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A Language and Its Dimensions: Intrinsic Dimensions of Language Fractal Structures
The present paper introduces a novel object of study - a language fractal
structure. We hypothesize that a set of embeddings of all -grams of a
natural language constitutes a representative sample of this fractal set. (We
use the term Hailonakea to refer to the sum total of all language fractal
structures, over all ). The paper estimates intrinsic (genuine) dimensions
of language fractal structures for the Russian and English languages. To this
end, we employ methods based on (1) topological data analysis and (2) a minimum
spanning tree of a data graph for a cloud of points considered (Steele
theorem). For both languages, for all , the intrinsic dimensions appear to
be non-integer values (typical for fractal sets), close to 9 for both of the
Russian and English language.Comment: Preprint. Under revie