It is rather in transcending this purely tangible extensiveness that the metropolis also becomes the seat of cosmopolitanism. … In the same way, economic, personal and intellectual relations in the city (which are its ideal reflection), grow in a geometrical progression as soon as, for the first time, a certain limit has been passed. Every dynamic extension becomes a preparation not only for a similar extension but rather for a larger one and from every thread which is spun out of it there continue, growing as out of themselves, an endless number of others. … At this point the quantitative aspects of life are transformed qualitatively. The sphere of life of the small town is, in the main, enclosed within itself. For the metropolis it is decisive that its inner life is extended in a wave-like motion over a broader national or international area.

DEFINE: Explains how 'the quantitative aspects of life are transformed qualitatively' — the mechanism by which mere size becomes cosmopolitan culture.

XREF: Echoes Metcalfe's law about network value scaling with the square of nodes — same geometric progression principle applies to city relations.

Georg Simmel, on individuality and social…, loc. 757