as well as two different random-order sequences. There are of course other options – the pessimistic might try reverse-frequency-order, where little-used symbols are discovered first; or a frequency-weighted random discovery process.

The data plotted are as follows:

-   Change in average symbol frequencies: the average and standard deviation of the symbol frequencies at each discovery event are calculated, then used to display the *change* in these between such knowledge at this event and the previous event. This is plotted on a log scale, with 1 added to the absolute value of the change, so that any visible peaks are indicative of a significant innovation event where many new words become available. A higher curve, being the average value plus one standard deviation (in the mean) is also shown.

-   Symbol entropy, calculated as $E_n = -\sum p_{i,n} \log_2 p_{i,n}$, where $p_{i,n}$ is the probability of symbol $i$ being in a word knowable at the $n$-th symbol discovery.

-   Symbol rankings: However, these are not the raw rankings according to the latest information from only this discovery event, but are averaged over the process so far, then re-ranked. Processing is done according to the default method in R, so that tied 