Cognitive activity modulates the distribution of human response latencies in different ways, and this is a central tool in experimental psychology. An issue that has received little attention is the `baseline' state of these latencies, against which different cognitive modulations could be compared. A recent theory predicts that the right tails of human response latency distributions should follow a power-law with a constant scaling parameter of two, independently of the task or participants under study. We demonstrate this through the analysis of six large-size databases of human latencies. This finding introduces a fundamental constant that describes the `resting state' of the cognitive system, and opens the possibility of directly measuring the amount of information processing performed in a task or condition.