Wednesday, June 28, 2017

Multifractals (fractals within fractals) in literary texts

From Science Daily:
James Joyce, Julio Cortazar, Marcel Proust, Henryk Sienkiewicz and Umberto Eco. Regardless of the language they were working in, some of the world's greatest writers appear to be, in some respects, constructing fractals. Statistical analysis carried out at the Institute of Nuclear Physics of the Polish Academy of Sciences, however, revealed something even more intriguing. The composition of works from within a particular genre was characterized by the exceptional dynamics of a cascading (avalanche) narrative structure. This type of narrative turns out to be multifractal. That is, fractals of fractals are created.

[...]  Physicists from the Institute of Nuclear Physics of the Polish Academy of Sciences (IFJ PAN) in Cracow, Poland, performed a detailed statistical analysis of more than one hundred famous works of world literature, written in several languages and representing various literary genres. The books, tested for revealing correlations in variations of sentence length, proved to be governed by the dynamics of a cascade. This means that the construction of these books is in fact a fractal. [...]

Multifractals are more highly advanced mathematical structures: fractals of fractals. They arise from fractals 'interwoven' with each other in an appropriate manner and in appropriate proportions. Multifractals are not simply the sum of fractals and cannot be divided to return back to their original components, because the way they weave is fractal in nature. The result is that in order to see a structure similar to the original, different portions of a multifractal need to expand at different rates. A multifractal is therefore non-linear in nature.

"Analyses on multiple scales, carried out using fractals, allow us to neatly grasp information on correlations among data at various levels of complexity of tested systems. As a result, they point to the hierarchical organization of phenomena and structures found in nature. So we can expect natural language, which represents a major evolutionary leap of the natural world, to show such correlations as well. Their existence in literary works, however, had not yet been convincingly documented. Meanwhile, it turned out that when you look at these works from the proper perspective, these correlations appear to be not only common, but in some works they take on a particularly sophisticated mathematical complexity," says Prof. Stanislaw Drozdz (IFJ PAN, Cracow University of Technology).
Stream of consciousness turned out to be particularly complex:
However, more than a dozen works revealed a very clear multifractal structure, and almost all of these proved to be representative of one genre, that of stream of consciousness. The only exception was the Bible, specifically the Old Testament, which has so far never been associated with this literary genre.

"The absolute record in terms of multifractality turned out to be Finnegan's Wake by James Joyce. The results of our analysis of this text are virtually indistinguishable from ideal, purely mathematical multifractals," says Prof. Drozdz. [...] "It is not entirely clear whether stream of consciousness writing actually reveals the deeper qualities of our consciousness, or rather the imagination of the writers."

The original research:

Stanisław Drożdż, Paweł Oświȩcimka, Andrzej Kulig, Jarosław Kwapień, Katarzyna Bazarnik, Iwona Grabska-Gradzińska, Jan Rybicki, Marek Stanuszek. Quantifying origin and character of long-range correlations in narrative texts. Information Sciences, 2016; 331: 32 DOI: 10.1016/j.ins.2015.10.023

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