Steven A. Walton

Technologies of Pow(d)er: Military Mathematical Practitioners’ Strategies and Self-Presentation

The category of “military mathematical practitioners” consists of those active soldiers and engineers who consciously broadcast their use of mathematical methods to achieve their goals in warfare. These are but a subset of mathematical practitioners more broadly, and they existed on a continuum from the practical to the theoretical, with each demonstrating a mix of the two. In this military case, I investigate the concerns in gunnery and fortification of Thomas Harriot, William Bourne, Thomas Digges, and Edmund Parker—an early-modern scientist, noted author on the mathematical arts, military administrator and author, and a polymath soldier and gunner, respectively—each of whom adopted a certain “mathematical posture” to distinguish themselves in these pursuits. Framed by the work of E.G.R. Taylor, Edgar Zilsel, and Erving Goffman, the examination of how mathematics were actually used by these military mathematical practitioners (which should not be conflated with their actual utility, which is shown here to be often quite lacking) demonstrates the relationship, often a gulf, between theory and practice in one area of the mathematics in later sixteenth-century England. The context, audience, method of development, instruments, and mode of presentation (print vs. manuscript vs. rhetoric) of the mathematical methods applied to warfare also provide evidence of how mathematics was both used and understood as useful in this period to build a self-image of competence and professionalism.

What is straight cannot fall: Gothic architecture, Scholasticism, and dynamics

It has long been shown that medieval builders primarily used geometrical constructions to design medieval architecture. The thought processes involved, however, have been considered to be remote from the natural philosophical speculations of the Scholastics, who, following Aristotle, had taken the basis of physics to be the study of dynamics, or change. However, investigations of the Expertises of Chartres, Florence, Milan, and other documents related to medieval building suggest that medieval architects, in speaking of their work, resort to recognizable dynamic arguments, structured similarly to the speculations of Scholastic philosophers. These dynamic explanations of structural behaviour persist at least into the 17th century, but thereafter lost out to the arguments based on statics made by modern scholars attempting to explain the endurance of these structures.

Impossible Engineering: Technology and Territoriality on the Canal du Midi

This important book assesses the level of unreliability—random measurement error—in individual survey items found in general-population surveys, on which much scholarship in sociology and kindred fields depends. Duane Alwin aspires to reduce measurement error at its source by identifying less error-prone methods of constructing and administering surveys. His study contributes to understanding survey quality by showing how reliability varies with item content and instrument design; many findings provide empirical grounding for well-established survey practices, while others suggest that some common data collection protocols may heighten error. The study rests on an original, unique data base of reliability estimates for nearly 500 individual survey items drawn from longitudinal surveys representing well-defined populations. Questions included measure both basic sociodemographic facts and subjective phenomena (beliefs, attitudes, selfperceptions). Alwin coded item properties (number of response alternatives, length), question content (factual or nonfactual), and survey context (inclusion in a topical series or ‘‘battery’’ of related questions, ordinal position within a questionnaire), and then assessed associations between these design features and reliability. As befits a study of data quality, much of Margins of Error justifies the measurement of its dependent variable, item reliability. Three chapters that outline and critique extant approaches to reliability assessment can be read profitably on their own. But the key here is that Alwin seeks reliability measures for single survey items, not composite scales. He stresses the distinction between multiple measures (verbatimreplicated items) and multiple indicators (distinct items related to a common underlying construct). He finds widely-applied ‘‘internal consistency’’ approaches based on classical test score theory (coefficient a) wanting, because they estimate the reliability of multiple-indicator composites rather than individual items, and because such composites need not be ‘‘univocal’’—that is, they combine indicators that often have imperfectly correlated true scores. A particular difficulty is that those methods understate item reliability by classifying stable, but measure-specific, variance in a survey response as erroneous rather than reliable. Alwin argues that cross-sectional designs cannot adequately estimate the reliability of single items, because respondent memory raises correlations among multiple measures or indicators. He advocates longitudinal designs that administer identically worded questions on at least three occasions, suggesting that those measurements be separated by intervals of up to two years to avoid memoryinduced inflation of reliability estimates. When these demanding data requirements are met, suitable analytic methods can distinguish reliability and stability, and incorporate stable item-specific variance within true score variance. Many results substantiate widely-used and -taught guidelines for constructing survey instruments. For example, reliability tends to be higher for factual questions than for items measuring subjective content, for selfreports than for proxy responses about others, and (usually) for shorter questions. In keeping with much recent methodological research on survey data, Alwin invokes cognitive considerations to interpret such associations; he suggests, for instance, that respondents may better comprehend short questions, and more readily access and retrieve information needed to answer factual ones. Of particular note is Alwin’s finding that the widespread survey practice of presenting items in batteries—sets of consecutive questions using the same response format—tends

The Heirs of Archimedes: Science and the Art of War through the Age of Enlightenment (review)

The result of two conferences in the late 1990s, this volume on early modern military science offers a baker’s dozen of first-rate essays from the leaders in the field. Arranged roughly chronologically, from Kelly DeVries’s look at fourteenthand fifteenth-century gunpowder fortification to Brett Steele’s work on military “progress” and Enlightenment Newtonians, each offers a focused look at a single topic, or one country, and as a group they touch on military developments from the Atlantic to the Caucasus, from Sweden to Cairo, and on land and sea. Given that eight of the contributions are more or less directly related to gunpowder production or defense against gunpowder weaponry, it seems that the volume is more fully invested in critiquing the mechanics of the Roberts/Parker “military revolution” thesis than it is the scientific one, as the subtitle suggests. Still, the contributors all take up and reinterpret central themes in early modern military history, and some the historiography of the scientific revolution. Some essays merely survey a particular topic, and only a few seem to have delved deeply into primary sources or forged deeply novel arguments. The first part, on “Global Development of Gunpowder Weaponry,” includes four surveys by respected scholars. In addition to DeVries’s, Frederic Baumgarner investigates French reluctance to arm with gunpowder weaponry, while Bart Hacker and Gábor Ágoston show that the Islamic empires and the Ottomans, respectively, were more progressive in this matter than we typically assume. Part 2 focuses principally on navigation and exploration and their connection to both the sciences and northern European military impulses. Naval hardware is relatively absent here, although Alex Hildred’s long chapter on the Mary Rose gives at least one in-depth look at a warship, albeit from a more archaeological than synthetic viewpoint. The other essays seem only to draw a weak connection between militarism of the sixteenth and seventeenth centuries and navigational science (other than that the former needed the latter to get where it was going). Lesley Cormack and Amir Alexander synergistically consider the English case in their respective essays, Cormack concluding that science in the guise of navigation “assumed new methodologies, epistemologies, and ideologies of utility and progress” (p. 196), Alexander contrasting the geometrical and logical mathematics of John Dee with the exploratory mathematics of Thomas Harriot and suggesting that the actors’ frameworks determined their outcomes in some ways. Michael Mahoney then concludes with a pithy essay on Christiaan Huygens and his navigational and chronometric research program of state. T E C H N O L O G Y A N D C U L T U R E

The Field and the Forge: Population, Production, and Power in the Pre-industrial West (review)

In his latest book, demographer John Landers turns his attention to the intersection of technology and economics, production, and people over the longue durée of the pre-industrial West. Taking as his focus the “organic economies” before the Industrial Revolution (those based principally on muscle power and wooden raw materials rather than the “minerals” of iron and coal—a concept linked to economist E. A. Wrigley), Landers seeks to understand how these societies organized materials, production processes, and human energy, and how that organization affected policy. That alone would pique interest in the book by historians of technology, but its major subtheme—so integral that I wonder why it did not make it into the title— is the connection of all of these to military technology and military power. The Field and the Forge is a new take on the continuing “military revolution” debate, for, as Landers quite rightly notes in his opening pages, the shift from sword and pike to firearms was one of the first transitions from organic (muscle) technology to mineral (and chemical) technology. The Field and the Forge is impressively wide-ranging: the author analyzes Romans and Carthaginians in one paragraph, then jumps to military victories at Austerlitz and Sebastapol in the next. On the one hand, although compressing these vastly different eras into a single macro-analysis poses obvious difficulties, Landers’s comparisons come together cogently and provide useful insights into the relationships between the larger societal and technological variables; on the other hand, it seems to me the problem is that his analysis is often a rather simplistic rehashing of the general story of the development of the technologies and the production methods under consideration. This “banalysis” is not incorrect; it is usually quite well written and relies on the standard summary works in relevant fields, but it seems that one would not be reading this book if one did not already