This issue of Science in Context presents a sampling of current work by art historians examining modern artists' engagement with science as well as the relationship of photography to both science and art. The essays' topics span the mid-to-later nineteenth century to the 1960s and, thus, in a series of case studies provide an introduction to aspects of artistic modernism. Indeed, it is impossible to understand fully many of the radical innovations of modern art without some knowledge of an artist's cultural context, and developments in science have often played a critical role in defining that milieu. Collected together, these essays also represent methodological models of historical work on art and science that serve as useful examples in this developing field.

Argument

The paper focuses on a research project launched by Norwegian psychiatrists immediately following World War II. The project sought to investigate the roots of quislingism (collaboration with the Nazis) through psychiatric research on the collaborators. Considered with hindsight, however, the methodology of the project seems puzzlingly shallow. The paper discusses whether this was due to a general lack of adequate methodology in the contemporaneous sciences, or whether the explanation must be sought in the project's social and historical context. Ultimately, I conclude that considerable weight must be placed on the latter explanation, and that the general political ostracism of the collaborators in the postwar years played a major role in the psychiatrists' attitude.

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

In 1867 Edouard Manet painted the execution of the Mexican emperor Maximilian of Habsburg. Manet broke with the classical tradition of history painting, for he depicted the actual shooting itself instead of choosing moments before or after the execution. Thus, the painting refers to a moment that in real time would have been far too brief to be perceptible. Manet presented a portrait of living actors whose execution has already taken place. This depiction of the imperceptible invites comparison to contemporaneous photographs of extremely short periods of time: attempts to capture flying cannon balls (Thomas Kaife), to take flashlight portraits of patients that would undermine their bodies' reaction time (Albert Londe), to visualize the successive stages of a drop falling into water (Arthur Worthington). Like Manet these scientists referred to an “optical unconscious” (Walter Benjamin). A closer look at their work reveals that they dealt with a space of knowledge that went beyond the classical dichotomy between objectivity and imagination, scientific and artistic pictures.

Argument

This paper contributes to inquiries into scientific personae by employing a rhetorical approach. It analyzes the persuasive strategies of Judith Rich Harris in The Nurture Assumption: Why Children Turn Out the Way They Do (1998). Rhetorical analysis of Harris' self-fashioning in this remarkable best-seller and the reactions of the press to her persona demonstrates the resilience of specific archaic cultural repertoires for constructing scientific identities. While historical studies investigate how repertoires for scientific self-fashioning evolve through time, rhetoric reveals how identity models from an earlier age may be appropriated in the present.

The first part of this paper surveys the current literature in the history of nineteenth-century mathematics in order to show that the question “Did the increasing abstraction of mathematics lead to a sense of anxiety?” is a new and valid question. I argue that the mathematics of the nineteenth century is marked by a growing appreciation of error leading to a note of anxiety, hesitant at first but persistent by 1900. This mounting disquiet about so many aspects of mathematics after 1850 is seldom discussed. The second part explores the issue of anxiety in mathematical life through an interesting account of an address made by a mathematician in 1911, Oscar Perron. The third and final part ventures some conclusions about the value of anxiety as a question for historians of mathematics to pursue.

Argument

Odilon Redon's dark-spirited charcoals and lithographs of the last quarter of the nineteenth century responded to developments in science, including the Pasteurian revolution. Rather than celebrating the progressive potential of science, Redon's noirs engaged national anxieties that attended scientific advances. His position was close to the Decadents of the 1880s who dwelled on themes of illness and decay. While the artist's original biographer André Mellerio referred to the artist's fascination with Pasteur and his microbial world, where in a single drop of water “there arises the spectacle of giants of a gripping horror and a frightful, predatory nature,” the topic has virtually disappeared from Redon literature. By recovering the scientific/medical issues that stimulated Redon's creation, this article restores the subjects of pathogenic organisms and contagious illness to their rightful place in Redon's oeuvre. Further, it provides the reader with a discussion of the cultural context in which Redon's interest was generated.

The celebrated “creation” of transfinite set theory by Georg Cantor has been studied in detail by historians of mathematics. However, it has generally been overlooked that his research program cannot be adequately explained as an outgrowth of the mainstream mathematics of his day. We review the main extra-mathematical motivations behind Cantor's very novel research, giving particular attention to a key contribution, the Grundlagen (Foundations of a general theory of sets) of 1883, where those motives are articulated in some detail. Evidence from other publications and correspondence is pulled out to provide clarification and a detailed interpretation of those ideas and their impact upon Cantor's research. Throughout the paper, a special effort is made to place Cantor's scientific undertakings within the context of developments in German science and philosophy at the time (philosophers such as Trendelenburg and Lotze, scientists like Weber, Riemann, Vogt, Haeckel), and to reflect on the German intellectual atmosphere during the nineteenth century.

Argument

The recent development of molecular genetics has created concern that society may experience a new eugenics. Notions about eugenics and what took place in the 1930s and 1940s are actively shaping questions about which uses of the new genetics should be considered illegitimate. Drawing upon a body of historiographical literature on Scandinavian eugenics, this paper argues that the dominant view of eugenics as morally and scientifically illegitimate is not tenable when it comes to the uses of compulsion, political motivation, and scientific acceptability. In spite of a general condemnation of eugenics, health authorities today are trying to prevent individuals with deviant behavior from reproducing or at least from rearing children. This may not be argued with reference to the risk of transmitting defective genes, but rather the risk of producing undesirable social problems. Drawing on a Foucauldian approach, the paper concludes that eugenics and new genetics should be seen as two historically specific forms of biopower.

Argument

The article describes a special type of scientific and philosophical “non-conformism” as exemplified in the versatile work of Richard von Mises (1883–1953). While the historical impact of von Mises' practical and organizational work in applied mathematics is beyond doubt, it is shown that von Mises' insistence on cognitive connectibility of various scientific domains was not, in the end, successful although it stimulated the theoretical discussion considerably. Von Mises developed a principally critical attitude towards what he considered “one-sided” in several streams of modernity and tended to be “anti-modern” even in those of his activities which belonged to “modernism.” Reasons can be found in his biographical experiences, in particular in his unorthodox academic education and repeated emigrations. Thus biographical research has considerable potential for historical explanation. The paper delves into the existing premises and sources for a scientific biography of Richard von Mises which is yet to be written, and publishes in the appendix a revealing biographical sketch (1959) authored by von Mises' widow, the applied mathematician Hilda Geiringer.

Argument

I propose that both Moholy-Nagy's suggestions that products of applied, particularly scientific, photography be employed as exemplars for art photography, and his practice of integrating such applied photographs with art photographs in his publications and exhibitions, laid the groundwork for an aestheticization of scientific photography within the twentieth-century artistic avant-garde. This photographic “New Vision,” formulated in the 1920s, also effected a kind of “scientization” of art photography. Rather than Positivist mechanism, however, I argue that the science at play was “biocentrism,” the early twentieth-century worldview that can be described as Naturromantik updated by biologism. His key inspiration in this regard was one of the most important figures of biocentrism, the biologist and popular scientific writer Raoul Heinrich Francé, and his conception of Biotechnik [bionics], in which he proposed that all human technologies are based in natural technologies.

The biological, pure and simple, taken as the guide.

– Moholy-Nagy (1938, 198)

This essay takes a close look at specially selected features of the Göttingen mathematical culture during the period 1895–1920. Drawing heavily on personal accounts and archival resources, it describes the changing roles played by Felix Klein and David Hilbert, as Göttingen's two senior mathematicians, within a fast-growing community that attracted an impressive number of young talents. Within the course of these twenty-five years Göttingen exerted a profound impact on mathematics and physics throughout the world. Many factors contributed to the creation of a special atmosphere that served as a model for several other important centers for mathematical research. Göttingen exemplified a dynamic new way of doing mathematics within a highly competitive community in which the spoken word often carried more weight than did information conveyed in written texts. This oral dimension of the Göttingen culture played an important, till now overlooked role in the early development of Einstein's general theory of relativity.

In 1926 and 1927, James W. Alexander and Kurt Reidemeister claimed to have made “the same” crucial breakthrough in a branch of modern topology which soon thereafter was called knot theory. A detailed comparison of the techniques and objects studied in these two roughly simultaneous episodes of mathematical research shows, however, that the two mathematicians worked in quite different mathematical traditions and that they drew on related, but distinctly different epistemic resources. These traditions and resources were local, not universal elements of mathematical culture. Even certain common features of the main publications such as their modernist, formal style of exposition can be explained by reference to particular constellations in the intellectual and professional environments of Alexander and Reidemeister. In order to analyze the role of such elements and constellations of mathematical research practice, a historiographical perspective is developed which emphasizes parallels with the recent historiography of experiment. In particular, a notion characterizing those “working units of scientific knowledge production” which Hans-Jörg Rheinberger has termed “experimental systems” in the case of empirical sciences proves helpful in understanding research episodes such as those bringing about modern knot theory.

Argument

By the time the members of the Surrealist group had fled Paris and dispersed at the beginning of World War II, they had taken account of quantum mechanics and were seeking various ways of assimilating its findings into Surrealist theory. This can be detected in writings issuing from the Surrealist milieu as early as the late 1920s. However, while writers and thinkers outside the field of physics swiftly expressed their awareness of the epistemological crisis brought about by quantum mechanics, Surrealism's artists began to conscript the concepts and imagery of modern physics into their work only at the end of the 1930s. Focusing on two “second generation” Surrealist painters, the Chilean Roberto Matta and the Viennese Wolfgang Paalen, this article discusses the peculiar difficulties faced by artists in finding a language for the “new reality” revealed by the physicists, and argues that the relocation of Surrealism in a discursive field which includes quantum physics discloses the rationale behind its artists' shift to a semi-abstract language.

Argument

“How should a modern artist react to the atomic age?” Time magazine posed this question in 1952 to open a review of an exhibition of paintings inspired by the “explosion of the atomic bomb” and by the “discovery of nuclear energy.” The energetic paintings of the Italian Spatial Movement were, according to Time, “almost as explosive as the bomb itself.” “Explosiveness” was a defining feature of much 1950s art, whose main impulse, gestural abstraction, has previously been understood as the urgent expression of the artist's subjectivity. This paper argues that explosiveness in art can also be seen as an “expression” of the realities of the nuclear era. Postwar artists were ambivalent about the explosive forces, both liberating and devastating, that lay within the atom. Toward the end of the 1950s, no longer content merely to represent atomic disintegration, some artists went so far as to propose the outright self-destruction of the work of art as the only fitting means of expression in the atomic age.

One must – and this is not an exaggeration – keep in mind that we are living in the atomic age, where everything material and physical could disappear from one day to another, to be replaced by nothing but the ultimate abstraction imaginable.

– Yves Klein 1958 (Klein 1973, 10)

Hermann Weyl (1885–1955) was one of the early contributors to the mathematics of general relativity. This article argues that in 1929, for the formulation of a general relativistic framework of the Dirac equation, he both abolished and preserved in modified form the conceptual perspective that he had developed earlier in his “analysis of the problem of space.” The ideas of infinitesimal congruence from the early 1920s were aufgehoben (in all senses of the German word) in the general relativistic framework for the Dirac equation. He preserved the central idea of gauge as a “purely infinitesimal” aspect of (internal) symmetries in a group extension schema. With respect to methodology, however, Weyl gave up his earlier preferences for relatively a-priori arguments and tried to incorporate as much empiricism as he could. This signified a clearly expressed empirical turn for him. Moreover, in this step he emphasized that the mathematical objects used for the representation of matter structures stood at the center of the construction, rather than interaction fields which, in the early 1920s, he had considered as more or less derivable from geometrico-philosophical considerations.

What follows shall provide an introduction to a predominantly philosophical and polemical, but historically revealing, paper on the foundations of the theory of probability. The leading Russian probabilist Aleksandr Yakovlevich Khinchin (1894–1959) (see fig. 1) wrote the paper in the late 1930s, commenting on a slightly older, but still competing approach to probability theory by Richard von Mises. Together with the even more influential Andrey Nikolayevich Kolmogorov (1903–1987), who was nine years his junior, Khinchin had revolutionized probability theory around 1930 by introducing the modern measure-theoretic approach, which is still standard today and which allowed for a sufficiently general treatment of important new notions such as “stochastic processes.” This development had its first culmination in Kolmogorov's booklet, Grundbegriffe der Wahrscheinlichkeitsrechnung, written in German in 1933, which has exerted an enormous influence world wide.

Officially inaugurated in 1925, the Hebrew University of Jerusalem was designed to serve the academic needs of the Jewish people and the Zionist enterprise in British Mandatory Palestine, as well as to help fulfill the economic and social requirements of the Middle East. It is intriguing that a university with such practical goals should have as one of its central pillars an institute for pure mathematics that purposely dismissed any of the varied fields of applied mathematics. This paper tells of the preparations for the inauguration of the Hebrew University during the years 1920–1925 and analyzes the founding phase of the Einstein Institute of Mathematics that was established there during the years 1924–1928. Special emphasis is given to the first terms in which this Institute operated, starting from the winter of 1927 with the activities of the director and one of the founders, the German mathematician Edmund Landau, and onward from 1928 when his successors, particularly Adolf Abraham Halevi Fraenkel and Mihály-Michael Fekete, continued Landau's heritage of pure mathematics. The paper shows why and how the Institute succeeded in rejecting applied mathematics from its court and also explores the controversial issue of center and periphery in the development of science, a topic that is briefly analyzed in the concluding section.

The paper presented here was written as early as sometime between 1939 and 1944 by the eminent mathematician Aleksandr Yakovlevich Khinchin, who is well known for his contributions to the theory of probability, statistical physics, theory of numbers, and theory of functions. For reasons unknown to me, it remained unpublished, although I remember that Khinchin had submitted it to the periodical Uspekhi matematicheskikh nauk. After he died, while I was putting in order the scientific and literary heritage of Khinchin, I remembered this work and began looking for it. Regrettably, I was unable to find any copies of a final version and the editorial office of Uspekhi did not have any record of the article. So I decided to make use of a copy that had been retyped in 1946 by my students, E. L. Rvacheva and D. G. Meyzler, even though it had some lacunae. I am convinced that even in this state, Khinchin's work is of considerable interest.