From the time of al-Khwārizmī in the ninth century to the beginning of the sixteenth century algebraists did not allow irrational numbers to serve as coefficients. To multiply $\sqrt {18} $ by x, for instance, the result was expressed as the rhetorical equivalent of $\sqrt {18{x^2}} $. The reason for this practice has to do with the premodern concept of a monomial. The coefficient, or “number,” of a term was thought of as how many of that term are present, and not as the scalar multiple that we work with today. Then, in sixteenth-century Europe, a few algebraists began to allow for irrational coefficients in their notation. Christoff Rudolff (1525) was the first to admit them in special cases, and subsequently they appear more liberally in Cardano (1539), Scheubel (1550), Bombelli (1572), and others, though most algebraists continued to ban them. We survey this development by examining the texts that show irrational coefficients and those that argue against them. We show that the debate took place entirely in the conceptual context of premodern, “cossic” algebra, and persisted in the sixteenth century independent of the development of the new algebra of Viète, Decartes, and Fermat. This was a formal innovation violating prevailing concepts that we propose could only be introduced because of the growing autonomy of notation from rhetorical text.

Argument

Sociologists and historians have long favored externalist over internalist accounts of practices in the clinical disciplines. This has been particularly true in the case of the so-called new patient or borderline personality, which a range of commentators have located in culturally resonant narratives of decline. I argue here that these narratives, while pleasing, do not hold up as history; most problematic is their assumption that the appearance of the borderline portends the emergence of altogether novel forms of modal personhood. Internalist accounts of the category's consolidation are equally problematic in asserting a coherence and a stable referent that repeatedly proves elusive. In the end, I suggest that a complex account of disciplinary practice that attends to knowledge production in the clinical encounter supports the conclusion that the new patient was new to psychoanalysis. Whether or not he was altogether new cannot be established, undermining the critics' certitude and prophecies of decline.

Darwin's narrative of the earthquake at Concepción, set within the frameworks of Lyellian uniformitarianism, romantic aesthetics, and the emergence of geology as a popular science, is suggestive of the role of the sublime in geological enquiry and theory in the early nineteenth century. Darwin's Beagle diary and later notebooks and publications show that the aesthetic of the sublime was both a form of representing geology to a popular audience, and a crucial structure for the observation and recording of the event from the beginning. The awesome spectacle of the earthquake proved in turn the magnitude of the forces at stake in earth history, and helped to make geology an epic conjoining the history of civilization with the history of the earth.

According to Hugo Münsterberg, the direct application of experimental psychology to the practical problems of education, law, industry, and art belonged by definition to the domain of psychotechnics. Whether in the form of pedagogical prescription, interrogation technique, hiring practice, or aesthetic principle, the psychotechnical method implied bringing the psychological laboratory to bear on everyday life. There were, however, significant pitfalls to leaving behind the putative purity of the early psychological laboratory in pursuit of technological utility. In the Vocation Bureau, for example, psychological instruments were often deemed too intimidating for a public unfamiliar with the inner workings of experimental science. Similarly, when psychotechnical means were employed by big business in screening job candidates, ethical red flags were raised about this new alliance between science and capital. This tension was particularly evident in Münsterberg's collaboration with the Paramount Pictures Corporation in 1916. In translating psychological tests into short experimental films, Münsterberg not only envisioned a new mass medium for the dissemination of psychotechnics, but a means by which to initiate the masses into the culture of experimental psychology.

Argument

This essay studies the convergence of brain research with the physiology of emotions during the early twentieth century. It argues that the brain entered the laboratory of emotions not as an object of knowledge, but as a technique for producing emotions, in spite of the laboratory. The new brain-generated emotion signaled an epistemic break in the nature of studied emotion. It restructured the relationships between physiological and psychological forms of knowledge. It embodied the historical and political concerns of physiologists with pain. And it excluded the affectively experiencing subject from the study of “emotion.” The essay also suggests that the brain-generated emotion was an object suspended in time and abstracted from history. Its unique a-temporal and de-contextualized characteristic transformed emotion into a product of a laboratory whose mode of production mimicked the modern factory. The constitutive elements that were assembled in creating the brain as emotion-generator were instrumental for the important studies of James Papez, Paul MacLean, and for the modern concept of Limbic System.

The time has come [to]…begin the vivisection of the human heart according to scientific methods.

Angelo Mosso, 1896

Argument

In this article, I compare Sabetai Unguru’s and Wilbur Knorr’s views on the historiography of ancient Greek mathematics. Although they share the same concern for avoiding anachronisms, they take very different stands on the role mathematical readings should have in the interpretation of ancient mathematics. While Unguru refuses any intrusion of mathematical practice into history, Knorr believes this practice to be a key tool for understanding the ancient tradition of geometry. Thus modern historians have to find their way between these opposing views while avoiding an unsatisfactory compromise. One approach to this, I propose, is to take ancient rhetoric into account. I illustrate this proposal by showing how rhetorical categories can help us to analyze mathematical texts. I finally show that such an approach accommodates Knorr’s concern about ancient mathematical practice as well as the standards for modern historical research set by Unguru 25 years ago.

Argument

According to Hermann von Helmholtz, free mobility of bodies seemed to be an essential condition of geometry. This free mobility can be interpreted either as matter of fact, as a convention, or as a precondition making measurements in geometry possible. Since Henri Poincaré defined conventions as principles guided by experience, the question arises in which sense experiential data can serve as the basis for the constitution of geometry. Helmholtz considered muscular activity to be the basis on which the form of space could be construed. Yet, due to the problem of illusion inherent in the subject’s self-assessment of muscular activity, this solution yielded new difficulties, in that if the manifold is abstracted from rigid bodies which serve as empirical justification of the geometrical notion of space, then illusionary bodies will produce fictive manifolds. The present article is meant to disentangle these difficulties.

The presence or absence of scientific research in productive organizations is a subject of professional concern to the scientific and engineering community, and of wider interest to political agencies in the United Kingdom. This paper will explore aspects of the economic visibility of scientific practices in productive organizations:how, by whom, and in what contexts research and development practices have been constructed, monitored, and disseminated as economic statistices within and beyond the modern industrial enterprise. The paper will focus on the construction of scientific practices as accounting and economic signifiers within their organizational context:the growth of mechanisms for the connection fo scientific practices to economic calculations. How companies account for R&D has been elevated by particular government agencies through the accountancy bodies, as a way of forging a relationship between economic calculation and the scientific practices of U.K.companies.

From 1893 to 1909 when it definitely sunk into the glacier, the Mont-Blanc Observatory (MBO) struggled to find its scientific purpose. In this article, we use recent literature on the social characterization of place to analyze this struggle. Our first goal is to investigate where the observatory may fit in the laboratory-field dyad. We investigate various kinds of conceptual “borderlands” between these places and look at the networking activities between particular knowledge production sites. We argue that part observatory, part laboratory, and part field station, the place of the MBO was “heterotopic” space in Foucault's sense. We then examine the social underpinnings that led to the foundation of this observatory in the context of French Third Republic at the turn of the century. Following some of the ways the MBO was connected to other scientific sites and surveying some of its visitors' scientific practices, we finally hint at the fact that some of these practices played a part in the emergence of a regime of science production that endured into the twentieth century (astrophysical aeronautical practices, spatial stations, polar exploration, etc.)

Why do similar scientific enterprises garner unequal public approbation? High energy physics attracted considerable attention in the late-twentieth-century United States, whereas condensed matter physics – which occupied the greater proportion of US physicists – remained little known to the public, despite its relevance to ubiquitous consumer technologies. This paper supplements existing accounts of this much remarked-upon prestige asymmetry by showing that popular emphasis on the mundane technological offshoots of condensed matter physics and its focus on human-scale phenomena have rendered it more recondite than its better-known sibling field. News reports about high energy physics emphasize intellectual achievement; reporting on condensed matter physics focuses on technology. And whereas frontier-oriented rhetoric of high energy physics communicates ideals of human potential, discoveries that smack of the mundane highlight human limitations and fail to resonate with the widespread aspirational vision of science – a consequence I call “the purloined letter effect.”

The present issue of Science in Context comprises a collection of articles dealing with various, specific aspects of the history of mathematics during the last third of the nineteenth century and the first half of the twentieth. Like the September issue of 2003 of this journal (Vol. 16, no. 3), which was devoted to the history of ancient mathematics, this collection originated in the aftermath of a meeting held in Tel-Aviv and Jerusalem in May 2001, under the title: “History of Mathematics in the Last 25 Years: New Departures, New Questions, New Ideas.” Taken together, these two topical issues are meant as a token of appreciation for the work of Sabetai Unguru and his achievements in the history of mathematics.

Argument

This essay explores how and why women involved themselves in the sciences in eighteenth-century Italy. Using the case study of Diamante Medaglia Faini, a poet who attempted to become a mathematician, it argues that the image of the woman natural philosopher was shaped by the visible presence of woman in scientific institutions in the mid-eighteenth century and by the tradition of popular scientific writing, best embodied in the works of Bernard le Bovier de Fontenelle and Francesco Algarotti, that made the woman natural philosopher an important literary protagonist. Becoming a scientist, in other words, was both a reality and a fiction. The tensions between these two different images shaped the terrain in which women pursued science.

The Copernican revolution with which Kant transformed the question of whether knowledge is possible into the query as to how knowledge is possible, constitutes one stage in the development of epistemology from a speculative to an observational science — i.e., one that proceeds from the investigation of concrete, existent objects rather than from a small number of presupposed concepts. This path, leading from speculation to examination of the concrete objects of research — for epistemology, to the investigation of the various individual sciences — is long and arduous, and even now it has been traversed only a small part of the way. Although epistemological research has for a long time had some relation to mathematics and physics, and a more concrete exploration of biology and the humanities has recently been launched as well, we undoubtedly still stand at the very beginning of this enterprise. One major task for the epistemological inquiry into a specific discipline is bound up with tracing the course of development of that science — in particular, the radical shifts and readjustments in a science that promise to furnish the epistemologist with valuable information. Seen from this angle, psychology also currently deserves the special attention of epistemology.

This paper is about the context of Albert Einstein's concerns at the time of a most intense intellectual effort — his own and that of a small group of scientists concerned with classical quantum theory. I describe contemporaneous interactions and differing views about the prospects for and the significance of the First Solvay Congress of 1911 as voiced by major participants. There are two axes around which the paper evolves: the Einstein-Nernst-Lorentz dialogue and the public institutional creation of the “Solvay” stage. In certain ways, this paper is about personal and institutional patronage: the working out of a difficult theoretical impasse requires individual and collective moral support. It is about the forging of the identity of a scientific problem and the personal and institutional setting, the public space, in which this problem was collectively addressed. But I also uncover heuristic playfulness and flexibility which accompanies theoretical change.

Following an international trend, Italy has reformed its university system, especially concerning methods and tools for research evaluation, which are increasingly focused on a number of bibliometric indexes. To study the effects of these changes, we analyze the changing profiles of economists who have won competitions for full professorship in the last few decades in the country. We concentrate on individual characteristics and on scientific production. We show that the identification of a univocal and standardized concept of “research quality” within the new research assessments has progressively imposed a strategy of “homologation,” especially for women. We find that women economists are at a higher risk of discrimination than their male colleagues and thus they are more likely to conform their research activities to the standardized profile imposed by the gender-blind application of simplistic bibliometric methods.

Hijōji (emergency) was an important keyword in the militarist Japan of the 1930s. Previous scholarship has assumed that such language sprung from the global financial crisis of 1929, and subsequent diplomatic events. Our article demonstrates, however, that a full-bodied language of emergency was crafted well before the collapse of the global economy, and against the backdrop of the Great Kanto Earthquake of 1923, which destroyed the Japanese capital. While previous “great earthquakes” had been opportunities to strengthen Japanese participation in the global project of science, this one led more dramatically to a crisis of reason, and indirectly contributed to the spiritual, anti-western, and anti-rational rhetoric of what became the “Showa Restoration.” This and other post-disaster landscapes, we argue, should be examined as compelling sites for the crafting of political language – sites of opportunity and meaning as well as trial. While the phrase “state of emergency” was coined under very different circumstances in post-war Britain, it gained power and charisma in Japan, and likely other places around the world, by its association with natural catastrophe. Thus did modern politics establish a new connection with the traditional realm of the sublime, and in the case of Japan, the supernatural. Emergency's ability to associate politics with nature would never disappear, and has perhaps even strengthened in the early twenty-first century.

The experimental development of a therapeutic serum against diphtheria between 1891 and 1894 was characterized by a scientific competition that pitted Emil Behring from the Institute for Infectious Diseases in Berlin against Émile Roux and Elie Metschnikoff from the Pasteur Institute in Paris. In general, their competition can be regarded as an extension of the fundamental differences that separated the research schools of Robert Koch and Louis Pasteur. However, to characterize the competition for a diphtheria-serum as “national rivalry” fails to account adequately for the mutual adoption of experimental practices by the Berlin and Parisian protagonists, whose contributions to the development of a therapeutic serum were intertwined in complex ways. Nor can it be characterized as “cooperation,” given their fierce public disputes over scientific concepts and the fact that these disputes also shaped the peculiarities of the experimental procedures in Berlin and Paris. A close analysis reveals a complex picture of the dynamic interaction between the conceptual and experimental activities of Behring, Roux, and Metschnikoff – interaction that defined as well as bridged the “French” and “Prussian” experimental systems of diphtheria-serum research.

This article gives the background to a public lecture delivered in Hebrew by Edmund Landau at the opening ceremony of the Hebrew University in Jerusalem in 1925. On the surface, the lecture appears to be a slightly awkward attempt by a distinguished German-Jewish mathematician to popularize a few number-theoretical tidbits. However, quite unexpectedly, what emerges here is Landau's personal blend of Zionism, German nationalism, and the proud ethos of pure, rigorous mathematics – against the backdrop of the situation of Germany after World War I. Landau's Jerusalem lecture thus shows how the Zionist cause was inextricably linked to, and determined by political agendas that were taking place in Europe at that time. The lecture stands in various historical contexts - Landau's biography, the history of Jewish scientists in the German Zionist movement, the founding of the Hebrew University in Jerusalem, and the creation of a modern Hebrew mathematical language. This article provides a broad historical introduction to the English translation, with commentary, of the original Hebrew text.

“The problem of university courses on infinitesimal calculus and their demarcation from infinitesimal calculus in high schools” (1927) is the published version of an address Otto Toeplitz delivered at a meeting of the German Mathematical Society held in Düsseldorf in 1926. It contains the most detailed exposition of Toeplitz's ideas about mathematics education, particularly his thinking about the role of the history of mathematics in mathematics education, which he called the “genetic method” to teaching mathematics. The tensions and assumptions about mathematics, history of mathematics, and historiography revealed in this piece dedicated to educational ideas are what make Toeplitz's text interesting in the study of historiography of mathematics. In general, the ways historiography of mathematics and teaching of mathematics, even without an immediate concern for history, are deeply entangled and, in our view, worth attention both in historical and educational research.

We examine the most famous controversy between economists — the one between Thomas Robert Malthus and David Ricardo — as a means of shedding fresh light on the current debate about economic methodology. By focusing on this controversy as the primary unit of analysis, we show how methodological considerations are but one of a whole set of stratagems employed by each opponent. We argue that each opponent's preference for a particular kind of stratagem expresses his own specific scientific style (within the general scientific and cultural style of an age). We also describe a dynamic dimension of the controversy, independent of the participants' intentions. Such a dimension is analyzed in one of the “cycles” of the controversy, which begins with a well-defined issue and expands to additional topics, without reaching a “solution” of the initial issue. The Controversy, thus, does not yield a solution of a given problem nor persuasion of the adversary — its presumable aims. Rather, its “benefit” seems to lie in an unintended result — the clarification and deepening of contrasting approaches to the discipline. Insofar as the history of a discipline requires a reconstruction of such contrasts, it is indispensable that it take into account the controversies where they emerge, and view both the positive doctrines and the methodological postures of the contenders as parts of a wider framework, within which the notion of a scientific style — which this paper attempts to clarify — looms large.