A dynamical system is "excitable" at some stage in its behavior (e.g. at a rest state or while it is nearly at rest prior to a spontaneous event) if a small, but not too small, stimulus of the right kind elicits an immediate big reaction that eventually leads back to the original state. During this return to excitability a typical system is not excitable. An excitable system need not have an attracting rest state; a spontaneous oscillator can be excitable, too, as is common in biological and in chemical excitable kinetics. In a medium characterized by such excitable dynamics at every point, the excitation can propagate as a travelling pulse. Undamaged cardiac muscle shares with other excitable media certain features of such pulse propagation in two and three dimensions. Among the new electrophysiological phenomena thus anticipated are paired mirror-image vortices ("rotors") organized around phase singularities. These should arise in the myocardium near the intersection of a moving critical contour of phase in the normal cycle of excitation and recovery with a momentary critical contour of local stimulus strength. Such intersections, and the corresponding aftermath of paired rotors, should only occur following certain combinations of stimulus size and stimulus timing. Plotting those combinations on a "vulnerability diagram", one delineates a domain for creation of rotors (corresponding to tachycardia) surrounded on all sides by a halo of combinations at which just a few repetitive responses follow stimulation. The experiments called for to check these implications have now been carried out in the special case of electrically-induced tachycardia in healthy canine ventricle. They support the two-dimensional theory, so a new experiment is suggested to demonstrate wholly intramural three-dimensional vortex filaments.