The time-delayed feedback control mechanisms of the nervous system are continuously subjected to the effects of uncontrolled random perturbations (herein referred to as noise). In this setting the statistical properties of the fluctuations in the controlled variable(s) can provide non-invasive insights into the nature of the underlying control mechanisms. We illustrate this concept through a study of stick balancing at the fingertip using high speed motion capture techniques. Experimental observations together with numerical studies of a stochastic delay differential equation demonstrate that on time scales short compared to the neural time delay ("fast control"), parametric noise provides a non-predictive mechanism that transiently stabilizes the upright position of the balanced stick. Moreover, numerical simulations of a delayed random walker with a repulsive origin indicate that even an unstable fixed point can be transiently stabilized by the interplay between noise and time delay. In contrast, on time scales comparable to the neural time delay ("slow control"), feedback and feedforward control mechanisms become more important. The relative contribution of the fast and slow control mechanisms to stick balancing is dynamic and, for example, depends on the context in which stick balancing is performed and the expertise of the balancer.