process of discovering all symbols and hence the whole dictionary.

Fink et al [@Fink-RPF-2016arxiv] used an elegant series of diagrams that ranked symbols (their ‘components’) based on their “average usefulness $\bar{u}_\alpha(n)$”, where the (ordinary) usefulness ${u}_\alpha$ of symbol $\alpha$ was a simple numerical count of how many words (their ‘products’) was present in. Here I prefer to focus on the usefulness as might be estimated due to the current state of knowledge, rather than an average usefulness [@Fink-RPF-2016arxiv] which involves a sum over all the alternative selections of other symbols. This less comprehensive averaging means we expect to see less stable rankings as the discovery process proceeds than Fink et al would, but it does not presume a knowledge of the (world) dictionary. Further, here I am most interested in the variation in the rates of change, not any absolute value.

The measures I consider when investigating the scaling of innovation are all normalized so that according to some simple assumptions, the full symbol discovery process on some dictionary will return that innovation measure to depend on the size of its symbol list, i.e. be $\SySize-1$. However, since the simple assumptions are in fact unlikely to hold in any given 