 Let us start at the top of EH. In Bernoulli systems the probabilities of the present state are totally independent of whatever happened in the past, even if the past is only one time step back. So knowing the past of the system does not improve our predictive abilities in the least; the past is simply irrelevant to predicting the future. This fact is often summarised in the slogan that Bernoulli systems are as random as a coin toss. We should emphasise, however, that this is true only for events in the Bernoulli partition; the characterisation of a Bernoulli system is silent about what random properties partitions other than the Bernoulli partition have.