However, since and real “innovation” process will only experience one possible symbol discovery order, in Sec. \[S-Discovery\] I present and comment on specific discovery processes, noting their main features and discussing and comparing the outcomes. Finally, in Sec. \[S-Conclusion\], I present my conclusions.

Dictionaries and Scaling {#S-Dictionaries}
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Here the dictionaries I investigate are compiled of words made from strings of symbols generated by a randomly driven algorithm. However, we might consider the symbols to represent ingredients to be assembled into recipes (“words”), and then the compendium of recipes make up a recipe-book (“dictionary”); or they might be gestures and movements which we assemble into dance moves, and then into a whole dance routine. At any point in the discovery process, we will know only a subset of all the allowed symbols, and hence only have found (“innovated”) a subset of the words; i.e. we will be working from not the total dictionary, but a sub-dictionary.

Here I consider how new words (“innovations”) become available as new symbols are found and used to to interrogate the dictionary, and thus allow us to expand our sub-dictionary. For this we rely on aggregate quantities made up from all changes occurring during the 