Sensitive dependence on initial conditions — & more
[ by Charles Cameron — on human impact, with a quick glance at Pundita’s wide-angle thinking ]
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The “butterfly effect” identified by meteorologist Edward Lorenz suggests that when you are dealing with highly complex systems such as weather patterns, what eventually happens may be “sensitively dependent on initial conditions”. Very small differences at one moment in such systems may result in very large differences later on. As Lorenz explains in the upper quote above, however, we’re dealing with a myriad of influences simultaneously, and it’s entirely possible that our own meteorological impact exceeds and outweighs that of the butterfly species…
I’ve chosen to post this particular pair of quotes, in fact, because both examples point to severely deleterious effects of human impact on our home environment in the larger sense — “the world we live in” — at a level where human individuals may not feel they have much of an individual impact, but where the cumulative effect is much greater: global warming? devastating storms? loss of rain forest? — narcarchy?
Narcarchy: hereby defined as rule by cartel — see this fascinating news piece, and note in particular the presence of a significant religious thread in the midst of the drug / crime / warfare picture.
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On the question of sensitive dependence on initial conditions, this graphic paints the picture nicely and with nuance, for those who “think in pictures”:
I found it attached to the Wikipedia entry on Lorenz’s Butterfly Effect which may also help if like me you’re a lay reader, mathematically speaking.
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I also wanted to juxtapose the two quotes above because they give me a chance to talk about “wide angle views” and their virtues, and to point you to a recent Pundita post that set me thinking along those lines. The post is Then and Now: Instructive parallels between 9/11/01-Benghazi and Katrina-Sandy storms, and part of my comment read as follows:
…you have an amazing breadth of thought going on here – especially in your paragraph:
It’s as if a new era arrived, with its vast changes in weather patterns and attack patterns, and nobody is yet fully processing the nature of the threats. I guess such an observation is actually old news. But Sandy coming on the heels of Benghazi struck me as a kind of exclamation mark to the fact that civilizations start to fall at the point where they’re no longer able to process the cumulative effects of their past.
Seeing parallels between Benghazi and 9/11, or between Sandy and Katrina, would be one thing – but managing to see parallel changes in both “weather patterns and attack patterns” is quite another — and even though people may want to question and qualify some of the details, the overall scope and view is breathtaking.
We need this kind of wide-angle thinking, it seems to me, and I offer my two quotes here in much the same spirit.
So if “sensitive dependence on initial conditions” is one analytic thought pattern I’m promoting here, “wide-angle thinking” and the capacity to zoom from significant detail to global context is surely another.
November 3rd, 2012 at 3:36 pm
In which I register passing but profound surprise that wordsmith such as yourself would see value in a neologism so unwieldy as “Narcarchy.”
In other news, Mandelbrot’s bio should be arriving at my doorstep on Monday. I have high hopes.
November 3rd, 2012 at 7:38 pm
Hi, Justin:
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Ha! — I pondered it myself of course, but decided that on balance I liked it. Your suggestion that it’s unwieldy is duly noted, though, and it’s good to know someone is “reading me for style” as well as content, since that’s half the battle as far as I’m concerned.
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The Mandelbrot should be fascinating!
November 3rd, 2012 at 8:19 pm
Hi Charles,
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If I can find it, I had a notebook entry several years ago where I took on the notion of “complexity.” Would it not be interesting to learn that our premise(s) create more complexity than actually exists? Human beings have an insatiable appetite for labeling stuff. When the labels are wrong, they have a tendency to roil the world. In the mid-19th century cholera was thought to be caused by miasma; actually it was a matter of faith until Dr. John Snow connected the disease to water, and the fact people relying on alcohol for hydration were less susceptible (Actually, Snow’s discovery was posthumous, if memory serves.).
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Much of science is so “sure” they have it right, not much light gets in—nor gets out. That said, I believe Mandelbrot’s discovery of fractals to be one of the most significant discoveries in history—-and I predict as we pull the next layer back on this front, much of what is now complex will not be so…
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BTW, Justin, many thanks for alerting on the Mandelbrot bio (I’m assuming it is new…)!
November 6th, 2012 at 5:21 am
“If a single flap ……” That’s a really big IF. What works in mathematical chaotic systems most likely doesn’t work in nature. You can yell all you want out in Yellowstone, but the weather in Boston will still be cold in December.
On the other hand, a few fanatical women yielding brooms and axes in bars – like Susan B. Anthony and the WCTU – eventually gave rise to Prohibition, which gave rise to organized crime.
Some fluttering has more effect than others.
PS: The foxnews article is a fascinating example of cause-and-effect – probably also of unintended consequences.
November 6th, 2012 at 5:32 am
PS: I just found a review of the new Mandelbrot autobio:
http://www.tabletmag.com/jewish-arts-and-culture/books/114766/a-math-genius-sad-calculus?all=1
“For this reviewer, reading The Fractalist is rather like reading about a poet who wrote in a foreign language for which no adequate translation is available.”
“What makes The Fractalist compelling, even for a non-mathematician, is its first half, which describes Mandelbrot’s childhood and adolescence as a Jew in wartime Europe. ”
November 6th, 2012 at 7:57 pm
Hi, ZZMike:
As I read him, Lorenz is saying much the same thing — a single butterfly flap could have unforeseen consequences, but in aggregate the numberless butterflies flapping their wings numberless times may well effectively cancel each other out.
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It was the idea that a small difference in initial conditions (with one flap of a butterfly’s wing as his example) may cause significantly different outcomes (in his example, causing a tornado in Texas) that was seminal, and which he was pointing to — but the paragraph I quoted was designed to suggest that while that might be true for any one flap, he wasn’t making predictions about the aggregate of millions…