planning—whether darkly as in the Gothic or consciously as in the ages of Alexander and Napoleon—reflects the same principle as the mathematic— in the one case the Leibnizian mathematic of infinite space, in the other the Euclidean mathematic of separate bodies.[94] But to the “habit” of a group belong, further, its definite _life-duration_ and its definite tempo of development. Both of these are properties which we must not fail to take into account in a historical theory of structure. The rhythm (Takt) of Classical existence was different from that of Egyptian or Arabian; and we can fairly speak of the _andante_ of Greece and Rome and the _allegro con brio_ of the Faustian spirit. The notion of life-duration as applied to a man, a butterfly, an oak, a blade of grass, comprises a specific time-value, which is quite independent of all the accidents of the individual case. Ten years are a slice of life which is approximately equivalent for all men, and the metamorphosis of insects is associated with a number of days exactly known and predictable in individual cases. For the Romans the notions of _pueritia_, _adolescentia_, _iuventus_, _virilitas_, _senectus_ possessed an almost mathematically precise meaning. Without doubt the biology of the future will—in opposition to Darwinism and to the exclusion in principle of causal fitness-motives for the origins of species—take these _pre-ordained_ life durations as the starting-point for a new enunciation of its problem.[95] The duration of a generation— whatever may be its nature—is a fact of almost mystical significance.