porter1990 statisctics are socially constructed.pdf

CHAPTER 3

THE QUANTIFICATION OF UNCERTAINTY AFTER 1700: STATISTICS SOCIALLY CONSTRUCTED?

Theodore M. Porter

Abstract--The quantification of uncertainty has since the time of Pascal and Fermat been tied to a program of social rationalization and enlightenment. Probability and statistics, though their historical roots are distinct, have always been united in this: that they provide a way of understanding and hence controlling the uncertainties of change. Mathematical probability arose out of legal traditions involving the valuation of evidence, and by the eighteenth century was generally conceived as the scientific surrogate for native good sense in a world where this was too often lacking. Statistics, a science of nineteenth-century origins, began as the application of numerical reasoning to the problems of society. Its job was to uncover the order of large numbers that prevailed beneath the conspicuous turbulence and unpredictability of surface events, and to provide the legislator with the knowledge needed to combat potential instabilities in social development. The ideas and techniques that were developed in the context of these social and philosophical projects have since become standard tools of the sciences, natural as well as social. Mathematical statistics might thus appear to reflect the social interests of those who have invented and applied it rather than to provide true knowledge about nature, or, in the current jargon, to be "socially constructed.·

This paper is a historical exploration of the mathematical assault on chance and risk in the centuries before acting under uncertainty became a preoccupation of specialized social and behavioral sciences. I seek to show how thoroughly the history of probability and statistics contravenes the standard view of the hierarchy of the sciences, to show that the origins of some of the most fundamental ideas and assumptions of mathematical statistics, statistical physics, and population genetics lie in the social sciences, and even in social ideologies. I aim also to clarify the relations between the content of the sciences and their social contexts by defining this sharply for the case of statistics. The paper will defend a thoroughly contextualist approach to the history of science, but not one that reduces science to institutional forms and social relations.

G. M. von Furstenberg, Acting under Uncertainty: Multidisciplinary Conceptions© Springer Science+Business Media Dordrecht 1990

46 Acting Under Uncertainty: Multidisciplinary Conceptions

Probability theory arose as the mathematics of uncertainty. The term itself reveals a monumental act of scientific imperialism. For originally "probability" had nothing to do with mathematics, or even numbers. As Edith Sylla explains in this volume, a doctrine had traditionally been called probable if, while lacking certainty, it came on authority reliable enough to be worthy of belief, and of being acted upon. In the aftermath of the striking new approach to gambling problems developed by Blaise Pascal and Pierre de Fermat, a few natural philosophers began to wonder if this non-demonstrative knowledge, probability, might be reduced to mathematics. Pascal ([1670] 1962) himself, in perhaps the most famous of his Pen sees, applied the reasoning of mathematical expectation to belief in God, arguing that the prospect of an infinite reward made Christian faith a sensible wager no matter how great the odds against its truth. Thus was mathematical probability, from its very inception, the instrument of a brave campaign to bring important decisions into the domain of calculation. Statistics, a science of early nineteenth-century origins, had only slightly less extravagant ambitions. It was to be the quantitative science of the state, or the method of science--counting and comparing numbers--as applied to society. Statisticians aimed to promote social reforms, leading towards a rational polity and a prosperous economy. By the end of the nineteenth century, statistics and probability had come together, forming what is still the standard mathematical tool for dealing with uncertainty.

These aims were not mere embellishments of a pure mathematical, or even a pure scientific, program of research. On the contrary, the history of mathematized rationality and of quantitative social science comes close to being a history of statistical mathematics in its formative" period. Such at least is the perspective offered in this paper. I am concerned here with the effort to subject variation and uncertainty to the guiding compass of mathematics in the centuries before acting under uncertainty became a specialization within the modern social sciences. The coverage is necessarily selective, and will emphasize the ways in which the social mission of providing a guide to action was interwoven with the invention of some key methods and concepts of what has become the statistical method.

This, then, is a highly contextual history. Statistics will be treated here as a social construct. Indeed, I am concerned here with the relations of statistics to the broader society, and not merely with social processes that are internal to the scientific community. This contextual

· The Quantification of Uncertainty After 1700 47

approach provides only a partial view of the history of science, but it is an essential one if science is to be understood as a part of history. It is not to be construed as an assault on the value of statistical methods, but as an exploration of growing role of quantification in modern history.

I. CLASSICAL PROBABILITY

Jakob Bernoulli's Ars Conjectandi ([1713] 1968) set out a program to make belief an exact science, to put numbers to all our uncertainties, to reduce rationality to mathematics. That campaign culminated in Pierre Simon Laplace's use of what is now called Bayes' Theorem to define what rationality means--whether in judicial decisions, business calculation, evaluation of historical testimony, or theory choice in science. Lorraine Daston's (1988) remarkable study of probability in the Enlightenment shows that mathematical probability was esteemed a scientific surrogate for good sense in a world where this was too often lacking. In place of the wise intuition of the enlightened few, it offered calculation of degrees of belief. It would substitute public demonstration for ineffable wisdom.

The classical probabilists made much of their epistemological modesty. Like Newton, they renounced fanciful hypotheses (see Molland's paper in this volume). They were willing, at least provisionally, to do without knowledge of deep causes, and to proceed instead by counting instances. They would learn about the causes of sex at birth through careful registration, and then by comparing empirical ratios from London and Paris, or city and country. They would use mortality records to decide on the advisability of inoculation for smallpox, while recognizing that the conclusion might not be applicable to any particular individual. And even for large numbers, they conceded the inevitability of error, just as there was always error in astronomical measurements. As Laplace ([1814] 1951) put it, famously, a perfect intelligence would have no need of probability, but for mortal man it is indispensable. In a world of uncertainty, it seemed an immense advantage to be able to quantify partial belief.

But if probability involved some compromise of the standards of rational demonstration that had traditionally been associated with philosophy, we must not associate this with diminished scientific


ambitions. Laplace did assert his humility too much. He accepted a loosened standard of rigor of scientific belief, but only in order to expand the domain of science beyond all limits. Probability could not eliminate uncertainty from the world, but it promised a rational way of managing it. The dream of mechanized decision criteria based on the maximization of probability values or mathematical expectations had already been dreamed in the eighteenth century. Ian Hacking (1975) has argued that probability emerged from the low sciences, such as alchemy and medicine. Here, knowledge was based on similitude rather than demonstration. Probability, he suggests, became possible upon the breakdown of this Renaissance world of signs and likenesses, and their replacement by the idea of evidence. The notion of evidence figures prominently also in Daston's account of early probability theory: she argues that probability arose mainly from legal and commercial reasoning. She points out that the earliest quantitative study of games of chance was conceived in terms of the fair contract, and expressed in terms of expectations. The shift to a style of reasoning whose elemental concept was that continuous magnitude between zero and one, the chance of an event, reflected the influence of a different branch of legal reasoning. Jurists had long made use of a theory of partial proofs, which were added together to make a full proof that would justify conviction (in both senses of the term). G. W. Leibniz and Jakob Bernoulli, both trained in the law, developed a mathematical grounding f or legal probabilities and sought to use this as a model for apportioning belief whenever certainty was not attainable.

Probability thus came to provide a model of enlightened good sense. Indeed it was more than a model. Probability theory was nothing else than the mathematics of good sense. Like mechanics, probability was part of "mixed mathematics," that most rationalistic branch of natural knowledge in the eighteenth-century classification of the sciences. Again like mechanics, probability was not merely required to produce agreement between premises and conclusions, but to make accurate predictions about the world. The relation of the calculus of probabilities to rational belief was much like that of optics to light. If it proved to condone judgments or actions that manifestly lacked good sense, then evidently there was something wrong with th~ theory, which required correction.

Daston's best example of the subordination of mathematics to enlightened good sense is the St. Petersburg paradox, first stated by Jakob Bernoulli's nephew Nicholas (printed in Montmort, 1713). This

The Quantification of Uncertainty After 1700 49

arises from a game in which Peter will toss a coin until it turns up heads. If this occurs on the first try, Paul owes him $1; if on the second, $2; if on the third, $4; and if not until the Ilth toss, Paul must pay him $2"·1. The question is: what is a fair price for Peter to pay Paul for the rights to the proceeds of this game?

Mathematicians quite naturally looked to probability for an answer. More than that, they required probability to give a good answer. It was after all the logic of good sense. Failure to do so would virtually amount to a falsification of the theory. And this is why the St. Petersburg problem was called a paradox. For probability did give a simple answer--one that, though un problematical mathematically, manifestly contradicted good sense. The fair price in a gambling problem was defined in probability theory as the mathematical expectation of gain. Here the expectation was [(1/2) + 2(1/4) + 4(1/8) + ... + 2"'1(1/2") + ... ] = [1/2 + 1/2 + 1/2 + ... ], which, since the game can continue indefinitely, is infinite. But, as Bernoulli remarked, no sensible person would pay more than a few dollars to play such a game.

Hence it was necessary either to give up the calculus of probabilities, or to tinker with it. Daniel Bernoulli ([1738] 1954), a cousin of Nicholas, chose the latter option. In a widely influential paper that is now best remembered as the first intimation of the theory of diminishing marginal utility, he defined a "moral expectation" which increased not linearly with wealth but only in proportion to its logarithm. After all, one dollar means much less to a person who already has millions than to one on the verge of starvation. Hence very small probabilities of proportionately large gains are worth almost nothing, so that the sequence declines sharply and the total moral expectation of the game is a modest number. Jean d'Alembert (see Daston, 1979) took a more radical course, proposing to solve the St. Petersburg problem with a change that radically undermined the conventional theory of probabilities. A very long run of tails, he argued, is mathematically possible but physically impossible. The probability of a new throw of heads must go down as the number of consecutive identical tosses goes up. Good sense supports this, he held, for if tails were tossed even 100 times in a row, nobody would believe the coin was fair. D'Alembert's solution, in contrast to Bernoulli's, was condemned unanimously by probability writers, and it caused something of a scandal that a mathematician so brilliant could be so stubbornly wrongheaded about probability. But we can at least see that he, like Bernoulli, was


troubled by the chasm between the mathematics of probability and good sense.

II. THE SOCIAL ORIGINS OF STATISTICS

The development of statistical mathematics, too, cannot be understood without taking into account the social and ethical aspirations of the "statists" who studied it. Statistics, like probability, was originally intended to provide a way of quantifying the most important aspects of human existence. Both aimed to make reason the guide of private and public action. There is, however, an important distinction to be made here. The eighteenth-century science of probability was normative and individualistic, concerned mainly with the rational apportionment of belief. The nineteenth-century science of statistics aimed first of all to describe the laws governing a social collective, albeit with the expectation that they would have implications for social reform. These aims, while not incompatible, reflected rather different sensibilities about how order was to be imposed on political, social, and economic life. Still, their shared goals and presuppositions would seem to outweigh this divergence. Quantification in each case meant subduing the irrational and inexplicable. It admitted a degree of uncertainty, or at least a level of existence (the individual) for which prediction was not possible. As compensation it offered a means of extraordinary range and flexibility for discovering order where it had hitherto gone unperceived and creating it where it had been lacking.

Although probabilists, and most notably M.-J .-A.-N. Condorcet (Baker, 1975), tried to make their science the foundation of policy, it had flourished principally in the rarified domain of mathematicians and natural philosophers. Statistics, in contrast, was located mainly outside the academies and universities. Emerging at first in Great Britain and France early in the nineteenth century, it looked rather more like a movement than a science. Official statisticians began collecting numbers to promote mobilization for war in the Napoleonic period. In the private sphere, "statists" were generally moved by poverty, disease, crime, and urban unrest. They campaigned vigorously for public education and for public health measures. They claimed the objectivity


of science, which they identified with numbers, but did so mainly in order to invoke its authority against their opponents.

The issue here is not whether ideological commitments stood behind the statistical movement. That much is unquestionable. What may appear more doubtful is whether that movement contributed markedly to the development of statistical method and statistical mathematics. After all, the statists were for the most part thoroughly practical men--men of business, the law, and medicine--and were often untrained in science. Very few had any knowledge of probability, or any formal conception of how to deal with uncertainty and error. And yet we can say with only slight exaggeration that these reformers and publicists introduced to the world the most basic concepts of statistical thinking. As worshipers of numbers, they took for granted that something important could be learned about the causes of crime, births out of wedlock, and mortality from laboriously-collected statistics. Since it was the "mass" of humanity with which they were concerned, they were untroubled by the impossibility of making predictions about individuals. Rather than seeking to explain this or that suicide, statisticians wondered why suicide in Prussia was up this year, or why the mean height of conscripts was higher in northern than southern France. They assumed, that is, the regularity of large numbers. They even believed that a science of society could be based on them.

There was, however, a critical intellectual shift that had provided a rationale for investigations of this sort. The statistical research of the nineteenth century was predicated on the new conception of "society" that was developed in the wake of the French and Industrial Revolutions. The threat of social turmoil had called the statistical movements into existence. The regularities they discovered off ered the statisticians hope that society was on track, that disorder was exceptional, or that undesirable activities such as crime somehow fit into the larger scheme of things. But the decisive importance of the concept of society, for our purposes, is that it provided statistics with a proper object, a level of existence above the individual. Society was an entity that statistical regularities could be properties of. Crime rates and suicide frequencies could scarcely be understood as normal characteristics of every man or woman. On the contrary, it was widely agreed that these were dependent on the state of society, and could be reduced, or increased, if the social order was reformed.

This view of statistical regularities, of crucial importance for the subsequent development of statistical thinking, was worked out around


1830. It must be understood that certain regularities of large numbers were well known in the eighteenth century. Jakob Bernoulli ([1713] 1968) had proven an important theorem about the convergence of frequencies of outcomes, say of coin tosses, to the underlying probabilities. The uniformity from year to year of the ratio of male to female births, of marital fertility and age of death, was well known to demographic quantifiers such as the Prussian pastor Johann Peter Siissmilch (1765). But these reflected the natural order of things, even the biological character of mankind. They did not lead to a general expectation of regularity in all social numbers, as we can see from the shock with which the first statistical tabulations of crime were greeted, even by men whom we might have expected to know better. A stable crime rate could be no natural consequence of free individual activity. Instead, it seemed to imply an alarming fatalism, some mysterious force that drove people to murder or suicide, even against their will. Such, for instance, was the reaction of the Belgian astronomer turned social statistician Adolphe Ouetelet (1829), who more than anyone else was responsible for formulating and popularizing the idea that immoral acts were subject to statistical laws.

Ouetelet's distress, however, was only momentary. For a troubled liberal, deeply fearful of revolution (especially after 1830), the paradoxical discovery of laws of crime was cause for celebration. And celebrate Ouetelet did, in a stream of memoirs and books intended for scientists, functionaries, rulers, and the general public (e.g. Ouetelet, 1835). He drew two general conclusions from his figures. First was the seemingly conservative, but in fact merely reassuring, one that society was on track. Human errors could not permanently derail society from the course of progress. His second, and most controversial, conclusion involved moral accountability. Society was more powerful than individuals, and hence also more responsible. The repetition of the same crimes with the same frequencies every year proved that society, not the individual criminal, was the real malefactor. It was the task of the legislator to put into law those ref orms whose advisability was shown by statistical study, and thus to reduce this terrible, needless slaughter. One or the other of these two morals, both enunciated by Ouetelet in the early 1830s, was drawn virtually every time the "laws of statistics" were discussed during the remainder of the century. Which one depended on ideological temperament. Ouetelet's English admirer, the militantly liberal historian Henry Thomas Buckle (1857), inferred from statistics that the laws of history were supreme, and that neither a


meddling state nor an obscurantist church could block the inevitable progress of society. German "socialists of the chair," eschewing the "atomistic" determinism of "social physics" and Manchestertum, preferred the opposite conclusion, that a benevolent state was both capable and morally obligated to institute the reforms needed to improve the social condition (e.g. Knapp, 1871; 1872).

We thus find sharp ideological conflict concerning the most basic of statistical assumptions, that conclusions can be drawn from large numbers when the constituent acts (such as suicide) are too unpredictable or too numerous to be studied individually. The same can be said of the first application of the normal curve to statistical variation, a step of scarcely less importance. That, too, was Quetelet's work, though here again we have less an act of pure originality than a creative conflation of ideas. The normal curve had been derived as the limit of the binomial distribution by Abraham De Moivre early in the eighteenth century. Laplace put it to use to estimate, for example, the error in population estimates made by multiplying the total of births registered in a year by the ratio of births to population in a certain district chosen to be typical of all France. In 1809, Gauss showed how the curve could be used to measure another kind of error, when an astronomical quantity (such as a relative stellar position) was estimated from repeated measurements. It is for this that the curve is commonly called the Gaussian, though it was known almost universally as the error curve until late in the nineteenth century. It was as a law of error that the normal curve became a standard tool of astronomers, geodesists, and surveyors (Stigler, 1986).

Quetelet (1846), whose great mission in statistics was to show that "social physics" used the same methods and exhibited the same principles as celestial mechanics, extended the range of the error law to the physical and moral variation of humans in society. The crucial result of this was to vindicate, and indeed exalt, the concept of /'homme moyen, the average man. If, as he inferred, all real individuals are accidental deviates from an archetype, then the laws of the corresponding society can be learned from the study of mean values alone, with due regard also to the average error. This was very convenient for social physics, which aimed to plot a trajectory for society through time by extrapolating from a series of measurements of the average man. It also had gratifying implications for the future prospects of society. If a society is adequately represented by mean values, and if these mean values exhibit impressive stability from year

54 Acting Under Uncertainty: MUltidisciplinary Conceptions

to year, then the threat of discontinuous change can be defined away. Deviation is mere error. What remains is the true mean, the point of virtue that is always to be found between vicious extremes. Thus was Aristotelian moral philosophy vindicated by statistical mathematics.

These may seem rather strained analogies. But they are not unusual. A fuller discussion (Porter, 1986) would show how Ouetelet built his social physics out of an elaborate metaphor connecting the physical, the social, and the ethical. His own conception of social progress appeared in this scheme as deriving both from physical and moral laws. He also generalized freely, usually on the basis of analogy. His evidence that human variation was normally distributed consisted of what in retrospect seems an indifferent fit between the astronomer's error law and some physical measurements, mainly from records of military conscription. From this he concluded that all human traits, including moral and psychological ones, are distributed in the same fashion as errors of observation in astronomy. For example, every individual has a quantitative "penchant for crime." The values of these individual penchants vary randomly from the mean penchant for crime (the total of crimes committed annually divided by the population). This idea seemed to many statisticians to carry the denial of individual responsibility too far. But such reasoning was entirely typical of Ouetelet's intellectual style.

Among the pioneers of mathematical statistics, Quetelet's analogical imagination was slightly unusual f or its lack of discipline, but not at all exceptional in its fertility. Analogies were crucial for the application of statistical concepts and methods to new subject areas. After Ouetelet, social science itself became a crucial source of such analogies, analogies that were applied back to physics and biology. Ouetelet's ideas formed the bridge between the social science of statistics and the modern branch of applied mathematics that has taken its name. Here, then, the hierarchy of the sciences that we have come to regard as customary fell apart, or rather was folded back on itself. What is more, these social analogies sustained the bond between the methods of statistics and the social perceptions through which they had originated, even after the cutting edge of statistical innovation had shifted back to the sciences of nature.


Ill. THE STATISTICS OF MOLECULES

Statistical physics is among the most successful fields to borrow methods from the social science of statistics. In the great pioneering work of statistical gas theory by James Clerk Maxwell ([1860] 1890), we already find strong hints of his debt to the statistical tradition. The first three propositions in this paper show that a system of colliding particles (a gas) must quickly lose all trace of its initial configuration of positions and velocities. The result is complete disorder. But, argued Maxwell in a leap reminiscent of the social statistician, the disorder of innumerable objects will have an order of its own. He proceeded to determine that the gas particles must in fact come to equilibrium at the distribution of velocities given by the astronomer's error law. Strikingly, his derivation of that curve was almost precisely the one introduced by the astronomer and polymath John Herschel (1850) in a review of one of Quetelet's books. Herschel considered his derivation appropriate because of its simplicity and generality, suitable for what Quetelet had shown to be the extraordinarily widespread applicability of the error curve. Thus did Quetelet's faith in universal social order contribute to the recognition of a kind of molecular order. To the untrained eye, the motions and collisions of many billions of molecules would seem to be utterly beyond the grasp of science. Even three (gravitating) bodies introduced rna thema tical com plexities so grea t tha t no formal solu tion was possible. Only one versed in statistics could take for granted that millions of colliding particles would yield order at a higher level. When Maxwell was writing, even the existence of molecules was still completely hypothetical.

Maxwell was, to be sure, no passive recipient of the technical virtuosity of social science. Already in 1860 he was able to use elegant combinatorial mathematics to deduce properties of gases that had no analogues in society. But he took an active interest in many of the same problems that engaged the statisticians. The publication of Buckle's History of Civilization in Eng/and (1857) had set off a fierce controversy about the compatibility of statistical regularity with free will. Quetelet (1847), ambiguously, and Buckle, quite forthrightly, had been inclined to assume that there was no room for the capriciousness of human freedom where mathematical order had been shown to prevail. The availability of mathematical rules governing chance and uncertainty, however, could also lead in the opposite direction. Late in


the nineteenth century, when the statistical method had become well established, a few scientists and philosophers began arguing that it was unnecessary to endorse determinism even as a working assumption. Now they had research methods that were no less capable of dealing with a universe of chance. From the 1860s, social thinkers in much of Europe and North America developed this view in a vigorous discussion. Holistically-inclined German historical economists defended the idea of a nondeterministic social science most strenuously. Precisely because statisticians take averages over large numbers of individuals, they held, the most impressive regularities are still quite compatible with the existence of radical, unexplained human diversity--if not pure chance, with which they were rather less enthralled (Porter, 1987).

In several essays from the early 1870s, Maxwell (e.g. 1873) repeated this argument in a gentle criticism of Buckle, and proceeded to draw out its implications for physics. Since the kinetic gas theory is obliged to use the statistical method if it is to make any sense of this chaos of colliding particles, it must fall short of a perfect, dynamical explanation. Thus physics can no more exclude the operation of an element of chance, or of some unknown cause, at the molecular level, than social science can deduce from statistics who will commit suicide. Against Buckle, Maxwell insisted that statistics is bound by its nature to uncertainty, and can in no way provide evidence against free will.

Others maintained the opposite view. In physics for example, Ludwig Boltzmann held stubbornly to his early faith in atomistic reductionism and the complete determination of physical processes by natural laws. Boltzmann, Maxwell's most brilliant successor in the kinetic gas theory, was an admirer of Buckle. In one of his landmark technical papers on the kinetic gas theory he offered the unexpected argument that the adoption of a statistical method in physics no more implies uncertainty in its results than does its employment by social scientists, who have shown the most remarkable regularities to prevail from year to year (Boltzmann, [1877] 1968). Statistics, then, was a highly flexible source of philosophical arguments. If some statisticians and physicists chose to interpret their results as reflecting variability and uncertainty, we must look at least partly to external factors to understand why. For German statisticians and historical economists like G. F. Knapp and Wilhelm Lexis, these seem to reflect mainly their political and social views, while Maxwell was moved more by religious and philosophical considerations. Still, we can hardly imagine these


debates assuming the shape they did in the absence of flourishing statistical approaches to physics and social science.

IV. SOCIAL BIOLOGY AND MATHEMATICAL STATISTICS

The social analogy also contributed crucially to the shape of statistical biology, or biometry. Just as Maxwell had learned of the application of the normal law to real variation from an interpreter of Quetelet, Francis Galton ([1909] 1911) reported in his Memories that another of the Belgian statistician's advocates, the geographer William Spottiswoode, first explained to him the properties of this remarkable curve. Galton's initial work as a statistical biologist involved social, or at least sociobiological, studies. His first use of higher mathematics was to apply the normal distribution to the physical and mental variation of humans, very much in the Quetelet tradition.

Galton's real originality in statistical methods began with an explicit social analogy. This was the theory of Pangenesis, introduced by his cousin Charles Darwin in 1868 and elaborated in an appendix to Galton's Hereditary Genius in 1869. Pangenesis explained heredity as the result of innumerable genetic elements, called gemmules, combining into an embryo. This process was, Galton reported, precisely comparable to the formation of a new town out of a great many individuals migrating from the vicinity. All the most important phenomena of heredity--atavism, sudden changes of racial type, "sports" of nature--could be understood in terms of an analogy of migrations and elections. He emphasized, in the liberal spirit that prevailed even in eugenics during its earliest years, that these were free individuals, so that no centralizing power was required. After all, it had been clearly shown by statistics that a stable ordering of social behavior could be maintained simply through the free choices of individuals.

Galton's analogy was strongly suggestive of a method of analysis. The science that dealt with these demographic phenomena was statistics; the same mathematics ought to be applicable to the biological problem. Galton knew exactly how to set it up from the analogy with sampling a popUlation. If a child was formed out of the gemmules passed down from his parents, any given trait, such as his height, ought to equal the


mean of his parents (corrected for sexual differences), plus an error term governed by the normal curve.

A few years later (Galton, 1877), when he actually performed the experiment on an organism for which sufficient experimental control was possible to give clean results, he found that this was not quite right. Indeed, he decided, it could not be right, at least as a general rule, for the addition of a new error term in every generation would cause the distribution to get wider and wider. In fact, Galton's attempt to apply the methods of social statistics to a biological problem led to a much more interesting conclusion than replication of old results. He got instead a linear regression. On average, the off spring were closer to the mean than their parents. Why, then, did the population not simply converge over time to the mean? Having asked this question, Galton was led to divide the variation in the offspring into a portion explained by the parental variation, plus a residual, unexplained portion that would appear even if both parents were at the mean. Here, for the first time, was a statistical method of correlating variables. For years, Galton always interpreted these results strictly in terms of biological categories: "reversion" to ancestors more remote than the parents, or later "regression" towards the mean of the race. Finally in 1888 (published as 1888-89), when the same mathematics arose in a quite different context, he suddenly realized that this was an abstract mathematical tool, applicable to interdependent variables from almost every field of knowledge. He gave it the name "correlation," and distinguished it from "regression" only by its much greater generality (Galton, 1890).

Thus Galton, like Maxwell, set out from a social analogy but was soon led by imperfections of the analogy to novel results of extraordinary importance. How he, a mediocre mathematician, could have been practically the founder of modern mathematical statistics, is an interesting problem. Victor Hilts (1973) suggested what has become the usual interpretation of Galton's statistical originality. In contrast to the social statisticians, Hilts argues, Galton was much less interested in mean values than in variation and its causes. The souls of statisticians, Galton (1889, p. 62) once wrote, "seem as dull to the charm of variety as that of the native of one of our flat English counties, whose retrospect of Switzerland was that, if its mountains could be thrown into its lakes, two nuisances would be got rid of at once." This emphasis on natural diversity, in turn, is usually connected with, and sometimes attributed to, Galton's commitment to eugenics, the improvement of the human race


through artificial selection. Eugenics provided, after all, the main incentive for Galton to take up statistical biology. If progress was to come through artificial selection rather than, as with Quetelet, the universal diffusion of knowledge, exceptional individuals must be of much greater interest than average ones.

An appreciation of the role of eugenics is crucial to any satisfactory account of Galton's statistical creativity. Yet it goes too far to argue, as for example Ruth Cowan (1972) has, that the influence of eugenics is almost a sufficient explanation of the genesis of the correlation concept. To believe that important scientific concepts were ripe for the picking by anyone armed with the appropriate social ideology is even less justifiable than the implication of some older histories that the great discoveries required no more than a willingness to value empirical facts over bookish preconceptions. Correlation involved some subtle difficulties, and even where the will to find such a tool was present, the way could prove elusive. Moreover, Galton was not so blinded by his ideological commitments, nor so indifferent to purely intellectual endeavors, as he appears in Cowan's portrayal. By the mid 1880s he had become convinced that regression to the mean reflected the inherent stability of certain types, and hence that real eugenic progress would have to come through discontinuous variation, of a sort that could not be grasped by his statistical formalism. This is why Galton's work provided as much encouragement to the anti-statistical Mendelians as to Karl Pearson and the biometricians when these two parties had their definitive falling out at the turn of the century (Provine, 1971). But Galton did not give up his statistical study of continuous variation on this account. It presented problems that greatly intrigued him, such as the asymmetry between parental regressions on offspring and offspring regressions on the parents, which he was so pleased to have figured out in about 1885.

There is another compelling reason not to assign exclusive explanatory value to eugenic ideology in accounting for Galton's statistical ideas. Eugenic concerns were not the only ones that could lead away from mean values towards diversity as the principal focus of statistical interest. In late nineteenth-century Germany, the paternalistic socialism that prevailed among statisticians and historical-school economists was seen as sharply at odds with Quetelet's social physics and its emphasis on the average man. German social thinkers stressed the mutual responsibility implied by a highly differentiated organicist state, and a society of average men would be


mlssmg precisely what was needed to make a moral community. Mathematically-inclined statisticians developed tools to comprehend a highly differentiated society. For example, Lexis (1877) worked out a much-noted formula for assessing the stability of statistical series. He concluded that such series were not so surprisingly stable, and that their fluctuations reflected the interdependence and diversity of human beings. By the late nineteenth century, statisticians in Germany and elsewhere routinely pursued the search for causes by asking about the relations between education and crime, or religion and suicide, or wealth and duration of life. For this the method of correlation might have been highly welcome. In England and America Galton's correlation concept was applied almost immediately to existing problems in social statistics, and also to meteorology, anthropology, economics, and education. In none of these fields, however, was it discovered independently. I have suggested here, and argued elsewhere (Porter, 1986, chapter 9), that Galton's path to correlation depended on some distinctive features of the problem of hereditary transmission. He began with a social analogy, but was quickly led beyond it. This reflects certain peculiarities of his subject matter, and while Galton came to it mainly because of eugenic concerns, we cannot reasonably speak of correlation as merely the product of eugenic ideology.

V. STATISTICS AS THE METHODOLOGY OF SCIENCE

After Galton, mathematical statistics became more like a discipline, rapidly generating a body of methods and a mathematical structure that had to be mastered by all serious practitioners. In these early years, we seem to have almost a holy line of statistical founders. Galton begat Karl Pearson; Pearson begat G. Undy Yule, W. S. Gosset ("Student"), and R. A. Fisher. Fisher fell out of favor, but then accomplished a heroic patricide. Pearson also begat Egon S. Pearson (literally) and the Polish mathematician Jerzy Neyman, whose criticism of Fisher initiated a new round of internecine strife. If in fact these are the blessed forefathers, we must concede a certain weakness of family loyalty. Indeed, few fields can match statistics for the duration and fierceness of its controversies. The differences that separated Fisher


from Pearson, then from Neyman and E. S. Pearson, and (more recently) both parties from the so-called Bayesians, were deep ones. Statistics was and remains a long way from consensus on fundamentals.

The one point on which Galton, Pearson, and Fisher seem to be united is a preoccupation with biometry--inspired to a considerable extent by eugenic concerns. But the biometric line is far from pure, and its dominance was never complete. Stephen Stigler (1986) shows how Pearson drew upon the economist Francis Edgeworth and then, with Yule, mined the astronomical tradition of error theory for its mathematics. Student developed his t-test for quality control in brewing. The various editions of Arthur Bowley's (1901) statistical textbook for social researchers may be contrasted with the textbook tradition started by Yule (1911), or with Fisher's (1925; 1935) classic books on statistics for research workers and on experimental design. Bowley relied on Edgeworth (e.g. 1885), and on the German tradition epitomized by Lexis and Ladislaus von Bortkiewicz (e.g. 1901). Social statistics was by this time rapidly becoming more mathematical, but decades passed before it incorporated the tools developed within the (broadly) biometric tradition.

Of all the founders Fisher seems closest to biology. His immense statistical prowess was instrumental in reconciling biometry with Mendelian genetics in the evolutionary synthesis (Fisher, 1930). His methodology of experimental design, however, was associated more closely with practical agriculture than with evolutionary biology. What he found in the agricultural literature could not have come from the Pearsonian corpus, for Pearson's statistics, like his philosophy, emphasized description and correlation rather than experiment and causation (Gigerenzer et aI., 1989; Box, 1978). Fisher's concept of degrees of freedom came from physics.

"Statistics," in fact, continues to encompass an extremely diverse subject matter. But if the field remains a fractious one, users and consumers of statistics now generally believe in a single, reasonably unified methodology for designing surveys or experiments and analyzing the data. In the extreme case, statistics has been treated as an answer to the dream of mechanized induction. As Gerd Gigerenzer, especially, has argued (1987; Gigerenzer et aI., 1989), textbook writers of the 1940s deserve most of the credit for this apparent unification of statistical methodology. They wrote mainly for the sciences of life, behavior, and society, many of whose practitioners were eager to believe that statistics provided an easy path to the grail of scientific respectability. The first


generation of statistics textbooks for the human SCIences were consciously written for researchers in fields where very little mathematical sophistication was either demanded or available. Accordingly, they provided a product that was as simple and unambiguous as possible. In place of the controversies and inconsistencies that still prevailed they created what has been called a hybrid statistics. For sociologists, psychologists, and researchers in education and medical therapeutics, this was simply Statistics. If its logical foundations were insecure, its recipes were certified as tested in the kitchens of mathematical specialists. In some subfields, experimental study with numerous repetitions yielding in the end a 0.05 significance level became practically the definition of sound research (Morrison and Henkel, 1970). Fisher encouraged this attitude with loose remarks, including one in The Design of Experiments (1935) which seemed to reduce science to the rejection of null hypotheses.

The statistics textbooks were also welcomed in bureaucratic circles. A unified statistical methodology would permit potentially controversial decisions to be taken out of the political domain. They could instead appear to be made objectively, that is, according to fixed rules, preferably using somewhat arcane methods sanctioned by science. For such purposes, mathematical statistics is second in importance only to cost-benefit analysis, to which it also often contributes. This can make public decision-making seem almost mechanical, as in the area of drug testing, which in the United States is governed by a rigid methodology of double-blind experiments (where possible) and analysis for statistical significance. Statistics is also central to the burgeoning new field of risk analysis, where it has achieved its greatest notoriety in the study of nuclear power plants. Here, as in the most controversial health matters, such as treatments for AIDS, the authority of quantitative objectivity tends to break down. But these examples should suffice to make it clear that the progress of statistics continues to be shaped by, as well as to shape, social needs and wants.

VI. THE QUESTION OF SOCIAL CONSTRUCTION

The prominent social role that has come to be played by probability and statistics is readily apparent. In recent years, scholars


have gone a long way towards writing a history of probability and statistics in these terms, challenging the older understanding assumed by most statistician-historians who treat the subject mainly in terms of the advance of technical methods. A few works on the history of statistics, and particularly on the British eugenist-statisticians, have been written as case studies of social construction. A broader literature, upon which I have drawn heavily here, suggests that other aspects of the history of statistics are no less conducive to a broadly social approach. Most of this work, to be sure, is not argued along the somewhat rigid lines associated with an uncompromising sociological interpretation. But this very diversity makes the history of statistics an excellent subject matter for investigating this historiographic movement. We need to ask not just what the idea of social construction contributes to the history of science, but also, and more crucially, what if any interpretations of social construction can be reconciled with this history.

There is a sense in which it is trivially true to call science a social construct. Science is, after all, made by human beings. Somewhat less trivially, modern science is impossible without an advanced economy and sophisticated forms of social organization. We are concerned here with a somewhat different, and not at all trivial, relationship between society and the content of science. Not all cultures place much value on scientific knowledge in the form it has customarily taken in elite western institutions during the last three centuries. There has been almost continuous resistance to it even within Europe and America. Charles Gillispie's (1960) classic Edge of Objectivity illustrates how prof ound were the differences separating rival programs for physics, chemistry, and biology, as late as the eighteenth and nineteenth centuries, even in France, Germany, and Britain. It took A. L. Lavoisier's pneumatic chemistry, he suggests, to discredit the mystical chemistry of p n e u rna, and in biology the strong claims of teleological and broadly romanticist approaches to nature remained influential decades after Darwin's 1859 Origin of Species.

Quantification and statistics are for many the defining characteristic of scientific knowledge. They also, however, have often been seen as eliminating from a subject precisely what is most important for science to understand. We now hear such criticism most often in relation to the social sciences, but the biological and physical sciences have by no means been exempt. As late as the 1830s, G. F. Ohm's mathematical analysis of the electric circuit was denounced by the Hegelian natural philosopher G. F. Pohl as unjustifiably austere and


abstract, rather like a traveler's description of a journey which gave nothing but the traveler's stops and the velocity in between (Jungnickel and McCormmach, 1986, p. 56). Both Auguste Comte and Claude Bernard rejected the use of statistics by medicine because they saw detailed explanation as essential, especially for a science whose object was to cure the individual patient (Porter, 1986). Statistics, in fact, has been affected by such considerations more than most fields, partly because it involves "mere" probability, and partly because of its imperialistic tendencies. A field so influential and so controversial can hardly be understood in purely internalistic terms, as the result of mathematical advances and factual discoveries.

To include sociological factors means first of all to examine carefully the workings of the scientific community responsible for advancing knowledge in the relevant discipline. The activity of disciplinary communities as makers of knowledge is the subject of a rapidly growing literature. Such studies aim to show that even the microlevel of science, ostensibly its most unproblematical, unideological aspect, can be illuminated by sociological analysis. What had once been seen as the un problematical domain of discovery is now portrayed as the locus of continuous struggle and controversy (Latour, 1987). Controversies, it is argued, expose real alternatives, and only in retrospect does knowledge seem to be driven by experiment, observation, and the logic of exact theory toward the "truths" that now fill our textbooks.

Harry Collins (1985) argues that knowledge should be viewed as emerging out of a process of negotiations within the scientific community. Like Latour, he prefers not to talk about nature in itself, arguing instead that scientific facts or laws only come into being when the relevant community of specialists reaches agreement on them. They are, however, far from denying the importance of observation and experiment; on the contrary, theirs is the perspective most responsible f or reviving interest in experimentation among historians, philosophers, and sociologists of science. Indeed, they may be less subversive than Latour's memorable epigrams would seem to imply. His interpretation of science as clever rhetoric requires that scientific instruments, and the "inscriptions" they produce, be the cleverest rhetoricians of all, which is to say he imports a kind of realism through the back door. Ian Hacking (1983) argues this way explicitly. Since modern experiments often produce phenomena which never occur outside of experiments, the "construction" of scientific facts can have a concrete meaning. When,


however, experimental control permits certain results to be obtained so reliably that they can be incorporated unproblematically into other experiments, then one is justified in speaking of the reality of those phenomena.

Collins (1985) disagrees. He holds that true replication is much rarer and more difficult than most discussions of the methods of science imply. One of his case studies, from physics, concerns the TEA laser, which is not particularly remarkable as high technology, but which nonetheless could never be duplicated, despite several attempts, except by scientists who had actually worked in a laboratory where it was already functioning. If this is typical, as a few other studies suggest and as much sociological literature now assumes, it tends to exalt tacit knowledge at the expense of the "public knowledge" of theory and even of scientific description. It also makes generalization from experimental results rather problematical, and casts some doubt on the extent to which scientific results deserve the authority which in the modern world is customarily attached to them (Barnes and Edge, 1982).

This line of interpretation offers definite promise as an approach to the history of statistics. Statisticians of the present century have been noteworthy for their passionate and enduring controversies, perhaps even to the extent of providing a counterexample to the usual assumption that an eventual establishment of consensus is the rule in science. For that reason, the patched-together version of statistics that prevails in the textbooks is more than usually vulnerable to deconstructive criticism. If, however, there are disagreements about the underlying logic, on the surface statistics appears as a method of astonishing power and flexibility, a clear triumph of a general method over recalcitrant particulars. Statisticians, after all, use similar mathematical tools to analyze data from every branch of science, and often from outside of science as well. In a certain sense, statistics is the quintessential form of public knowledge, one that depends on standardization of experimental or observational procedures and helps to render results strictly comparable. In the same sense, the rise of statistics has made knowledge more "objective"--that is, capable of being interpreted or further analyzed without the benefit of an intimate knowledge of the circumstances under which the results were obtained (Swijtink, 1987). To say this, of course, is not to refute Collins. Statistics only goes part way towards changing tacit into explicit knowledge, and the reduction of all results to numbers is often used to disguise the subjective aspects of an investigation. Still, the problem of


replication has more to do with the experimental or observational methods than with the statistical analysis. Many statistical procedures are so routine and mechanical that they can be done by computers.

Collins and Latour provide valuable insights, but their exclusive concern with subdisciplinary communities is inadequate for a topic so broad as the rise of probability and statistics over the last three centuries. More useful f or our purposes is the perspective made famous by sociologists at Edinburgh under the label "sociological strong program." This label, despite a recent move by its advocates in the microsociological direction (Shapin, 1982), continues to be associated with an interest in macrosociological determinants of scientific knowledge. A number of studies have gone so far as to deny the autonomy of the discipline or subdiscipline in favor of explanations involving a different unit of analysis, usually social class. Donald MacKenzie's (1981) recent study is the most noteworthy of these. He argues that eugenics gained credence in Britain because it best met the ideological needs of the professional middle classes. He seeks then to show that the outcomes of certain key episodes in the history of statistics--Galton's studies of correlation, the Biometrician-Mendelian controversy, the debate between Pearson and Yule over contingency analysis--were determined by eugenic ideology.

Advocates of the strong program do not stand alone in drawing such connections. They have only been most forceful, and perhaps dogmatic. Be that as it may, their research has greatly enriched our perspective on science. It enables us to see that not just scientific theories and techniques, but also the standards of truth or methodological soundness by which particular contributions are judged, have varied over time and place, even among the elite scientific communities of the modern west. Moreover, it shows that the content of science is often closely related to circumstances falling within the domain of political, social, economic, intellectual, and religious history. Edinburgh sociologists are correct to deny that the course of scientific change is to be explained simply in terms of factual discoveries and the working out of the logic of theories. The historically contingent intrudes at every level in the making of science.

This line of interpretation is wonderfully helpful in interpreting the history of statistics, which exhibits the permeability of science to external influences more strikingly and more frequently than do most fields. A considerable struggle was required for statistical reasoning to become acceptable to the scientific community at all. The model of


statistical laws came from social science, where, ironically, it survived partly on borrowed authority from the physical sciences. The mathematical tools of probability and statistics reflected the social views and related intellectual ambitions of their inventors: to reduce good sense to calculus, or to mechanize scientific inference; to collapse natural diversity into a system of mean values, to depict a highly differentiated, organic society, or to probe the causes of the perpetuation of variability from parents to offspring; to demonstrate that even life, mind, and society are rigidly determined by natural laws, or to show that there is room for chance, or free will, even in the laws of physics; to deny uncertainty, to celebrate it, or to subject it to mathematical order.

An approach to science that assumes the autonomy of disciplines must be thoroughly inadequate in regard to the history of statistics. Concepts arising as a part of natural or social science informed its mathematical structure. An almost dizzying play of analogies promoted its extension into new territories. The unification and integration of statistical methods was promoted by the longstanding dream that probability might one day be accepted as the logic of uncertainty, or of social decisions, and thus cut the ground away from demagogues and disputants. Nevertheless, rival alternatives have repeatedly been formulated, giving rise to some of the most vitriolic debates in the history of science.

Granting this, we might still wonder how far we should go with the Edinburgh sociologists. Their claims seem to derive from an urge to debunk science. Or rather, they subordinate science to sociology by arguing that science is the appropriate form of knowledge for societies like ours. The last phrase is hard to make precise. Does the existence of other forms of knowledge as depicted by anthropology suffice to call science a form of ideology? It is hard to see how history can provide an adequate grounding for this, an epistemological claim (Gordon, 1989). Less abstractly, the sociological interpretation of scientific change seems almost to invite an objection much like Samuel Johnson's refutation of Berkeley. Science works. Our high technology would be inconceivable without it. How can it be a mere ideology?

This is by no means unanswerable. A simple response, consistent with the social constructivist viewpoint, is that the criterion of truth implicit here--technological fruitfulness, or perhaps prediction and control--is itself socially conditioned. It rests on a special attitude towards nature, one whose emergence in the modern west is a historical


problem of the greatest interest. But the objection cannot be dismissed as completely misdirected. Radical social constructionists tend to be satisfied with an explanation of scientific change only when they have found an ideological factor, or perhaps a struggle for resources and authority within the scientific community, to which decisive importance can be assigned. This cannot be the only way to write about science. We can note that science, as a social activity, necessarily has a rhetoric, the more so as controversies arise frequently in the making of knowledge. We can observe that respect for science is still far from universal, and often more dependent on its relations to wealth and power than on the explanations it gives. We might go so far as to call call the norms and ideals that regulate science cultural preferences. But these are, at the least, longstanding and reasonably stable cultural preferences. Some of the most crucial have been with us since the seventeenth century, or even classical antiquity, and are presupposed in any activity upon which we would confer the name "science." The body of knowledge, techniques, standards, and organizational forms that constitute the modern scientific enterprise has considerable coherence and durability.

Science can reasonably be called a social construct, but it does not require a separate act of social creation every time it moves. To suggest, as Latour does, that the reasons for a particular scientific position become sound only in retrospect is to imply that every scientific controversy, every unresolved issue, could equally well be decided one way as another. This view would have science perpetually inhabiting a state of nature. It would cancel out everything called knowledge as soon as it is created. The absurdity of doing so is implicitly recognized even in the most radically sociological accounts of scientific change, including Latour's. If scientific ideas and methods had no standing--if they were powerless to affect the future development and uses of science--their history could not be of the slightest importance. Science may be socially constructed, but it is not reinvented every moment.

VII. CONCLUSION: CONSTRUCTING STATISTICS

The recent move by social constructivists to put less emphasis on the relations of science to its social and intellectual context reflects


a concern to avoid appearing crudely reductionistic. This, however, misses the point. A social interpretation is crude when it refuses to respect the content of science, seeing in it nothing but a pale reflection of social relations. A more nuanced view of social construction is fully compatible with attentiveness to the interactions between science and the broader culture. Such an approach must certainly be balanced with study of the micro-processes that characterize disciplinary (and subdisciplinary) communities in the big science of our day. Even that science is not wholly insulated, however, and it rests on the shoulders of a scientific enterprise that often was closely bound up with philosophical, religious, and political concerns.

Few subjects could illustrate this point better than the history of statistics. It was long on the fringes of science, both because of its close ties to eff orts to expand science into the human domain and because its methods were hard to reconcile with traditional ideals of scientific demonstration. Again and again, ideas and ideologies from outside the sciences have exerted a formative influence on it. The process by which its fundamental concepts originated and gained acceptance is of the highest interest, for its influence on the social and natural sciences has been extraordinary. Its acceptability was not a foregone conclusion; as late as 1900 it was possible to reject statistical models in physics on the ground that they added nothing to our knowledge of the macroscopic laws of thermodynamics but uncertainty.

The history of statistical method, I have argued here, is inseparable from the history of politics and society. Even so, it offers scant support for those who see nothing but clever rhetoric and power struggles in the making of science. If statistical mathematics had almost no disciplinary autonomy before 1900, the fields with which it interacted, including even social science, did. Quetelet, Maxwell, and Galton had to meet certain minimal expectations of the scientific audiences to which they addresed their work. These expectations need not lead inexorably to some unique formulation of a problem, much less to a single set of answers. (Consider, for example, how different is the physicist's from the chemist's atom.) But they do set limits, strenuous ones, on acceptable scientific work.

The standards of acceptable science are very hard to state formally. They are not identical in every discipline, and there have been sharply variant national traditions. They evolve over time. Modern statistics, for example, has changed them considerably; it had to, for by the standards of science prevailing up to about 1800, statistical

70 Acting Under Uncertainty: MUltidisciplinary Conceptions

explanation was no explanation at all. But since the seventeenth century, at least, successful science has involved convincing other scientists or natural philosophers that one has attained a certain mastery over nature. This can mean agreement between a theory and existing data, or the prediction of new phenomena, or demonstrated experimental control. Such requirements are easy to belittle, for nature does not present itself naked for observation and measurement. It is now a truism that scientific description is necessarily theory-laden. Still, to say this is not to imply that nature is utterly passive, or that every theoretical framework (or experimental apparatus) stands up equally well.

How else can we interpret the shock that we find expressed at some of the real turning points in the early history of probability and statistics? The classical probabilists were genuinely alarmed to find that their reasonable calculus was subject to a paradox like the St. Petersburg problem. Ouetelet reported his astonishment upon learning that even crime was subject to a considerable degree of statistical regularity. Maxwell anticipated that his statistical gas theory would be written off as interesting but misdirected speCUlation until experiment confirmed what seemed the implausible prediction that gaseous friction should be independent of density. Galton expressed wonder on several notable occasions, among them his recognition while graphing some anthropometric data that hereditary "regression" and biological "correlation" (of parts) have the same mathematical solution (Galton, 1890). He concluded that he had reached a solution to the problem of "co-relation," which was much more abstract than any biological theory.

The existence of scientific surprise does not imply that the facts speak for themselves and must in the end triumph over mere theory. Surprise, too, is an interpretation, and (for example) subsequent statisticians have had great difficulty seeing "astonishing" regularity in Ouetelet'sfavorite results. But it does reflect a certain engagement with one's materials. Our protagonists were perhaps more than normally susceptible to the delight and consternation of surprise because they occupied a field with strong centrifugal tendencies. Working, as they did, outside and between disciplinary traditions, they were perpetually confronting the materials of one discipline with methods and conceptions borrowed from another. Far from the well-worn paths, the fit between method or theory and object was imperfect and unpredictable.


Perhaps, then, it is precisely because statistical mathematics had so little autonomy that the confrontation between expectations and subject matter was so often surprising. This is almost the same reason that statistics was so readily accessible to ideas and influences from outside the scientific community. It suggests that an intense struggle to master a recalcitrant subject matter and an openness to a wide variety of influences, including perhaps social ideologies, are far from contradictory. It makes good sense that we should see such influences in a new, ill-defined field, and especially in one whose strongly expansionist tendencies brought it into contact with a variety of objects and intellectual traditions. Both surprise and openness were encouraged also by the curious status of statistics, an insecure social science aiming to imitate the methods of physics, while actually developing new conceptions that would eventually prove valuable in the study of nature.

If statistics is unusual, however, it is not unique. A balanced account of any development in science must integrate technical, microsociological, and broader contextual factors. To say that statistics, or any area of science, is "socially constructed" is not to say very much. The phrase does suggest, however, that history, philosophy, and sociology of science should pay attention to the relations between knowledge and the societies within which it is nurtured and applied. The history of statistics, at least, cannot be adequately understood in any other way.

REFERENCES

Baker, Keith (1975), Condorcet: From Natural Philosophy to Social Mathematics. Chicago: University of Chicago Press.

Barnes, Barry and Edge, David, eds. (1982), Science in Context, Cambridge: MIT Press.

Bernoulli, Daniel ([1738] 1954), "Exposition of a New Theory on the Measurement of Risk," Econometrica, January, 22, pp. 23-36.

Bernoulli, Jakob ([1713] 1968), Ars Conjectandi, Brussels: Culture et Civilisation.


Boltzmann, Ludwig ([1877] 1968), "Ueber die Beziehung zwischen dem zweiten Hauptsatz der mechanischen Warmetheorie und der Wahrscheinlichkeitsrechnung," in Ludwig Boltzmann, Wissenschaftliche Abhandlungen, Fritz Hasenohrl, ed., 3 vols., reprinted New York: Chelsea, vol. 2, pp. 164-223.

Bortkiewicz, Ladislaus von (1901), "Anwendungen der Wahrscheinlichkeitsrechnung auf Statistik," in Encyclopadie der mathematischen Wissenschaften, Leipzig: B. G. Teubner, vol. I, part 2, pp. 821-51.

Bowley,Arthur L. (1901), Elements of Statistics, London: P. S. King. Box, Joan Fisher (1978), R. A. Fisher: The Lif e of a Scientist, New

York: Wiley. Buckle, Henry Thomas (1857), History of Civilization in England,

vol. 1, London: J. W. Parker. Collins, H. M. (1985), Changing Order, London: Sage. Cowan, Ruth S. (1972), "Francis Galton's Statistical Ideas: The

Influence of Eugenics," Isis, December, 63, pp. 509-28. Cullen, Michael (1975), The Statistical Movement in Early

Victorian Britain, Hassocks: Harvester. Daston, Lorraine J. (1979), "D'Alembert's Critique of Probability

Theory," Historia Mathematica, August, 6, pp. 259-79. Daston, Lorraine J. (1988), Classical Probability in the

Enlightenment, Princeton: Princeton University Press. Edgeworth, Francis (1885), "Methods of Statistics," Journal of the

Royal Statistical Society, Jubilee Volume, pp. 181-217. Fisher, Ronald A. (1925), Statistical Methods for Research

Workers, Edinburgh: Oliver and Boyd. Fisher, Ronald A. (1930), The Genetical Theory of Natural

Selection, Oxford: Clarendon. Fisher, Ronald A. (1935), The Design of Experiments, Edinburgh:

Oliver and Boyd. Galton, Francis (1869), Hereditary Genius, London: Macmillan. Galton, Francis (1877), "Typical Laws of Heredity," Proceedings of

the Royal Institution of Great Britain, 8, pp. 282-301. Galton, Francis (1888-89), "Co-relations and their Measurement, Chiefly

from Anthropometric Data," Proceedings of the Royal Society of London, meeting of December 20, 1888,45, pp. 135-45.

Galton, Francis (1889), Natural Inheritance, London: Macmillan.


Galton, Francis (1890), "Kinship and Correlation," North American Review, April, 50, pp. 419-31.

Galton, Francis ([1909] 1911), Memories of my Life, London: Macmillan.

Gigerenzer, Gerd (1987), "Probabilistic Thinking and the Fight against Subjectivity," in Krtiger, Gigerenzer and Morgan, pp. 11-33.

Gigerenzer, Gerd et al. (1989), The Empire of Chance: How Probability Changed Science and Everyday Life, Cambridge: Cambridge University Press.

Gillispie, Charles C. (1960), The Edge of Objectivity, Princeton: Princeton University Press.

Gillispie, Charles C. (1963), "Intellectual Factors in the Background of Analysis by Probabilities," in A. C. Crombie, ed., Scientific Change, New York: Basic Books, pp. 431-53.

Gordon, Scott (1989), The Proper Study of Mankind: An Introduction to the History and Philosophy of Social Science, Brookfield, Vt.: Edward Elgar.

Hacking, Ian (1975), The Emergence of Probability, Cambridge: Cambridge University Press.

Hacking, Ian (1983), Representing and Intervening: Introductory Lectures on the Philosophy of Science, Cambridge: Cambridge University Press.

[Herschel, John] (1850), "Quetelet on Probabilities," Edinburgh Review, July, 92, pp. 1-57.

Hilts, Victor L. (1973), "Statistics and Social Science," in R. N. Giere and R. S. Westfall, eds., Foundations of Scientific Method: The Nineteenth Century, Bloomington: Indiana University Press, pp. 206-33.

Jungnickel, Christa and McCormmach, Russell (1986), Intellectual Mastery of Nature: Theoretical Physics from Ohm to Einstein, vol. 1, The Torch of Mathematics 1800-1870, Chicago: University of Chicago Press.

Knapp, Georg Friedrich (1871), "Die neueren Ansichten tiber Moralstatistik," lahrbucher fur Nationalokonomie und Statistik, 16, pp. 237-50.

Knapp, Georg Friedrich (1872), "A. Quetelet als Theoretiker," lahrbucher fur NationalOkonomie und Statistik, 17, pp. 89-124.


Kruger, Lorenz; Daston, L. J. and Heidelberger, M., eds. (1987), The Probabilistic Revolution, vol. 1: Ideas in History, Cambridge: MIT Press.

Kruger, Lorenz, Gigerenzer, G. and Morgan, M., eds. (1987), The Probabilistic Revolution, vol. 2: Ideas in the Sciences, Cambridge: MIT Press.

Laplace, Pierre Simon ([1814] 1951), Philosophical Essay on Probabilities, F. W. Truscott and F. L. Emory, trans., New York: Dover.

Latour, Bruno (1987), Science in Action, Cambridge: Harvard University Press.

Lexis, Wilhelm (1877), Zur Theorie der Massenerscheinungen in der menschlichen Gesellschaft, Freiburg: Wagner.

MacKenzie, Donald (1981), Statistics in Britain, 1865-1930: The Social Construction of Scientific Knowledge, Edinburgh: Edinburgh University Press.

Maxwell, James Clerk ([1860] 1890), "Illustrations of the Dynamical Theory of Gases," in James Clerk Maxwell, Scientific Papers, W. D. Niven, ed., 2 vols., Cambridge: Cambridge University Press, vol. 1, pp. 377-409.

Maxwell, James Clerk ([1873] 1882), "Science and Free Will," in Lewis Campbell and William Garnett, Life of James Clerk Maxwell, London: Macmillan, pp. 434-44.

Montmort, Pierre Remond de (1713), Essai d'Analyse sur les J eux de Hazard, Paris: Quillau, 2nd Ed.

Morrison, D. E. and Henkel, R. E., eds. (1970), The Significance Test Controversy, Chicago: Aldine.

Pascal, Blaise ([1670] 1962), Pensees, Louis Lafuma, ed., Paris: Delmas.

Porter, Theodore M. (1986), The Rise of Statistical Thinking, 1820-1900, Princeton: Princeton University Press.

Porter, Theodore M. (1987), "Lawless Society: Social Science and the Reinterpretation of Statistics in Germany, 1850-1880," in Kruger, Daston and Heidelberger, eds., pp. 351-75.

Provine, William B. (1971), The Origins of Theoretical Population Genetics, Chicago: University of Chicago Press.

Quetelet, Lambert-Adolphe-Jacques (1829), "Recherches Statistiques sur Ie Royaume des Pays-Bas," Nouveaux Memoires de l'Academie Royale des Sciences et Belles-Lettres de Bruxe II e s, 5, separate pagination.


Quetelet, Lambert-Adolphe-Jacques (1835), Sur I'Homme et Ie Developpement de ses Facultes, ou Essai de Physique Sociale, Paris: Bachelier.

Quetelet, Lambert-Adolphe-Jacques (1846), Lettres sur la Theorie des Probabilites, Brussels: Hayez.

Quetelet, Lambert-Adolphe-Jacques (1847), "De I'Influence de Libre Arbitre de I'Homme sur les Faits Sociaux," Bulletin de la Commission Centrale de Statistique (of Belgium), 3, 135-55.

Shapin, Steve (1982), "History of Science and its Sociological Reconstructions," History of Science, September, 20, pp. 157-211.

Stigler, Stephen M. (1986), The History of Statistics: The Measurement of Uncertainty before 1900, Cambridge: Harvard University Press.

Sussmilch, Johann Peter (1765), Die gOttliche Ordnung in den Veriinderungen des menschlichen Geschlechts, 2 vols., Berlin: Verlag der Buchhandlung der Realschule, 3d Ed.

Swijtink, Zeno G. (1987), "The Objectification of Observation: Measurement and Statistical Methods in the Nineteenth Century," in Kruger, Daston and Heidelberger, eds., pp. 261-85.

Yule, G. Udny (1911), An Introduction to the Theory of Statistics, London: Griffin.

porter1990 statisctics are socially constructed.pdf

Documents

Transcript of porter1990 statisctics are socially constructed.pdf