The paper discusses the interplay of experience and representation in disciplinarily structured science using the example of the fundamental changes in the concepts of space and time brought about by the advanced formalism of twentieth-century physics, which enabled the integration of a growing corpus of experiential knowledge. In particular the question of why certain parts of experiential knowledge had an impact on concepts of space and time, while other parts did not have such an impact, is addressed.

We propose to use “endangerment sensibility” to designate the perception that vast portions of the world are in danger of extinction or destruction, together with the complex of concepts, values and practices dealing with human and non-human entities considered threatened. We then sketch main issues associated with the endangerment sensibility in three areas that are crucial across all domains from biodiversity to cultural heritage: diversity as a constitutive value; listing as a fundamental epistemic practice; and emotions as integral to both the values and the sciences of endangerment. Exploring “endangerment” in such a perspective highlights the extent to which it is rooted in historically situated ethical, political, emotional and epistemic configurations. Wir verwenden den Begriff “Sensibilität der Gefährdung” als Bezeichnung der Wahrnehmung, dass weite Teile der Welt Gefahr laufen, vernichtet zu werden, sei es durch Aussterben oder Zerstörung. Wir schließen in den Begriff all jene Konzepte, Werte und Praktiken ein, die sich auf als gefährdet eingestufte menschliche wie nichtmenschliche Einheiten beziehen. Wir skizzieren drei Kernpunkte, welche die Sensibilität der Gefährdung von der Biodiversität bis zum Kulturellen Erbe prägen: Erstens Diversität als grundlegende Wertschätzung; zweitens Listung als fundamentale epistemische Praxis; und drittens Gefühle als integralen Bestandteil der Werte wie auch der Wissenschaften der Gefährdung. Aus dieser Perspektive bringt die Erforschung der “Gefährdung” als Phänomen der Wahrnehmung zum Vorschein, inwieweit die betreffenden Sensibilitäten jeweils in historisch situierten ethischen, politischen, emotionalen und epistemischen Konstellationen wurzeln.

The relationship between the determination of the circumference of the Earth and the geographical mapping performed by Ptolemy in his Geography is discussed. A simple transformation of the Ptolemaic coordinates to the circumference of the Earth measured by Eratosthenes, based on the assumption that the metrical values of the stadion used by both Ptolemy and Eratosthenes are equivalent, drastically improves the positions of the locations given in Ptolemy’s catalogue at least for a great part of the oikoumenē. Comparing the recalculated positions of the identified localities with their actual positions, it turns out that the distances extracted by Ptolemy from ancient sources are remarkably precise. This in turn confirms the high precision of Eratosthenes’s result for the circumference of the Earth. It is shown that many distortions of Ptolemy’s world map can be explained as pure mathematical consequences of a mapping onto the surface of a sphere of wrong size.

Post-revolutionary Cuba is a unique case among underdeveloped countries. This small plot of land – less than one thousand of the emerged Earth surface with barely 1.5 per thousand of the World population, with scarce resources – decided in 1959 to develop an advanced scientific system, with the explicit goal of both solving the most urgent problems for the development of the country and for its population (primarily the health problems), and to overcome the condition of subalternity. This process was very original also for the free and open-minded recourse to every kind of support and collaboration, with Soviet and Western scientists and institution, besides a typical Cuban inventiveness. The success of this project was striking. In the following three decades Cuba built an advanced and articulated scientific system, and achieved an excellence level in leading scientific fields. Among these, one can mention electronics and superconductivity, but probably the most striking top-level results were achieved, quite surprisingly, in a capital-intensive and typically American field like biotechnology. This last success has called the attention of the most qualified international Journals, such as Nature, Science and the specialized literature. Even more remarkable is that the development of Cuban biotechnology was completely independent from any collaboration and support from the Soviet Union, which was backward in this field. At the turn of the 1980s, however, the collapse of the Soviet Union left Cuba in an extremely difficult economic situation, seriously putting at risk the achievements of the Revolution, and posing again the threat of subalternity. Most analysts even predicted the downfall of the Cuban economy and regime. The American embargo was intentionally worsened. Actually, the Cuban scientific system withstood the tremendous shock despite the loss of every support, confirming the maturity and autonomy it had attained, even though the economic difficulties inevitably undermined many scientific sectors. In face of such a critical situation, the Cuban government reconfirmed and reinforced the choice of supporting its most advanced and profitable scientific sectors, especially in the biomedical sector, as a strategy to overcome the present difficulties. This strategy proved to be once again a well chosen choice. The present essay presents a wide-ranging reconstruction of the complex process of Cuban scientific development, based on, and reviewing the relevant literature that has addressed this problem. The explicit thesis is that the Cuban way of addressing and overcoming subalternity is unique in contemporary history. An original contribution is the first reconstruction of the unique role of Italian biologists in the training and growth of Cuban geneticists and biotechnologists between mid 1960s and mid 1970s.

In 1878 the mathematician Joseph Boussinesq pointed out a structural analogy between some features of living beings and singular solutions of differential equations. Sudden transitions between ordinary and singular solutions could represent sudden release of energy in biological process and in the fulfilment of free will. He assumed that a guiding principle rather than a physical action might lead the system beyond the threshold of singular points. Deterministic processes, which corresponded to ordinary solutions, gave way to indeterministic processes, which corresponded to singular solutions. Alongside the mathematical pathway, a different conceptual stream had already emerged in the second half of the nineteenth century. Both physicists and physiologists made use of concepts like triggering actions and guiding principles in order to represent explosions and unstable equilibrium in inanimate matter, and the complex interaction between volitions and motions in human beings. A third conceptual stream was represented by philosophical debates on the problematic link between deterministic physical laws and free will. The new issues stemming from the fields of mathematics, physics, and life sciences found room in philosophical journals, but the interest of philosophers gradually faded away towards the late 1880s. At the same time, the majority of mathematicians and physicists had never shown a systematic interest in this subject matter. We find in Boussinesq an original and almost isolated attempt to merge mathematical, physical, biological issues into a consistent philosophical framework. However questionable his research programme might be, it was actually a daring and systematic one. In the twenty-first century, some philosophers of science rediscovered the problematic link between determinism and singular solutions of differential equations. The memory of late nineteenth-century debates had already disappeared, but recently Marij van Strien has put forward a direct comparison between those debates and recent theses on determinism.

The cultural meaning of Renaissance debates on ephemerides cannot be restricted to the technical dimension of astronomical computation. Predictive precision was in fact the presupposition for astrological forecasts. Given the intellectual and ethical relevance of astrology in that epoch, a criticism of the reliability of ephemerides invested also the tenability of astrological beliefs, and questioned social and cultural practices linked to it. The interconnection of mathematical-astronomical, astrological, philosophical and ethical issues in debates over heavenly predictions is witnessed by the fierceness of the Turin controversy of 1580-1581 opposing the astrology critique Benedetto Altavilla and the ducal mathematician Giovanni Battista Benedetti. The preprint includes a transcription of selected passages from four Turin publications by these authors as an appendix: Benedetto Altavilla, Animadversiones in Ephemeridas, Taurini, apud haeredes Nicolai Bevilacquae, 1580; idem, Breve discorso intorno gli errori dei calculi astronomici, Turino, appresso gli heredi del Bevilacqua, 1580; idem, In Nome di Dio, broadside (11 August 1581); Giovan Battista Benedetti, Lettera per modo di discorso... all’illustre Bernardo Trotto, intorno ad alcune nuove riprensioni, ed emendazioni, contra alli Calculatori delle Effemeridi, Torino, appresso gl’heredi del Bevilacqua, 1581.