I
will discuss problems in which the number of unique items discovered up
to time t grows as t^z, with z < 1. We found such sub-linear
scaling in the search for new words in books and in the search for new
papers in citation networks. Besides presenting these findings, the
goal of this talk is to show: the consequence of such sublinear growth,
how it appears and can be modelled, and the importance of the
fluctuations around the average growth.