The supertasks described by Perez Laraudogoitia, involving the dynamics of a system containing an infinite number of particles in a bounded region of space, are characterized by the nonconservation of energy and by the spontaneous motion of particles (“self-excitation”'). We argue that these features arise from the inadequacy of the local, particle-by-particle description used to analyze the supertasks. A global analysis, involving embeddings in Hilbert spaces, clarifies these supertasks and avoids what we regard as their nonphysical features.