Figure 5

Ratios of lengths for consecutive messages. Histogram of natural multiplicative changes of length of consecutive messages in BBC discussions, defined as $m_i=L(P_i)/L(P_{i-1})$, on a logarithmic scale. Multiplication factors form a well defined distribution with high variation. The presence of significant number of situations when $L(P_i)/L(P_{i-1})$ is greater than 2 or smaller than 0.5 shows that even for the messages for which the content could not be analyzed, there must have been large differences in the form of new material added or large cuts. This makes the explanation of the lognormal distribution based on gradual accumulation of multiplicative changes implausible, and confirms direct analysis of the smaller datasets. Gray line is a best-fit normal distribution based on logarithm of $m_i$.