Computational Efficiency in Naming Big Numbers

The ability to develop complex numerals is human-specific. Thinking beyond experience is a by-product of a uniquely human, non-adaptive, cognitive capacity. Comparative studies of mathematical capabilities in nonhuman animals show that they may only deal with small numbers, perhaps directly or via subitizing. I argue that the ability for the human mind to compute complex numerals is a consequence of the great leap from finite and continuous systems, such as the gestural system, to systems of discrete infinity, such as human language, mathematics and music.

 I provide evidence from Romance, Slavic, as well as from Arabic that the computational procedure deriving complex numerals relies on recursive merger. Numerals, however, do not merge directly; their combination is mediated by  (covert) operators, ADD, MULT, which in turn gives rise to indirect recursion. I argue further that asymmetric selection can be seen as part of the laws reducing the complexity of otherwise unstructured sequences of numerals. I explore the hypothesis that more abstract asymmetry based principles reducing complexity can be extended to complex arithmetic expressions and musical partitions.