Arquivo da tag: Fractais

The world’s greatest literature reveals multi fractals and cascades of consciousness (Science Daily)

Date: January 21, 2016

Source: The Henryk Niewodniczanski Institute of Nuclear Physics Polish Academy of Sciences

Summary: 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, 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.

Sequences of sentence lengths (as measured by number of words) in four literary works representative of various degree of cascading character. Credit: Source: IFJ PAN 

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.

As far as many bookworms are concerned, advanced equations and graphs are the last things which would hold their interest, but there’s no escape from the math. 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. In the case of several works their mathematical complexity proved to be exceptional, comparable to the structure of complex mathematical objects considered to be multifractal. Interestingly, in the analyzed pool of all the works, one genre turned out to be exceptionally multifractal in nature.

Fractals are self-similar mathematical objects: when we begin to expand one fragment or another, what eventually emerges is a structure that resembles the original object. Typical fractals, especially those widely known as the Sierpinski triangle and the Mandelbrot set, are monofractals, meaning that the pace of enlargement in any place of a fractal is the same, linear: if they at some point were rescaled x number of times to reveal a structure similar to the original, the same increase in another place would also reveal a similar structure.

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).

The study involved 113 literary works written in English, French, German, Italian, Polish, Russian and Spanish by such famous figures as Honore de Balzac, Arthur Conan Doyle, Julio Cortazar, Charles Dickens, Fyodor Dostoevsky, Alexandre Dumas, Umberto Eco, George Elliot, Victor Hugo, James Joyce, Thomas Mann, Marcel Proust, Wladyslaw Reymont, William Shakespeare, Henryk Sienkiewicz, JRR Tolkien, Leo Tolstoy and Virginia Woolf, among others. The selected works were no less than 5,000 sentences long, in order to ensure statistical reliability.

To convert the texts to numerical sequences, sentence length was measured by the number of words (an alternative method of counting characters in the sentence turned out to have no major impact on the conclusions). The dependences were then searched for in the data — beginning with the simplest, i.e. linear. This is the posited question: if a sentence of a given length is x times longer than the sentences of different lengths, is the same aspect ratio preserved when looking at sentences respectively longer or shorter?

“All of the examined works showed self-similarity in terms of organization of the lengths of sentences. Some were more expressive — here The Ambassadors by Henry James stood out — while others to far less of an extreme, as in the case of the French seventeenth-century romance Artamene ou le Grand Cyrus. However, correlations were evident, and therefore these texts were the construction of a fractal,” comments Dr. Pawel Oswiecimka (IFJ PAN), who also noted that fractality of a literary text will in practice never be as perfect as in the world of mathematics. It is possible to magnify mathematical fractals up to infinity, while the number of sentences in each book is finite, and at a certain stage of scaling there will always be a cut-off in the form of the end of the dataset.

Things took a particularly interesting turn when physicists from the IFJ PAN began tracking non-linear dependence, which in most of the studied works was present to a slight or moderate degree. 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.

The most multifractal works also included A Heartbreaking Work of Staggering Genius by Dave Eggers, Rayuela by Julio Cortazar, The US Trilogy by John Dos Passos, The Waves by Virginia Woolf, 2666 by Roberto Bolano, and Joyce’s Ulysses. At the same time a lot of works usually regarded as stream of consciousness turned out to show little correlation to multifractality, as it was hardly noticeable in books such as Atlas Shrugged by Ayn Rand and A la recherche du temps perdu by Marcel Proust.

“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. It is hardly surprising that ascribing a work to a particular genre is, for whatever reason, sometimes subjective. We see, moreover, the possibility of an interesting application of our methodology: it may someday help in a more objective assignment of books to one genre or another,” notes Prof. Drozdz.

Multifractal analyses of literary texts carried out by the IFJ PAN have been published in Information Sciences, a journal of computer science. The publication has undergone rigorous verification: given the interdisciplinary nature of the subject, editors immediately appointed up to six reviewers.

Journal Reference:

  1. 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 textsInformation Sciences, 2016; 331: 32 DOI: 10.1016/j.ins.2015.10.023

Risk (Fractal Ontology)

Joseph Weissman | Thursday, November 1, 2012

Paul Klee, “Insula Dulcamara” (1938); Oil on newsprint, mounted on burlap

I began writing this before disaster struck very close to home; and so I finish it without finishing it. A disaster never really ends; it strikes and strikes continuously — and so even silence is insufficient. But yet there is also no expression of concern, no response which could address comprehensively the immense and widespread suffering of bodies and minds and spirits. I would want to emphasize my plea below upon the responsibility of thinkers and artists and writers to create new ways of thinking the disaster; if only to mitigate the possibility of their recurrence. (Is it not the case that the disaster increasingly has the characteristics of the accident; that the Earth and global techno-science are increasingly co-extensive Powers?) And yet despite these necessary new ways of thinking and feeling, I fear it will remain the case that nothing can be said about a disaster, if only because nothing can ultimately be thought about the disaster. But it cannot be simply passed over in silence; if nothing can be said, then perhaps everything may be said.

Inherent to the notion of risk is the multiple, or multiplicity. The distance between the many and the multiple is nearly infinite; every problem of the one and the many resolves to the perspective of the one, while multiplicity always singularizes, takes a line of pure variation or difference to its highest power. A multiplicity is already a life, the sea, time: a cosmos or style in terms of powers and forces; a melody or refrain in its fractured infinity.

The multiple is clear in its “being” only transitorily — as the survey of a fleet or swarm or network; the thought which grasps it climbs mountains, ascends vertiginously towards that infinite height which would finally reveal the substrate of the plane, the “truth” of its shadowy depths, the mysterious origins of its nomadic populations.

No telescopic lens could be large enough to approach this distance; and yet it is traversed instantaneously when the tragic arc of a becoming terminates in disaster; when a line of flight turns into a line of death, when one-or-several lines of organization and development reach a point beyond which avoiding self-destruction is impossible.

Chaos, boundless furnace of becoming! Fulminating entropy which compels even the cosmos itself upon a tragic arc of time; are birth and death not one in chaos or superfusion?

Schizophrenia is perhaps this harrowing recognition that there are only machines machining machines, without limit, bottomless.

In chaos, there is no longer disaster; but there are no longer subjects or situations or signifiers. Every subject, signifier and situation approaches its inevitable as the Disaster which would rend their very being from them; hence the nihilism of the sign, the emptiness of the subject, the void of the situation. Existence is farce — if loss is (permitted to become) tragedy, omnipresent, cosmic, deified.

There is an infinite tragedy at the heart of the disaster; a trauma which makes the truth of our fate impossible-to-utter; on the one hand because imbued with infinite meaning, because singular — and on the other, in turn, meaningless, because essentially nullified, without-reason. That the disaster is never simply pure incidental chaos, a purely an-historical interruption, is perhaps the key point: we start and end with a disaster that prevents us from establishing either end or beginning — a disaster which swiftly looms to cosmic and even ontological proportions…

Perhaps there is only a life after the crisis, after a breakthrough or breakdown; after an encounter with the outside. A life as strategy or risk, which is perhaps to say a multiplicity: a life, or the breakthrough of — and, perhaps inevitably, breakdown before — white walls, mediation, determinacy.

A life in any case is always-already a voice, a cosmos, a thought: it is light or free movement whose origin and destination cannot be identified as stable sites or moments, whose comings and goings are curiously intertwined and undetermined.

We cannot know the limits of a life’s power; but we know disaster. We know that multiplicities, surging flocks of actions and passions, are continually at risk.

The world presents itself unto a life as an inescapable gravity, monstrous fate, the contagion of space, time, organization. A life expresses itself as an openness which is lacerated by the Open.

A life is a cosmos within a cosmos — and so a life opens up closed systems; it struggles and learns not in spite of entropy but on account of it, through a kind of critical strategy, even a perversely recursive or fractal strategy; through the micro-cosmogenetic sieve of organic life, entropy perversely becomes a hyper-organizational principle.

A life enters into a perpetual and weightless ballet — in a defiance-which-is-not-a-defiance of stasis; a stasis which yet presents a grave and continuous danger to a life.

What is a life, apart from infinite movement or disaster? Time, a dream, the sea: but a life moves beyond rivers of time, or seas of dreaming, or the outer spaces of radical forgetting (and alien memories…)

A life is a silence which may become wise. A life — or that perverse machine which works only by breaking down — or through…

A life is intimacy through parasitism, already a desiring-machine-factory or a tensor-calculus of the unconscious.

A life lives in taut suspension from one or several lines of becoming, of flight or death — lines whose ultimate trajectories may not be known through any safe or even sure method.

A life is the torsion between dying and rebirth.

Superfusion between all potentialities, a life is infinite-becoming of the subjectless-subject. Superject.

Journeying and returning, without moving, from the infinity and chaos of the outside/inside. A stationary voyage in a non-dimensional cosmos, where everything flows, heats, grinds.

Phenomenology is a geology of the unconscious, a problem of the crystalline apparatus of time. Could there be at long last a technology of time which would abandon strip-mining the subsconscious?

A chrono-technics which ethico-aesthetically creates and transforms virtual and actual worlds, traces possibilities of living, thinking, thinking; diagnoses psychic, social and physical ecosystems simultaneously.

A communications-strategy, but one that could point beyond the vicious binary of coercion and conflation — but so therefore would not-communicate.

There is a a recursive problem surrounding the silence and darkness at the heart of a life; it is perhaps impossible to exhaust (at least clinically) the infinitely-deferred origin of those crystalline temporal dynamisms which in turn structure any-moment-whatsoever.

Is there a silence which would constitute that very singular machinic ‘sheaf’, the venerated crystalline paradise of the moved-unmoving?

Silence, wisdom.

The impossibility of this origin is also the interminability of the analysis; also the infinite movement attending any moment whatsoever. It is the history of disaster, of the devil.

There is only thinking when a thought becomes critically or clinically engaged with a world, a cosmos. This engagement discovers its bottomlessness in a disaster for thought itself. A disaster for life, thought, the world; but also perhaps their infinitely-deferred origins…

What happens in the physical, economic, social and psychic collapse of a world, a thought, a life? Is it only in this collapse, commensurate with the collision, interference of one cosmos with another…?

Collapse is never a final state. There is no closed system of causes but a kind of original fracture. The schizophrenic coexistence of many separate worlds in a kind of meta-stable superfusion.

A thought, a cosmos, a world, a life can have no other origin than the radical corruption and novel genesis of a pure substance of thinking, living, “worlding,” “cosmosing.” A becoming refracts within its own infinite history the history of a life, a world, a thought.

Although things doubtless seem discouraging, at any moment whatsoever a philosophy can be made possible. At any time and place, this cyclonic involution of the library of Babel can be reactivated, this golden ball propelled by comet-fire and dancing towards the future can be captured in a moment’s reflection…

The breakdown of the world, of thought, of life — the experience of absolute collapse, of the horror of the vacuum, is already close the infinite zero-point reached immediately and effortlessly by schizophrenia. Even in a joyous mode when it recognizes the properly affirmative component of the revelation of cosmos as production, production as multiplicity, multiplicity as it opens onto the infinite or the future. (Only the infinity of the future can become-equal to a life.)

That spirit which fixes a beginning in space and time, fixes it without fixing itself; it exemplifies the possibility of atemporality and the heresy of the asignifying, even while founding the possibility of piety and dogma.

The disaster presents thought and language with their cosmic doubles; thought encounters a disaster in the way a subject encounters a radical outside, a death.

Only selection answers to chaos, to the infinite horizon of a life — virtually mapping infinite potential planes of organization onto a singular line of development. Only selection, only the possibility of philosophy, points beyond the inevitability of disaster.

The disaster and its aversion is the basic orientation of critical thought; thinking the disaster: this impossible task is the critical cultural aim of art and writing. Speaking the truth of the disaster is perhaps impossible. A life encounters disaster as the annihilating of the code itself; not merely a decoding but the alienation from the essence of matter or speech or language. The means to thinking the disaster lie in poetic imagination, the possibility of the temporal retrojection of narrative elements; the disaster can be thought only through “unthinking” it: in the capacity of critical or poetic imagination to explore the means by which a disaster was retroactively averted. The counterfactual acquires a new and radical dimension: not the theological dimension of salvation, but a clinical dimension — the power to of think the transformation of the conditions of the disaster.