Anschauen, Anfassen, Auffassen.

Eine Wissensgeschichte Mathematischer Modelle

verfasst von: Anja Sattelmacher

Verlag: Springer Fachmedien Wiesbaden

Buchreihe : Mathematik im Kontext

Enthalten in: Springer Professional "Wirtschaft+Technik" , Springer Professional "Technik" , Springer Professional "Wirtschaft"

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Über dieses Buch

Das Herstellen, Sammeln und Verbreiten mathematischer Modelle war im 19. und frühen 20. Jahrhundert weit verbreitete Praxis an Universitäten und technischen Hochschulen.Anhand ausgewählter Modelle im Kontext ihrer Sammlungen lässt sich zeigen, dass das Wissen über mathematische Modelle im Prozess der Modellierung, des Sammelns, des Veräußerns und des Ausstellens generiert wurde. Dabei flossen sowohl künstlerische Praktiken als auch reformpädagogische Überlegungen in dieses Wissen mit ein. Im Zentrum der Studie stehen Mathematikprofessoren, die die Verwendung von Modellen im Kontext der akademischen Lehre auf unterschiedliche Weise vorantrieben. Weniger bekannt ist hingegen, dass auch Frauen einen wichtigen Anteil an der Produktion von Modellen hatten. Das Buch leistet mit den Auswertungen zahlreicher Quellen aus unterschiedlichen Archiven sowie einer ethnographischen Beobachtung eines Modellbauers einen wichtigen Beitrag für eine praxeologisch orientierte Wissenschaftsgeschichte.

Inhaltsverzeichnis

Frontmatter

Kapitel 1. Einleitung

Zusammenfassung

This chapter introduces the themes, theses and asumptions made in this book: a history of knowledge of mathematical models between 1830 and 1910 in France and Germany. Taking the example of a portrait of the family of Hermann Wiener (1857–1939), mathematician and modeler around 1907, the chapter reveals that mathematical models have to be understood as products of cultural techniques that evolved within their very own epistemic environments, the family context being one of them. Furthermore, the production of mathematical models was intertwined with important cultural techniques, such as drawing, cutting, folding and many more. Hence, materiality plays a crucial role: the decision to produce a model in a certain material had an impact on its use, its circualtion and its perception.

Anja Sattelmacher

Kapitel 2. Über Modelle Sprechen

Zusammenfassung

Around 1870 the notion of mathematical intuition (‚Anschauung‘) became common ground for education of math students in Germany. It was especially the mathematician Felix Klein (1849–1925) who promoted this term in his writings and who put it into close relation to the use of models in mathematical teaching. The central thesis of this chapter is that the history of mathematical models can only be understood by revealing the term, its origin and its implications. ‘Anschauung’ in the 19th century meant to see and to understand at the same time. It was often used to justify the importance to work with models and to enhance practical approaches to the study of mathematics. Henceforth, it is important to note that the concept of ‘Anschauung’ has its roots in the sensualist philosophy of the 18^th century and was widely promoted by Immanuel Kant. Historians of mathematics have often emphasized that within 19th century mathematics, there was a polarization between intuitive and formalized mathematics. The chapter discusses these discurses in context with the evolution of mathematical modelling.

Anja Sattelmacher

Kapitel 3. Modelle Zeichnen

Zusammenfassung

The history of mathematical models is deeply intertwined with the cultural techniques of drawing. As this chapter shows, it was the techniques of constructive drawings and the evolution of descriptive geometry in early 19th century France that laid the foundations for different modelling techniques. One of the driving forces of this development was Gaspard Monge (1746–1818), who was among the founders of the École Polytechnique in Paris. He strengthended the role of technical education within French secondary education and professionalized the technical drawing within the study of architecture and engineering. One of his students, Théodore Olivier, introduced the first geometrical models into mathematical teaching. Today they are housed in the Conservatoire des Arts et Métiers in Paris.

Anja Sattelmacher

Kapitel 4. Modelle Sammeln

Zusammenfassung

Mathematical model collections in the 19th century emerged from a combination of different collecting traditions. They carried elements of technical collections, teaching collections, and commercially based collections, such as sample warehouses. And they spanned an entire century – from 1830 to 1930 – during which both the practice of collecting and the visual presentation of models in display cases and collection catalogs changed fundamentally. Looking at the collections allows us to understand models as part of a framework in which scientific, political, and even commercial interests merged. All the different types of collections mathematical models can be found at have in common that they often changed between commercial and scientific interests. As it will be shown, especially collection catalogues played an important role for the distribution of models within Germany and beyond.

Anja Sattelmacher

Kapitel 5. Modelle Anfertigen

Zusammenfassung

Mathematical models underlie a material epistemology that changed over time. One and the same model - produced in different materials - could perform different functions. Exemplary for many more model materials, the focus in this chapter lies on the three materials of plaster, cardboard and wire. While an ellipsoid made of plaster was immobile and opaque, the same model made of cardboard was movable; if it was made of wire rod and provided with hinges, it was even transparent. A hyperboloid made of brass and thread, on the other hand, had the advantage over the plaster model that it could be moved. Thanks to existing works on material iconography and iconology, we know that material has value and must be treated as an object of study in its own right. Accordingly, besides scientific aspects, socio-economic and aesthetic issues always played a role for the choice of material.

Anja Sattelmacher

Kapitel 6. Modelle Abbilden

Zusammenfassung

Mathematical models, as it became evident in the years between 1875 and 1905, changed their external appearance, becoming movable, transparent, lighter and larger. This can be seen, for example, in Hermann Wiener’s models, which differed significantly in form and function from the plaster and cardboard models of his cousin Alexander Brill (1842–1935). Around 1900, mathematical model collections no longer had display cabinets with models alone, but increasingly had rooms and apparatus for projecting images and models. The chapter discusses the emergence of a new perception paradigm that caused mathematicians to experiment with new projection techniques for mathematical teaching and that deeply relied on the acquired knowledge on three-dimensional models at the time.

Anja Sattelmacher

Kapitel 7. Schluss

Zusammenfassung

Mathematical models did not simply disappear after 1914. Their form of appearance rather changed. Whereas they had previously been displayed in collection showcases, on catalog pages or projection screens, there was now an increased focus on techniques of visualization that demonstrated the mathematical properties of movement. Among these techniques were also some attempts to use the medium film for intuitive mathematical teaching. The math teacher Ludwig Münch (1852–1922) and the math professor Richard Baldus (1885–1945) showed how geometry could be visualized through experimental animations. Other examples are the mathematical slide collection in Göttingen and Erwin Papperitz’s (1857–1938) projection apparatus which evolved around 1912. After losing impact after the First World War, in the years from 1960s onwards, the notion of ‘mathematical models’ gained importance, this time, through computer-controlled visualization techniques which often referred to material 3-dimensional modelling techniques that were developed in the 19^th and early 20^th century.

Anja Sattelmacher

Backmatter

Titel: Anschauen, Anfassen, Auffassen.
verfasst von: Anja Sattelmacher
Verlag: Springer Fachmedien Wiesbaden
Electronic ISBN: 978-3-658-32528-2
Print ISBN: 978-3-658-32527-5
DOI: https://doi.org/10.1007/978-3-658-32528-2