The main purpose of this article is to present new material concerning Leibniz's use of indivisibles and infinitesimals in his early mathematical texts. Most of these texts are contained in hitherto unpublished manuscripts and are soon to be printed in volume VII, 4 of the Academy Edition. They present examples which illustrate how Leibniz operated with concepts such as indivisibles and infinitesimals in that period of his development.

Der Beitrag beschäftigt sich aus philosophischer Perspektive mit der kontroversen öffentlichen Diskussion zur documenta fifteen. Einigen Stellungnahmen in dieser Debatte liegen implizit Prämissen einer kantisch geprägten ästhetischen Theorie zugrunde; ihnen stehen anders situierte Diskussionsstrategien aus außereuropäischen Kontexten gegenüber. Im Text wird der kantische universalistische Gedanke eines ästhetischen Gemeinsinns kritisch im Sinne einer postkolonialen Kritik gelesen. Gibt es andere universale Annäherungen an künstlerisches Arbeiten, die stärker von einer Haltung des Zuhörens geprägt sind? Entsprechend den in diesem Feld möglichen Differenzen variiert auch (...) das Verständnis, was es bedeutet, in einem Künstler:innenkollektiv zu arbeiten. (shrink)

L’article se propose de réfléchir à l’intériorité du sujet créateur dans l’art à partir de la réflexion de Croce sur la connaissance intuitive. Dans le contexte de pratiques de simulation transversales, Croce semble entrevoir une esthétique qui réhabilite l’individualité et l’intériorité du créateur dans une perspective contemporaine.

Noise has become an increasingly noticeable and significant symptom of our civilization. Fundamentally an acoustic phenomenon, noise has wider implications. It is the legitimate object of scientific investigations in the fields of psychology and physiology. It can be properly evaluated by its role in music and in general aesthetics. It leads to basic questions of sociology. We shall pursue the implications in these various fields one by one. In this process, as elsewhere, music provides the bridge from facts to commitments (...) . Siegmund Levarie is professor of music at the City University of New York. The author of books on Mozart, Guillaume de Machaut, harmony, and Italian music, he has also collaborated with Ernst Levy on Tone: A Study in Musical Acoustics and the forthcoming A Dictionary of Musical Morphology. (shrink)

Physics was the leading science of the twentieth century and the book retraces important discoveries, made between 1895 and 2001, in 100 self-contained episodes. Each is a short story of the scientists involved, their time and their work. The book is richly illustrated byabout 600 portraits, photographs, and figures.

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 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, 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. (shrink)

"Der geschichtliche Sinn, welcher schon das Altertum auszeichnete, bewahrte sich auch auf unserm Gebiete, und es hat schon in fruher Zeit nicht an Versuchen gefehlt, den Entwicklungsgang des Wissens bis zu einem gewissen Termine zu schildern. Nach Diogenes von Laerte, einem freilich nicht immer vollig zuverlassigen Gewahrsmann, hat schon ein Schuler des Aristoteles, der als Naturforscher bekanntere Theophrast, Geschichtswerke uber Arithmetik, Geometrie und Astronomie verfasst, von denen sich jedoch hochstens insofern eine Spur erhalten hat, als nach den ausgezeichneten Untersuchungen von (...) Diels bei einer ganzen Reihe spatlateinischer und spatgriechischer Autoren Anklange an historische Angaben Theophrasts zu finden sind. Ahnliches gilt von der angeblich geometrischen Schrift des Xenokrates, deren ebenfalls Diogenes Erwahnung tut." [...] Der bedeutende Philosoph und Philosophiehistoriker Dr. Wilhelm Windelband (1848-1915) gilt als Begrunder der sudwestdeutschen Schule (auch Badische Schule ), die eine Richtung des Neukantianismus darstellt. Windelbands Hauptaugenmerk galt der Abgrenzung von Natur- und Kulturwissenschaften. Sein wichtigster Schuler war Heinrich Rickert. Sigmund Gunther lebte von 1848 - 1923 und gilt als einer der wichtigsten Mathematikhistoriker. Er wurde mit der Dissertation "Studien zu theoretischen Photometrie" promoviert. In dem vorliegenden Werk gehen beide Autoren ausfuhrlich auf die geschichtlichen Hintergrunde der Naturwissenschaften und der Philosophie ein. Das Buch erschien ursprunglich als funfter Band im "Handbuch der klassischen Altertums-Wissenschaft" und wurde 1888 erstmals veroffentlicht. Der Verlag der Wissenschaften verlegt historische Literatur bekannter und unbekannter wissenschaftlicher Autoren. Dem interessierten Leser werden so teilweise langst nicht mehr verlegte Werke wieder zugangig gemacht. Das vorliegende Buch ist ein unveranderter Nachdruck der Originalausgabe.". (shrink)

The correspondence between Richard von Mises and George Pólya of 1919/20 contains reflections on two well-known articles by von Mises on the foundations of probability in the Mathematische Zeitschrift of 1919, and one paper from the Physikalische Zeitschrift of 1918. The topics touched on in the correspondence are: the proof of the central limit theorem of probability theory, von Mises' notion of randomness, and a statistical criterion for integer-valuedness of physical data. The investigation will hint at both the fruitfulness and (...) the limits of several of von Mises' notions such as ``collective'', ``distribution'' and ``complex adjuncts'' (characteristic functions) for further developments in probability theory and in ``directional statistics''. By pointing to the selectiveness of Pólya's criticism, the historical analysis shows the differing expectations of the two men with respect to the further development of the theory of probability and its applications. The paper thus gives a glimpse of the provisional state of the theory around 1920, before others such as P. Lévy (1886–1971) and A. N. Kolmogorov (1903–1987) stepped in and created a new paradigm for probability theory. (shrink)

The article discusses the “paradox of the late (around 1940) arrival of academic applied mathematics in the U.S.” as compared to Europe, in particular Germany. A short description of both the indigenous traditions in the U.S. and (in some more detail) of the transfer of scientific ideas, persons, and ideals originating in Europe, particularly in Germany, is given, and some theses, relevant literature, and a tentative solution of the “paradox” are provided.

ArgumentIn the decade between 1983 and 1993, Herbert Mehrtens in West Berlin and I in East Berlin communicated closely about our parallel work on mathematics under the National Socialist (NS) regime. For a short period (1988–89), we worked on a joint book on this topic. We agreed that the book should be based primarily on empirical historical material, using a theoretical approach largely guided by Mehrtens’ work on social systems in mathematics (Mehrtens1981, 1987a). However, parallel work for his habilitation thesis (...) on modernity in mathematics increasingly captivated Mehrtens’ interests. This, together with ongoing resistance among older mathematicians and the insecurities of our individual careers during times of considerable political change, particularly in East Germany, led to the failure of our joint project.This paper aims at reconstructing—mostly by drawing on correspondence—parts of the dialogue between Mehrtens and me at the time. Our dialogue was influenced by our different upbringing and socialization in the two parts of Germany, and by different, though complementary, views about the combination of empirical and theoretical approaches to the historiography of mathematics.In the epilogue, I describe how my later work in the decades from the 1990s on the history of mathematics profited much from Mehrtens’ early theoretical and empirical work but was less influenced by his book on modernity. That later work of mine was, however, mostly done at a time when Mehrtens had largely left the field and considered himself increasingly as a “cultural scientist” (Kulturwissenschaftler). (shrink)