  Ab initio calculations in Nuclear physics for atomic nuclei require a
specific knowledge of the interactions among their constituents, protons and
neutrons. In particular, NN interactions can be constrained down to scale
resolutions of $\Delta r \sim 0.6 {\rm fm}$ from the study of phase shifts
below the pion production threshold. However, this allows for ambiguities and
uncertainties which have an impact on finite nuclei, nuclear- and
neutron-matter properties. On the other hand the nuclear many body problem is
intrinsically difficult and the computational cost increases with numerical
precision and number of nucleons. However, it is unclear what the physical
precision should be for these calculations. In this contribution we review much
of the work done in Granada to encompass both the uncertainties stemming from
the NN scattering database in light nuclei such as triton and alpha particle
and the numerical precision required by the solution method.
