[en] The generalized uncertainty principle arises from the Heisenberg uncertainty principle when gravity is taken into account, so the leading order correction to the standard formula is expected to be proportional to the gravitational constant G_N = L²_Pl. On the other hand, the emerging picture suggests a set of departures from the standard theory which demand a revision of all the arguments used to deduce heuristically the new rule. In particular, one can now argue that the leading order correction to the Heisenberg uncertainty principle is proportional to the first power of the Planck length L_Pl. If so, the departures from ordinary quantum mechanics would be much less suppressed than what is commonly thought