The articles collected in this volume have their origin in an international workshop dedicated to “Experience and Knowledge Structures in Arabic and Latin Sciences.” Specialists from Great Britain, France, Denmark, Spain, Morocco, the United States, and Germany gathered in Berlin in 1996 in the context of an interdisciplinary research project on the history of mechanical thinking at the Max Planck Institute for the History of Science. The workshop initiated a process of discussion focused on problems of the intercultural transmission and transformation of knowledge. The present double issue is an outcome of this ongoing discussion.

Argument

Focus of this paper is on the historiographical fate of Nicholas Copernicus and Galileo Galilei in Nazi Germany. Both played interesting roles in Nazi propaganda and the legitimization of Nazi political goals. In the “Third Reich,” efforts to claim Copernicus as a German astronomer were closely linked to revisionist policies in Eastern Europe culminating in the war-time expansion. The example of Galileo’s condemnation by the Catholic Church in 1633 became a symbol of its unjustified opposition to new “scientific” results, namely Nazi racial theory. After Catholic opposition against Nazi racial theory had reached a peak in 1937, the Galileo affair was turned into an instrument of Nazi propaganda against the Catholic Church.

Auch der Historiker steht in der Zeit, nicht über ihr.

Das Ewigkeitspostament hat er verloren.

Siegfried Giedion

Argument

Historians have accorded a privileged status to the analytic ideal of elements as a distinctive marker of “modern” chemistry. Boyle’s and Lavoisier’s have been used to characterize their modernity, which has in turn justified their status as the founding fathers of modern chemistry. It has been difficult, however, to establish a viable connection between these two fathers or the genealogy of their definitions. I argue in this paper that French didactic tradition gave rise to the definition Boyle stated in the Sceptical Chymist, or the analytic/philosophical ideal of elements. He did not endorse the definition he gave, but criticized its lack of analytic rigor and philosophical sophistication. His critique served as a negative heuristic, leading to Nicolas Lemery’s analytic ideal of “chemical principles” as distinct from “natural principles.” Lemery’s definition survived in French didactic tradition, as is evidenced in Macquer’s and Guyton’s textbooks which provided direct precedents for Lavoisier’s analytic ideal of “elements or principles.”

This article describes how the decimal place value system was transmitted from India via the Arabs to the West up to the end of the fifteenth century. The arithmetical work of al-Khwārizmī's, ca. 825, is the oldest Arabic work on Indian arithmetic of which we have detailed knowledge. There is no known Arabic manuscript of this work; our knowledge of it is based on an early reworking of a Latin translation. Until some years ago, only one fragmentary manuscript of this twelfth-century reworking was known (Cambridge, UL, Ii.6.5). Another manuscript that transmits the complete text (New York, Hispanic Society of America, HC 397/726) has made possible a more exact study of al-Khwārizmī's work. This article gives an outline of this manuscript's contents and discusses some characteristics of its presentation.

Argument

Recent writers in the brain sciences and the philosophy of mind contrast modern biological theories of consciousness with a mind-body dualism supposedly dominant half-a-century ago which they regard as scientifically sterile. Reference to C. S. Sherrington often signals the rejected dualism. This paper re-examines Sherrington’s highly qualified position and links it to the arguments of British scientists for whom he was a figurehead in the 1930s and 1940s. I interpret the mind-body literature as ancillary to debates about cultural values. From this perspective, dualism represents a defense of a threatened conservative culture. Dismissal of scientists’ supposed “dualism” does little to illuminate the tension in their thought between defense of values traditionally associated with mind and hope for an integrated mind-body science. This leads to comments on Sherrington’s own concept of integration. The conclusion relates these points to the new research in the brain sciences evident by the end of the 1940s.

in spite of koyré's conclusions, there are sufficient reasons to claim that galileo, and with him the beginnings of classical mechanics in early modern times, was closely related to practical mechanics. it is, however, not completely clear how, and to what extent, practitioners and engineers could have had a part in shaping the modern sciences. by comparing the beginnings of modern dynamics with the beginnings of statics in antiquity, and in particular with archimedes — whose rediscovery in the sixteenth century was of great consequence — i will focus on the question of which devices played a comparable role in dynamics to that of the lever and balance in statics. i will also examine where these devices came from. in this way, i will show that the entire world of mechanics of that time — “high” and “low,” practical and theoretical — was of significance for shaping classical mechanics and that a specific relationship between art and science was and is constitutive for modern sciences.

we present a number of findings concerning galileo's major discoveries which question both the methods and the results of dating his achievements by common historiographic criteria. the dating of galileo's discoveries is, however, not our primary concern. this paper is intended to contribute to a critical reexamination of the notion of discovery from the point of view of historical epistemology. we claim that the puzzling course of galileo's discoveries is not an exceptional comedy of errors but rather illustrates the normal way in which scientific progress is achieved. we argue that scientific knowledge generally develops not as a sequence of independent discoveries accumulating to a new body of knowledge but rather as a network of interdependent activities which only as a whole makes the individual steps understandable as meaningful “discoveries.”

Argument

The cerebral localization of mental functions is one of the centerpieces of modern brain research. Though the localization paradigm in its cultural and social interwovenness has been characterized as successful in the last third of the nineteenth century by a variety of historians of the neurosciences, there is also general agreement that localization came under threat around 1900. Besides the so-called holistic protest against the localization of mental functions, the neuroanatomical approach itself was challenged by experimental psychology, psychiatric nosology, and psychoanalysis. This story underestimates the fact that anatomically-based localization remained powerful in response to these multiple challenges. This meant a neuroanatomical revision of tools, concepts, and practices. But this meant also a shift in the cultivation of the cortex from a more philosophical agenda to rather concrete political claims. More specifically, the idea of the cortex as the noblest part of man was supplemented by suggestions concerning its “Höherzüchtung.” I will analyze this re-orientation and radicalization in two steps. First, I briefly discuss the anatomical and philosophical account of Theodor Meynert and then turn to Paul Flechsig who in the late nineteenth century inscribed the ability to create culture and civilization into the cortex. Second, I focus on the neuroanatomists Oskar and Cécile Vogt, who began their careers around 1900 and expanded the cultivation of the cortex. Even before World War I, they proclaimed a “cerebral hygiene.” Consequently, the Vogts linked their innovative neuroanatomical researches with the rising field of genetics, racial hygiene, and eugenics. In the early Weimar Republic, the Vogts openly supported socialist ideas and were engaged in establishing an Institute for Brain Research in Soviet Moscow, where Lenin’s brain was analyzed. By the end of the Weimar Republic, the rhetoric of the Vogts was bluntly authoritarian. Based on a few anatomical examinations of so-called elite brains and the brains of criminals, they made concrete suggestions for eugenics and the breeding of “one-sidedly gifted leaders.” Given the remarkable popularity of the Vogts around 1930, their program is an important example of the hubris of predicting and guiding future developments on the basis of scientific authority. It can be regarded as an ironic nemesis that the Vogts – never sympathizing with the political aims of the National Socialists – were forced to finish their careers as influential Kaiser Wilhelm scientists in Nazi-Germany.

Der Mensch wird immer mehr ein Hirntier werden. (Vogt 1912, 309)

Argument

Studies of Helmholtz’s popular lectures on science have concentrated on reconstructing his vision of the scientific enterprise, of its nature, its benefits, and its “civilizing power.” This paper offers a different perspective by focusing on Helmholtz’s attempts to expose his own scientific work to a wider public. Drawing on recent discussions about how to study science popularization, it analyzes how he made his work on sensory physiology accessible to various audiences. It is argued that the exposition of the theory of vision comprises a complex, multilayered transformation of epistemic messages, which includes the recasting of arguments, recontextualizations, shifting emphasis, and significant changes in style. The popular writings on vision were directed to several different audiences, and, as such, manifest a delicate balance between conflicting agendas. An analysis of the texts indicates that neither the traditional two-step model of science popularization nor the more recent attempt to regard popularization as an “expository continuum” provides appropriate historiographical frameworks to study the popularization of scientific knowledge.

This paper investigates the affiliation of Book I of the Latin translation of Euclid's Elements attributed to Hermann of Carinthia with the Arabic transmission of the Greek mathematical work. It argues that it is a translation of a text of the Arabic secondary transmission, that is, of an Arabic edition mixed with comments. Two methodological claims are made in the paper. The first insists that the determination of a text whose transmission was as multifaceted and complex as the Euclidean Elements needs to be based on a systematic investigation of entire books rather than on selected theorems or diagrams of global, mostly structural relevance. The second claim starts from the experience that almost all results regarding the place of a particular document in a chain of transmission are conjectural. It acknowledges that individual results are more or less persuasive, depending upon the qualitative status of the argument. It suggests that the quantitative accumulation of similarities, differences, errors, regularities, or peculiarities allows one to recognize patterns and thus improves the reliability of judgment.

Argument

Hermann von Helmholtz’s distinction between “pure intuitive” and “physical” geometry must be counted as the most influential of his many contributions to the philosophy of science. In a series of papers from the 1860s and 70s, Helmholtz argued against Kant’s claim that our knowledge of Euclidean geometry was an a priori condition for empirical knowledge. He claimed that geometrical propositions could be meaningful only if they were taken to concern the behaviors of physical bodies used in measurement, from which it followed that it was posterior to our acquaintance with this behavior. This paper argues that Helmholtz’s understanding of geometry was fundamentally shaped by his work in sense-physiology, above all on the continuum of colors. For in the course of that research, Helmholtz was forced to realize that the color-space had no inherent metrical structure. The latter was a product of axiomatic definitions of color-addition and the empirical results of such additions. Helmholtz’s development of these views is explained with detailed reference to the competing work of the mathematician Hermann Grassmann and that of the young James Clerk Maxwell. It is this separation between 1) essential properties of a continuum, 2) supplementary axioms concerning distance-measurement, and 3) the behaviors of the physical apparatus used to realize the axioms, which is definitive of Helmholtz’s arguments concerning geometry.

For more than a century, there has been some discussion about whether medieval Arabic al-jabr (and hence also later European algebra) has its roots in Indian or Greek mathematics. Since the 1930s, the possibility of Babylonian ultimate roots has entered the debate. This article presents a new approach to the problem, pointing to a set of quasi-algebraic riddles that appear to have circulated among Near Eastern practical geometers since c. 2000 BCE, and which inspired first the so-called “algebra” of the Old Babylonian scribal school and later the geometry of Elements II (where the techniques are submitted to theoretical investigation). The riddles also turn up in ancient Greek practical geometry and Jaina mathematics. Eventually they reached European (Latin and abbaco) mathematics via the Islamic world. However, no evidence supports a derivation of medieval Indian algebra or the original core of al-jabr from the riddles.

the article deals with the interrelation between galileo and the visual arts. it presents a couple of drawings from the hand of galileo and confronts them with viviani's report that galileo had not only wanted to become an artist in his youth but stayed close to the field of visual arts throughout his lifetime. in the ambiance of these drawings the famous moon watercolors are not in the dark. they represent a very acute and reasonable tool to convince the people who trusted images more than words. the article ends with panofsky's argument that it was galileo's anti-mannerist notion of art that evoked a repulsion of kepler's ellipses. it tries to show that it was again an aesthetical prejudice that hindered einstein from accepting panofsky's theory.

Argument

When electricity became a commodity in 1900, it furnished Germany with new attractions and revolutionized everyday life with all kinds of tools and gadgets; it also opened up a new space for investigating psycho-physical interaction, reviving ideas of a close linkage between psychic life and electricity. The paper traces the emergence of this electro-psychological framework beyond “electroencephalography,” the recording of electrical brain waves, to “diagnoscopy,” personality profiling by electric phrenology.

Diagnoscopy opens a window onto the scientific and public cultures of electricity and psychical processes in Weimar Germany. It garnered enormous attention in the press and was quickly taken up by several institutions for vocational guidance, because it offered a rapid and technological alternative to laborious psychological testing or “subjective” interviewing. Academic psychology and leading figures in brain research reacted with horror; forging counter measures which finally resulted in this technique being denounced as quackery. A few years later, the press celebrated electroencephalography as a mind-reading device, whereas the neuroscientists remained initially skeptical of its significance and the very possibility of an “electroencephalogram” (EEG) before they adapted electroencephalography as a tool for representing various neuro-psychiatric conditions in patterns of recorded signals.

The blending of psychophysiology and electrical engineering marks the formation of an electric epistemology in scientific as well as public understanding of the psyche. The transformations of electrodiagnosis from diagnoscopy to the EEG are indicative of a cultural shift in which electricity changed its role from being the power source for experimental apparatuses to becoming a medium of psychic processes.

Argument

After more than half a century of eclipse, the mind (in contradistinction to brain and behavior) emerged in the 1950s as a legitimate object of experimental and quantitative research in natural science. This paper argues that the neural nets project of Warren S. McCulloch, in frequent collaboration with Walter Pitts, spearheaded this cognitivist turn in the 1940s. Viewing the project as a spiritual and poetic quest for the transcendental logos, as well as a culturally situated epistemology, the paper focuses on McCulloch’s and Pitts’ efforts of logical modeling of the mind and on the social conditions that shaped that mission.

From McCulloch’s “experimental epistemology,” the mind–purposes and ideas–emerged out of the regularities of neuronal interactions, or nets. That science of mind thus became a science of signals based on binary logic with clearly defined units of perception and precise rules of formation and transformation for representing mental states. Aimed at bridging the gulf between body and mind (matter and form) and the technical gulf between things man-made and things begotten, neural nets also laid the foundation for the field of artificial intelligence.

Thus this paper also situates McCulloch’s work within a larger historical trend, when cybernetics, information theory, systems theories, and electronic computers were coalescing into a new science of communication and control with enormous potential for industrial automation and military power in the Cold War era. McCulloch’s modeling the mind as a system of command and control contributed to the actualization of this potential.

We build our castles in the air,

And from the air they tumble down,

Unless we carry them up there

Until they crack the pate they crown.

And we must lug them everywhere,

From garden walk to crowded town;

We build our castles in the air,

And from the air they tumble down.

And lucky, if when sere and brown,

Before our eyes too lofty stare,

We scape with life and pate, though bare,

On which to plant an honest frown.

We build our castles in the air,

And from the air they tumble down.

Warren S. McCullochOf McCulloch’s literary work only two thin volumes, One Word After Another (1945) and The Natural Fit (1959), have been published. Most of his poetic output was unpublished and is deposited at the American Philosophical Society (hereafter APS) in the McCulloch Papers, BM 139. The poem, originally published in The Natural Fit, is quoted after McCulloch 1989, vol. 3, 917. For commentary on his poetry, see Vasalis 1989.

in 1612, lodovico cigoli completed a fresco in the pauline chapel of the basilica of santa maria maggiore in rome depicting apocalypse 12: “a woman clothed with the sun, and the moon under her feet.” he showed the crescent moon with spots, as his friend galileo had observed with the newly invented telescope. considerations of the orthodox view of the perfect moon as held by philosophers have led historians to ask why this clearly imperfect moon in a religious painting raised no eyebrows. we argue that when considered in the context of biblical interpretation and the rhetoric of the counter-reformation, the imperfect moon under the woman's feet was entirely consistent with traditional interpretations of apocalypse 12.

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.

In two articles published in 1881 and 1884, the young academics, Martin Klamroth and Johan L. Heiberg, engaged in a brief debate on the textual choices that should govern the publication of a new critical edition of Euclid's Elements. This short debate seemed to settle the problem in Heiberg's favor as to what should be taken as the definitive text of Euclid's Elements. But the issue ought to be considered once again for there are good reasons for the claim that Klamroth was right, and that Heiberg was wrong. If so, we have been consulting, and continue to consult, the wrong text in our efforts to interpret the Euclidean tradition. In order to substantiate this claim, the textual issue debated by Klamroth and Heiberg is rehearsed again, and the principal reasons brought forth by Heiberg against Klamroth's position are reconstructed. Specimens from three broad areas of evidence – structural, linguistic, and technical – will be considered. They reveal how the medieval tradition of the text advocated by Klamroth displays textual superiority to the Greek tradition promoted by Heiberg. Such a reorientation of the texts has the potential to change significantly our understanding of ancient mathematics.