  We show that the rate for upward showers from an isotropic cosmic neutrino
flux at neutrino telescopes like IceCube is independent of the neutrino-nucleon
cross section. For bins that span a relatively narrow range in energy, neither
scaling the cross section, nor changing its power-law energy behavior affects
the upward shower rate, which depends only on the flux. The neutrino flux can
be completely known since its spectral shape can be determined by comparing the
rates in neighboring bins. We also show that the downward shower rate varies
linearly with cross section with a proportionality constant determined by the
energy-dependence of the cross section, independent of the power-law behavior
of the flux. The normalization and energy dependence of the cross section can
be known by comparing the downward rates in neighboring bins.
