  We reconsider the persistence of information under the dynamics of the
logistic map in order to discuss communication through a nonlinear channel
where the sender can set the initial state of the system with finite
resolution, and the recipient measures it with the same accuracy. We separate
out the contributions of global phase space shrinkage and local phase space
contraction and expansion to the uncertainty in predicting and postdicting the
state of the system. Thus, we determine how the amplification parameter, the
time lag, and the resolution influence the possibility for communication. A
novel representation for real numbers is introduced that allows for a
visualization of the flow of information between scales.
