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Mathematical Structures in Classical Books

Posted January 28, 2016 10:09 AM by Bayes

I came across this very interesting article regarding fractal structures in classical literature and thought I'd pass it along. - R

Scientists find evidence of mathematical structures in classic books

James Joyce's Finnegans Wake has been described as many things, from a masterpiece to unreadable nonsense. But it is also, according to scientists at the Institute of Nuclear Physics in Poland, almost indistinguishable in its structure from a purely mathematical multifractal. The academics put more than 100 works of world literature, by authors from Charles Dickens to Shakespeare, Alexandre Dumas, Thomas Mann, Umberto Eco and Samuel Beckett, through a detailed statistical analysis. Looking at sentence lengths and how they varied, they found that in an "overwhelming majority" of the studied texts, the correlations in variations of sentence length were governed by the dynamics of a cascade - meaning that their construction is a fractal: a mathematical object in which each fragment, when expanded, has a structure resembling the whole.

Fractals are used in science to model structures that contain re-occurring patterns, including snowflakes and galaxies. "All of the examined works showed self-similarity in terms of organisation of the lengths of sentences. Some were more expressive - here The Ambassadors by Henry James stood out - others to far less of an extreme, as in the case of the French 17th-century romance Artamene ou le Grand Cyrus. However, correlations were evident, and therefore these texts were the construction of a fractal," said Dr Paweł Oświęcimka from the Institute of Nuclear Physics of the Polish Academy of Sciences, one of the authors of the new paper Quantifying Origin and Character of Long-range Correlations in Narrative Texts. Some works, however, were more mathematically complex than others, with stream-of-consciousness narratives the most complex, comparable to multifractals, or fractals of fractals. Finnegans Wake, the scientists found, was the most complex of all.

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#1

Re: Mathematical Structures in Classical Books

01/29/2016 10:50 AM

Interesting. I suppose I'm not surprised as Fractals turn up in nature all over the place so why not in the way one expresses oneself?

It's disappointing the article didn't give a demonstration of the fractalness (is that a word?) in some of the novels. The four graphs showing sentence length vs. sentence number appears as just noise...not clearly evidence of the fractal nature of the work.

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#5
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Re: Mathematical Structures in Classical Books

01/29/2016 5:55 PM

As well as Fibonacci numbers

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#2

Re: Mathematical Structures in Classical Books

01/29/2016 4:00 PM

One of the strange places that fractals show up is in the process of adding sand to a sand pile (the abelian sand pile model). The size of the avalanches form a fractal pattern.

http://nautil.us/issue/23/dominoes/the-amazing-autotuning-sandpile

So, my theory is that authors have all these words, sentences, and paragraphs building up inside of them until they fall out!

Seriously, there might be a connection...

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#3
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Re: Mathematical Structures in Classical Books

01/29/2016 4:17 PM

I like it! Writing, especially stream of consciousness writing, does tend to feel like avalanches of ideas to paper (or computer screen now I guess).

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#4

Re: Mathematical Structures in Classical Books

01/29/2016 4:20 PM

How did this group come up with this research idea in the first place? Fascinating!

It's Friday afternoon so my brain is doing odd things ... my first thought is that maybe there's a rule that any given work of fiction can be labeled as a classic or, well, vacation reading solely by the fractal test. Wouldn't that be interesting? Is there something about this structure that appeals to a reader, even though the reader is most likely unaware that the structure exists within the words?

I remember reading Chaos (James Gleick) back when it first came out, how astonished I was when I saw the examples of fractals from such a variety of sources.

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#6
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Re: Mathematical Structures in Classical Books

01/30/2016 1:17 PM

Hey, I was wondering the same thing. I'm not sure how it fits in with nuclear physics. I guess they're free to work on what interests them.

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#7
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Re: Mathematical Structures in Classical Books

02/03/2016 1:15 PM

We were thinking the same thing? Then we are BOTH geniuses! Or maybe you're my husband in disguise? We often think of the same thing at the same time but the thoughts are more likely what to have for dinner.

Probably someone saw a word-co-occurrence graph for a classic novel and thought s/he saw rudiments of a fractal. Or someone realized that plots have sub-plots and so on ad infinitum. If I ever find out the answer I'll let you know!

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