  An observability condition number is defined for physical systems modeled by
network dynamics. Assuming the dynamical equations of the network are known and
a noisy trajectory is observed at a subset of the nodes, we calculate the
expected distance to the nearest correct trajectory as a function of the
observation noise level, and discuss how it varies over the unobserved nodes of
the network. When the condition number is sufficiently large, reconstructing
the trajectory from observations from the subset will be infeasible. This
knowledge can be used to choose an optimal subset from which to observe a
network.
