Is there a best way to measure? Perhaps: maximizing ephemeral information suggests the coarsest generating partition.

We imagine the act of measurement as that of partitioning (coarse graining) an underlying dynamical system, producing a sequence of symbols: the raw data. Provided we choose a generating partition—and there are many such choices—symbolic dynamics allows modeling that underlying system (in terms of its hidden states and a dynamic between them) from only this raw data.

Taking the tent map as an example, we find that while the uncertainty generated by a single measurement—the Shannon entropy rate h_μ—does not (by definition) depend on the choice of generating partition, the amount of that uncertainty which affects future measurements—the bound information b_μ—does. Of the generating partitions, then, which should we choose? Is there a best one?

Here, we offer an answer: preliminary evidence suggests the supremum over all partitions of the ephemeral information—r_μ = h_μ − b_μ, uncertainty generated by a single measurement which does not affect the future—may be a dynamical invariant, effectively selecting the coarsest generating partition.