In dynamic percolation, the sites flip between the states open and closed according to independent Poisson clocks. We will describe a recent theorem obtained with Jeff Steif, which says that on the planar triangular grid, critical site percolation has exceptional times in which an infinite cluster exists. This contrasts with the fact that at any fixed time almost surely all clusters are finite. One of the tools used is a new inequality relating the Fourier coefficients of a boolean function with the existence of a randomized algorithm that calculates the function but is unlikely to examine any specific input bit.