Winfree reported 20 years ago the intriguing finding that a light stimulus of a critical strength applied at a critical circadian phase could essentially stop the circadian clock in Drosophila pseudo-obscura by resetting the circadian oscillator close to its singularity (a phaseless position at which the amplitude of circadian oscillation is zero). Since then, similar observations of attenuated circadian amplitude in response to critical stimuli have been limited to unicells, insects and plants. Our recent demonstration that the phase of the human circadian pacemaker could be inverted using an unconventional three-cycle stimulus led us to investigate whether critically timed exposure to a more moderate stimulus could drive that oscillator towards its singularity. Here we report that exposure of humans to fewer cycles of bright light, centred around the time at which the human circadian pacemaker is most sensitive to light-induced phase shifts, can markedly attenuate endogenous circadian amplitude. In some cases this results in an apparent loss of rhythmicity, as expected to occur in the region of singularity.