Chaos: When the present determines the future, but the approximate present does not approximately determine the future. – Edward Lorenz
The May 2013 issue of Physics Today contains an interesting article on this subject, taking us back to that time when the MIT meteorologist Edward Lorenz first appreciated that differences in fine details of initial weather conditions could lead over time to radically different numerical weather predictions over time. The article merits reading (savoring might be a better word; the authors Adilson E. Motter and David K. Campbell have done a splendid job in the telling) in its entirety. But there’s a special immediacy to Lorenz’ recounting of his own discovery.
Here’s the excerpt:
“At one point I decided to repeat some of the computations in order to examine what was happening in greater detail. I stopped the computer, typed in a line of numbers that it had printed out a while earlier, and set it running again. I went down the hall for a cup of coffee and returned after about an hour, during which time the computer had simulated about two months of weather. The numbers being printed were nothing like the old ones. I immediately suspected a weak vacuum tube or some other computer trouble, which was not uncommon, but before calling for service I decided to see just where the mistake had occurred, knowing that this could speed up the servicing process. Instead of a sudden break, I found that the new values at first repeated the old ones, but soon afterward differed by one
and then several units in the last decimal place, and then began to differ in the next to the last place and then in the place before that. In fact, the differences more or less steadily doubled in size every four days or so, until all resemblance with the original output disappeared somewhere in the second month. This was enough to tell me what had happened: the numbers that I had typed in were not the exact original numbers, but were the rounded-off values that had appeared in the original printout. The initial round-off errors were the culprits; they were steadily amplifying until they dominated the solution.”
The rest… so goes the cliché… is history. Lorenz’ work is quite possibly the biggest scientific breakthrough in 20th-century physics not to have been recognized by a Nobel Prize. If not, it’s at least a contender for that distinction. It has served as a portal into one of the most consequential and intriguing branches of physics, addressing phenomena ranging from Poincare’s three-body problem, to Saturn’s rings, the behavior of some electrical circuits, and a range of biological wonders, as well as stock market behavior, to name a few areas of application.
And speaking of clichés, the authors remind us that Lorenz gave us another one:
“Lorenz realized that if the atmosphere were to behave like his model, forecasting the weather far in the future would be impossible. At a 1972 meeting of the American Association for the Advancement of Science, in a talk titled “Predictability: Does the flap of a butterfly’s wings in Brazil set off a tornado in Texas?” Lorenz used a butterfly as a metaphor for a tiny, seemingly inconsequential perturbation that could change the course of weather. The metaphor caught on, and sensitive dependence famously came to be dubbed the butterfly effect.”
The butterfly serves to remind us that in a similar way, our individual actions, though seemingly inconsequential, can be hugely far-reaching. Two groups of people come to mind on this particular weekend.
Mothers. The world has a billion or so. Individually, it might seem that each is lost in the mass. But, in fact, each has an extraordinary impact on one or more sons or daughters, who then by virtue of both their mother’s nature and her nurture, grow up to shape our future and all its possibilities. I’m thankful every day for all the mothers in my life. My own mother… this is my first Mother’s Day without her. I love and miss you, Mom! Her chain of mothers going back to that 20-year-old mom who came to the United States from Londonderry, Ireland in 1643 with her 21-year-old husband… and beyond. My dad’s mother, who gave birth to him (birthweight 13 lbs, 27” tall) in 1918 when mothers and their children didn’t often survive such an experience. And all the others. Without them I wouldn’t be here…without them I wouldn’t be who I am. Then there’s my daughter. My daughter-in-law. My wife… and all her mothers. All the mothers who’ve been my work colleagues. And their mothers. Without them, I wouldn’t be who I am either. And then there are all those mothers-to-be. Parenthetically, if anybody understands chaos theory, that would be mothers of young children. They knew about chaos long before Ed Lorenz.
Happy Mother’s Day, y’all.
Meteorologists. This second group numbers only in the (many) thousands. Especially on my mind are the 4000 or so who work for the National Weather Service, doing shifts at more than a hundred NWS forecast offices across the country. Individually, you too might be forgiven for feeling lost in the mass. You’ve had a rough ride the past decade or so, and especially in recent years and months… with all manner of budget woes, aging infrastructure, the looming shadow of furloughs, unfilled positions, outside criticism and more. But draw encouragement from that butterfly.
Like that butterfly, every day you influence those around you, who in turn influence those around them, and so on… and that influence ripples around the world. You can wait for the NWS culture to change from the top down… and that’s like to happen over time given the new team at the top. But in the words of Mahatma Gandhi, you can be the change you want to see in the world…and in the National Weather Service… without waiting another day. And unlike the butterfly, which doesn’t know whether its flapping wings are creating a storm or snuffing one, you can be intentional. You get to choose the change you create. The NWS has one of the best missions in government. Protect lives and property? It doesn’t get any better than that. You have much to be proud of…including your role in it.
So… all around… a tip of the hat this weekend to the butterfly. To chaos. And those mothers who manage it and those meteorologists who predict it.
Londonderry, eh? The English deliberately populated Ulster with Scottish protestants (mostly from the Border region) from the early 17th C, a way of keeping in check the Irish. My mother’s ancestors were “Ulster-Scots” who in the 17thC built a stone cottage in a hamlet near Limavady, close to ‘Derry: she was born there in 1912, and the cottage was still in the family the last I heard. Many of the Ulster-Scots moved on, North America being a prime destination. Perhaps your ancestor was one of them.
Thanks, Michael…perceptive as usual. My sense always has been that things were hot for Protestants in northern Ireland at that time, as you suggest. My ancestors probably left because they felt they had to. Come St. Patrick’s Day every year, I’m loathe to wear green, because I’m thinking I should probably wear orange. I’m loathe to wear orange, because it might incite… so I pretty much stay on the sidelines… 🙂
Bill, that prompts me to share a story. My grandmother was born into a Catholic family in County Kerry in the 1880s. In accordance with family tradition, her parents put her into a convent when she turned 18. Not her cup of tea – she ran off to Belfast, where she found lodgings and an office job. One day, there was a knock on the door. Four southern nuns said “Yer comin’ back with us!” “No, I’m not!” she replied.
The nuns grabbed her and frog-marched her to the train station. A passer-by saw what was happening and ran to find a policeman – enter my Protestant grandfather. He rescued her from the nuns, and they got married. In 1915, Sinn Fein were out to kill my grandfather. He was offered transfers to Liverpool (still in danger there) or Newcastle upon Tyne. He chose the latter, which is how I’m a Geordie.
🙂 That’s what I call living on the real world… circa 1900. Thanks for sharing a wonderful story, Michael. It’s interesting to reflect on how all seven billion of us are each the product of thousands of such stories down through our entire family line…