The remarkable degree of accuracy with which some of the Old Kingdom pyramids are oriented towards the cardinal directions is one of the most challenging problems in the history of science. The progressive deviation of the orientation of the 4th Dynasty pyramids from true north was long understood to be a consequence of the pyramids having been aligned to a star whose celestial position changed due to the effect of the general precession of the rotational axis of the Earth. Instead of a single star, recent proposals considered a possible orientation towards some notable vertical or horizontal stellar configurations. The main idea behind these recent attempts at explanation was to justify the gradual deviation of the pyramid alignments by way of the selected target stellar configuration exhibiting a similar azimuthal trend. Considering conventional Egyptian chronologies of this period to be only relative, and the astronomically determined data to be fully reliable, the researchers tried to make the two trends match perfectly by shifting the conventional Old Kingdom chronologies by some, often significant, number of years. Too little attention, however, was paid to allowing for systematic and random errors in the surveying of stars and in the orientation of pyramids towards the observed asterism, which may obfuscate the real accuracy of the methods and conceal the actual targets of observations. In this text, we consider recent proposals and analyze their errors. We propose and discuss two new solutions whose systematic errors are minimal among all the known proposals: one based upon the horizontal alignment of Alioth and Mizar, and another one upon the vertical alignment of Kochab and ζ UMi. In contrast to other methods, the latter pair has the advantage that it could have been observed at lower altitudes. Both variants show an impressive degree of agreement with the trend in the orientation of the pyramids for von Beckerath’s (lower estimates) as well as for Baines and Malek’s chronologies of the period. It appears to us that the preserved Egyptian astronomical diagrams are fully consistent with our new proposals.

The following collects observations I made during the reading of Fibonacci’s Liber abbaci in connection with a larger project, “abbacus mathematics analyzed and situated historically between Fibonacci and Stifel”. It shows how attention to the details allow us to learn much about Fibonacci’s way of working. In many respects it depends critically upon the critical edition of the Liber abbaci prepared by Enrico Giusti and upon his separate edition of an earlier version of its chapter 12 – not least on the critical apparatus of both. This, and more than three decades of esteem and friendship, explain the dedication.

Vortrag im Rahmen der Ringvorlesung der International Max Planck Research School „Knowledge and Its Resources: Historical Reciprocities“, 17. Februar 2022:
Wenn man Wissen als Ressource bezeichnet oder von den Ressourcen des Wissens spricht, als handele es sich um Stoffe, über die man verfügen kann, übersieht man allzu leicht die komplexen und dynamischen Strukturen, die die Geschichte des Wissens charakterisieren. In meinem Vortrag möchte ich diese Strukturen näher beschreiben, und zugleich die zentrale Rolle deutlich machen, welche die Wissensgeschichte als Teil der Gattungsgeschichte für die kulturelle Evolution und für unsere Zukunft im Anthropozän spielen kann.

The pioneering work, Scienza e Industria 1848–1915: Gli sviluppi scientifici connessi alla seconda rivoluzione industriale (Science and Industry 1848–1915: Scientific developments related to the second industrial revolution) by Angelo Baracca, Stefano Ruffo, and Arturo Russo is reproduced in this preprint. Published in Italian by Laterza in 1979, it is an unjustly forgotten treasure of a highly fertile and innovative period of the history of science. The introduction to the preprint describes the historical circumstances in which this book and the approach it proposes emerged. It covers a wide range of subjects, from the different ways in which the Second Industrial Revolution unfolded in Great Britain and in continental Europe to the upheaval in modern science, in particular in chemistry in the latter half of the nineteenth century and in physics at the beginning of the twentieth century. Although each of these themes has meanwhile become the subject of detailed historical investigations, the survey and overall picture that Scienza e Industria provides is still intriguing: it connects the new knowledge economy of the Second Industrial Revolution with the conceptual revolutions in modern physics by pointing to the mediatory role of chemistry.

The present article continues an earlier analysis of occurrences of two algebraic unknowns in the writings of Fibonacci, Antonio de’ Mazzinghi, an anonymous
Florentine abbacus writer from around 1400, Benedetto da Firenze, and another anonymous Florentine writing some five years before Benedetto, and Luca Pacioli.
The following article investigates how Benedetto da Firenze explores in 1463 the use of four or five algebraic unknowns in symbolic calculations, describing it afterwards in rhetorical algebra; in this way he thus provides a complete parallel to what was so far only known from Johannes Buteo’s Logistica from 1559. It also discusses why Benedetto may have seen his innovation as a merely marginal improvement compared to techniques known from Fibonacci’s Liber abbaci, therefore omitting to make explicit that he has created something new.

Die Rolle wissenschaftlicher Expertinnen und Experten in der Corona-Krise ist wiederholt kritisiert worden, insbesondere von geisteswissenschaftlicher Seite.  Ein Hauptvorwurf, der auch an die Adresse der Nationalen Akademie der Wissenschaften Leopoldina gerichtet ist, lautet, wissenschaftliche Experten seien anmaßend, wenn sie als politische Berater mit ihrer wissenschaftlichen Kompetenz und mit Sachzwängen argumentieren. Die Brisanz des Arguments wird noch durch die Behauptung zugespitzt, der wissenschaftliche Experte benötige für seine politische Beraterrolle besondere persönliche Qualitäten, für die ihm die Wissenschaft kein Rüstzeug liefere. Diese Mystifizierung der Figur des Experten dient dann als Rechtfertigung eines vorgefassten, tiefsitzenden Skeptizismus gegenüber naturwissenschaftlichem Spezialistentum und Expertise. Ein Rückblick in die Geschichte entzieht dieser Mystifizierung die empirische Grundlage. Die Geschichte zeigt: Experten oder „Sachverständige“ zeichnen sich vor allem durch praktisch relevantes, empirisches Wissen aus, das im technischen Umgang mit „Sachen“, Experimente eingeschlossen, erworben wurde; diese Sachkompetenz war meist der ausschlaggebende Faktor für ihre Beratertätigkeit. In der anschließenden Diskussion des Begriffs Sachzwang argumentiere ich gegen die weit verbreitete Ansicht, Sachzwänge seien technokratische Totschlagargumente.  Das Argumentieren mit Sachzwängen legt nur offen, welche Konsequenzen und Handlungsoptionen sich aus vorhandenem Sachwissen ergeben, es impliziert jedoch keine Normen und damit auch keine Vorabentscheidung über Handlungsziele.

The role of experts in the recent corona crisis has often been criticized, especially by scholars from the humanities. A major objection is that experts claim their political advice is based on scientific knowledge and that related constraints are presumptuous. The objection—addressed also to the German National Academy of Science—is accompanied by the argument that the advisory role of scientific experts presupposes certain personal qualities of the expert that cannot be acquired in the scientific community. This mystification of the figure of expert then serves as justification for preconceived general skepticism toward scientific expertise. The historical part of this paper shows that experts have long been recognized as persons with outstanding empirical knowledge acquired in technical activities, including experimentation; their role as political advisors is based primarily on the fact that this kind of knowledge is recognized as practically useful knowledge. The historical figure thus does not lend itself to mystifying definitions. The historical part is complemented by a discussion of the concept of natural and technical constraints of actions (Sachzwänge). I argue that this kind of knowledge neither implies norms nor goals of action. Hence it always leaves open different possibilities of action.

One of the truly decisive figures in the flourishing of general relativity that began in the 1950s, the eminent physicist John A. Wheeler (1911-2008) is best known today to the general public because of the adoption of the phrase ‘black hole’. Still, that seems quite a thin reason for scientific fame – the question, then, is: what did Wheeler actually do in that field? A proper answer has to take into account a plurality of levels, from Wheeler's peculiarly visual style to his interactions with his own school and other groups, from the pioneering uses of computers to his early visions of quantum gravity. That is what this paper offers, while tracing Wheeler's evolving positions – from rejection to enthusiastic acceptance and popularisation – during the fifteen years (ca 1952-1967) preceding the moment black holes became ‘black holes’.

Turning everyday ordinary happenings into struggling moments for existence—from breathing to socializing—is how the Covid-19 pandemic will mark history. What we ask here is not how the ordinary becomes abnormal but how it becomes political and diplomatic.  We argue that the spread of the Covid-19 virus, which is measured through virologic and epidemiological models, overlaps with feverous diplomatic and political activities taking place among big geopolitical powers. Yet, this is not new in history of health. The first encounters between diplomats and health professionals were elicited by the social and economic challenges caused, on a global scale, by the cholera epidemics of the nineteenth century. Indeed, health sciences and diplomacy have been historically co-produced. Such a historical perspective on science and health diplomacy facilitates our understanding of international institutions such as the World Health Organization as highly political and diplomatic endeavors. The Diplomatic Studies of Science, a new interdisciplinary research field underpinned by a historical perspective on science diplomacy, sheds light on the multiple factors contributing to the worsening of the global COVID-19 crisis we are facing nowadays.