69 The Collection of Mathematical Models DANIEL LORDICK The ambiguous concept of what constitutes a mathematical model When scientists today talk of a mathematical model, they usually do not refer to objects such as those presented in this Collection, but to a formalized description − employing mathematical means − of a sub-problem from the world we experience. The more precisely an event is “modeled,” the better it can be predicted. Accurate weather forecasts, analyses of financial markets and the characterization of complicated processes from physics, chemistry and biology become possible when the power of computers is harnessed. Despite these obvious successes in almost all areas of life, despite their key role in advanced technology, and despite many attempts at mediation, mathematicians and the rest of society remain thoroughly divided: Their formalistic science is often regarded as incomprehensible and remote, not least because of its highly condensed language. By way of contrast, the Collection of Mathematical Models offers a distinctly sensual treasure, making the inner beauty and elegance of formulae and abstract structures tangible even to the layperson. These material models are also the actual work of mathematicians and serve as a means of communicating mathematical content, alongside formulae, texts and graphics. In the recent past, the immediate persuasive power of the material models in conveying knowledge has been the starting point for numerous projects that have taken the Dresden Collection to new heights beyond the boundaries of mathematics. The models have been on display in various exhibitions, with some now on loan to Saxon museums; they serve as the subject matter of artistic works and, last but not least, have been researched in a pilot project of the German Research Foundation (DFG). At the same time, however, the aesthetic appeal of the objects camouflages the remarkable conflicts that have contributed to the very eventful history of the Collection during its inner-mathematical push and pull between reference to reality and abstraction. Whereas Galileo Galilei still proclaimed that the universe was written in the language of mathematics, Albert Einstein already viewed the interplay between science and reality in a much more differentiated way. Even the title of the oldest specialist journal still in publication, the “Journal für die reine und angewandte Mathematik”, founded in 1826, describes the polarity according to which pure mathematics is regarded as belonging to the humanities, while everything that emerges from this ivory tower and moves towards application and “Anschauung” is implicitly devalued and classified as “impure”. So, it may seem like a contradiction that the models of the 19th century largely originate from pure mathematics. An obvious limitation of material models consists in their inevitable attachment to the three-dimensional visual space. Small wonder, then, that material models are rather insignificant for current mathematical research, dealing as it does with higher-dimensional structures. As a direct form of depiction, objects are suitable only for a small section of matheAs far as the laws of mathematics refer to reality, they are not certain; and as far as they are certain, they do not refer to reality. Albert Einstein in his lecture on “Geometry and Experience” (1921) Objects from the Collection of Mathematical Models.
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