The hypothesis of the molecular clock proposes that molecular evolution occurs at rates that persist through time and across lineages, for a given gene. The neutral theory of molecular evolution predicts that the clock will be a Poisson process, with equal mean and variance. Experimental data have shown that the variance is typically larger than the mean. Hypotheses have been advanced to account for the hypervariance of molecular evolution. Four recent papers show that none of the predictive hypotheses that have been proposed can be generally maintained. The conclusion is that molecular evolution is dependent on the fickle process of natural selection. But it is a time-dependent process, so that accumulation of empirical data often yields an approximate clock, as a consequence of the expected convergence of large numbers.