Occasionally, experimental biologists obtain results which mystify them so deeply that the paradoxical nature of their finding is acknowledged in the paper reporting it. This constitutes a more-or-less explicit invitation to those who did not perform the experiments - and even those who do not perform experiments at all - to propose explanations that eluded the experimenter. A much more frequent scenario, however, is that the experimenter asserts confidently that his or her data can be explained by a particular model but are at odds with some other model. In such circumstances, it is often overlooked that the stated falsification of the latter model is error-prone: just as the mystified experimenter saw no explanation when in fact there is one, the other experimenter may see only one explanation of the data when there are two. The main reason this phenomenon is neglected is, of course, the fact that here the theoretician (or other experimenter) must take the initiative in critiquing a conclusion that, far from troubling the experimenter, may by the time of its publication be a cornerstone of his or her research program, so whose refutation may be decidedly unwelcome. For precisely this reason, such critiques - especially, perhaps, when they come from those who do not do bench work at all and thus have a complementary approach to the analysis of data - are fundamental to maximising the rate of progress in fields of biology that otherwise risk languishing in ever-better-studied cul-de-sacs for many years. Computational biology, including simulation, plays an especially important role in this, whereas its ability to contribute to biology in other ways is often less than its proponents claim. Here I discuss some representative examples of falsification-falsification, including a previously unpublished analysis of mitochondrial DNA population dynamics in cell culture, in the hope of stimulating more theoreticians - and perhaps also more experimentalists - to engage in it.