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Multifractal analysis of sentence lengths in English literary texts

Paper · 2012 · Iwona Grabska-Gradzinska, Andrzej Kulig, Jarosław Kwapien et al.

Summary

The paper asks whether the rhythm of sentence lengths in English fiction has fractal or multifractal structure, meaning nonlinear long-range dependence rather than only linear correlation. The authors took 30 literary books from Project Gutenberg. They converted each book into a sequence of sentence lengths counted in words, preserving the original order. Sentence boundaries were full stops, colons, semicolons, question marks and exclamation marks; commas were ignored. The main tool was MFDFA, and WTMM served as a cross-check. Shuffled versions of each series acted as surrogates to separate genuine multifractality from artifacts caused by heavy tails or nonstationarity.

Each text was placed in one of four groups: no fractal scaling, monofractal, spurious multifractal-like behaviour at small scales, or genuinely multifractal. Most books were not multifractal, and some showed no scaling at all. Only a handful qualified as true multifractals. This tempers the broader claims about the fractal nature of language and shows how carefully such signals must be read.

Key points

  • The corpus has 30 English books, which the paper attributes to 17 authors. They include 5 by Dickens, 4 by Austen, and 3 each by Joyce, Conan Doyle and Twain. Single works come from Wilde, Christie, Melville, Carroll, Darwin, Shelley, Stoker and others.
  • The shortest signal is Alice in Wonderland. The longest are Ulysses and Bleak House.
  • Sentence-length distributions can be leptokurtic, so the Rényi parameter q was limited to −3…3.
  • A text counted as multifractal if its singularity spectrum f(α) was clearly wider than about 0.1. The authors say this threshold comes from their own experience.
  • Results from MFDFA and WTMM agreed more closely as the evidence for multifractality grew stronger.
  • Only the genuinely multifractal example showed a power-law stretch in its autocorrelation function.
  • Twain's and Conan Doyle's books had fairly stable fractal properties from one book to another, whereas Austen's books differed among themselves.

Interesting ideas

  • I1. Every text is compared against a shuffled copy of itself, and multifractality counts only if it clearly exceeds what the shuffled copy shows. This kind of null baseline exposes effects that come merely from the value distribution.
  • I2. A primary method is paired with a weaker independent one, and confidence rises when the two agree. The weaker method alone is avoided because it is unreliable on short inputs.
  • I3. Results are sorted into four outcome classes rather than a yes/no verdict, one of which is an explicit "looks positive but is spurious" class. This keeps borderline artifacts from being counted as successes.
  • I4. Sentence units are cut at colons and semicolons as well as terminal punctuation, on the view that each unit carries a distinct piece of information, while commas are deliberately excluded.
  • I5. The range of moments is restricted when the data are heavy-tailed, since extreme values would otherwise dominate the statistics.

For Mova

How these ideas could serve Mova, our small open language model — its files, stages and tests:

  • I1 (learn): Evaluations could be rerun on inputs with shuffled sentences or clauses, so that any gain that survives the shuffle is flagged as not depending on discourse order.
  • I2 (learn): Silver labels from witness parsers could be weighted by cross-method agreement, and a witness known to be weak on short sentences could be given less trust there.
  • I3 (learn): Self-induced repair rules could be judged with a similar graded outcome set, which would separate rules that truly help from ones that only appear helpful on easy cases.
  • I4 (tokens): The sentence splitter could expose a configurable segmentation level, with clause-like chunks at ";" and ":", for downstream steps that want smaller information units.
  • I5 (learn): When computing aggregate metrics over corpora with very long sentences, robust or clipped statistics could stop a few outliers from distorting parser comparisons.

Our summary of the paper, in our own words — not its text. The work belongs to its authors; read it at the links above.

📚 Shelves 6The field of science this work belongs to (OpenAlex fields).Biochemistry, Genetics and Molecular Biology · 116 worksMolecular Biology · 114 worksPhysics and Astronomy · 25 worksStatistical and Nonlinear Physics · 22 worksEconomics and Econometrics · 2 worksEconomics, Econometrics and Finance · 2 works

🧭 Topics 1Research subjects and languages the work is about.English · 1,373 works

Cite

Cite as Iwona Grabska-Gradzinska, Andrzej Kulig, Jarosław Kwapien, Paweł Oswi\kecimka and Stanisław Drozdz. 2012. Multifractal analysis of sentence lengths in English literary texts. arXiv:1212.3171 · AWERProcedia Information Technology & Computer Science 03, 1700, 2013.

The paper itself, not this page. BibTeX from the library's record of the work. DOI 10.48550/arxiv.1212.3171 · arXiv 1212.3171

@misc{grabskagradzinska2012multifractal,
  title = {{Multifractal analysis of sentence lengths in English literary texts}},
  author = {Iwona Grabska-Gradzinska, Andrzej Kulig, Jaroslaw Kwapien, Pawel Oswikecimka and Stanislaw Drozdz},
  year = {2012},
  doi = {10.48550/arxiv.1212.3171},
  eprint = {1212.3171},
  archivePrefix = {arXiv},
  url = {https://doi.org/10.48550/arxiv.1212.3171}
}

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