case, the difference between the calculated value and the nominal ‘assumed value’ will provide information about the innovation process. The measures are:

1.  *Changes in ranks* $\delta_r$, a count of how many symbol-usefulness rankings changed at every new discovery, scaled down by $\SySsub$, i.e. the number of known symbols $\SySsub$. This is chosen so that if every known symbol changes rank at every new discovery, for each of the $\SySize-1$ discoveries, then $\delta_r=\SySize-1$.

2.  *Linear ranks shift* $\delta_\omega$, a sum of all the absolute values of changes in symbol-usefulness at every new discovery, scaled down by $\SySsub^2/2$. This is chosen so that if every known symbol changes usefulness by an average $\SySsub/2$ at every new discovery, then $\delta_\omega=\SySize-1$.

3.  *Nonlinear ranks shift* $\delta_\chi$, a sum of all the changes in symbol-usefulness *squared* at every new discovery, scaled by $\SySsub^3/4$. This is chosen so that if every known symbol changes usefulness by an average $\SySsub/2$ at every new discovery, then $\delta_\chi=\SySize-1$; with the squaring acting to de-emphasize the smaller changes.

I now summarize and describe the dictionary generation methods I tested, and how the aggregate quantities varied with symbol count $\SySize$, dictionary size $\DcSize$, and any generator-specific parameters. Each result in 