The superior colliculus (SC) encodes a saccade via the spatial position of an ensemble of active neurons on its motor map. Downstream circuits control muscles with the temporal code of firing frequency and duration. The moving hill hypothesis resolves the SC-tobrainstem spatiotemporal transformation (STT) enigma by proposing feedback to the SC which "pushes" a hill of activity (height ϭ frequency) caudorostrally such that its instantaneous position encodes the angular error [gaze-position error (GPE)] between gaze and target. This mechanism, proposed for cat but controversial in primate, has not been tested in the head-unrestrained monkey. We do this here. During large ϳ60°control gaze shifts in the dark, a hill of activity began in the caudal SC and moved rostrally, but too sluggishly to encode veridical GPE. At gaze end the peak had not reached the rostral pole and only arrived there ϳ80 ms later. No moving hill accompanied ϳ20°gaze shifts, in agreement with previous studies of head-fixed monkeys. To investigate feedback to the SC, we perturbed large gaze shifts producing initial and corrective gaze saccades separated by 50 -800 ms of gaze immobility, the gaze plateau. Map activity was dramatically remodeled: the sluggishly moving hill stopped during the plateau, at the site encoding the corrective gaze saccade, thereby providing a tonic stationary spatially encoded memory signal of plateau GPE. A burst occurred before the corrective saccade. Conclusion: Feedback to map moves activity which encodes a low-pass filtered GPE signal, a process too slow to implement the STT but adequate for corrective gaze saccades.