  A feature of human creativity is the ability to take a subset of existing
items (e.g. objects, ideas, or techniques) and combine them in various ways to
give rise to new items, which, in turn, fuel further growth. Occasionally, some
of these items may also disappear (extinction). We model this process by a
simple stochastic birth--death model, with non-linear combinatorial terms in
the growth coefficients to capture the propensity of subsets of items to give
rise to new items. In its simplest form, this model involves just two
parameters $(P, \alpha)$. This process exhibits a characteristic 'hockey-stick'
behaviour: a long period of relatively little growth followed by a relatively
sudden 'explosive' increase. We provide exact expressions for the mean and
variance of this time to explosion and compare the results with simulations. We
then generalise our results to allow for more general parameter assignments,
and consider possible applications to data involving human productivity and
creativity.
