Hertz's Theory of Mechanistic Images. A precursor of Mathematical Models?

Jesper Lützen, Institute for Mathematics, University of Copenhagen 

In Die Prinzipien der Mechanik in neuem Zusammenhange Dargestellt (1894) Heinrich Hertz gave a differential geometric foundation for mechanics which was meant as a basis for all accounts of the natural world. The philosophical introduction to the book discussed the nature of such theories or images as Hertz called them. In the talk I shall analyse Hertz's notion of images. In particular I shall discuss how Hertz's own work as a physicist influenced it and how it was shaped by the particular ideas about mechanics presented in the book. I shall also discuss in how far Hertz's image theory was a precursor of the 20th century notion of a mathematical model. In particular I shall emphasize their lack of ontological commitment and connect it to previous considerations about the nature of mathematical descriptions of the natural world.