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I only want to mention Planck, according to whom this new conception of the notion of time "surpasses in boldness everything previously suggested in speculative natural phenomena and even in the philosophical theories of knowledge: non-euclidean geometry, which only comes seriously into consideration in pure mathematics, would be child's play in comparison."^[1]

The intent of this lecture is to show that Lobachevskian geometry is seemingly the adequate instrument to handle the theory of relativity. The analogy between the two fields was noted by me, even before I was led to an intense study of Einstein's theory by Minkowski's Cologne lecture. In a lecture concerning the first period of development of non-euclidean geometry^[2] I also mentioned the investigations concerning the admissible curvature measure of space or the length of the absolute unit distance of hyperbolic space. All lengths with which we have to deal, vanish against the unit distance and therefore the formulas of Lobachevskian geometry reduce themselves in regions of our empirical space to expressions of ordinary euclidean geometry. To make clear the relation of those geometries by an analogy from physics, I alluded to the relation of the mechanics of electrons to Newtonian mechanics; also the formulas of hyperbolic geometry asymptotically approach to the formulas of euclidean geometry. Later some additional but superficial analogies were noticed by me. The Lorentz contraction appeared to me as being an analogy to the deformation of lengths in well known interpretation of Lobachevskian geometry, where the straight lines were represented as half circles, and the line element it taken in the form $d\sigma ={\tfrac {ds}{y}}$. In general this line element cannot be moved without deformation. This led me to the assumption, whether the Lorentz contraction can be interpreted as the consequence of the geometrical anisotropy of space. In relativity theory the parallelogram of velocities is not valid; in Lobachevskian geometry there is no parallelogram at all. In relativity theory which banned the absolute from physics, there exists an absolute

1. Planck, Acht Vorlesungen über theoretische Physik, p. 117
2. Published in Rad jugoslavenske akademije 169, 110-194, 1907