  Modeling a temporal process as if it is Markovian assumes the present encodes
all of the process's history. When this occurs, the present captures all of the
dependency between past and future. We recently showed that if one randomly
samples in the space of structured processes, this is almost never the case.
So, how does the Markov failure come about? That is, how do individual
measurements fail to encode the past? And, how many are needed to capture
dependencies between the past and future? Here, we investigate how much
information can be shared between the past and future, but not be reflected in
the present. We quantify this elusive information, give explicit calculational
methods, and draw out the consequences. The most important of which is that
when the present hides past-future dependency we must move beyond
sequence-based statistics and build state-based models.
