5 NEW USES FOR NUMBERS

NUMBERS AND MEASURES

Historians note two features of the use of numbers in the late eighteenth and early nineteenth centuries. First, the messianic “quantifying spirit” of the age¹ pushed numerical considerations into new domains. For example, numerical methods were introduced into areas of medicine that had previously seemed non-numerical, such as the treatment of insanity. Second, measurements at this time attained a new high level of accuracy, making this an “age of precision.”²

Both features are evident in the field of statecraft, in the actual counts that replaced estimates of national populations and in attempts to ascertain the actual production and consumption of food.

The quantifying spirit of the age particularly appears in the introduction of national censuses. In 1789 the new American Constitution called for a decennial census. The first federal census was taken in 1790. National censuses were taken in Sweden in 1792 (replacing earlier estimates of the size of the population), in Holland in 1795, in Norway and Denmark in 1797, and in England in 1801.³ The American historian of statistics, Helen Walker, surmised that fear of divine punishment for a sin like King David’s was removed by the obvious flourishing of the United States after the census of 1790.

In France, an attempt had been made in 1697 to estimate the size of the population. Instructions were sent out to the 32 “intendants” or regional governors appointed by Louis XIV, ordering them to “report the number of towns, villages, hamlets, and inhabitants within their jurisdictions.” The intendants, however, “had neither the means nor the inclination” for the collection of this kind of demographic data. They returned a “medley of back numbers” taken from tax records and “counts of hearths” rather than making a true head count. Nine of the 32 intendants made no report at all.⁴

In 1800 the French government established a Bureau de Statistique Générale and in that same year issued a decree that there be a census of all the inhabitants of France. This census has been described as a “great Failure.” The actual count was made under the direction of Lucien Bonaparte, Napoleon’s brother, then Minister of the Interior. Lucien apparently believed that the census could be completed in a few months, but in fact the head count and tabulation of data required two years.⁵

These census figures seem to us to be innocent data, but in the eighteenth century the knowledge of such numbers could be of strategic importance in estimating a nation’s potential military strength. Such security considerations apparently induced Sweden during the 1760s to keep its census data secret under the control of an Office of Tables.

In an essay on the quantifying spirit in the thought of the late eighteenth century, John Heilbron has called attention to a “newly discovered effective emphasis on precision.”⁶ This precision appears as an increase in the number and variety of concepts quantified, and as an increase in the accuracy of measurements. Precision and accuracy of measurement imply that a concept has been reduced to numbers. Not surprisingly, some leading thinkers of the time envisioned that all of human thought might be expressed mathematically.

Two examples display the enormous increase in precision at this period. From the time of Tycho Brahe (1546–1601) in the late sixteenth century to the age of John Flamsteed (1646–1719), accuracy in astronomical observations increased from about 1 minute of arc to 20 seconds, a factor of 3. In contrast, during the eighteenth century accuracy improved by a factor of 200. This same increase in precision can be seen in the measurement of time. The first pendulum clocks, built in the late seventeenth century, were good to some 10 seconds a day, but by 1800 chronometers were good to one-fifth of a second per day.

A CONCERN WITH NUMBERS IN FRANCE: LAVOISIER’S ESSAY ON POLITICAL ARITHMETIC

Antoine-Laurent Lavoisier (1743–1794), one of France’s most distinguished scientists, is generally known as a primary founder of the modern science of chemistry. He established the division of substances into elements, compounds, and mixtures, a distinction that we still use.⁷ He spearheaded the creation of a new rational nomenclature of varieties of matter according to their chemical composition. For example, the traditional pre-Lavoisier name for a certain substance was “blue vitriol.” In the new system, the name was based on the chemical composition. Blue vitriol turns out to be a compound of copper, sulfur, and oxygen—a fact expressed in the name “copper sulfate.” If the substance had been a compound of copper and sulfur without oxygen, the name would have been “copper sulfide.” So great were the innovations introduced into chemistry by Lavoisier and his associates that the change is generally known as the Chemical Revolution.

One of the most fundamental principles of Lavoisier’s chemistry was the use of numbers, notably in relation to what we often call today the principle of conservation of mass: in a chemical reaction, mass is neither created nor destroyed. In other words, in every chemical reaction, the weight of all the reacting substances is always equal to the weight of all the product substances. This principle implies that an experimenter must not only keep account of all the reacting solids and liquids, but also the gases—that is, all of the products. In particular, Lavoisier’s rule directed attention to the reacting and product gases. This rule led to quantitative experiments. Lavoisier was not the first person to use numbers in chemistry but he was a pioneer in using such numerical measurements as the basis of his system of chemistry.

Lavoisier’s law implies the indestructibility of matter in chemical reactions: matter is neither created nor destroyed. In Lavoisier’s own words: “Nothing is created in the operations either of art or of nature, and it can be taken as an axiom that in every operation an equal quantity of matter exists both before and after the operation.”⁸

When Lavoisier first announced this law, chemists generally believed in something called “phlogiston” which supposedly entered into chemical reactions (such as combustion) but had no weight. It was a radical step, therefore, for Lavoisier to base a system of chemistry on a balance of weights and to maintain that chemistry is not concerned with weightless “substances.” In a very real sense, this was indeed a chemical revolution.

Lavoisier was an enthusiastic supporter of the French Revolution in its early and moderate phase. In a letter to Benjamin Franklin in 1790 he referred to the new chemistry as a revolution, saying he would consider it “well advanced and even completely accomplished if you range yourself with us.” Lavoisier continued, “After having brought you up to date on what is going on in chemistry, it would be well to speak to you about our political revolution. We regard it as done and without any possibility of return to the old order.” Clearly the two revolutions were linked in his mind. However, during the later stages of the Revolution, Lavoisier was arrested because under the former government he had been a staff member of the “ferme générale” or tax collection agency, and on 8 May 1794 he was decapitated on the guillotine.

Before the Terror, however, Lavoisier worked in many areas for the new government. Because of his concern with numbers and precision, Lavoisier was made a member of the commission to establish the metric system (adopted in 1799).

One of Lavoisier’s assignments led him directly into numerical statecraft: making a study of “the territorial wealth of France,” a census of the land actually under cultivation for farm production. His report was published by order of the National Assembly in 1791 as the lead chapter in a work entitled Collection de divers ouvrages d’arithmétique politique par Lavoisier, Delagrange et autres (Paris: An IV [1791]). The second work in this collection was written by the eminent mathematician Joseph-Louis Lagrange (1736–1813), a close friend of Lavoisier’s.

The new French Republic needed Lavoisier’s survey because taxation was based on property, on land actually under cultivation or in use for raising livestock. His method of estimating the amount of land under cultivation was ingenious.⁹ He assembled data on the annual consumption of food and wine in urban and in rural households and then computed how much land would have to be under cultivation to produce this quantity of food and drink. He also insisted that this method of computing the area of land under cultivation was possible because there were at that time no sizable imports or exports of food. Yet, the lack of reliable figures for the total population of France significantly flawed his method. Jean-Claude Perrot, a scholar who has made a detailed study of Lavoisier’s work, points out that Lavoisier underestimated the size of the population of France by 2.5 million.¹⁰

Lavoisier estimated the total population of France to be some 25 million, of whom he supposed 8 million lived in towns. He recorded how many people were engaged in various activities. For example, he found that 2.5 million people were engaged in viniculture. He reported that in France the annual consumption of grains (wheat, rye, barley), including both seed and comestible grains, came to 1,400 “livres pesant.”

To estimate how many horses and oxen were employed in agriculture, Lavoisier started with the amount of grain consumed by the French population. He reckoned the area of cultivated land of average productivity needed to produce that amount of grain, the number of plows needed to cultivate that area, the number of oxen or horses required to draw a plow through soil of average density, the relative efficiency of plows drawn by oxen and horses, and the proportion of oxen and horses employed in plowing as an average over the country. He calculated the area of land plowed by each kind of draft animal, and finally calculated an estimate of their actual numbers.¹¹

He recognized that to get the total number of horses in France he would also have to estimate the number of horses not used in agriculture, such as those in cities and in haulage. At this point in his analysis, he admitted that these numbers were obviously “fort hypothétique” (extremely hypothetical). He concluded with estimates of the total number of cattle, sheep, and pigs. One of his remarkable conclusions was that only one-third of the arable land of France was actually under cultivation.

Lavoisier ended by calling for a permanent office of facts and figures, a statistical bureau, to keep regular records of agriculture, commerce, and the size of the population of France.¹² According to Lavoisier, only in one country—France—could such a bureau be established and maintained. This project, he concluded, depended on “the will of the Assemblée Nationale.” He added that with the establishment of such a bureau and the collection of factual data, the “science of political economy” would cease to exist because all problems would be solved with no disagreements whatsoever.¹³

SIR JOHN SINCLAIR’S CENSUS OF SCOTLAND

Sir John Sinclair’s (1754–1835) statistical account of Scotland affords further evidence of the growing concern with national and social numbers at the end of the eighteenth century. In the words of Sinclair’s biographer, this was a time marked by a tendency of “the government to go around counting things.”¹⁴ This was in part “the result of a developing social conscience in the political part of the nation.” But it also came from “an immediate need to check up on food and manpower supplies in a war that was revealing shortages of both.” A number of individuals began to search for exact—that is, numerical—information concerning social conditions. For example, in 1794 Jeremy Bentham was “drawing up a table of the property and population of the country.” Recall that the first census in Britain took place in 1801.

Sinclair, a wealthy Scot and a member of Parliament, was particularly interested in agriculture and had a passion for numerical information. His census was planned to be more than a mere head count. Such a count had been made a half-century earlier by Dr. Alexander Webster (1707–1784),¹⁵ who obtained his numerical data from parish ministers, the same source of information to be used by Sinclair half a century later. Sinclair’s method was to send out a questionnaire to every minister in Scotland. He had the backing of the Church of Scotland and used both financial pressure and cajolery to get these informants to return the forms. He used his own funds to staff a secretariat to process the forms as they came in to the central office. Obviously, some ministers were more conscientious than others, and so the standard of reporting was rather uneven. One obvious fault of this system was that the head count did not include Roman Catholics, freethinkers, Jews, and those who simply were not churchgoers. But in Scotland at this time these would not represent large percentages of the total population.

The publication of these ministerial reports came to 21 volumes published from 1791 to 1799, of which volume 20 contained a description of Sinclair’s method and a summary of results. These reports of the ministers were not edited or printed in regional groups. Rather, Sinclair put them into print as they came in to the central office.

A mere description in words cannot give the reader any sense of the monumental scale of this undertaking and the wealth of social and economic data Sinclair’s volumes contain. A single example will give some sense of the information in Sinclair’s census. A Mr. Smill of Dornock in Dunfriesshire reported concerning the annual finances of a “common labourer” with a wife and four children. Table 5.1 gives the family’s living expenses for a year. The annual earnings of this man came to 14 pounds, 8 shillings, less than his living costs. This difference was made up by the wife’s earnings, working as an agricultural laborer during harvest and haying seasons, and spinning wool during the winter and spring. Whatever their faults, these data are of such value to social and economic historians that the contents of these volumes are currently being edited for publication reorganized by locality and with detailed indexes.

One final aspect of these volumes should be noted. Sinclair boldly titled these volumes Statistical Account of Scotland. Here I use the adverb “boldly” because at that time the adjective “statistical” had not as yet come into general use in the modern sense. As Sinclair wrote:

Many people were at first surprised, at my using the new words, Statistics and Statistical, as it was supposed, that some term in our own language, might have expressed the same meaning. But, in the course of a very extensive tour, through the northern parts of Europe, which I happened to take in 1786, I found, that in Germany they were engaged in a species of political inquiry, to which they had given the name of Statistics; and though I apply a different idea to that word, for by Statistical is meant in Germany, an inquiry for the purpose of ascertaining the political strength of a country, or questions respecting matters of state, whereas, the idea I annex to the term, is an inquiry into the state of a country, for the purpose of ascertaining the quantum of happiness enjoyed by its inhabitants, and the means of its future improvement; yet, as I thought that a new word might attract more public attention, I resolved on adopting it, and I hope that it is now completely naturalized and incorporated with our language.

At the dawn of the nineteenth century the word “statistics” had two unrelated meanings. In Germany, the term “Statistik” referred to a nonmathematical form of statecraft, the collection of information of the sort that used to be taught as political geography. At the same time, numerical statecraft was being pursued in a form which agrees with the word “statistics” as we understand it today. Toward the end of the nineteenth century, this confusing situation was described by the words “two roots,” to indicate that there were two unrelated forms of study which are related to the emergence of the modern concept of statistics. However, someone who pursued statistics was still called a “statist” as late as 1878 when a French calculating machine was brought to the attention of English statisticians.¹⁶

TABLE 5.1 ANNUAL EXPENSES OF A “COMMON LABOURER” OF DUNFRIESSHIRE

	£ (1 pound = 20 shillings)	s (1 shilling = 12 pence)	d (1 penny)
House-rent, with a small garden or kailyard	1	0	0
Peats or fuel	0	6	0
A working jacket and breeches, about	0	5	0
Two shirts, 6s. a pair of clogs, 3s. 2 pair of stockings, 2s.	0	11	0
A hat, 1s. a handkerchief, 1s. 6d.	0	2	6
A petticoat, bedgown, shift and caps for the wife	0	9	0
A pair of stockings, 1s. clogs, 2s. 6d. apron, 1s. 6d. napkin, 1s. 6d. for ditto	0	6	6
A shirt 2s. clogs, 2s. stockings, 2s. for each of the four children	1	0	0
Other clothes for the children, about 4s. each	0	16	0
School wages, etc. for the four children	0	10	0
Two stone of oat meal, per week at 20d. per stone	8	13	4
Mi l k, 9d. per week; butter, 3d. per ditto	2	12	0
Salt, candle, thread, soap, sugar and tea	0	13	0
The tear and wear of the man and wife’s Sunday clothes	0	10	0
Total outlays	17 £	14 s.	4 d.

From Sir John Sinclair, ed., The Statistical Account of Scotland, 1791–1799 (Edinburgh: W. Creech, 1799; reprint East Ardsley,England: E. P. Publishing, 1977)

PINEL’S MEDICAL NUMBERS

The growing concern with numbers at the opening of the nineteenth century is apparent in the changes in the treatment of the insane in France. This development is all the more remarkable in that, until the development of pharmaceutical treatments for biologically based mental illness, this area of medicine had not been considered to be a science using quantitative evidence. The writings of Sigmund Freud (1856–1939), for example, do not contain references to numerical evidence.

Philippe Pinel (1749–1826) is honored in the history of medicine because he radically altered the ways in which people who were “insane” were treated. At the time of the French Revolution, men and women who were suffering from mental disorders were apt to be chained in dungeons and generally treated as if they were savage beasts. In 1793, when Pinel received a post at l’hôpital de Bicêtre, an institution in Paris which housed insane inmates, he found that one male patient had been restrained by chains for 36 years!¹⁷ Pinel introduced a new point of view, arguing that such patients were “sick” and should be treated with kindness. A famous painting by Tony Robert-Fleury shows Pinel freeing a patient from shackles. The painting is entitled Pinel délivrant les aliénés with the masculine “aliénés” even though it is a young woman who is being freed.¹⁸ Pinel believed that all individuals should be protected against forcible restraint.¹⁹ It has been suggested that Pinel’s treatment of the insane was in harmony with the ideals of the French Revolution, which made it a duty to protect all individuals, even the insane, against chains.

Our concern, however, is not with Pinel’s role as a founder of psychiatry, nor as “the greatest hospital superintendent of all times.”²⁰ Rather, our focus is his “passion for statistical information.” Pinel described his method as the new “calculus of probability,” but, as one scholar notes, his research involved “little more than a judicious use of arithmetic,” so that “calculation of proportions” is a better description of the procedure. Pinel kept careful daily records of his patients and he made from them numerical tabulations “from which comparisons could be made between subgroups.… [He was] one of the great disease classifiers.”²¹

Pinel was, above all, an empiricist, and as such he did not bow down to established authorities. He wanted to avoid getting “lost in vague arguments about objects inaccessible to human understanding.” Pinel’s major work was his Traité médicophilosophique sur l’aliénation mentale (Paris: Brosson, 1809). In the introduction he stated his philosophy as follows: “[A] wise man has something better to do than to boast of his cures, namely to be always self-critical.”²²

In his research Pinel faced two problems: how to classify the mental disorders he encountered in patients and how to evaluate the success or failure of his therapeutic measures. He applied numerical methods to both.

In his analysis of Pinel’s work, the late William Coleman observed that Pinel argued that his numerical method “had already served with good effect for the study of objects of social life.” Numerical methods would “kill ungrounded speculation” and allow medicine (“the healing art”) to escape from “blind empiricism” and to become a “true science.”²³ As an example of his “numerical method,” Pinel reported on patients he had treated over a four-year period. He divided his therapeutic outcomes into two categories: cured and discharged, or not cured.

Pinel did not succeed in establishing the treatment of mental disorders on a sound numerical basis—the task was too complex and too little understood for one person to achieve this end. But his example does show us how the goal of a numerically based science had permeated even the least mathematical part of medicine, treatment of mental illness.

One of Pinel’s American students was a Boston physician, Dr. George Parkman (1799–1849). Dr. Parkman later gained notoriety in the annals of crime as being the only person to have been murdered by a Harvard professor. Dr. John White Webster, a professor of chemistry, cut up Parkman’s corpse and fed the pieces into a furnace in his chemistry laboratory, hoping to destroy the evidence against him. But Dr. Parkman’s teeth, found in Dr. Webster’s furnace, were enough to convict Webster.

LOUIS AND THE NUMERICAL METHOD

Historians and statisticians generally agree that Pierre Charles Alexandre Louis (1787–1872) should be honored as a primary author of the “numerical method.” By “numerical method” he meant that the stages of disease and therapeutic outcomes should be expressed in terms of numbers and not merely as a set of verbal descriptions. These numbers could be classified in such terms as the age of the patient and stages of development. This method seems so sensible that it is difficult to see why it was resisted by the medical establishment.

Louis has been described as “the father of medical statistics”²⁴ and as “one of the pioneers of clinical statistics.”²⁵ They take note, however, that some of his work can be faulted for drawing conclusions on insufficient evidence.²⁶

Louis obtained an M.D. in 1813 and then practiced medicine in Russia, returning to Paris in 1820. He became associated with several hospitals in Paris. He stressed the importance of accurate data, including not only the symptoms of a patient’s disease but, when the patient had died, detailed information—when possible—from an autopsy. It has been estimated that Louis performed 2,000 autopsies, devoting at least two hours to each one. Above all, he sought for quantitative information and developed what he called the numerical method. In 1827, he took a year off (in Brussels) where he used his freedom from hospital duties to analyze his data.

Among his publications, three stand out, two being his studies of tuberculosis and of typhoid fever, both of which depend on statistics and display his numerical method. His most celebrated publication was his refutation of the claims of a contemporary, F. J. V. Broussais (Paris, 1835), concerning the use of bloodletting in the treatment of pneumonia and other diseases.

Louis acquired an enthusiastic following, who accepted the doctrine of the numerical method. In 1832 his students formed a Société Médicale d’Observation. Louis was appointed “permanent President.”

In 1835, Louis explained his new method in Recherches sur les effets de la saignée dans quelques maladies inflammatoires, et sur l’action de l’émétique et des vésicatoires dans la pneumonie as follows:

Between the one who counts the facts, grouped according to their resemblance, in order to know what to believe regarding the value of therapeutic agents and him who does not count but always says “more or less frequent,” there is the difference between truth and error, between something that is clear and truly scientific and something that is vague and without value—for what place is there in Science for that which is vague?²⁷

In this classic work, Louis analyzed the effectiveness of blood-letting. At that time (1835) blood-letting, an ancient medical practice, was used extensively to treat patients suffering from pneumonia and other diseases. In the nineteenth century bloodletting was not performed surgically by making an incision in a vein, but rather was carried out by applying leeches or bloodsuckers to the patient’s body. It has been estimated that a single treatment might require the application of as many as 50 leeches.

Louis’s statistical evidence demonstrated the ineffectiveness of blood-letting. In asserting this, he placed himself in opposition to the French medical establishment. His primary opponent was a distinguished doctor, B. J. V. Broussais. In the late 1820s, Broussais himself used 100,000 leeches in a single year.²⁸ Today Broussais has an odd distinction: he is said to have been “the first physician to be destroyed by statistics.”²⁹ Nevertheless, Louis was not able to change the outlook of the French medical profession all at once. Even those who agreed with his ideas in general understood that the numerical method yielded only probabilities, not certainties, and that his answers were at best statistical.

For Americans, Louis is an important figure because he had a number of students from the United States, particularly from New England. Sir William Osler estimated that Louis trained at least 37 American doctors.³⁰ Among the New England doctors who studied under Louis, the best known was Oliver Wendell Holmes, Sr., father of the jurist Oliver Wendell Holmes, Jr., and author of The Autocrat of the Breakfast Table.

Louis’s influence on American medicine went beyond merely training some American students. His major publications were translated into English and published in American editions by Bostonian doctors: Henry I. Bowditch produced a revised translation of Louis’s 1835 work on phthisis (tuberculosis) and in 1841 translated his study of typhoid. G. C. Putnam translated Louis’s treatise on pneumonia in 1836, and in 1839 George C. Shattuck translated his tract on yellow fever.³¹

James Jackson, Sr., who was introduced to Louis’s method by his son, hailed the Frenchman as the man he had been searching for, for 35 years: a medical investigator who actually practiced the Baconian ideals of measuring, weighing, and numbering. Louis alone had taken the gigantic step necessary actually “to pursue the method of Bacon thoroughly and truly in the study of medicine.”³²

Louis’s research was publicized in American medical schools by Elisha Bartlett’s popular Essay on the Philosophy of Medical Science (1844, 1852, 1856). Bartlett stressed the importance of Louis’s numerical method, saying, “It is only by the aid of these principles [of observation, statistics, and mathematics], legitimately applied, that most of the laws of our [medical] science are susceptible of being rigorously determined.”³³ The book was favorably reviewed by two of Louis’s students, Josiah Clark Nott of Mobile and Alfred Stille of Philadelphia.³⁴ Stille wrote to George C. Shattuck of Boston that Bartlett’s views were “those of my own medical creed, & yours, & of all of us who have been brought up in the school of … Louis.”³⁵ Osler hailed Bartlett’s Essay as a “classic in medical literature.”³⁶

Coleman, on the other hand, finds that Louis’s actual “grounding in numerical data” was “slight.” For example, in his tests of the efficacy of blood-letting, he “used only two series of cases, one of 78 patients (of whom 28 died) and another of 29 patients (4 of whom died).”³⁷

Louis’s response to such criticism was that he required both clear and simple facts, and reasoned generalization based uniquely on those facts. As he wrote in 1837 to one critic, Jean Cruveilhier, “all [knowledge] comes from experience, it is true, but experience is nothing if it does not form collections of similar facts. Now, to make collections is to count.”³⁸

NEW USES FOR NUMBERS: INNOVATIONS BY CONDORCET AND LAPLACE

The late eighteenth and early nineteenth centuries witnessed tremendous advances in the mathematical theory of probability, the mathematics used to analyze statistical data. This new science ultimately gave rise to a variety of spin-off disciplines that altered our daily life. Two contributors to the development of the theory of probability were Condorcet and Laplace.

Antoine de Caritat, Marquis de Condorcet (1743–1794), was a mathematician and a social theorist. He was a friend of Benjamin Franklin’s and of Thomas Jefferson’s, both of whom had contact with him in his role as secretary of the French Academy of Science.

Like Lavoisier, Condorcet was an enthusiastic supporter of the French Revolution in its early stages. But as the Revolution turned into the Terror, Condorcet, like Lavoisier, was condemned and died on the guillotine. Yet Condorcet, while awaiting certain arrest and inevitable death, wrote one of the most optimistic books ever written about the future of mankind. This philosophical masterpiece, Esquisse d’un tableau des progrès de l’esprit humain, was published posthumously by his wife.

Pierre-Simon, Marquis de Laplace (1749–1827), was the most important mathematician since Isaac Newton. He was a gifted contributor to both pure and applied mathematics, and it was he who transformed Newton’s “rational mechanics” into “celestial mechanics” with his treatise Mécanique céleste (1799–1825). Laplace made many important contributions to probability theory and wrote a very influential book on the philosophy of probability, Théorie analytique des probabilities (1812).

Laplace applied the theory of probability to judicial voting. Whereas in the British system of law, a unanimous vote of a jury of 12 was required to establish guilt, in France a simple majority would suffice. Laplace believed that the British system implied a bias toward the protection of society and that the French system was unjust to the accused. He recommended a compromise, requiring the agreement of 9 out of 12 jurors, which he thought would provide a better system of justice.

The history of the development of the theory of probability is beyond the scope of this book. Our interest here is in numbers, and in this field Condorcet has been noted for his use of the new science of probability to analyze the voting process. But perhaps his most important contribution was to have made Laplace aware of this problem.³⁹

So in place of a discussion of probability, we must turn our attention next to the politically even more consequential emergence of the new science of statistics.