  We probe the numerical errors made in renormalization group calculations by
varying slightly the rescaling factor of the fields and rescaling back in order
to get the same (if there were no round-off errors) zero momentum 2-point
function (magnetic susceptibility). The actual calculations were performed with
Dyson's hierarchical model and a simplified version of it. We compare the
distributions of numerical values obtained from a large sample of rescaling
factors with the (Gaussian by design) distribution of a random number generator
and find significant departures from the Gaussian behavior. In addition, the
average value differ (robustly) from the exact answer by a quantity which is of
the same order as the standard deviation. We provide a simple model in which
the errors made at shorter distance have a larger weight than those made at
larger distance. This model explains in part the non-Gaussian features and why
the central-limit theorem does not apply.
