In discussions of the possible connections between Copernicus and his Islamic predecessors, the so-called Ṭūsī-couple, invented by the 13th-century Persian polymath Naṣīr al-Dīn al-Ṭūsī, has often been invoked by various modern historians to bolster their cases for or against transmission from Islamic astronomy to Copernicus. This paper seeks to clarify the possible routes of transmission by first explaining the various versions of the Ṭūsī-couple that were meant to produce either straight-line or curvilinear oscillations from circular motions, and then summarizing what is known about this transmission, providing new evidence as well as reinterpreting existing evidence. It becomes clear that there are a variety of avenues by which the various couples could have come into Europe, such as through Byzantium, through Spain, and through Italy, and that Copernicus acknowledges the earlier existence of at least one version of the couple in a draft of De Revolutionibus. The paper concludes with a historiographical note that maintains that the long, complex development and use of the Ṭūsī-couples within an Islamic context, and the lack of anything comparable in Europe before Copernicus, provides a compelling argument for transmission rather than parallel discovery within a Latin/European context.

To develop a more fine-grained picture of how the theory of general relativity was received and elaborated from 1914 until 1924, we move outside the personal networks of its creator, Albert Einstein. We set aside the question when and why Einstein himself came to recognize that the new field physics required higher mathematics and focus on the cross-fertilization between mathematics and physics that contributed to the theory. The breakdown of disciplinary boundaries had a greater impact on academic politics in Germany, as the intrusion of mathematics heightened tensions that had long been brewing within the German physics community. A second factor contributing to the tensions was the increasing prominence in the community of German physicists of those of Jewish extraction. We examine these phenomena in two localities, Göttingen and Berlin that serve as focal points for polarization in the natural sciences. First, we discuss the openness in their scientific approach and in their recruitment policy of the paladins of Göttingen—Felix Klein and David Hilbert—and then proceed to trace the fruits of that policy in the successor generation that was largely composed of Jews. We then look at Einstein in Berlin, and more specifically, at how his “conversion” to Zionism in 1920 crystallized his idiosyncratic views on cultural politics that alienated him from others in the Berlin community, including some of his Jewish colleagues. We examine four incidents that undergird his solidarity with Hilbert, a “Gesinnungsgenosse,” who believed that belonging to the international community of scientists took precedence over any sense of patriotic duty or ethnic identity.

The Max Planck Society (MPG) has presented itself since its reestablishment in 1948 as a refuge for basic research in the Federal German Republic. This programmatic claim developed under the political conditions of the middle 1940s, during which the end of the Second World War overlapped with the beginning of the Cold War and the western part of the subjugated “Third Reich” very quickly was drawn in as the inevitable junior partner of the western alliance. Within an American-dominated discourse, what had up until then been a hybrid concept changed into a dichotomous one: basic research was described as being clearly distinguishable from applied research, that is, as not immediately relevant for politics, economics, or the military. It was moreover elevated to a symbol of freedom, created by the western democracies to use against the totalitarian Stalinist opponent. With this semantic charge, the concept of basic research forged during the Cold War did three things for the MPG: as far as dealing with the past was concerned, it helped obscure the hybrid character of research, which the Kaiser Wilhelm Society had demonstrated as part of the NS-regime, especially in armaments research. With regard to contemporary politics, during the immediate postwar period it helped legitimate the organizational integrity of the MPG, its institutional independence, and the scientific autonomy of its members. For the future, the commitment to basic research remained a constantly renewing, yet diffuse mission. Debates about closing, reforming, or reestablishing Max Planck institutes show that the research plans were supposed to satisfy the claims about “basic research,” but also that this yardstick could never be calibrated in a binding way. Basic research served as a vague yet undisputed parameter for strategic scientific decisions within the MPG and its positioning in the scientific system of the Federal Republic.

Esoteric Knowledge remains a central problem of ancient science, since much of the scholarly heritage of ancient schooling was only meant for a small circle of adherents, rather than for the general public. For this reason, knowledge was restricted within schools or within professions, only accessible to those with a personal connection to experts and savants. The expression ‘esoteric’ is used today rather indiscriminately. Within the category of ‘esoteric knowledge’ one understands a variety of related expressions, such as ‘mystical’ or ‘occult’, as well as the more concrete ‘absolute’ or ‘elevated’ knowledge, which can also be considered as ‘hidden’, ‘secret’, or ‘inaccessible’, and even ‘fanciful’ or carried away. The confused pattern of these definitions is the reason why a closer look at the historical development of this concept is so important. This Preprint provides case studies of esoteric knowledge, within the realms of philosophy (e.g. esoteric vs. exoteric knowledge), religious knowledge (early Christian thought, Gnosticism, cultic practices), geography, divination, alchemy, dream interpretation, and iconography. Examples of esoteric knowledge presented here extend from Mesopotamia and Egypt into Graeco-Roman and early medieval models, in Akkadian, Egyptian, Syriac, Greek and Latin sources, indicating the durability and continuity of this concept.

Modern ship model testing has a long international prehistory of several centuries. This paper deals with its precursors from the 17th c. to its maturing by the beginning of the 20th c., also in Germany. The prerequisites for a practicable, design relevant model test methodology were created in many steps with important contributions by prominent scientists such as Huygens, Mariotte, Newton, Van Zwijndrecht, Chapman, D'Alembert, Beaufoy, John Scott Russell, Reech, Rankine, William and Robert Froude, David Taylor and many others. These developments characterize the status reached by the turn to the 20th c. when several German model basins were founded, too.

Around 1930, it was discovered that certain Babylonian cuneiform texts contain calculations that agree with what turns up in the solution of second-degree equations. Since the meaning of most of the terminology had to be derived from the numbers contained in the texts, this led to a reading of these as numerically based algebra. This interpretation stood unchallenged until the author of the present book discovered around 1982 that it was incompatible the global structure of the terminology. As it turns out, two different and non-synonymous operations had both been understood as addition; two different subtractive operations had been conflated, and four different operations had been seen as one and the same multiplication. Instead, the structure points to a technique based on a geometry of squares and rectangles with measurable sides and areas. Avoiding such philological detail as would only be informative for readers that are familiar with basic Assyriology (yet with appendixes meant for these), the book analyses a number of texts in "conformal translation", that is, a translation in which the same Babylonian term is always translated in the same way and, more important, different terms are always translated differently. All of these texts are from the second half of the Old Babylonian period, that is, 1800-1600 BCE. It is indeed during this period that the "algebraic" discipline, and Babylonian mathematics in general, culminates. Even though a few texts from the late period show some similarities with what comes from the Old Babylonian period, they are but remnants. Beyond analyzing texts, this preprint gives a general characterization of the kind of mathematics involved, and locates it within the context of the Old Babylonian scribe school and its particular culture. Finally, it describes the origin of the discipline and its impact in later mathematics, not least Euclid's geometry and genuine algebra as created in medieval Islam and taken over in European medieval and Renaissance mathematics.

If the emergence of physics as a definite academic discipline was a heritage of the late nineteenth century, the emergence of a new theoretical practice, and the settlements of chairs of theoretical physics were the most interesting outcome of that process. The hallmark of the new theoretical practice was the awareness that the alliance between the mathematical language and the experimental practice celebrated by Galileo had to be updated. Besides “definite demonstrations” and “sound experiments” there was a third component, which could be labelled conceptual or theoretical: it dealt with principles, models, and patterns of explanation. That conceptual component, neither formal nor empirical, came to be looked upon as a fundamental component of scientific practice. It is worth remarking that, in that fin de siècle, science had finally managed to realize, at least in part, Bacon’s dream, and the myth of scientific progress emerged. In the debates on science which took place in France from the early 1870s to the early 1890s two main issues were at stake: determinism and reductionism. On the one hand we find some scientists, historians, and philosophers who relied on simplified epistemological and historiographical frameworks, and put forward an optimistic cult of human progress. On the other hand, a sophisticated point of view on science was put forward by scientists and philosophers who did not deny the effectiveness of scientific progress but were able to go beyond the simplified conception of scientific practice as an unproblematic alliance between mathematical and empirical procedures. In 1892 the young physicist Pierre Duhem published the first paper explicitly devoted to meta-theoretical issues or, to make use of a more recent expression, to philosophy of science. At that time he had already published a book on thermodynamic potentials and their applications to different fields of physical sciences, and a demanding paper, where he had put forward an original mathematical approach to thermodynamics on the track of Analytical Mechanics. Theoretical physics, the history of physics, and meta-theoretical remarks on science were mutually interconnected in Duhem’s actual praxis. The historical and epistemological remarks he began to publish systematically in the 1890s were subsequently collected in the book he published in 1906, La théorie physique, son objet, et sa structure. He represented the scientific enterprise as a three-stages task: from the knowledge of “specific facts”, the human mind was able to derive some “experimental laws” by induction, and then create a scientific theory. If the objects of experimental laws were facts, the objects of physical theories were experimental laws. In any case, a theory had nothing to do with the truth: it could not be qualified as true or false, but “suitable or unsuitable, good or bad”. The plurality of theoretical frameworks corresponding to a set of laws was consistent with this essential feature of theories. Moreover he put forward three fundamental theses on experimental physics: first, a physical experiment was not a purely empirical process; second, it could not be so powerful as to lead to the refutation of a single hypothesis; third, it was less reliable, even though more precise, than ordinary experience. After the Second World War some themes which had been put forward in the late XIX-century philosophy of science re-emerged in an unexpected way. In reality, Duhem’s books and papers had almost been forgotten, but a new interest in some of his meta-theoretical theses emerged in the context of a philosophical tradition that was deeply linked to logic. In 1951 Willard van Orman Quine sharply criticised both the dichotomy analytic/synthetic and reductionism, but he neither quoted from nor mentioned Duhem. In 1960 Adolf Grünbaum put forward a refutation of what he called “Duhemian argument”, but the core of Duhem’s meta-theoretical remarks got lost in a net of logical deductions which were extraneous to their context. Only from the 1970s onwards historians, historians of science, and philosophers of science began to be attracted by late XIX-century context in general, and Duhem’s philosophy of science in particular. Late XIX-century philosophy of science stemmed from a remarkable epistemological and historiographical awareness, and that awareness would deserve to be further explored.

The strong impetus towards self-reflection of science during the 1960ies culminated around 1970 in the foundation of many relevant research institutions in different countries. Although included into that general trend, the MPI for the Exploration of Living Conditions in the Sci-entific-Technological World at Starnberg, established under the direction of Carl Friedrich von Weizsäcker in 1970, pursued a unique idea, somewhat apart from the mainstream charac-terizing most institutes in the emerging field of science research (science of science, science studies, social studies of science, etc.). Meanwhile science research usually was focused on science as a sub-system of modern societies, for the Starnberg institute the typical subject was the “scientific-technological world” – mankind in global context increasingly based on sci-ence as a leading source of innovation and evolution. As a key concept for describing and analyzing the living conditions in the scientific-technological world, von Weizsäcker employs the idea of ambivalence. Obviously it means a proto-theoretical, fuzzy concept that cannot be introduced explicitly per definition; starting with an intuitive perception, “ambivalence” should gradually gain meaning by using it in dif-ferent argumentative contexts. Following a circular course (Kreisgang) – a procedure typical for von Weizsäcker’s style of thought – , he moves successively from explicit ambivalence in the application sphere of science through ambivalent features in scientists’ behaviour and ac-tion up to the general ambivalence of human existence prior to rationality and science, dis-closed at an anthropological level of deliberation situated between philosophy and common sense. He criticized profoundly the wide-spread conviction about the alleged neutrality of science becoming ambivalent only due to application under contrary goals; von Weizsäcker’s approach allowed to overcome the essentially inadequate and ethically questionable opinion mentioned above and to understand scientific cognition even at the level of “pure science” as an ambivalent enterprise. The given paper mainly discusses an essay by von Weizsäcker written in the starting year of the Starnberg institute (October 1970) under the title “Living conditions, Reflection on the interrelation of subjects”. The essay was a response to many conceptual proposals, presented by his (mostly young) scientific co-workers, and intended, at the same time, to inspire further discussion about the future profile of the institute. Von Weizsäcker’s remarkable effort to pay attention to the different ideas of his collaborators and to fit them into a more general network gave him reason to sketch a complex conceptual structure capable to integrate a broad range of suggestions; so the concept of ambivalence may be characterized as an indispensable mo-ment of central importance in the intellectual architecture of the Starnberg institute.

The paper reviews Einstein's engagement as a mediator and popularizer of science. It discusses the formative role of popular scientific literature for the young Einstein, showing that not only his broad scientific outlook but also his internationalist political views were shaped by these readings. Then, on the basis of recent detailed studies, Einstein’s travels and their impact on the dissemination of relativity theory are examined. These activities as well as Einstein’s own popular writings are interpreted in the context of his understanding of science as part of human culture.

This paper focuses on the linguistic representation of spatial concepts in two unrelated languages with a non-written tradition. It explores the degree to which environmental experience and spatial orientation is reflected in language, i.e., it is in line with anthropological linguistic approaches placing language in its social and cultural context, and its cultural practices. Spatial knowledge is not only encoded in concepts or categories, but is embodied in the lived histories of human beings, and their cultural and linguistic practices. The cultures under survey present an alpine region (Eipo, Papua Province, Indonesia) and vast prairies (Dene Chipewyan, Alberta, Canada). The mental and perceptual course maintaining in these cultures rely on cognitive maps, i.e., the orientation techniques are processes of inference within the structure of cognitive maps. We adopt cognitive maps as known from navigation techniques of dead reckoning of orientation. This kind of navigation is based on dynamic cognitive maps and mental triangulation so that the navigator has a spatial conception of their position at any time. It is argued here that this is of special importance also for orienting oneself in the alpine regions of Eipo or the vast prairies extensions of the Dene. Our question concerns the relationship between non-linguistic information and spatial language. The point of departure is that non-linguistic information has its impact upon spatial language and categorization, i.e., reference of space and its relation to semiotic systems. We present language data indicating the influence and constructive process of environmental landmarks and cultural heritage upon shaping of spatial categorization in the two languages.