  Identification of causal structures and quantification of direct information
flows in complex systems is a challenging yet important task, with practical
applications in many fields. Data generated by dynamical processes or
large-scale systems are often symbolized, either because of the finite
resolution of the measurement apparatus, or because of the need of statistical
estimation. By algorithmic application of causation entropy, we investigated
the effects of symbolization on important concepts such as Markov order and
causal structure of the tent map. We uncovered that these quantities depend
nonmontonically and, most of all, sensitively on the choice of symbolization.
Indeed, we show that Markov order and causal structure do not necessarily
converge to their original analog counterparts as the resolution of the
partitioning becomes finer.
