Motivated by recent criticisms of the low reliability and high costs of sci- ence funding allocation by grant peer review, the paper investigates the alternative of funding science by lottery, and more generally the possible introduction of a for- mal random element in the funding process. At first it may seem that randomness will lower expected efficiency, by allocating funds to less meritorious projects. By focusing on the notion that we want funded research projects to ultimately make our lives better, and the observation that the causal effect of research projects is subject to change over time, the paper argues that the introduction of random- ness can counteract a bias towards the familiar present in grant peer review, and thus increase the overall efficiency of science funding. The time-dependant nature of scientific merit is exemplified by the historical processes leading to the discov- ery of the structure of DNA. The argument regarding the relative effectiveness of random allocation is supported by a computer simulation of different funding mechanisms on a hypothetical dynamic epistemic landscape.