When a butterfly flaps its wings

[Image source: https://nationalparanormalassociation.blogspot.com/2012/01/butterfly-people-of-joplin-missouri.html . Photo taken after the tornado struck Joplin, Missouri, on 22 May 2011. Many survivors reported sightings of "butterfly people", thought to be angels.]

The meteorologist Edward Lorenz discovered that in certain systems, characterized by nonlinearity (i.e. exponential development), tiny changes to initial conditions lead eventually to enormous differences. He discovered it by accident, when intending to repeat a computer simulation of weather over two months: a tiny initial difference caused by rounding produced an entirely different outcome. (This is why weather forecasting is only worthwhile for a maximum of two weeks.)

Peter Dizike's excellent account of Lorenz's discoveries, suitable for non-meteorologists:
https://www.technologyreview.com/s/422809/when-the-butterfly-effect-took-flight/
(Dizike's links to Lorenz' articles are broken. But here is Lorenz's seminal 1963 paper, "Deterministic Nonperiodic Flow":
https://eapsweb.mit.edu/sites/default/files/Deterministic_63.pdf
Unless you are a mathematician, you'll struggle...)

Lorenz's initial account of the effect was in 1963. In his 1960s papers, he used the analogy of a seagull's wing.

But in 1972 he gave a paper, for a wider audience, "Predictability: Does the Flap of a Butterfly's Wings in Brazil Set Off a Tornado in Texas?" -- and a meme was born.

The butterfly analogy was suggested by his colleague Philip Merilees, possibly thinking of Ray Bradbury's classic SF story "A Sound of Thunder" (1952), which also involves a butterfly. (In the story, an incautious time-traveller treads on a butterfly back in the Jurassic era: he returns to the "present" of 2055 to find it utterly different from the way he left it.)

*

But the two are different in spirit. 

Lorenz's paper suggested that, in theory and rarely and unpredictably and undetectably, a small event might end up precipitating a great event. 

Bradbury's story imagined that a small event probably will, over time, infect all subsequent history.

"All right," Travis continued, "say we accidentally kill one mouse here. That means all the future families of this one particular mouse are destroyed, right?"

   "Right"

   "And all the families of the families of the families of that one mouse! With a stamp of your foot, you annihilate first one, then a dozen, then a thousand, a million, a billion possible mice!"

   "So they're dead," said Eckels. "So what?"

   "So what?" Travis snorted quietly. "Well, what about the foxes that'll need those mice to survive? For want of ten mice, a fox dies. For want of ten foxes a lion starves. For want of a lion, all manner of insects, vultures, infinite billions of life forms are thrown into chaos and destruction. Eventually it all boils down to this: fifty­nine million years later, a caveman, one of a dozen on the entire world, goes hunting wild boar or saber­toothed tiger for food. But you, friend, have stepped on all the tigers in that region. By stepping on one single mouse. So the caveman starves. And the caveman, please note, is not just any expendable man, no! He is an entire future nation. From his loins would have sprung ten sons. From their loins one hundred sons, and thus onward to a civilization. Destroy this one man, and you destroy a race, a people, an entire history of life. It is comparable to slaying some of Adam's grandchildren. The stomp of your foot, on one mouse, could start an earthquake, the effects of which could shake our earth and destinies down through

Time, to their very foundations. With the death of that one caveman, a billion others yet unborn are throttled in the womb. Perhaps Rome never rises on its seven hills. Perhaps Europe is forever a dark forest, and only Asia waxes healthy and teeming. Step on a mouse and you crush the Pyramids. Step on a mouse and you leave your print, like a Grand Canyon, across Eternity. Queen Elizabeth might never be born, Washington might not cross the Delaware, there might never be a United States at all. So be careful. Stay on the Path. Never step off!"

   "I see," said Eckels. "Then it wouldn't pay for us even to touch the grass?"

   "Correct. Crushing certain plants could add up infinitesimally. A little error here would multiply in sixty million years, all out of proportion. Of course maybe our theory is wrong. Maybe Time can't be changed by us. Or maybe it can be changed only in little subtle ways. A dead mouse here makes an insect imbalance there, a population disproportion later, a bad harvest further on, a depression, mass starvation, and finally, a change in social temperament in far­flung countries. Something much more subtle, like that. Perhaps only a soft breath, a whisper, a hair, pollen on the air, such a slight, slight change that unless you looked close you wouldn't see it. Who knows? Who really can say he knows? We don't know. We're guessing. . . "

*

Either way, the butterfly's wing-flap has held great appeal for a crowded secular world in which so many citizens sense the insignificance of their own lives, their seeming inability to have any kind of influence or control over the march of events. 

If for life to be meaningful it must have material consequence, then how pleasing it is to imagine that no effort is required, that our small lives will cause magnificent tornadoes! And no-one can blame us for the unpredictable outcomes, and the powers-that-be will be very sorry they ignored us. . .

But of course this isn't only, or even primarily, about human ego and need for attention. 

The mythical image of the potent butterfly's wings has also flourished because it resists our sense of the helplessness of nature in the face of human destructiveness. Our physical sense that, when it comes to preserving the rainforest, bulldozers matter, and butterflies really don't. Perhaps the image even encapsulates an argument for leaving nature in peace: that we can't predict the consequences. 

The image has also appealed to our sense of a globally connected world. Lorenz' title placed the butterfly in Brazil and the tornado in Texas. In his paper, Lorenz speculated that a Brazilian butterfly might not be able to cause a Texan tornado, because the very different nature of weather in the tropics tends to confine other weather systems to their own hemispheres. But later meme-users have often emphasized the long-distance aspect, replacing the original locations with others, as entertainingly compiled by John Burckardt:

https://people.sc.fsu.edu/~jburkardt/fun/misc/butterfly.html

And finally, unpredictability itself is something that humans value. A wave of something like joy passes through us whenever the weather forecast gets it wrong. 

As a species we can't seem to stop making more powerful and better technology. But we also hate and fear the power of technology. The way we don't control it ourselves, the terrifying speed of its flow across the planet. We think we might have to kill technology before it kills us. 

*

But now, some fifty years down the line, the butterfly has bedded into proverbial human discourse and no longer carries such emotional weight. 

It can simply signal any unusual outcome, as in Adam Collins' preamble to Sri Lanka v. S. Africa, 28/6/19 (Guardian OBO):

"A week ago, this looked like a stinker between two sides with no chance. But then the butterfly flapped its wings: Sri Lanka beat England and the race for the top four was turned on its head..."

Or it can refer to a known but insufficient cause, the tail wagging the dog, as in Lauren Rudd's financial editorial in the Pittsburgh Post-Gazette, 24 March 2013:

"Nonetheless, it seems the butterfly flapped its wings and the result was a drop in the market cap of some of our nation's largest corporations, all because Cyprus might levy a tax of 7.5 billion Euros ($10 billion) on bank deposits. Talk about irrationality. Do you really believe Cyprus's actions justify a 1 percent decline in Exxon's share price? It is nuts to think that because of Cyprus, Exxon should now be valued $4 billion less than a week prior. . . ."

The image has appeal for traders who know that small events in one country can affect markets across the globe. E.g. Brad W. Setser's post of 27 February, 2006 "A butterfly flapped its wings in Iceland ..."

Naturally, Covid-19 has brought the image vividly back to life. 

"The butterfly that flapped its wings in Wuhan might ruin Nigeria's economy," wrote Tobi Lufadeju on LinkedIn (16 March 2020). 

One powerful aspect of the image is that it mysteriously deflates the significance of the big outcome. Like, If it was only a butterfly that caused it, then the tornado can't be such a big deal after all. Which is another thought that we often need to grab on to: that everything will be all right, that after all Tutto nel mondo è burla, life is an incomprehensible joke, we mustn't let it get to us.