and Wales, an office established in 1837. Stuff was managed by the Board of Trade, an old institution with a chequered lineage.
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We do not here want a history of institutions like the Board of Agri- culture in London or the Royal Statistical Bureau in Berlin. We need notice only that new kinds of authorities were created, with new kinds of mandate. The transition was commonly effected by coopting the talents of the amateurs.
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One characteristic feature of the new kind of bureau was little affected by its administrative home. It published and published and published, combining the eighteenth-century enthusiasm for making numbers public with the power of orderly government.
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I shall lay great stress on the very first published civic statistics of a 'modern' sort, those begun by Paris and the Department of the Seine in the 1820s.
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Prussia, as the most powerful and as one of the first in the statistical field, established the technology that was to be used, although other German states such as Baden and Wiirttemberg were by no means inactive. Other nations and groups of nations followed other paths. Yet each, in its own way, created similar institutions to create its own public numbers.
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The institutions brought a new kind of man into being, the man whose essence was plotted by a thousand numbers:
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Published tabulations freeze the assembled numerical facts of a nation in cold print. The tables exhibit regularities from year to year. Can that new kind of thing, a statistical law of human nature, be far behind? Yes and no. It depends where you are.
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Statistical law needed two things. One was the avalanche of printed
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numbers that occurred throughout Europe. Without the post-war bur- eaucracies there would have been no tabulations in which to detect law-like regularity. But there also had to be readers of the right kind, honed to find laws of society akin to those laws of nature established by Newton.
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Why, if you are a conservative, who regards law as a social product, are you disinclined to think that statistical laws can be read into the printed tables of numerical data, or obtained from summaries of facts about individuals? Because laws are not the sort of thing to be inferred from individuals, already there and counted. Laws of society, if such there be, are facts about the culture, not distillations of individual behaviour.
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Why, if you are a liberal who regards law (in the political sphere) as a product of the will of individuals, are you content to find statistical laws in facts about crime and conviction published by the ministry of justice? Because social laws are constituted by the acts of individuals.
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This model indicates where many nineteenth-century incoherencies arise. To begin with, if, as many today will tell you, probabilistic law applies to populations, ensembles, or Kollectivs, ought not the collectivist, holistic attitude be the one that invites the notion of statistical law? Conversely, if the liberal thinks that statistical laws are laws of society, akin to laws of nature, then what freedom is left to the individuals en masse? This question of statistical fatalism reared its confusing head in mid-century.
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The moral sciences aimed at studying people and their social relation- ships. But how? Not by anticipating empirical psychology or survey- samplc sociology. Condorcet's moral science meant chiefly two things, and thereby hangs a tale not yet unravelled even today. He mapped out what have become two distinct terrains. One is moral-science-as-history, the other, moral-science-as-(probability, statistics, decision theory, cost- benefit analysis, rational choice theory, applied economics, and the like).
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By 1670 it was evident to the enlightened leaders of the brief Dutch Republic that mortality data should be used to guide rates for selling life annuities - the standard way of raising capital for the state. The idea did not really take off, for reasons well elaborated by Lorraine Daston, but it was a viable idea of actuarial data as applied science.
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Even though mortality statistics were of little practical importance until the nineteenth century, they were conceptually significant. They gave rise to the idea of a law of mortality, and to the very phrase 'law of mortality'.
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Laws of birth and mortality abounded. Lambert serves me only as an example. Because death curves were not seen as a matter of maurs, or customs, they gave little foothold for moral science or social mathematics.
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But they did furnish data for the solution of problems in social mathema- tics: ideally, for example, the correct rates at which a government should sell life annuities when a given rate of interest is prevalent.
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Only after 1829, when there were printed tabu- lations of French jury decisions, could Poisson form the idea of proba- bilistic laws of voting behaviour. It was the printed numbers that turned Condorcet's a priori studies into Poisson's empirical ones.
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He appears to have been a sensible administrator who asked what we now think of as the right theoretical questions. For example, his paper on the mathematical statistics of the population was the first attempt, in France, to obtain systematic breakdowns of the laws of mortality not just according to age but also by sex, marital status, and, tentatively, location and even occupation. 24Such a question entailed new echelons of clerks, enumerators, calculators, printers that would in time create the avalanche of numbers. Duvillard was also a prophet.
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When the wars were at an end, the city of Paris set the model for publication of social data, and the avalanche of printed public numbers was under way. But without Condorcet's enlightenment vision of law, of moral science, and of the sweet despotism of reason, those number-collecting offices might merely have manufactured tables in the Prussian style. French numeration and social mathematics were instead sired by Newtonian ambitions of laws of society.
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Fraud, drink and agitation were not the main difficulties. The problem was actuarial. No one had any idea of what premiums to charge. Moreover, except when insurance companies got into the act, the English clubs were small and local.
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There were experts. The most famous , Richard Price, had died in 1791, but he had left the Northampton tables, which provided a law of mortality based on the eighteenth-century records of the city of Northampton.* They became the British standard for a century, enacted into laws regarding premiums for life insurance and life annuities.
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Price's tables may have been unjust but they made a deep impression upon the English mind. We now think that work done in Sweden was much better. 7The Select Committee asked nearly all its expert witnesses about what it called the 'Swedish tables', but the experts knew little.
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Britain, like many other states, raised much capital by selling life annuities. There had been a gigantic annuity sale in 1808. In 1816 the national debt was £900 million. After the Napoleonic wars Britain conducted its affairs by deficit financing. By the standard of all other states its debt was grotesque. Finlaison's job was to ensure that the annuity side of the debt was serviced, given that millions upon millions of pounds had been purchased at disastrous bargain basement rates.
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The British became convinced that there are regular laws of sickness akin to those for mortality.
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He was a Duvillard de Durand whose time had come. His system of reporting and analysis of the incidence of birth, life and death became the model for the world. He was also the first functionary to install and deploy a computer on his premises, for the purpose of calculating and printing out annuity rates and the like.
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Pen
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Numerical regularities about disease, unknown in 1820, were common- place by 1840. They were called laws, laws of the human body and its ailments. Similar statistical laws were gaining a hold over the human soul. The analogy was close, for laws of behaviour aimed at sick souls.
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So many more things were being made and had to measure up, in 1826, that a need for vastly more comprehensive systems of standards was felt.
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Quite aside from an absence of thoughts about 'fundamental' constants, there was no category of physical constants or constants of nature until the 1820s. Babbage's letter to Brewster of 1832 was important not because it was influential (although Babbage was at his apogee in those years) but because it was representative.
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Babbage was not the first to want to compile lists of constants. His indefatigable contemporary, Johann Christian Poggendorf, editor of Annalen der Physik und Chimie (and later creator of the definitive nineteenth-century biographical and bibliographical science reference work) had just published tables of what Babbage calls 'the constant quantities belonging to our (solar] system'…
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8 Babbage's exercise, he suggested, would be useful when ordering type fonts. The letter frequencies had more to do with Babbage's ingenious but bizarre interests in cryptography.
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The letter on constants of nature and of art is thus a more personal document than at first appears. Nevertheless this odd letter epitomizes the moment, 1832. The British Association printed Babbage's letter as a separate pamphlet. The first of the great Quetelet-organized statistical congresses republished it in 1853, as did the Smithsonian Institution in 1856. Joseph Henry, in his secretarial report to the Smithsonian as late as 1873, referred to Babbage's letter as the model for tables of specific gravities, boiling points and melting points. 13Babbage's odder items were passed by. He remained a symbol of a new way to think about nature and our works: numerically.
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The first half of the nineteenth century generated a world becoming numerical and measured in every corner of its being. In our own 'information age' quirky Charles Babbage has become posthumously famous for elaborating the general principles of the digital computer. Instead I single him out as the self-conscious spokesman for what was happening in his times.
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Near the end of his essay on measurement, Kuhn emphasizes his 'paper's most persistent thesis: 'The road from scientific law to scientific measurement can rarely be traveled in the reverse direction. To discover quantitative regularity one must normally know what regularity one is seeking and one's instruments must be designed accordingly.'
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What then are laws? Any equations with some constant numbers in them. They are positivist regularities, the intended harvest of science. Collect more numbers, and more regularities will appear. Now it is time to see how the empty silos of human beha\•iour began to overflow with laws of human nature.
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I call the Anglo-French squabbling about suicide the beginning of numerical sociology because (a) there were numbers and (b) the numbers of suicide were seen as a moral indicator of the quality of life. The issue was immediately joined.
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The practice of recording weekly mortality and causes of death originated in London, and was made famous in Graunt's 1662 Observa- tions on the Bills of Mortality. They had become the model for Europe, but had declined at home. Burrows lamented 'the annual barbarously ignorant Bill of Mortality of London'. Graunt's days were long gone. 'Too many are content with viewing effects only and search no further. From such cause, perhaps, the value of statistical enquiries has been under-rated.'
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Physicians had regarded disease as imbalance in the whole body, but by 1800 disease was primarily to be located in an injured, defective or irritated tissue or organ.
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…not only did people discover statistical laws about suicide, crime, divorce, prostitution and other bad behaviour, but also they thought there was an explanation of the nature of statistical law that made it safe for determinism. This was a curious marriage of astronomical, mathematical and medical lore…
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By 1830 innumerable regularities about crime and suicide seemed visible to the naked eye. There were 'invariable' laws about their relative frequency by month, by method, by sex, by region, by nation. No one would have imagined such statistical stabilities had it not been for an avalanche of printed and public tables.
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The model was set by the annual Recherches statistiques sur la ville de Paris et le departement de la Seine.
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Guerry's 1832 essay on the 'moral statistics' of France. Like many other French books that I shall mention, it won the Prix Montyon, at that time awarded annually for work of a statistical nature. It is a superb object of noble dimensions with fine maps indicating the geographical distribution of crime. The hygienic movement gave us our present conception of graphical representation, the ancestor of today's computer- ized spreadsheets.
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Guerry knew the importance of mechanizing this work and designed a calculator for handling his data. It is
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…xperimental basis of the philosophy of legislation 77 fitting that he called it an ordom1ateur statistique. The present French name for the computer, the ordinateur, was reinvented in response to a request by IBM France to replace the franglais computeur.9
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Guerry called his work comparative statistics. That statistics should be comparative is part of their original mandate to measure the power and wealth of the state, as compared with other states.
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One obituary notice related that the numerals in the cards on which Guerry kept his notes would, if written down in a line, stretch for 1,160 metres.
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Numbers were a fetish, numbers for their own sake. What could be done with them? They were supposed to be a guide to legislation. There was the nascent idea of statistical law, but hardly any statistical inference.
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Here is a way in which the new stausucs seemed to matter. In 1785 Condorcet applied probability theory to judicial questions. In 1815 Laplace made some powerful a priori deductions about conviction rates. Once judicial statistics were available, his protege Poisson used statistical inferences to overturn his conclusions. There is then a simple three-stage story of probability arithmetic and the French jury.
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Witnesses, assemblies and juries have played a significant role in the development of probability ideas. We tend to forget why they mattered. They were part of the notion so well surveyed by Daston, that there could be a 'reasonable calculus'.
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I claimed in The Emergence of Probability that our idea of probability is a Janus-faced mid-seventeenth- century mutation in the Renaissance idea of signs. It came into being with a frequency aspect and a degree-of-belief aspect.
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The avalanche of printed enumerations of social conditions began in the 1820s with the Recherches statistiques of Paris and the Seine directed by Joseph Fourier.
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The powerhouse of the statistical movement was Adolphe Quetelet, the greatest regularity salesman of the nineteenth century. As soon as Parisian judicial statistics were published he noticed 'the terrifying exactitude with which crimes reproduce themselves'.2 The number of criminals is con- stant; the relative proportions of different sorts of crime remains the same.
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Quetelet changed the game. He applied the same curve to biological and social phenomena where the mean is not a real quantity at all, or rather: he transformed the mean into a real quantity.
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It was Quetelet's less-noticed next step, of 1844, that counted far more than the average man. He transformed the theory of measuring unknown physical quantities, with a definite probable error, into the theory of measuring ideal or abstract properties of a population. Because these could be subjected to the same formal techniques they became real quantities. This is a crucial step in the taming of chance. It began to turn statistical laws that were merely descriptive of large-scale regularities into laws of nature and society that dealt in underlying truths and causes.
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Quetelet had precious few examples of Gaussian distributions. 'Male height is still almost unknown even in the most civilized countries of Europe.' 15 And why should one collect such information? It is interesting only if one believes, with Quetelet, that it signifies some underlying real characteristic of a population.
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The law of error had chiefly mattered to astronomers. Quetelet exported it to the human sciences, wrapping it in an obscure metaphysics of minute underlying causes.
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A determi- nistic world view was threatened on many fronts by the phenomena suggested by the new statistics, and there was no coherent way to understand the burgeoning phenomena. The talk about underlying causes was only one element in the papering over of conceptual cracks.
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Statistical information leads to the discovery of statistical laws. We who collect the information change the boundary conditions and thereby change the laws of society.
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Instead of engendering political self-doubt, the connections
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between information, control and statistical law created a metaphysical quandary, which was called statistical fatalism.
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One thing is clear. Had there not been that avalanche of numbers in 182(}....40, and the accompanying conception of statistical law, we would have no such problem.
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We obtain data about a governed class whose deportment is offensive, and then attempt to alter what we guess are relevant conditions of that class in order to change the laws of statistics that the class obeys. This is the essence of the style of government that in the United States is called 'liberal'.
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It was statistical fatalism. Accord- ing to that doctrine, if a statistical law applied to a group of people, then the freedom of individuals in that group was constrained.
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In the West the spirit of positivism made out that all laws were mere regularities. A belief in causes over and above regularities was an illegitimate residue of the meta- physical age.
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The years 1826-9 exemplify a shift in that era of enthusiasm from mere counting to increasingly minute classifications of the people counted. Balzac was familiar with this. His father had been fascinated with the Malthusian debate, and made statistical reformers such as Benoiston de Chateauneuf known to his son, who in turn put them into the 1829 Physiology.
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Le Play did not systematically publish his results until 1855, when he put 36 families on view (he had many more in storage). He called the whole method one of writing monographies. These studies are different in kind from any statistical work that I have hitherto described. Yet they were numerical. How? The core of each monograph was a household budget, be it that of a Basque fisherman or of a master bleacher in the Clichy suburb of Paris. Every item of a year's income in cash and kind was faithfully recorded. Likewise each sort of annual expense was tabulated, not just rent and food, but candles and cabbages.
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The monographs were divided into three, with the household budgets as the core. The first part was a thorough account of the location and practices of the family in its site (history, rank, religion, health habits, clothing, dwelling, recreation, together with the state of manufacture and agriculture in the region). The third part contained social and moral reflections on the immediate causes of the condition of the family as reported. In the middle was the monographie proper, namely the descrip- tion of the family summed up in its domestic budget.
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An era of optimism about the possible uses of statistics ended in 1848, prompting many kinds of backlash.
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One was political. The statisticians were typically advocates of liberal utilitarian reform. People who had no truck with their philosophy, or with its pretensions to resolving current social issues, held them in contempt slightly mingled with fear.
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People and the world became not less governed but more controlled, for a new kind of law came into play. That is why I speak of chance being tamed.
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Pen
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Think of Paul Eluard, king of Dada, composing and publishing poems that consist simply of words, first written on slips of paper, and then drawn from a hat. We've really escaped necessity here, publishing purely random words! Yet in exactly the same decade L.J.C. Tippett first collected and finally published tables of random sampling numbers under the auspices of Karl Pearson's journal, Biometrika. 22These were systematically random numbers, taken from the digits of dates of births and deaths in parish registers. These cradle and tombstone digits of pure chance were intended to increase the efficacy of data analysis, to bring order into chaos, to derive firm bounds for any error that might be produced by chance fluctuations. Dada and Biometrika: two sides, we might say, of the same coin.
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As a word, 'determinism' came into use in the 1780s, and assumed its present most common meaning in the 1850s. As a word, 'normal' is much older, but it acquired its present most common meaning only in the 1820s.
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When was the last great debate involving human nature? 1829.
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The industrializing world demanded standardization. We recall Babbage and the constants of nature and art, as enumerated in chapter 7. He hardly distinguished standards of art that are imposed by engineers from con- stants and norms that are to be recorded from nature.
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Comte thus expressed and to some extent invented a fundamental tension in the idea of the normal - the normal as existing average, and the normal as figure of perfection to which we may progress. This is an even richer source of hidden power than the fact/value ambiguity that had always been present in the idea of the normal. The tension makes itself felt in different ways. If we think ahead to sociology and to statistics, in the modern comprehension of those terms - that is, if we think ahead to the work encrusted around names such as Durkheim and Galton - we feel the tension acutely.
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Words have profound memories that oil our shrill and squeaky rhetoric. The normal stands indifferently for what is typical, the unenthusiastic objective average, but it also stands for what has been, good health, and for what shall be, our chosen destiny. That is why the benign and sterile-sounding word 'normal' has become one of the most powerful ideological tools of the twentieth century.
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17So just at the time of the antisemitic agitation, there were fewer data about the Jewish population. Thus it became increasingly easy to invent 'statistical axioms' about the mass-immigration of Jews.
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Peirce is the strongest possible indicator that certain things which could not be expressed at the end of the eighteenth century were said at the end of the nineteenth.
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