In the past statistical theory advanced entirely by deductive reasoning, the theoretical route. However inductive logic, the experimental method, is also feasible now, with modern technology. Computer simulations help to clarify the issues in cases where there are long-standing conceptual problems; we have applied this technique to the problem of the marginal totals in Fisher's exact test. It becomes clear that both margins should be fixed. We conclude that there are advantages if the strategy natural to the mathematician, on the one hand, and the scientist, on the other, are used concurrently.