[1806.07722] Stylized innovation: generating timelines by interrogating incrementally available randomised dictionaries

A key challenge when trying to understand innovation is that it is a dynamic,
ongoing process, which can be highly contingent on ephemeral factors such as
culture, economics, or luck. This means that any analysis of the real-world
process must necessarily be historical – and thus probably too late to be most
useful – but also cannot be sure what the properties of the web of connections
between innovations is or was. Here I try to address this by designing and
generating a set of synthetic innovation web “dictionaries” that can be used to
host sampled innovation timelines, probe the overall statistics and behaviours
of these processes, and determine the degree of their reliance on the structure
or generating algorithm. Thus, inspired by the work of Fink, Reeves, Palma and
Farr (2017) on innovation in language, gastronomy, and technology, I study how
new symbol discovery manifests itself in terms of additional “word” vocabulary
being available from dictionaries generated from a finite number of symbols.
Several distinct dictionary generation models are investigated using numerical
simulation, with emphasis on the scaling of knowledge as dictionary generators
and parameters are varied, and the role of which order the symbols are
discovered in.