Cosmic Neutrinos and the Energy Budget of Galactic and Extragalactic Cosmic Rays

Although kilometer-scale neutrino detectors such as IceCube are discovery instruments, their conceptual design is very much anchored to the observational fact that Nature produces protons and photons with energies in excess of 10^{20} eV and 10^{13} eV, respectively. The puzzle of where and how Nature accelerates the highest energy cosmic particles is unresolved almost a century after their discovery. We will discuss how the cosmic ray connection sets the scale of the anticipated cosmic neutrino fluxes. In this context, we discuss the first results of the completed AMANDA detector and the science reach of its extension, IceCube.