The terrible turn of events – Literature and the butterfly effect

A comfortable destiny

 “If everything were predetermined, we could lead carefree lives. If there was an inevitable destiny to which we would definitely slave without hope of escape, then we could not do nor say anything outside of the predetermined. And of course this would be done lightly”. When the future appears bleak and fearful, casting its dark, heavy shadow over the present, when one finds himself crushed under circumstances imposed by mechanisms that cannot be comprehended, then destiny comes as a comforting thought. In his novel “the Class” (1927) Hermann Ungar  (1893 – 1929) appears willing to embrace this concept of destiny and predeterminism as a refuge, presenting it as a much more preferable alternative to the curse of free will. Free will, says Josef Blau, the book’s main character, means that “one has to choose for himself what to say and what to do amongst many possibilities […that…] violate the harsh, unknown law and insult the dark forces…”. How could one possibly feel innocent at any time, wonders Blau, subject to this meaningless, incomprehensible cosmic domino of events with obscure beginning and unknown conclusion and, what is more disturbing, with even more obscure rules. For him every minuscule act, every tiny event, every single word uttered, even every breath taken might unsuspectedly activate a long chain of irreversible effects, each one inevitably triggered by its previous and which, in the long run, might grow to a catastrophic outcome. Future is anyway unknown and a rigid destiny would at least remove all responsibility from these petty details of life rendering it livable without the burden of one’s own share of the all the evil in the world.

Hermann Ungar (1893 – 1929)

The inevitable unpredictability

If there is a destiny such as Blau much wished for, the rigid tracks of which the universe and our lives move upon, then only God’s omniscience is believed to extend indefinitely towards both directions of time. Prediction is still far beyond human capabilities and perceived most of the time as a near impossible accomplishment, “especially if it is about the future” as is believed Niels Bohr (among others) once said tongue – in – cheek. Science itself however is an attempt, futile or not, to ultimately and hopefully understand the world to such a degree that god – like predictions will be made possible. From the seemingly trivial prediction of tomorrow’s weather to the sublime movements of heavenly bodies, scientific predictions, though often not perceived as such, have today become a part of everyday life. Yet simple statements such as “next week wet weather is expected” and “five solar eclipses will occur again in 2206” are perceived quite differently, indicating that not all natural phenomena provide equally fertile ground for prediction. Indeed, while the former is viewed as a prediction with some degree of certainty and a considerable amount of uncertainty, the latter is rather viewed as an announcement. On one hand, solar eclipses are the inevitable result of the periodic movement of the Earth and Moon relative to the Sun, unaltered for time periods far longer than the human time scale – unless a highly unlikely major cosmic event disrupts it. As such, solar eclipses are highly predictable, just as it is quite straightforward to predict the overlapping of the hour and the minute hand on a normally working, analogue clock. Predictions for such periodically behaving phenomena simply demand the extension of the observed movements into the future, exactly the way they were recorded in the past and no god – like abilities are required to achieve this. On the other hand, though a general periodic weather pattern does exist for sufficiently long time periods (for example the succession of seasons as observed in the last century or so), on a smaller, day to day basis, no periodic pattern exists and one cannot proceed to accurate predictions be simply extending past events. Weather phenomena rather demand the continual updating and processing of a wide range of meteorological data using quite complex mathematical models and the number – crunching power of computers. Still, the results prove to be subjects to uncertainty which rapidly increases towards the future until, very soon, they become unreliable. A future weather calendar recording the exact weather conditions of a specific location for every day until the year 2206 is simply impossible contrary to solar eclipses, that are well known and expected for years even more remote into the future. The American meteorologist and mathematician Edward Lorenz (1917 – 2008) expressed it concisely by remarking that “any physical system that behaves non periodically is unpredictable” – and the weather is exactly such a system.

Minuscule and important

The notorious Lorenz system, a three-dimensional, nonlinear, deterministic system of ordinary differential equations. The variables x, y, z represent the system’s state, t is the time variable while β, ρ, σ are parameters.

In the early 1960’s Lorenz worked on a mathematical model simulating atmospheric convection when he stumbled upon a curiosity that became later known as “the butterfly effect”, an odd sounding expression that appears at the same time equally scientific and poetic. His innocent – looking system comprised of three differential equations that could be studied with the aid of his primitive computer, producing equally primitive graphs representing various weather scenarios. Surprisingly, and as was coincidentally discovered by Lorenz, starting the system with slightly different initial data resulted to graphs that were only for a short time similar and soon greatly diverged from each other until they became totally disparate. It seemed, for certain values of the parameters and for certain initial conditions, that minuscule discrepancies in the data hugely mattered as they could lead the system astray to a completely different weather scenario. In fact, real meteorological data always contain errors as measuring instruments have a finite accuracy and certainly a much smaller degree of accuracy than the tiny discrepancies Lorenz experimented with in his model. It seems that it was some unnamed meteorologist’s idea to relate such tiny discrepancies to a seagull by commenting that if Lorenz’s results were true then even the minuscule atmospheric disturbance of a seagull’s wing flap could eventually change the weather forever and render long term weather prediction impossible – a remarkably felicitous simile. Following his colleagues’ admonitions, in later presentations and talks Lorenz swapped his seagull with a butterfly shifting his metaphor towards a more poetic yet even more impressive and straight to the point formulation. And in 1972 Lorenz presented a talk at the meeting American Association for the Advancement of Science with the quite eloquent title “Does the flap of a butterfly’s wings in Brazil set off a tornado in Texas?” Quite remarkably, solutions of the Lorenz system represented in three-dimensional phase space outline a geometric entity known as the “Lorenz attractor”, a fractal object with the exotic property of possessing non-integer dimension, and whose shape is strongly reminiscent of a butterfly. Its convoluted structure accurately describes the destiny of the system’s state yet nearly identical initial conditions, i.e. nearly identical starting points, soon follow diverge paths and are subject to completely different destinies, jumping irregularly from one to the other of the butterfly wings. Lorenz’s discovery gave rise to a whole mathematical theory which seemed to embrace not only meteorology but also biology, economics, physics and in fact nearly any non – periodic phenomenon one cared to deal with. At the core of all these was nonlinearity, the mathematical property displayed by systems of which input and output are not proportional. In such systems doubling the input does not necessarily cause a doubling of the output; feeding the system with the sum of inputs does not necessarily produce the sum of the outputs. Such systems are in a mathematical sense hard or even impossible to be dealt with and in the long run are greatly affected by even the tiniest of discrepancies in the input. Though deterministic, i.e. governed by a specific, rigorous, mathematical mechanism, and thus given certain conditions their outcome is predefined, it is the uncertainty in conditions of the real world that practically renders them untraceable after a certain point. Even the most accurate meteorological instruments cannot deal with the irrational real world data, burdened with infinite decimals, and anyway they cannot take into account all possible seagulls or butterflies that could cause a turn of events towards any direction. Certainly, mathematical models of complex natural phenomena such as the weather, however accurate, are only simplified abstractions of reality. Yet their nonlinear character does capture a real property of nature that produces complexity and rich structures even from innocent – looking systems like Lorenz’s weather model. Unfortunately for anyone attempting to mimic God, it also produces long term unpredictability.

The terrible turn of events

Adalbert Stifter

In his “Abdias” (1842), the Austrian writer Adalbert Stifter imagined “a chain of flowers hanging above the infinity of the universe”, a chain of causes and effects, of wonderful mysteries that could one day be solved using reason, “the soul’s eye, the most wonderful flower of all, crowning man’s head”. If, one day, we succeed in following the links correctly we will arrive “to the hand upon which the end rests” and nothing will appear the result of chance anymore. Chance is nothing more than an illusion and “the unexpected arises only from existing imperfections”. Stifter’s deterministic universe appears thus fully predictable once one finds a way to deal with the omnipresent tiny imperfections blurring the path. The idea of a universe where small or even seemingly negligible events may in the long run greatly and unpredictably affect the future was before Lorenz brought forward by various writers as a philosophical curiosity, a paradox or an attempt to understand what is commonly reffered to as destiny. And, like in Stifter’s works, this uncertainty caused by the minuscule imperfections, gave birth to a potential of dangers, imaginary or not, a fear of some terrible turn of events that might be triggered and arise out of the unimportant. Italo Calvino in his short story “Numbers in the Dark” (written somewhere between 1943 and 1958) describes the effect of a tiny mistake been greatly magnified when subjected to deterministic, computer processing, a situation not very different than the one Lorenz observed with his weather model:

”  «There never was another like Annibale De Canis», and the man with the green visor moves the candle to show, above a pile of registers and beside an old abacus with rickety rods, the photograph of a man with a moustache and goatee beard posing with a Pomeranian dog. «Yet this infallible man, this genius, see here 16 November 1884» – and the accountant turns the pages of the ledger to open it where a dried up goose – feather has been left as a bookmark – «yes, here, a mistake, a stupid mistake of four hundred and ten lire in an addition». At the bottom of the page the total is ringed in red pen. «And nobody realized, only I know about it, and you’re the first person I’ve told: keep it to yourself and don’t forget! And then, even if you did go around telling people, you’re only a boy and no one would believe you… But now you know what that mistake of four hundred and ten lire has become? Billions! Billions! The calculating machines and electronic brains and whatnot can grind out numbers all the like. The mistake is right at the core, beneath all their numbers and it’s growing bigger and bigger and bigger!» They had shut up the little room now and were climbing the spiral staircase, walking back down the corridor. «The company has grown big, huge, with thousands of shareholders, hundreds of subsidiaries, endless overseas agencies, and all of them grinding out nothing but wrong figures, there’s not a grain of truth in any of their accounts. Half the city is built on these mistakes! No, not half the city, what am I saying? Half the country! And the exports and imports? All wrong, the whole world is distorted by this mistake, the only mistake in the life of Annibale De Canis, that master of book – keeping, that giant of accounting, that genius!»  “

Guilty until proven innocent

This gloomy point of view, of the potentially evil outcome of any act, however minuscule and unimportant, permeates Hermann Ungar’s “Class”: “Any word uttered could not be taken back”, says Josef Blau . “It took its way with no return. It changed the world. It provoked fate. It became the cause for developments that no one could prevent”. The world, according to Blau, is thus trapped, entangled by an invisible thread, the slightest disturbance of which at any point may, after an unpredictable domino of effects, provoke a terrible disaster to some other remote and seemingly unrelated end. All humanity, every single human being becomes therefore guilty, simply by existing and Blau states a cruel presumption of guilt: “If only he could hold even his breath and not at all disturb the course of events! Only one who does not breathe remains innocent … […] If only everyone could hold their breath, as every breath changed the world, if only they could hold their breath and remain innocent! With the first breath, the first baby cry, the evil begins”. When his own path comes across a terrible turn of events, Blau traces guilt upon his own trivial and seemingly unrelated to the catastrophe acts, that become thus a butterfly’s wing flap: “Pupil Laub was dead. His death was not his inevitable destiny. Pupil Laub’s death started somewhere, at some point his life’s path took a turn towards death. From that point on there was no salvation, there was no possibility for a new start. But how did things get there? What was the initial cause of evil? Could it be Josef Blau’s act of buying a cigar? … […]… Josef Blau acknowledged his guilt: he had acted knowing that every single act bears the seed of a whole series of other acts, which in turn have their own consequences and so on without end.“

Windswept

Beyond Ungar’s dreary approach and the theoretical example connecting the imaginary butterfly’s wing flap to hurricanes occuring at the some other part of the earth (which has become rather commonplace), Lorenz’s butterfly is only a metaphor of the sensitivity on initial conditions displayed by certain deterministic systems. The Lorenz system may generate an infinity of different scenarios or outcomes, depending on the choice of initial conditions. An immobile “butterfly” simply corresponds to a specific aftercourse amongst an infinity of others while the same butterfly flapping its wings corresponds to a different trajectory of the same system that might provide, in the long run, a completely disparate aftercourse or scenario. In the encyclopedic “Ulysses”, written by James Joyce from 1914 to 1921, a similar concept might be thought as implied by the detail of the elusive Macintosh (or the man with the macintosh), a mysterious personage appearing four times in the background (in “Hades”, “Wandering Rocks”, “Eumeus” and “Ithaca”) and having no direct involvement in the plot. Yet the most direct, concise and felicitous reference is made in the windswept “Aeolus” chapter (of all places), when Leopold Bloom’s internal monologue is suddenly switched on by the simple lighting of a match, providing a quite remarkable – yet coincidental – allusion to Lorenz’s weather model and the butterfly effect:

“I have often thought since on looking back over that strange time that it was that small act, trivial in itself, that striking of a match, that determined the whole aftercourse of both our lives.”

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