Information is extensive. Central is the concept of additivity: the combination of two independent datasets with the same amount of information contains twice as much information as the separate individual datasets. The notion of extensiveness emerges naturally in our interactions with the world around us when we count and measure objects and structures. Basic conceptions of more abstract mathematical entities, like sets, multisets and sequences, were developed early in history on the basis of structural rules for the manipulation of symbols (Schmandt-Besserat 1992). The mathematical formalisation of extensiveness in terms of the log function took place in the context of research in to thermodynamics in the nineteenth (Boltzmann 1866) and early twentieth century (Gibbs 1906). When coded in terms of more advanced multi-dimensional numbers systems (complex numbers, quaternions, octonions) the concept of extensiveness generalizes in to more subtle notions of additivity that do not meet our everyday intuitions. Yet they play an important role in recent developments of information theory based on quantum physics (Von Neumann 1932; Redei &amp; Stöltzner 2001, see entry on  quantum entanglement and information). 