Subjects stood upright with the index finger of the right hand either touching a nearby surface gently or not touching it at all and with the eyes either open or closed. Trajectories of the center of pressure (COP) were analyzed as fractional Brownian motion. The extracted parameters were the effective diffusion (D) coefficients and Hurst (H) exponents for short-term time intervals (corresponding to positively correlated random walks) and long-term time intervals (corresponding to negatively correlated random walks). Gentle tactile contact reduced the effective stochastic activity measured by D to the same extent as the availability of vision. Further, touch interacted with time interval in the same way as vision, with the correlated activity closer to H = 0.5 at both time scales when the finger contacted the nearby surface. The results corroborate and extend major features of recent investigations of haptic influences on posture and recent analyses of vision’s influence on the fractional Brownian motions of the COP. Discussion focused on (a) the equivalence of expropriospecific information (about the body’s orientation to the environment) registered haptically and visually and (b) the possibility that postural sway may reflect exploratory motions in the short term (obtaining information about the postural system) and performatory motions in the long term (using this information).