The Butterfly Effect 2

[Orestes Hardy]

Atthe time, weather statisticians thought you should be able to predict future weather based on looking at historical records to see what had happened when conditions were the same as they are now. Lorenz was skeptical. He was running a computer program to test various weather simulations and he discovered that rounding off one variable from .506127 to .506 dramatically changed the two months of weather predictions in his simulation.

His point was that long-range weather forecasting was virtually impossible, in large part because humans don't have the ability to measure nature's incredible complexity. There are simply too many minute variables that can act as pivot points, cascading into much bigger consequences.

So, while people often think the butterfly effect means that tiny changes can have big consequences (and we can track this progression to see what change caused what), Lorenz was trying to say that we can't track these changes. We don't really know exactly what would cause a weather pattern to go one way over another.

Later, other scientists realized the importance of Lorenz's discovery. His insights laid the foundation for a branch of mathematics known as chaos theory, the idea of trying to predict the behavior of systems that are inherently unpredictable.

"Climate change is expected to have some large impacts, such as too hot for some species or too dry for others, but there are a nearly infinite amount of smaller, indirect effects that will also occur," emails Alessandro Filazzola, a community ecologist and data scientist, and post-doctorate fellow at the University of Alberta.

"In our research, we looked at one of those indirect effects and saw how future climate will slowly cause mismatch in spatial location of a butterfly and its host plant. As a caterpillar, this butterfly only feeds on this type of plant species so any mismatch in range will cause a decline in the butterfly."

"For instance, the animals that feed on that butterfly and the animals that feed on those animals, or what about other insect species all together, or even other butterflies? Our project was quite controlled because our butterfly species only eats the one type of plant, but the logic is maintained when you consider the entire ecosystem (just trickier to measure)."

For example, limiting the construction of hydroelectric dams might reduce certain types of environmental damage. But in eliminating this potential source of clean energy, we tend to fall back on fossil fuels that accelerate global warming. Biofuel subsidies, meant to reduce our dependence on fossil fuels, have increased rainforest destruction, freshwater waste and food price increases that have affected the poorest segments of the human population.

"Better understanding of indirect effects is probably one of the most important steps in trying to mitigate these effects. More simply though, just keeping nature as close to its original state is really the most important thing," he says. "Ecosystems are vastly complex, and the loss of a single species might not have a perceived effect, but it could have cascading effects on the entire system." For instance, re-introducing the wolf to Yellowstone Park increased beaver populations, increased the numbers of willow and aspen plants and provided food for birds, coyotes and bears, among other benefits.

"The items I buy, the people I interact with, the things I say, I believe can each have their cascading effects that ripple through society," he says. "That is why it is important to try and be a good person, to create a positive influence. One thing I also think about is how these indirect effects are often not as small and removed as I believe many would think."

In chaos theory, the butterfly effect is the sensitive dependence on initial conditions in which a small change in one state of a deterministic nonlinear system can result in large differences in a later state.

The term is closely associated with the work of mathematician and meteorologist Edward Norton Lorenz. He noted that the butterfly effect is derived from the metaphorical example of the details of a tornado (the exact time of formation, the exact path taken) being influenced by minor perturbations such as a distant butterfly flapping its wings several weeks earlier. Lorenz originally used a seagull causing a storm but was persuaded to make it more poetic with the use of a butterfly and tornado by 1972.[1][2] He discovered the effect when he observed runs of his weather model with initial condition data that were rounded in a seemingly inconsequential manner. He noted that the weather model would fail to reproduce the results of runs with the unrounded initial condition data. A very small change in initial conditions had created a significantly different outcome.[3]

The idea that small causes may have large effects in weather was earlier acknowledged by French mathematician and physicist Henri Poincar. American mathematician and philosopher Norbert Wiener also contributed to this theory. Lorenz's work placed the concept of instability of the Earth's atmosphere onto a quantitative base and linked the concept of instability to the properties of large classes of dynamic systems which are undergoing nonlinear dynamics and deterministic chaos.[4]

In The Vocation of Man (1800), Johann Gottlieb Fichte says "you could not remove a single grain of sand from its place without thereby ... changing something throughout all parts of the immeasurable whole".

Chaos theory and the sensitive dependence on initial conditions were described in numerous forms of literature. This is evidenced by the case of the three-body problem by Poincar in 1890.[5] He later proposed that such phenomena could be common, for example, in meteorology.[6]

In 1950, Alan Turing noted: "The displacement of a single electron by a billionth of a centimetre at one moment might make the difference between a man being killed by an avalanche a year later, or escaping."[7]

The idea that the death of one butterfly could eventually have a far-reaching ripple effect on subsequent historical events made its earliest known appearance in "A Sound of Thunder", a 1952 short story by Ray Bradbury. "A Sound of Thunder" features time travel.[8]

In 1961, Lorenz was running a numerical computer model to redo a weather prediction from the middle of the previous run as a shortcut. He entered the initial condition 0.506 from the printout instead of entering the full precision 0.506127 value. The result was a completely different weather scenario.[9]

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.

In 1963, Lorenz published a theoretical study of this effect in a highly cited, seminal paper called Deterministic Nonperiodic Flow[3][11] (the calculations were performed on a Royal McBee LGP-30 computer).[12][13] Elsewhere he stated:

One meteorologist remarked that if the theory were correct, one flap of a sea gull's wings would be enough to alter the course of the weather forever. The controversy has not yet been settled, but the most recent evidence seems to favor the sea gulls.[13]

Following proposals from colleagues, in later speeches and papers, Lorenz used the more poetic butterfly. According to Lorenz, when he failed to provide a title for a talk he was to present at the 139th meeting of the American Association for the Advancement of Science in 1972, Philip Merilees concocted Does the flap of a butterfly's wings in Brazil set off a tornado in Texas? as a title.[1] Although a butterfly flapping its wings has remained constant in the expression of this concept, the location of the butterfly, the consequences, and the location of the consequences have varied widely.[14]

The butterfly effect presents an obvious challenge to prediction, since initial conditions for a system such as the weather can never be known to complete accuracy. This problem motivated the development of ensemble forecasting, in which a number of forecasts are made from perturbed initial conditions.[15]

Some scientists have since argued that the weather system is not as sensitive to initial conditions as previously believed.[16] David Orrell argues that the major contributor to weather forecast error is model error, with sensitivity to initial conditions playing a relatively small role.[17][18] Stephen Wolfram also notes that the Lorenz equations are highly simplified and do not contain terms that represent viscous effects; he believes that these terms would tend to damp out small perturbations.[19] Recent studies using generalized Lorenz models that included additional dissipative terms and nonlinearity suggested that a larger heating parameter is required for the onset of chaos.[20]

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