Space structure vibration modes: How many exist? Which ones are important?

This paper attempts to shed some light on the two issues raised in the title: How many vibration modes does a real structure have? and Which of these modes are important? The author argues that the "absurd subspace" (all but the first billion modes) is not a strength of continuum modeling, but, in fact, a weakness. Partial differential equations are not real structures, only mathematical models. This paper also contends that the partial differential equation model and the finite-element model are, in fact, the same model, the latter being a numerical method for dealing with the former. Modes should be selected on dynamical grounds other than frequency alone.