  As we discuss, a stationary stochastic process is nonergodic when a random
persistent topic can be detected in the infinite random text sampled from the
process, whereas we call the process strongly nonergodic when an infinite
sequence of independent random bits, called probabilistic facts, is needed to
describe this topic completely. Replacing probabilistic facts with an
algorithmically random sequence of bits, called algorithmic facts, we adapt
this property back to ergodic processes. Subsequently, we call a process
perigraphic if the number of algorithmic facts which can be inferred from a
finite text sampled from the process grows like a power of the text length. We
present a simple example of such a process. Moreover, we demonstrate an
assertion which we call the theorem about facts and words. This proposition
states that the number of probabilistic or algorithmic facts which can be
inferred from a text drawn from a process must be roughly smaller than the
number of distinct word-like strings detected in this text by means of the PPM
compression algorithm. We also observe that the number of the word-like strings
for a sample of plays by Shakespeare follows an empirical stepwise power law,
in a stark contrast to Markov processes. Hence we suppose that natural language
considered as a process is not only non-Markov but also perigraphic.
