By Robin E. Rider
The intent of this afterword is to suggest some sources and directions that might prove helpful in further investigation of what we call the quantifying spirit. To keep the task within bounds, the emphasis is on publications of the 1980s. The essays in or into historiography in The ferment of knowledge. Studies in the historiography of eighteenth-century science afford a convenient point of departure. Its editors hoped that a historiographical approach would gather together the "detailed and discrete publications" that chronicle the complexity of 18th-century science—complexity that bedevils attempts to craft synthetic accounts of 18th-century knowledge about nature. To that end, they assembled a dozen detailed, not always discrete responses to the historiographic challenge, a challenge individual contributors defined in quite different ways.
Several essays in The ferment of knowledge speak directly to themes of the present volume. Henk Bos, for example, underscores the "direct and intense interaction" of mathematics with its applications in the 18th century. Simon Schaffer discusses, among other topics, Buffon's view of "natural philosophy as the discourse of order," drawing our attention to Foucault's distinction between a "general science of order" and mathematization. In making frequent reference to a study of the méthode numérique in 18th-century medicine, W. Bynum alerts us to quantification of medical experience
from the 1760s on. D.S.L. Cardwell highlights the significance of the "quantification of power" in 18th-century technology; for Cardwell, the roots of the Smeatonian method—"rational, systematic and comprehensive," aimed at "testable and preferably quantitative" answers—likely lie in Newtonianism. Roy Porter contends that quantification proved of dubious value "for explicating the environment" of the terraqueous globe, but he sets considerable store by the 18th-century view of nature as economical, "uniform, organized and integrative." He also underscores the challenge posed by "the growth of knowledge"—"the sheer quantity of newly available information" to be managed, lest chaos reign. In Rom Harré's discussion of scientific epistemology, the model of mathematical thought makes several appearances: Locke's views on certainty, seen as grounded in geometry; d'Alembert's adherence to the Cartesian doctrine of "mathematical abstractionism"; Adam Smith's "philosophical economics," aimed at optimizing the quantity of happiness. Maurice Crosland, in his stress on Lavoisier and the chemical revolution, plays familiar themes of classification and measurement.
J.L. Heilbron's essay offers the clearest invocation of the quantifying spirit. Heilbron reasons from the development of 18th-century electricity to a periodization of experimental natural philosophy in which quantification plays a crucial role. In the emphasis on experimental physics in the latter part of the century, in the preference for an instrumentalist approach stripping away metaphysical niceties, we hear tunes sounded in several chapters of the present volume.
The editors of The ferment of knowledge also asked their contributors to mark out fruitful directions for further research. From the desiderata listed by the contributors emerge several common concerns relevant to the influence of mathematics and the uses of quantifica-
tion. Many of the authors urge that the disciplinary map be redrawn along lines more faithful to 18th-century categories of knowledge; most request greater attention to social, political, or economic context. Several recommend listening carefully to language, to the forms of discourse. All find plenty for historians to do.
The sheer quantity of scholarship on 18th-century science published in the past decade or so speaks to needs and opportunities in this field, and tempts quantification of the art of bibliography. Beginning with the Isis Critical bibliography for 1981, the 18th century broke free, as a chronological classification, from the 17th. Though the total number of entries in the CB s has varied considerably for the 1980s (and though the numbers are softened by individual decisions regarding compilations of articles), the market share for the 18th century has held fairly steady at 9 to 10 percent of all CB entries, with a peak of 397 entries; annual figures for the 17th century have shown more variation. If we take into account all the entries in the Cumulative bibliography for the years 1976–85, we find that entries for 18th-century topics outnumber those for thee 17th century by about one-third (2,008 versus 1,572). Anniversaries of late 18th-century events have helped to swell the totals. Just as the 250th anniversary of Newton's death proved the occasion for another round of scholarly attention to his work and influence, the 200th anniversaries of scientific or political events or of the deaths of other 18th-century scientific figures have recently triggered reassessments, new editions of classic works, and bibliographies deserving of attention. In what follows, the stress is put on other manifestations of the quantifying spirit and the ways in which the message of quantification was spread.
Other Expressions of the Spirit
The opinions of Fontenelle are frequently trotted out in characterizations of the Englightenment. Fontenelle commended the esprit géométrique for its promise of certainty and rationality, which might improve polity, morality, literature, and oratory as it had enriched astronomy and mechanics. By the end of the 18th century, a wealth of treatises and textbooks had praised the merits of mathematics and the solidity of reasoning in Euclidean geometry, often in terms borrowed from the previous century. Recent scholarship has pointed to John Arbuthnot's arguments in favor of the utility of mathematics, the appeal of the axiomatic approach and the persistence of Cartesian methods as mixed with mathematics, and the wide-ranging
influence of what one author calls the mathematical method-model.
What was reasonable or certain in the 17th and 18th centuries was intimately bound up with questions of probability and risk, in contexts ranging from law to morality, economics to public health. The richness of the analysis and examples in recent studies on probability will warrant careful attention in subsequent exploration of the esprit géométrique and the quantifying spirit. As the 18th-century controversy over inoculation against smallpox makes clear, the stakes could be high in disputes over the validity of quantitative arguments.
Such arguments could still carry weight even when the numbers were soft or when measurement was out of the question, as in discussions of moral arithmetic, meandering rivers, or thermometers for female emotional response, as calibrated from modesty through impudence. Here it is necessary to attend to what quantification promised: useful comparisons whatever the scale, informative models without measurement, precision (clarity, distinctness, intelligibility) rather than a close fit with the real world.
Although moral barometers scarcely belong to the realm of exact science, comparisons of soft and hard quantification may prove instructive. In particular, it is worthwhile measuring the play of the quantifying spirit in the 18th century against conspicuous accomplishments in the mathematization of science in the 17th century and the successes of mathematical physics in the late 18th and early 19th centuries. The articles in Nature mathematized explore examples of 17th-century exact science that enlightened thinkers subsequently found so persuasive. A recent issue of Revue d'histoire des sciences investigates the "conquest of new territories" by mathematical science between 1780 and 1830. And Jean Dhombres links the achievements of mathématisation with the nature of the French scientific community in the half-century between 1775 and 1825 in another recent article.
Inculcating the Spirit
It is a commonplace to see organized science as "entirely recast under the dominion" of the scientific academies and societies of the 18th century. Scientific academies and societies played a significant role in establishing the importance and extending the application of mathematical or quantitative methods. Much recent literature addresses questions of the founding and organization of academies and societies, and may thus enlighten us about the 18th-century disciplinary map. It may also contain clues about the place of mathematics and the mathematically adept in these institutions and about the ways in which academic prestige or authority could encourage the use of mathematics. Recent studies look at academies and societies in general and in particular. Studies of the use of mathematical
methods in the 18th century might follow the lead of works that discuss the place of particular sciences in specific academic contexts.
Studies that examine the role of individuals in academies and hence in the life of science, especially in conjunction with archival or edited correspondence, promise useful information. Historians have begun, for example, to trace the powerful academic influence of Leonhard Euler. Analysis of the éloges of the Paris Academy of Sciences yields insights both about its perpetual secretaries, including Fontenelle and Condorcet, and about the scientific ideologies and standards they promoted. The publications and prizes of academies and societies served to spread the quantifying spirit, and deserve more attention.
Educational institutions and strategies also played a role. The significance of science, especially mathematics, in the technical training establishment in France was sketched in older works that remain useful. Such works have recently been supplemented by studies of the royal engineering corps and military school in France; a comparative perspective is afforded by analysis of military and engineering training in old and New Spain. All need to be read against the evidence assembled in the work of Charles Gillispie, in biographical dictionaries of 18th-century engineers, in documentary histories of engineering, and in general histories of education. The roles played by academicians in beefing up the technical curricula bear more scrutiny. Data and studies of the teaching of mathematics and
science in colleges and universities offer possibilities for comparison.
The mathematical content, rhetoric, and appeal of popular courses and self-help books also helped to secure a place for quantification in popular culture. Studies of public courses and of the marketing of science thus warrant further investigation. So too do mathematical periodicals, textbooks for the self-taught, and the corps of mathematical author/practitioners.
For the end of the century, consideration of education and of the French Revolution raises twin issues of continuity and reform, both
pertinent to the place of mathematics in a revolutionary curriculum. Numerous studies unravel the organization and ideology of new institutions and trace their teachers, students, and lessons.
It is in the nature of bibliographical essays to point to topics or directions of research worth pursuing. Out of the diversity of the chapters in this volume on The quantifying spirit , as well as from a
survey of recent literature on the 18th century, emerge a number of possibilities, which may be collected under headings of economics and polity, discourse, and evidence of opposition.
Economics and Polity
In the discussions (in the "Introductory essay" and chapters 5, 6, 10, 11, and 12) of political arithmetic, economic development and policy, and meteorology, as well as in the work of Keith Baker and Charles Gillispie, we see signposts pointing to economics and polity as loci for the operation of the quantifying spirit. Vital statistics had economic value to tax collectors, conscription agents, and actuaries, and government bureaus and functionaries sought to police health as they managed princely coffers, coal, bread, and trees. The expanding literature on vital statistics and on public medicine in the 18th century thus promises a reasonable return on scholarly investment.
Cameralism and political economy, as they developed in theory and practice and in local and national settings, should not be ignored, nor studies of Adam Smith, influences on him, and impact of his ideas. The economic writings and policies of Physiocrats and Idéologues, especially as they relate to the philosophes and to intellectual movements in the Enlightenment, merit another look with the quantifying spirit in mind. The economic and political import of
scientism and the place of mathematics in scientism have relevance as well.
Mathematical metaphors and images frequently found their way into discourse in the 18th century, whatever the topic, and hence illustrate both the cultural appeal of quantification and a means by which the quantification message was reinforced and spread. Studies of language for other scientific fields explore the malleability and power of metaphor, and suggest useful approaches for considering the language of quantification.
If there was a quantifying spirit or esprit géométrique in the 18th century, there was surely a critical spirit as well, and the voices raised in favor of rethinking the place and power of mathematics and quantification ought also to be heeded. Buffon's criticism of mathematics and Diderot's quotable doubts about the future of mathematics speak to the prevailing faith in mathematics and mathematicians. Even d'Alembert wrote with some skepticism about the "esprit de calcul," which he saw as the dominant "goût de philosophie" in the 18th century. Tracts that decried the "abuse of mathematics in natural science," need to be set against 18th-century pæans in praise of mathematics.
The bibliographical burden can be made more enjoyable by seeing how mathematics and quantification fared in 18th-century scientific satires. Jonathan Swift's Gulliver watched savants labor to extract sunbeams from cucumbers; he heard their scheme for establishing a
universal language by abolishing all words; and he talked with an innovative projector in speculative learning. This worthy had secured the services of forty pupils to crank the handles on a frame twenty feet square: it carried a grid of "all of the Words of their language," based on careful computation of the proportions obtaining among the various parts of speech. Commanded first to crank, then to read and record the results, the pupils might thereby generate automatically books on all arts and sciences. That is not the method by which this book or this essay was composed.