Is Natural Language a Perigraphic Process? The Theorem about Facts and Words Revisited

摘要

As we discuss, a stationary stochastic process is nonergodic when a randompersistent topic can be detected in the infinite random text sampled from theprocess, whereas we call the process strongly nonergodic when an infinitesequence of independent random bits, called probabilistic facts, is needed todescribe this topic completely. Replacing probabilistic facts with analgorithmically random sequence of bits, called algorithmic facts, we adaptthis property back to ergodic processes. Subsequently, we call a processperigraphic if the number of algorithmic facts which can be inferred from afinite text sampled from the process grows like a power of the text length. Wepresent a simple example of such a process. Moreover, we demonstrate anassertion which we call the theorem about facts and words. This propositionstates that the number of probabilistic or algorithmic facts which can beinferred from a text drawn from a process must be roughly smaller than thenumber of distinct word-like strings detected in this text by means of the PPMcompression algorithm. We also observe that the number of the word-like stringsfor a sample of plays by Shakespeare follows an empirical stepwise power law,in a stark contrast to Markov processes. Hence we suppose that natural languageconsidered as a process is not only non-Markov but also perigraphic.