One of the fundamental puzzles of flavor physics is the origin of the difference between the quark and lepton masses and mixings. Quark and charged lepton masses are significantly hierarchical and have values reasonably close to the weak scale, while neutrino masses have a seemingly milder hierarchy and are some ten orders of magnitude smaller. At the same time, all of the mixing angles in the quark sector are small, while two angles in the lepton sector are close to maximal. A beautiful understanding of the smallness of the neutrino masses may be obtained by the see-saw mechanism, whereby one takes advantage of the key qualitative distinction between the neutrinos and the other fermions: Right handed neutrinos are gauge singlets, and may therefore have large Majorana masses. The standard see-saw mechanism, however, does not address the apparent lack of hierarchy in the neutrino masses, nor the large lepton mixing angles. In this talk, I will show that the singlet natu
re of the right-handed neutrinos may be taken advantage of in one further way in order to solve these remaining problems: Unlike particles with gauge interactions, whose numbers are constrained by anomaly cancellation, the number of gauge singlet particles is essentially undetermined. If large numbers of gauge singlet fermions are present at high energies- as is suggested, for example, by various string constructions- then the effective low energy neutrino mass matrix may be determined as a sum over many distinct Yukawa couplings- reducing hierarchy, and yielding large mixing angles. Assuming a statistical distribution of fundamental parameters, I will show that the probability that this scenario leads to viable low energy phenomenology is high, with only a few qualitative assumptions guided by the known quark and lepton masses.