  The "equation-free'' approach has been proposed in recent years as a general
framework for developing multiscale methods to efficiently capture the
macroscale behavior of a system using only the microscale models. In this
paper, we take a close look at some of the algorithms proposed under the
"equation-free'' umbrella, the projective integrators and the patch dynamics.
We discuss some very simple examples in the context of the "equation-free''
approach. These examples seem to indicate that while its general philosophy is
quite attractive and indeed similar to many other approaches in concurrent
multiscale modeling, there are severe limitations to the specific
implementation proposed by the equation-free approach.
